TSTP Solution File: ITP114^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:03 EDT 2024
% Result : Theorem 63.66s 25.05s
% Output : Refutation 64.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 382
% Syntax : Number of formulae : 708 ( 308 unt; 58 typ; 0 def)
% Number of atoms : 1778 ( 768 equ; 6 cnn)
% Maximal formula atoms : 81 ( 2 avg)
% Number of connectives : 5638 ( 198 ~; 22 |; 60 &;4492 @)
% ( 0 <=>; 866 =>; 0 <=; 0 <~>)
% Maximal formula depth : 34 ( 5 avg)
% Number of types : 7 ( 6 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 9 con; 0-4 aty)
% Number of variables : 1335 ( 42 ^1192 !; 56 ?;1335 :)
% ( 45 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(extended_ereal_type,type,
extended_ereal: $tType ).
thf(extended_enat_type,type,
extended_enat: $tType ).
thf(real_type,type,
real: $tType ).
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(a_type,type,
a: $tType ).
thf(type_type,type,
type:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(numeral_type,type,
numeral:
!>[TA: $tType] : $o ).
thf(uminus_type,type,
uminus:
!>[TA: $tType] : $o ).
thf(ord_type,type,
ord:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : $o ).
thf(order_type,type,
order:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(boolean_algebra_type,type,
boolean_algebra:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere142940540dd_abs_type,type,
ordere142940540dd_abs:
!>[TA: $tType] : $o ).
thf(real_V2090557954_space_type,type,
real_V2090557954_space:
!>[TA: $tType] : $o ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : $o ).
thf(topolo259154727pology_type,type,
topolo259154727pology:
!>[TA: $tType] : $o ).
thf(topolo503727757_space_type,type,
topolo503727757_space:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(extended_enat2_type,type,
extended_enat2: nat > extended_enat ).
thf(extended_case_enat_type,type,
extended_case_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extended_rec_enat_type,type,
extended_rec_enat:
!>[TA: $tType] : ( ( nat > TA ) > TA > extended_enat > TA ) ).
thf(extend1396239628finity_type,type,
extend1396239628finity:
!>[TA: $tType] : TA ).
thf(extended_the_enat_type,type,
extended_the_enat: extended_enat > nat ).
thf(extended_MInfty_type,type,
extended_MInfty: extended_ereal ).
thf(extended_PInfty_type,type,
extended_PInfty: extended_ereal ).
thf(extended_ereal2_type,type,
extended_ereal2: real > extended_ereal ).
thf(extended_size_ereal_type,type,
extended_size_ereal: extended_ereal > nat ).
thf(extend1771934483f_enat_type,type,
extend1771934483f_enat: extended_enat > extended_ereal ).
thf(extend1716541707_ereal_type,type,
extend1716541707_ereal: extended_ereal > real ).
thf(abs_abs_type,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(lower_107104146le_lsc_type,type,
lower_107104146le_lsc:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(lower_582600101lsc_at_type,type,
lower_582600101lsc_at:
!>[TA: $tType,TB: $tType] : ( TB > ( TB > TA ) > $o ) ).
thf(lower_1879122655c_hull_type,type,
lower_1879122655c_hull:
!>[TA: $tType] : ( ( TA > extended_ereal ) > TA > extended_ereal ) ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(neg_numeral_sub_type,type,
neg_numeral_sub:
!>[TA: $tType] : ( num > num > TA ) ).
thf(numeral_numeral_type,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(order_Greatest_type,type,
order_Greatest:
!>[TA: $tType] : ( ( TA > $o ) > TA ) ).
thf(order_antimono_type,type,
order_antimono:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(order_strict_mono_type,type,
order_strict_mono:
!>[TA: $tType,TB: $tType] : ( ( TB > TA ) > $o ) ).
thf(divide_divide_type,type,
divide_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(f_type,type,
f: a > extended_ereal ).
thf(g_type,type,
g: a > extended_ereal ).
thf(x_type,type,
x: a ).
thf(233,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_neg__le__0__iff__le) ).
thf(1105,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(164,axiom,
( ( extend1771934483f_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_ereal__of__enat__zero) ).
thf(893,plain,
( ( extend1771934483f_enat @ ( zero_zero @ extended_enat ) )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(226,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_le__trans) ).
thf(1083,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(113,axiom,
order @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_23) ).
thf(555,plain,
order @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(147,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_dual__order_Otrans) ).
thf(666,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_le__cases) ).
thf(1110,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(23,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_enat_Osimps_I6_J) ).
thf(365,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_rec_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(262,axiom,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( abs_abs @ extended_ereal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_abs__ereal__pos) ).
thf(1190,plain,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( abs_abs @ extended_ereal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(5,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add_Oinverse__inverse) ).
thf(333,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(208,axiom,
! [A: extended_enat] :
( ( ord_less_eq @ extended_enat @ A @ ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ extended_enat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ile0__eq) ).
thf(1031,plain,
! [A: extended_enat] :
( ( ord_less_eq @ extended_enat @ A @ ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ extended_enat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(81,axiom,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_enat_Osimps_I4_J) ).
thf(481,plain,
! [TA: $tType,A: nat > TA,B: TA,C: nat] :
( ( extended_case_enat @ TA @ A @ B @ ( extended_enat2 @ C ) )
= ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
boolean_algebra @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Lattices_Oboolean__algebra_11) ).
thf(352,plain,
boolean_algebra @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(200,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_bot__nat__0_Oextremum) ).
thf(1005,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(296,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_neg__le__iff__le) ).
thf(1290,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(222,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_nat__le__linear) ).
thf(1068,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(65,axiom,
topolo259154727pology @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Oorder__topology) ).
thf(449,plain,
topolo259154727pology @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(246,axiom,
! [A: real] :
( ( ( extended_ereal2 @ A )
= ( zero_zero @ extended_ereal ) )
= ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_ereal__eq__0_I1_J) ).
thf(1142,plain,
! [A: real] :
( ( ( extended_ereal2 @ A )
= ( zero_zero @ extended_ereal ) )
= ( A
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(60,axiom,
ord @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_24) ).
thf(440,plain,
ord @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(135,axiom,
! [A: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( zero_zero @ extended_ereal ) )
= ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_ereal__less__eq_I4_J) ).
thf(614,plain,
! [A: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( zero_zero @ extended_ereal ) )
= ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(44,axiom,
topolo259154727pology @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30) ).
thf(408,plain,
topolo259154727pology @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(189,axiom,
! [A: extended_ereal] :
( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_ereal__uminus__uminus) ).
thf(977,plain,
! [A: extended_ereal] :
( ( uminus_uminus @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(100,axiom,
( ( numeral_numeral @ extended_enat )
= ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_numeral__eq__enat) ).
thf(523,plain,
( ( numeral_numeral @ extended_enat )
= ( ^ [A: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(125,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_eq__iff) ).
thf(582,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(91,axiom,
linorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_13) ).
thf(500,plain,
linorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(253,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= B )
= ( A
= ( uminus_uminus @ extended_ereal @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ereal__uminus__eq__reorder) ).
thf(1164,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= B )
= ( A
= ( uminus_uminus @ extended_ereal @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(75,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_3) ).
thf(472,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(172,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_less__eq__neg__nonpos) ).
thf(913,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(318,axiom,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_abs__eq__infinity__cases) ).
thf(1354,plain,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(149,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zero__le) ).
thf(670,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(275,axiom,
! [A: real] :
( ( extended_ereal2 @ A )
!= ( extend1396239628finity @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_PInfty__neq__ereal_I1_J) ).
thf(1222,plain,
! [A: real] :
( ( extended_ereal2 @ A )
!= ( extend1396239628finity @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(178,axiom,
! [A: extended_ereal,B: real,C: real] :
( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_le__ereal__le) ).
thf(930,plain,
! [A: extended_ereal,B: real,C: real] :
( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
=> ( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(264,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA > extended_ereal] :
( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
=> ( ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
=> ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( lower_1879122655c_hull @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_lsc__hull__greatest) ).
thf(1196,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA > extended_ereal] :
( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
=> ( ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
=> ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( lower_1879122655c_hull @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(166,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
= ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_ereal__uminus__le__reorder) ).
thf(898,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
= ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(198,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_compl__le__swap2) ).
thf(1001,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(282,axiom,
! [A: real] :
( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( extend1396239628finity @ extended_ereal ) ) )
& ( ~ ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_ereal__divide__ereal) ).
thf(1243,plain,
! [A: real] :
( ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( extend1396239628finity @ extended_ereal ) ) )
& ( ~ ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
=> ( ( divide_divide @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(214,axiom,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_ereal__divide__zero__left) ).
thf(1046,plain,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(320,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_neg__numeral__le__numeral) ).
thf(1359,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( abs_abs @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_abs__0__eq) ).
thf(565,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( abs_abs @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(58,axiom,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_enat_Oinject) ).
thf(436,plain,
! [A: nat,B: nat] :
( ( ( extended_enat2 @ A )
= ( extended_enat2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(35,axiom,
topolo503727757_space @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Topological__Spaces_Otopological__space_1) ).
thf(389,plain,
topolo503727757_space @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(217,axiom,
( ( extend1396239628finity @ extended_ereal )
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_MInfty__neq__PInfty_I1_J) ).
thf(1055,plain,
( ( extend1396239628finity @ extended_ereal )
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(295,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_sub__non__positive) ).
thf(1287,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( neg_numeral_sub @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(121,axiom,
! [A: real] :
( ( extended_ereal2 @ A )
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_MInfty__neq__ereal_I1_J) ).
thf(570,plain,
! [A: real] :
( ( extended_ereal2 @ A )
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(298,axiom,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA > extended_ereal,B: TA] :
( ( ( A @ B )
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( lower_582600101lsc_at @ TA @ extended_ereal @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_lsc__at__MInfty) ).
thf(1298,plain,
! [TA: $tType] :
( ( topolo503727757_space @ TA )
=> ! [A: TA > extended_ereal,B: TA] :
( ( ( A @ B )
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( lower_582600101lsc_at @ TA @ extended_ereal @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(26,axiom,
linorder @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Olinorder_6) ).
thf(372,plain,
linorder @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( abs_abs @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_abs__eq__0) ).
thf(504,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( abs_abs @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( abs_abs @ TA @ A )
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_abs__of__nonpos) ).
thf(619,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( abs_abs @ TA @ A )
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(108,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_numeral__eq__iff) ).
thf(542,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(168,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_dual__order_Oeq__iff) ).
thf(902,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ B @ A )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(115,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_double__compl) ).
thf(559,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(248,axiom,
! [A: set @ extended_ereal] :
? [B: extended_ereal] :
( ! [C: extended_ereal] :
( ( member @ extended_ereal @ C @ A )
=> ( ord_less_eq @ extended_ereal @ B @ C ) )
& ! [C: extended_ereal] :
( ! [D: extended_ereal] :
( ( member @ extended_ereal @ D @ A )
=> ( ord_less_eq @ extended_ereal @ C @ D ) )
=> ( ord_less_eq @ extended_ereal @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_ereal__complete__Inf) ).
thf(1147,plain,
! [A: set @ extended_ereal] :
? [B: extended_ereal] :
( ! [C: extended_ereal] :
( ( member @ extended_ereal @ C @ A )
=> ( ord_less_eq @ extended_ereal @ B @ C ) )
& ! [C: extended_ereal] :
( ! [D: extended_ereal] :
( ( member @ extended_ereal @ D @ A )
=> ( ord_less_eq @ extended_ereal @ C @ D ) )
=> ( ord_less_eq @ extended_ereal @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(132,axiom,
( ( extend1396239628finity @ extended_ereal )
= extended_PInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_infinity__ereal__def) ).
thf(606,plain,
( ( extend1396239628finity @ extended_ereal )
= extended_PInfty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(203,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( neg_numeral_sub @ TA @ A @ B ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_sub__non__negative) ).
thf(1013,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( neg_numeral_sub @ TA @ A @ B ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(49,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ( type @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype) ).
thf(416,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ( type @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(64,axiom,
uminus @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Groups_Ouminus_16) ).
thf(448,plain,
uminus @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(278,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_bot__nat__0_Oextremum__unique) ).
thf(1232,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(306,axiom,
! [A: a] : ( ord_less_eq @ extended_ereal @ ( g @ A ) @ ( f @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms) ).
thf(1319,plain,
! [A: a] : ( ord_less_eq @ extended_ereal @ ( g @ A ) @ ( f @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( uminus_uminus @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_abs__minus__cancel) ).
thf(421,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( uminus_uminus @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(78,axiom,
real_V2090557954_space @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0) ).
thf(475,plain,
real_V2090557954_space @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(300,axiom,
( ( abs_abs @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
= ( extend1396239628finity @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_abs__ereal_Osimps_I3_J) ).
thf(1302,plain,
( ( abs_abs @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
= ( extend1396239628finity @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(311,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_compl__le__swap1) ).
thf(1334,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
=> ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(83,axiom,
semiring_char_0 @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32) ).
thf(485,plain,
semiring_char_0 @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(16,axiom,
topolo503727757_space @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29) ).
thf(353,plain,
topolo503727757_space @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(294,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_eq__refl) ).
thf(1283,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(169,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_order__subst1) ).
thf(905,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(11,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom) ).
thf(348,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(122,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_strict__mono__leD) ).
thf(574,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_ord__le__eq__trans) ).
thf(602,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(255,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Nat_Oex__has__greatest__nat) ).
thf(1169,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(272,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_antimono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_antimonoE) ).
thf(1215,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_antimono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(67,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0) ).
thf(453,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(39,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zero__neq__numeral) ).
thf(396,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(317,axiom,
! [A: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) )
= ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_ereal__of__enat__ge__zero__cancel__iff) ).
thf(1351,plain,
! [A: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) )
= ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(192,axiom,
( ( uminus_uminus @ extended_ereal @ extended_MInfty )
= extended_PInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_uminus__ereal_Osimps_I3_J) ).
thf(988,plain,
( ( uminus_uminus @ extended_ereal @ extended_MInfty )
= extended_PInfty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(94,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_add_Oinverse__neutral) ).
thf(507,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( uminus_uminus @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(102,axiom,
ordere142940540dd_abs @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs) ).
thf(527,plain,
ordere142940540dd_abs @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(55,axiom,
! [TA: $tType] :
( ( neg_numeral @ 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_162_dbl__simps_I1_J) ).
thf(428,plain,
! [TA: $tType] :
( ( neg_numeral @ 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)],[55]) ).
thf(266,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( abs_abs @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_abs__minus__le__zero) ).
thf(1201,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( abs_abs @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(59,axiom,
linord1659791738miring @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring) ).
thf(439,plain,
linord1659791738miring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(145,axiom,
! [A: num,B: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( numeral_numeral @ extended_ereal @ A ) @ ( extend1771934483f_enat @ B ) )
= ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_numeral__le__ereal__of__enat__iff) ).
thf(661,plain,
! [A: num,B: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( numeral_numeral @ extended_ereal @ A ) @ ( extend1771934483f_enat @ B ) )
= ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(176,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_abs__ge__zero) ).
thf(925,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(249,axiom,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_ereal__divide__Infty_I1_J) ).
thf(1153,plain,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(31,axiom,
zero @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(381,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_neg__less__eq__nonneg) ).
thf(910,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(185,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_le__cases3) ).
thf(957,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(314,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA > extended_ereal] :
( ( A
= ( lower_1879122655c_hull @ TA @ B ) )
= ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
& ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
& ! [C: TA > extended_ereal] :
( ( ( lower_107104146le_lsc @ TA @ extended_ereal @ C )
& ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( B @ D ) ) )
=> ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( A @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_lsc__hull__iff__greatest) ).
thf(1343,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA > extended_ereal] :
( ( A
= ( lower_1879122655c_hull @ TA @ B ) )
= ( ( lower_107104146le_lsc @ TA @ extended_ereal @ A )
& ! [C: TA] : ( ord_less_eq @ extended_ereal @ ( A @ C ) @ ( B @ C ) )
& ! [C: TA > extended_ereal] :
( ( ( lower_107104146le_lsc @ TA @ extended_ereal @ C )
& ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( B @ D ) ) )
=> ! [D: TA] : ( ord_less_eq @ extended_ereal @ ( C @ D ) @ ( A @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(212,axiom,
topolo259154727pology @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40) ).
thf(1042,plain,
topolo259154727pology @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(273,axiom,
( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( extend1396239628finity @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_abs__ereal_Osimps_I2_J) ).
thf(1217,plain,
( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( extend1396239628finity @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(53,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_compl__eq__compl__iff) ).
thf(424,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(43,axiom,
linord1659791738miring @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19) ).
thf(407,plain,
linord1659791738miring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(323,axiom,
preorder @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Opreorder_41) ).
thf(1370,plain,
preorder @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(280,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_le__funD) ).
thf(1238,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(158,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
= ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_divide__le__0__abs__iff) ).
thf(862,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
= ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(12,axiom,
linord1659791738miring @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31) ).
thf(349,plain,
linord1659791738miring @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(82,axiom,
ord @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_4) ).
thf(484,plain,
ord @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(162,axiom,
( ( abs_abs @ extended_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_abs__ereal__zero) ).
thf(889,plain,
( ( abs_abs @ extended_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(225,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ( A @ ( order_Greatest @ nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_GreatestI__nat) ).
thf(1079,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ( A @ ( order_Greatest @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(153,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_order_Otrans) ).
thf(682,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(188,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_neg__numeral__le__iff) ).
thf(974,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) )
= ( ord_less_eq @ num @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__numeral__extra_I3_J) ).
thf(916,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(73,axiom,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A != extended_PInfty )
=> ( A = extended_MInfty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_ereal_Oexhaust) ).
thf(467,plain,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A != extended_PInfty )
=> ( A = extended_MInfty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(251,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_le__fun__def) ).
thf(1159,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(70,axiom,
preorder @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_12) ).
thf(461,plain,
preorder @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(87,axiom,
neg_numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Oneg__numeral) ).
thf(493,plain,
neg_numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(270,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_enat__ord__simps_I1_J) ).
thf(1210,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(111,axiom,
real_V2090557954_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space) ).
thf(551,plain,
real_V2090557954_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(241,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( order_antimono @ nat @ TA )
= ( ^ [A: nat > TA] :
! [B: nat,C: nat] :
( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_decseq__def) ).
thf(1128,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( order_antimono @ nat @ TA )
= ( ^ [A: nat > TA] :
! [B: nat,C: nat] :
( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(99,axiom,
! [A: real] :
( ( extended_ereal2 @ A )
!= extended_PInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_ereal_Odistinct_I1_J) ).
thf(519,plain,
! [A: real] :
( ( extended_ereal2 @ A )
!= extended_PInfty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(142,axiom,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ D ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_times__ereal_Oinduct) ).
thf(650,plain,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extended_ereal2 @ D ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(239,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_Greatest__equality) ).
thf(1121,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA] :
( ( A @ B )
=> ( ! [C: TA] :
( ( A @ C )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ( order_Greatest @ TA @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(190,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_GreatestI2__order) ).
thf(980,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA > $o,B: TA,C: TA > $o] :
( ( A @ B )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ord_less_eq @ TA @ D @ B ) )
=> ( ! [D: TA] :
( ( A @ D )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less_eq @ TA @ E @ D ) )
=> ( C @ D ) ) )
=> ( C @ ( order_Greatest @ TA @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(230,axiom,
! [A: real,B: extended_ereal] :
( ( ord_less_eq @ real @ A @ ( extend1716541707_ereal @ B ) )
= ( ( ( ( abs_abs @ extended_ereal @ B )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B ) )
& ( ( ( abs_abs @ extended_ereal @ B )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_ereal__le__real__iff) ).
thf(1096,plain,
! [A: real,B: extended_ereal] :
( ( ord_less_eq @ real @ A @ ( extend1716541707_ereal @ B ) )
= ( ( ( ( abs_abs @ extended_ereal @ B )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B ) )
& ( ( ( abs_abs @ extended_ereal @ B )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ A @ ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(238,axiom,
! [A: real,B: extended_ereal,C: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B )
=> ( ( ord_less_eq @ real @ C @ A )
=> ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_ereal__le__le) ).
thf(1118,plain,
! [A: real,B: extended_ereal,C: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ B )
=> ( ( ord_less_eq @ real @ C @ A )
=> ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(90,axiom,
linordered_field @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(499,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(245,axiom,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_real__of__ereal_Ocases) ).
thf(1138,plain,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(18,axiom,
! [A: real] :
( ( extend1716541707_ereal @ ( extended_ereal2 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_real__of__ereal_Osimps_I1_J) ).
thf(356,plain,
! [A: real] :
( ( extend1716541707_ereal @ ( extended_ereal2 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(74,axiom,
linorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_22) ).
thf(471,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(309,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
= ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_ereal__uminus__divide) ).
thf(1329,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( divide_divide @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
= ( uminus_uminus @ extended_ereal @ ( divide_divide @ extended_ereal @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(207,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_order__class_Oorder_Oantisym) ).
thf(1028,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(321,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_order__refl) ).
thf(1361,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(7,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_neg__equal__iff__equal) ).
thf(339,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(179,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_antisym) ).
thf(933,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(259,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_le__minus__iff) ).
thf(1182,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(85,axiom,
zero @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ozero_38) ).
thf(489,plain,
zero @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(110,axiom,
! [A: real] :
( ( extended_ereal2 @ A )
!= extended_MInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_ereal_Odistinct_I3_J) ).
thf(547,plain,
! [A: real] :
( ( extended_ereal2 @ A )
!= extended_MInfty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(167,axiom,
ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ a @ g @ x ) @ ( g @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_calculation) ).
thf(901,plain,
ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ a @ g @ x ) @ ( g @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(79,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ( topolo503727757_space @ TA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space) ).
thf(476,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ( topolo503727757_space @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(204,axiom,
( ( extend1716541707_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_real__of__ereal__0) ).
thf(1016,plain,
( ( extend1716541707_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(269,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( abs_abs @ TA @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_abs__of__nonneg) ).
thf(1207,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( abs_abs @ TA @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(152,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_le__antisym) ).
thf(679,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(211,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_order__class_Oorder_Oeq__iff) ).
thf(1039,plain,
! [TA: $tType] :
( ( order @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(138,axiom,
! [A: extended_ereal,B: real] :
( ( ( extend1716541707_ereal @ A )
= B )
=> ( ! [C: real] :
( ( A
= ( extended_ereal2 @ C ) )
=> ( B != C ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( zero_zero @ real ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( zero_zero @ real ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_real__of__ereal_Oelims) ).
thf(622,plain,
! [A: extended_ereal,B: real] :
( ( ( extend1716541707_ereal @ A )
= B )
=> ( ! [C: real] :
( ( A
= ( extended_ereal2 @ C ) )
=> ( B != C ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( zero_zero @ real ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( zero_zero @ real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(37,axiom,
zero @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_27) ).
thf(393,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(231,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_abs__le__self__iff) ).
thf(1099,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(97,axiom,
preorder @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_21) ).
thf(515,plain,
preorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(242,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_abs__leI) ).
thf(1131,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(263,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_not__MInfty__nonneg) ).
thf(1192,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(219,axiom,
( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_ereal__uminus__zero) ).
thf(1060,plain,
( ( uminus_uminus @ extended_ereal @ ( zero_zero @ extended_ereal ) )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(141,axiom,
( ( extend1396239628finity @ extended_ereal )
!= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Infty__neq__0_I1_J) ).
thf(647,plain,
( ( extend1396239628finity @ extended_ereal )
!= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(288,axiom,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ereal__cases) ).
thf(1263,plain,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(227,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_abs__ge__self) ).
thf(1086,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(20,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
( ( abs_abs @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_abs__neg__numeral) ).
thf(360,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
( ( abs_abs @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) )
= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(175,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( B
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( extend1716541707_ereal @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_real__of__ereal__positive__mono) ).
thf(921,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( B
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( extend1716541707_ereal @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(254,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_dual__order_Orefl) ).
thf(1167,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(260,axiom,
( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
!= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Infty__neq__0_I3_J) ).
thf(1185,plain,
( ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) )
!= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(96,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(513,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA )
=> ( ord @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(274,axiom,
! [A: real] :
( ( A
= ( zero_zero @ real ) )
= ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
& ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( uminus_uminus @ real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_real__eq__0__iff__le__ge__0) ).
thf(1219,plain,
! [A: real] :
( ( A
= ( zero_zero @ real ) )
= ( ( ord_less_eq @ real @ ( zero_zero @ real ) @ A )
& ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( uminus_uminus @ real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(156,axiom,
! [A: extended_ereal,B: real] :
( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ B )
= ( ( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) ) )
& ( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ ( zero_zero @ real ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_real__le__ereal__iff) ).
thf(856,plain,
! [A: extended_ereal,B: real] :
( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ B )
= ( ( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) ) )
& ( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ord_less_eq @ real @ ( zero_zero @ real ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(299,axiom,
linorder @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Olinorder_42) ).
thf(1301,plain,
linorder @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(62,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add) ).
thf(444,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_abs__idempotent) ).
thf(375,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(244,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A ) )
= ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_ereal__0__le__uminus__iff) ).
thf(1135,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( uminus_uminus @ extended_ereal @ A ) )
= ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(47,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_neg__equal__zero) ).
thf(412,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(116,axiom,
topolo503727757_space @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Otopological__space_17) ).
thf(562,plain,
topolo503727757_space @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(201,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( abs_abs @ extended_ereal @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_abs__ereal__ge0) ).
thf(1007,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( abs_abs @ extended_ereal @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(41,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_verit__negate__coefficient_I3_J) ).
thf(402,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ( uminus_uminus @ TA @ A )
= ( uminus_uminus @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(124,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_abs__le__iff) ).
thf(579,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
= ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(285,axiom,
( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_real__of__ereal_Osimps_I3_J) ).
thf(1256,plain,
( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(276,axiom,
! [A: extended_enat,B: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( extend1771934483f_enat @ A ) @ ( extend1771934483f_enat @ B ) )
= ( ord_less_eq @ extended_enat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_ereal__of__enat__le__iff) ).
thf(1226,plain,
! [A: extended_enat,B: extended_enat] :
( ( ord_less_eq @ extended_ereal @ ( extend1771934483f_enat @ A ) @ ( extend1771934483f_enat @ B ) )
= ( ord_less_eq @ extended_enat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(109,axiom,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Topological__Spaces_Otopological__space) ).
thf(545,plain,
! [TA: $tType,TB: $tType] :
( ( topolo503727757_space @ TA )
=> ( topolo503727757_space @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(139,axiom,
! [A: extended_ereal] :
( ( ( extend1716541707_ereal @ A )
= ( zero_zero @ real ) )
= ( ( A
= ( extend1396239628finity @ extended_ereal ) )
| ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
| ( A
= ( zero_zero @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_real__of__ereal__eq__0) ).
thf(641,plain,
! [A: extended_ereal] :
( ( ( extend1716541707_ereal @ A )
= ( zero_zero @ real ) )
= ( ( A
= ( extend1396239628finity @ extended_ereal ) )
| ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
| ( A
= ( zero_zero @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(32,axiom,
ord @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_15) ).
thf(382,plain,
ord @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(304,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_neg__numeral__le__zero) ).
thf(1312,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(134,axiom,
! [A: real] :
( ( uminus_uminus @ extended_ereal @ ( extended_ereal2 @ A ) )
= ( extended_ereal2 @ ( uminus_uminus @ real @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_uminus__ereal_Osimps_I1_J) ).
thf(611,plain,
! [A: real] :
( ( uminus_uminus @ extended_ereal @ ( extended_ereal2 @ A ) )
= ( extended_ereal2 @ ( uminus_uminus @ real @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(89,axiom,
order @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oorder_7) ).
thf(498,plain,
order @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(218,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_le__imp__neg__le) ).
thf(1058,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(310,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_less__eq__nat_Osimps_I1_J) ).
thf(1332,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(229,axiom,
! [A: set @ extended_ereal] :
? [B: extended_ereal] :
( ! [C: extended_ereal] :
( ( member @ extended_ereal @ C @ A )
=> ( ord_less_eq @ extended_ereal @ C @ B ) )
& ! [C: extended_ereal] :
( ! [D: extended_ereal] :
( ( member @ extended_ereal @ D @ A )
=> ( ord_less_eq @ extended_ereal @ D @ C ) )
=> ( ord_less_eq @ extended_ereal @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_ereal__complete__Sup) ).
thf(1090,plain,
! [A: set @ extended_ereal] :
? [B: extended_ereal] :
( ! [C: extended_ereal] :
( ( member @ extended_ereal @ C @ A )
=> ( ord_less_eq @ extended_ereal @ C @ B ) )
& ! [C: extended_ereal] :
( ! [D: extended_ereal] :
( ( member @ extended_ereal @ D @ A )
=> ( ord_less_eq @ extended_ereal @ D @ C ) )
=> ( ord_less_eq @ extended_ereal @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(286,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__zero__eq) ).
thf(1258,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(183,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_ord__eq__le__subst) ).
thf(947,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(13,axiom,
canoni770627133id_add @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28) ).
thf(350,plain,
canoni770627133id_add @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(150,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_ord__eq__le__trans) ).
thf(672,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(63,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
( ( abs_abs @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_abs__numeral) ).
thf(445,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
( ( abs_abs @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(180,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_ereal__infty__less__eq2_I2_J) ).
thf(936,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(291,axiom,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_abs__ereal_Oinduct) ).
thf(1271,plain,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(324,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_ereal2__cases) ).
thf(1371,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( ? [C: real] :
( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [C: real] :
( B
!= ( extended_ereal2 @ C ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( B
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(42,axiom,
ord @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Oord_8) ).
thf(406,plain,
ord @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(51,axiom,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zero__enat__def) ).
thf(419,plain,
( ( zero_zero @ extended_enat )
= ( extended_enat2 @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(316,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_le__refl) ).
thf(1349,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(213,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_order__subst2) ).
thf(1043,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(256,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA] : ( ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A @ B ) @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_lsc__hull__le) ).
thf(1175,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal,B: TA] : ( ord_less_eq @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A @ B ) @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(193,axiom,
order @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oorder_43) ).
thf(990,plain,
order @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(196,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_strict__mono__less__eq) ).
thf(996,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TB @ ( A @ B ) @ ( A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(88,axiom,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A != extended_PInfty )
=> ( A = extended_MInfty ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_uminus__ereal_Ocases) ).
thf(494,plain,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A != extended_PInfty )
=> ( A = extended_MInfty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(313,axiom,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A
= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_abs__ereal_Ocases) ).
thf(1339,plain,
! [A: extended_ereal] :
( ! [B: real] :
( A
!= ( extended_ereal2 @ B ) )
=> ( ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A
= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(106,axiom,
numeral @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Num_Onumeral_37) ).
thf(535,plain,
numeral @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(129,axiom,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
=> ( ! [D: extended_ereal] : ( A @ D @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_plus__ereal_Oinduct) ).
thf(594,plain,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
=> ( ! [D: extended_ereal] : ( A @ D @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(252,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_not__numeral__le__zero) ).
thf(1162,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(308,axiom,
! [A: nat > $o,B: nat] :
( ? [C: nat] : ( A @ C )
=> ( ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ C @ B ) )
=> ( A @ ( order_Greatest @ nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_GreatestI__ex__nat) ).
thf(1325,plain,
! [A: nat > $o,B: nat] :
( ? [C: nat] : ( A @ C )
=> ( ! [C: nat] :
( ( A @ C )
=> ( ord_less_eq @ nat @ C @ B ) )
=> ( A @ ( order_Greatest @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(165,axiom,
! [A: extended_ereal] :
( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= ( uminus_uminus @ real @ ( extend1716541707_ereal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_real__of__ereal) ).
thf(895,plain,
! [A: extended_ereal] :
( ( extend1716541707_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= ( uminus_uminus @ real @ ( extend1716541707_ereal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(182,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_ereal__infty__less__eq2_I1_J) ).
thf(943,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( B
= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(257,axiom,
! [A: nat > nat,B: nat] :
( ( order_strict_mono @ nat @ nat @ A )
=> ( ord_less_eq @ nat @ B @ ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_strict__mono__imp__increasing) ).
thf(1177,plain,
! [A: nat > nat,B: nat] :
( ( order_strict_mono @ nat @ nat @ A )
=> ( ord_less_eq @ nat @ B @ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(4,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dbl__simps_I2_J) ).
thf(330,plain,
! [TA: $tType] :
( ( neg_numeral @ TA )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_abs__zero) ).
thf(462,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(236,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ( ord_less_eq @ nat @ B @ ( order_Greatest @ nat @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Greatest__le__nat) ).
thf(1112,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ( ord_less_eq @ nat @ B @ ( order_Greatest @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(9,axiom,
group_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add) ).
thf(345,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(112,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_neg__equal__0__iff__equal) ).
thf(552,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(297,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( ord_less_eq @ extended_ereal @ B @ A )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_neq__PInf__trans) ).
thf(1293,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( ord_less_eq @ extended_ereal @ B @ A )
=> ( B
!= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(148,axiom,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_ereal__less__eq_I2_J) ).
thf(668,plain,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(265,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( uminus_uminus @ extended_ereal @ B ) )
= ( ord_less_eq @ extended_ereal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_ereal__minus__le__minus) ).
thf(1198,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( uminus_uminus @ extended_ereal @ B ) )
= ( ord_less_eq @ extended_ereal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(40,axiom,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_enat__0__iff_I1_J) ).
thf(399,plain,
! [A: nat] :
( ( ( extended_enat2 @ A )
= ( zero_zero @ extended_enat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(271,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_zero__le__numeral) ).
thf(1213,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(160,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= B )
=> ( ! [C: real] :
( ( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( extended_ereal2 @ ( uminus_uminus @ real @ C ) ) ) )
=> ( ( ( A = extended_PInfty )
=> ( B != extended_MInfty ) )
=> ~ ( ( A = extended_MInfty )
=> ( B != extended_PInfty ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_uminus__ereal_Oelims) ).
thf(868,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= B )
=> ( ! [C: real] :
( ( A
= ( extended_ereal2 @ C ) )
=> ( B
!= ( extended_ereal2 @ ( uminus_uminus @ real @ C ) ) ) )
=> ( ( ( A = extended_PInfty )
=> ( B != extended_MInfty ) )
=> ~ ( ( A = extended_MInfty )
=> ( B != extended_PInfty ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(69,axiom,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ extended_PInfty )
=> ( ( A @ extended_MInfty )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_ereal_Oinduct) ).
thf(455,plain,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ extended_PInfty )
=> ( ( A @ extended_MInfty )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(133,axiom,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( zero_zero @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_ereal__divide__Infty_I2_J) ).
thf(608,plain,
! [A: extended_ereal] :
( ( divide_divide @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( zero_zero @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(117,axiom,
numeral @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Num_Onumeral_26) ).
thf(563,plain,
numeral @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(283,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( zero_zero @ extended_ereal ) )
= ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_ereal__uminus__le__0__iff) ).
thf(1250,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ ( zero_zero @ extended_ereal ) )
= ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(232,axiom,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_ereal__real_H) ).
thf(1102,plain,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(56,axiom,
preorder @ num,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_5) ).
thf(431,plain,
preorder @ num,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(144,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_le__0__eq) ).
thf(658,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(38,axiom,
( ( extended_size_ereal @ extended_MInfty )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_ereal_Osize__gen_I3_J) ).
thf(394,plain,
( ( extended_size_ereal @ extended_MInfty )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(191,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_le__funI) ).
thf(986,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(209,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B )
=> ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( divide_divide @ extended_ereal @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_zero__le__divide__ereal) ).
thf(1034,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ B )
=> ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( divide_divide @ extended_ereal @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(86,axiom,
! [A: real] :
( ( extended_size_ereal @ ( extended_ereal2 @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_ereal_Osize__gen_I1_J) ).
thf(490,plain,
! [A: real] :
( ( extended_size_ereal @ ( extended_ereal2 @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(301,axiom,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ~ ! [B: real] :
( A
!= ( extended_ereal2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_abs__neq__infinity__cases) ).
thf(1304,plain,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ~ ! [B: real] :
( A
!= ( extended_ereal2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(104,axiom,
linorder @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Olinorder_34) ).
thf(531,plain,
linorder @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(292,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= ( uminus_uminus @ extended_ereal @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ereal__uminus__eq__iff) ).
thf(1277,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= ( uminus_uminus @ extended_ereal @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(8,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_equation__minus__iff) ).
thf(342,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( uminus_uminus @ TA @ B ) )
= ( B
= ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(215,axiom,
! [A: extended_ereal] :
( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_ereal__infinity__cases) ).
thf(1049,plain,
! [A: extended_ereal] :
( ( A
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( A
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(76,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_2) ).
thf(473,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(224,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_dual__order_Oantisym) ).
thf(1076,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(267,axiom,
uminus @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ouminus_45) ).
thf(1203,plain,
uminus @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_less_eq @ ( $o > TA ) )
= ( ^ [A: $o > TA,B: $o > TA] :
( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__rel__bool__arg__iff) ).
thf(589,plain,
! [TA: $tType] :
( ( ord @ TA )
=> ( ( ord_less_eq @ ( $o > TA ) )
= ( ^ [A: $o > TA,B: $o > TA] :
( ( ord_less_eq @ TA @ ( A @ $false ) @ ( B @ $false ) )
& ( ord_less_eq @ TA @ ( A @ $true ) @ ( B @ $true ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(177,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_bot__nat__0_Oextremum__uniqueI) ).
thf(927,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(28,axiom,
topolo503727757_space @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Otopological__space_9) ).
thf(374,plain,
topolo503727757_space @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(136,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_le0) ).
thf(617,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(98,axiom,
extended_PInfty != extended_MInfty,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_ereal_Odistinct_I5_J) ).
thf(516,plain,
extended_PInfty != extended_MInfty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(247,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ( order_antimono @ nat @ TA @ A )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_decseqD) ).
thf(1145,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: nat > TA,B: nat,C: nat] :
( ( order_antimono @ nat @ TA @ A )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ TA @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(205,axiom,
! [A: extended_ereal] :
( ( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= ( zero_zero @ extended_ereal ) ) )
& ( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_ereal__real) ).
thf(1018,plain,
! [A: extended_ereal] :
( ( ( ( abs_abs @ extended_ereal @ A )
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= ( zero_zero @ extended_ereal ) ) )
& ( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
=> ( ( extended_ereal2 @ ( extend1716541707_ereal @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(101,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Groups_Ouminus) ).
thf(525,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TA )
=> ( uminus @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(199,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_linear) ).
thf(1003,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(206,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ! [C: real] :
( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) )
=> ( ord_less_eq @ extended_ereal @ B @ ( extended_ereal2 @ C ) ) )
=> ( ord_less_eq @ extended_ereal @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_ereal__le__real) ).
thf(1025,plain,
! [A: extended_ereal,B: extended_ereal] :
( ! [C: real] :
( ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ C ) )
=> ( ord_less_eq @ extended_ereal @ B @ ( extended_ereal2 @ C ) ) )
=> ( ord_less_eq @ extended_ereal @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(223,axiom,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_real__of__ereal_Oinduct) ).
thf(1070,plain,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ ( extend1396239628finity @ extended_ereal ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(250,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A )
= ( A
= ( extend1396239628finity @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_ereal__infty__less__eq_I1_J) ).
thf(1156,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) @ A )
= ( A
= ( extend1396239628finity @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(161,axiom,
( extended_MInfty
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_MInfty__eq__minfinity) ).
thf(887,plain,
( extended_MInfty
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(186,axiom,
numeral @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Num_Onumeral_46) ).
thf(971,plain,
numeral @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(3,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_minus__equation__iff) ).
thf(327,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ A )
= B )
= ( ( uminus_uminus @ TA @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(184,axiom,
! [A: real,B: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( extended_ereal2 @ B ) )
= ( ord_less_eq @ real @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_ereal__less__eq_I3_J) ).
thf(954,plain,
! [A: real,B: real] :
( ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ A ) @ ( extended_ereal2 @ B ) )
= ( ord_less_eq @ real @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(289,axiom,
ord @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Orderings_Oord_44) ).
thf(1267,plain,
ord @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(45,axiom,
topolo259154727pology @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10) ).
thf(409,plain,
topolo259154727pology @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(195,axiom,
! [A: num,B: nat] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_numeral__le__enat__iff) ).
thf(993,plain,
! [A: num,B: nat] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( extended_enat2 @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(261,axiom,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal] : ( lower_107104146le_lsc @ TA @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_lsc__lsc__hull) ).
thf(1188,plain,
! [TA: $tType] :
( ( real_V2090557954_space @ TA )
=> ! [A: TA > extended_ereal] : ( lower_107104146le_lsc @ TA @ extended_ereal @ ( lower_1879122655c_hull @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_uminus__apply) ).
thf(441,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_eq__imp__le) ).
thf(585,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(279,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_enat__ord__number_I1_J) ).
thf(1235,plain,
! [A: num,B: num] :
( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ A ) @ ( numeral_numeral @ extended_enat @ B ) )
= ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ A ) @ ( numeral_numeral @ nat @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(123,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ( divide_divide @ extended_ereal @ A @ B )
= ( zero_zero @ extended_ereal ) )
= ( ( A
= ( zero_zero @ extended_ereal ) )
| ( ( abs_abs @ extended_ereal @ B )
= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_ereal__divide__eq__0__iff) ).
thf(576,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ( divide_divide @ extended_ereal @ A @ B )
= ( zero_zero @ extended_ereal ) )
= ( ( A
= ( zero_zero @ extended_ereal ) )
| ( ( abs_abs @ extended_ereal @ B )
= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(19,axiom,
topolo259154727pology @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18) ).
thf(359,plain,
topolo259154727pology @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(312,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_abs__le__zero__iff) ).
thf(1336,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(6,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_verit__minus__simplify_I4_J) ).
thf(336,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( uminus_uminus @ TA @ ( uminus_uminus @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(143,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_not__zero__le__neg__numeral) ).
thf(656,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(130,axiom,
! [A: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_i0__lb) ).
thf(600,plain,
! [A: extended_enat] : ( ord_less_eq @ extended_enat @ ( zero_zero @ extended_enat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(216,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_verit__la__disequality) ).
thf(1052,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA,B: TA] :
( ( A = B )
| ~ ( ord_less_eq @ TA @ A @ B )
| ~ ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(34,axiom,
! [TA: $tType] :
( ( ring_char_0 @ 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_93_neg__numeral__eq__iff) ).
thf(386,plain,
! [TA: $tType] :
( ( ring_char_0 @ 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)],[34]) ).
thf(157,axiom,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
=> ( ! [D: extended_ereal] : ( A @ D @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_less__ereal_Oinduct) ).
thf(859,plain,
! [A: extended_ereal > extended_ereal > $o,B: extended_ereal,C: extended_ereal] :
( ! [D: real,E: real] : ( A @ ( extended_ereal2 @ D ) @ ( extended_ereal2 @ E ) )
=> ( ! [D: extended_ereal] : ( A @ ( extend1396239628finity @ extended_ereal ) @ D )
=> ( ! [D: extended_ereal] : ( A @ D @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ! [D: real] : ( A @ ( extended_ereal2 @ D ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( ! [D: real] : ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extended_ereal2 @ D ) )
=> ( ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) @ ( extend1396239628finity @ extended_ereal ) )
=> ( A @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(281,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) )
=> ( order_antimono @ TA @ TB @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_antimonoI) ).
thf(1240,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB] :
( ! [B: TA,C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) )
=> ( order_antimono @ TA @ TB @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(194,axiom,
( ( uminus_uminus @ extended_ereal @ extended_PInfty )
= extended_MInfty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_uminus__ereal_Osimps_I2_J) ).
thf(991,plain,
( ( uminus_uminus @ extended_ereal @ extended_PInfty )
= extended_MInfty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(72,axiom,
( ( extended_size_ereal @ extended_PInfty )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_ereal_Osize__gen_I2_J) ).
thf(465,plain,
( ( extended_size_ereal @ extended_PInfty )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(66,axiom,
! [A: real,B: real] :
( ( ( extended_ereal2 @ A )
= ( extended_ereal2 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_ereal_Oinject) ).
thf(450,plain,
! [A: real,B: real] :
( ( ( extended_ereal2 @ A )
= ( extended_ereal2 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(258,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_le__funE) ).
thf(1180,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(307,axiom,
! [A: extended_enat,B: nat] :
( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_enat__ile) ).
thf(1321,plain,
! [A: extended_enat,B: nat] :
( ( ord_less_eq @ extended_enat @ A @ ( extended_enat2 @ B ) )
=> ? [C: nat] :
( A
= ( extended_enat2 @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(163,axiom,
( ( zero_zero @ extended_ereal )
= ( extended_ereal2 @ ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_zero__ereal__def) ).
thf(891,plain,
( ( zero_zero @ extended_ereal )
= ( extended_ereal2 @ ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(240,axiom,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_order__trans) ).
thf(1126,plain,
! [TA: $tType] :
( ( preorder @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(202,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( zero_zero @ real ) )
= ( ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) )
| ( A
= ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_real__of__ereal__le__0) ).
thf(1010,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ real @ ( extend1716541707_ereal @ A ) @ ( zero_zero @ real ) )
= ( ( ord_less_eq @ extended_ereal @ A @ ( zero_zero @ extended_ereal ) )
| ( A
= ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(24,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(368,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(234,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( extend1716541707_ereal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_real__of__ereal__pos) ).
thf(1108,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ A )
=> ( ord_less_eq @ real @ ( zero_zero @ real ) @ ( extend1716541707_ereal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(21,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0) ).
thf(363,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(114,axiom,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_enat__0__iff_I2_J) ).
thf(556,plain,
! [A: nat] :
( ( ( zero_zero @ extended_enat )
= ( extended_enat2 @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(284,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_compl__le__compl__iff) ).
thf(1253,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( uminus_uminus @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(220,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_numeral__le__iff) ).
thf(1062,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(14,axiom,
uminus @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ouminus_25) ).
thf(351,plain,
uminus @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(36,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__neq__neg__numeral) ).
thf(390,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(50,axiom,
ord @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oord_36) ).
thf(418,plain,
ord @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(120,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_not__numeral__le__neg__numeral) ).
thf(568,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: num,B: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_fun__Compl__def) ).
thf(378,plain,
! [TA: $tType,TB: $tType] :
( ( uminus @ TB )
=> ( ( uminus_uminus @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA] : ( uminus_uminus @ TB @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_numeral__neq__neg__numeral) ).
thf(510,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( numeral_numeral @ TA @ A )
!= ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(302,axiom,
topolo503727757_space @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39) ).
thf(1308,plain,
topolo503727757_space @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(80,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_neg__0__equal__iff__equal) ).
thf(478,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
= ( ( zero_zero @ TA )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(33,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_equal__neg__zero) ).
thf(383,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(154,axiom,
! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_ereal3__cases) ).
thf(684,plain,
! [A: extended_ereal,B: extended_ereal,C: extended_ereal] :
( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ? [D: real] :
( A
= ( extended_ereal2 @ D ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( extend1396239628finity @ extended_ereal ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ? [D: real] :
( B
= ( extended_ereal2 @ D ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( extend1396239628finity @ extended_ereal ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ! [D: real] :
( C
!= ( extended_ereal2 @ D ) ) ) )
=> ( ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( extend1396239628finity @ extended_ereal ) ) ) )
=> ~ ( ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( ( B
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
=> ( C
!= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(107,axiom,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ extended_PInfty )
=> ( ( A @ extended_MInfty )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_uminus__ereal_Oinduct) ).
thf(536,plain,
! [A: extended_ereal > $o,B: extended_ereal] :
( ! [C: real] : ( A @ ( extended_ereal2 @ C ) )
=> ( ( A @ extended_PInfty )
=> ( ( A @ extended_MInfty )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Lattices_Oboolean__algebra) ).
thf(346,plain,
! [TA: $tType,TB: $tType] :
( ( boolean_algebra @ TA )
=> ( boolean_algebra @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(303,axiom,
! [A: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= ( zero_zero @ extended_ereal ) )
= ( A
= ( zero_zero @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_ereal__uminus__zero__iff) ).
thf(1309,plain,
! [A: extended_ereal] :
( ( ( uminus_uminus @ extended_ereal @ A )
= ( zero_zero @ extended_ereal ) )
= ( A
= ( zero_zero @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(237,axiom,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
=> ( ord_less_eq @ extended_ereal @ ( abs_abs @ extended_ereal @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_ereal__abs__leI) ).
thf(1116,plain,
! [A: extended_ereal,B: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ B )
=> ( ( ord_less_eq @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) @ B )
=> ( ord_less_eq @ extended_ereal @ ( abs_abs @ extended_ereal @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(243,axiom,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_compl__mono) ).
thf(1133,plain,
! [TA: $tType] :
( ( boolean_algebra @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ ( uminus_uminus @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(197,axiom,
( ( '!' @ extended_ereal )
= ( ^ [A: extended_ereal > $o] :
( ( A @ ( extend1396239628finity @ extended_ereal ) )
& ! [B: real] : ( A @ ( extended_ereal2 @ B ) )
& ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_ereal__all__split) ).
thf(999,plain,
( ( '!' @ extended_ereal )
= ( ^ [A: extended_ereal > $o] :
( ( A @ ( extend1396239628finity @ extended_ereal ) )
& ! [B: real] : ( A @ ( extended_ereal2 @ B ) )
& ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(293,axiom,
! [A: real] :
( ( ( zero_zero @ extended_ereal )
= ( extended_ereal2 @ A ) )
= ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_ereal__eq__0_I2_J) ).
thf(1280,plain,
! [A: real] :
( ( ( zero_zero @ extended_ereal )
= ( extended_ereal2 @ A ) )
= ( A
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(57,axiom,
! [A: real,B: real] :
( ( A = B )
=> ( ( extended_ereal2 @ A )
= ( extended_ereal2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_ereal__cong) ).
thf(432,plain,
! [A: real,B: real] :
( ( A = B )
=> ( ( extended_ereal2 @ A )
= ( extended_ereal2 @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(410,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA )
=> ( preorder @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(277,axiom,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_ereal__infty__less__eq_I2_J) ).
thf(1229,plain,
! [A: extended_ereal] :
( ( ord_less_eq @ extended_ereal @ A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) )
= ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_abs__le__D1) ).
thf(854,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(159,axiom,
! [A: extended_ereal] :
( ! [B: real] : ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_ereal__bot) ).
thf(865,plain,
! [A: extended_ereal] :
( ! [B: real] : ( ord_less_eq @ extended_ereal @ A @ ( extended_ereal2 @ B ) )
=> ( A
= ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(27,axiom,
preorder @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_33) ).
thf(373,plain,
preorder @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(118,axiom,
numeral @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral) ).
thf(564,plain,
numeral @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1,conjecture,
ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(326,plain,
~ ( ord_less_eq @ extended_ereal @ ( g @ x ) @ ( f @ x ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(174,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_minus__le__iff) ).
thf(918,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B )
= ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(146,axiom,
! [A: extended_enat] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ereal__of__enat__nonneg) ).
thf(664,plain,
! [A: extended_enat] : ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extend1771934483f_enat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(315,axiom,
! [A: real] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_ereal__less__eq_I5_J) ).
thf(1346,plain,
! [A: real] :
( ( ord_less_eq @ extended_ereal @ ( zero_zero @ extended_ereal ) @ ( extended_ereal2 @ A ) )
= ( ord_less_eq @ real @ ( zero_zero @ real ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(48,axiom,
linorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder) ).
thf(415,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(322,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_ord__le__eq__subst) ).
thf(1363,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA )
& ( ord @ TB ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(305,axiom,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_linorder__wlog) ).
thf(1314,plain,
! [TA: $tType] :
( ( linorder @ TA )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(77,axiom,
semiring_char_0 @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_20) ).
thf(474,plain,
semiring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(325,axiom,
zero @ extended_ereal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Real_Oereal___Groups_Ozero_47) ).
thf(1410,plain,
zero @ extended_ereal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(105,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_neg__numeral__neq__numeral) ).
thf(532,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: num,B: num] :
( ( uminus_uminus @ TA @ ( numeral_numeral @ TA @ A ) )
!= ( numeral_numeral @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(221,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ( ( order_antimono @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA,C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_antimono__def) ).
thf(1065,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ( ( order_antimono @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA,C: TA] :
( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(287,axiom,
( ( extend1716541707_ereal @ ( extend1396239628finity @ extended_ereal ) )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_real__of__ereal_Osimps_I2_J) ).
thf(1261,plain,
( ( extend1716541707_ereal @ ( extend1396239628finity @ extended_ereal ) )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(290,axiom,
! [A: extended_ereal] :
( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= ( abs_abs @ extended_ereal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_abs__ereal__uminus) ).
thf(1268,plain,
! [A: extended_ereal] :
( ( abs_abs @ extended_ereal @ ( uminus_uminus @ extended_ereal @ A ) )
= ( abs_abs @ extended_ereal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(54,axiom,
order @ extended_enat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_35) ).
thf(427,plain,
order @ extended_enat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(103,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zero__reorient) ).
thf(528,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(140,axiom,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_antisym__conv) ).
thf(644,plain,
! [TA: $tType] :
( ( order @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(319,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_abs__ge__minus__self) ).
thf(1357,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(170,axiom,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_ereal__less__eq_I1_J) ).
thf(908,plain,
! [A: extended_ereal] : ( ord_less_eq @ extended_ereal @ A @ ( extend1396239628finity @ extended_ereal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(92,axiom,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_the__enat_Osimps) ).
thf(501,plain,
! [A: nat] :
( ( extended_the_enat @ ( extended_enat2 @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo259154727pology @ TB ) )
=> ( ( lower_107104146le_lsc @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA] : ( lower_582600101lsc_at @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_lsc__def) ).
thf(369,plain,
! [TA: $tType,TB: $tType] :
( ( ( topolo503727757_space @ TA )
& ( topolo259154727pology @ TB ) )
=> ( ( lower_107104146le_lsc @ TA @ TB )
= ( ^ [A: TA > TB] :
! [B: TA] : ( lower_582600101lsc_at @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(84,axiom,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_strict__mono__eq) ).
thf(486,plain,
! [TA: $tType,TB: $tType] :
( ( ( linorder @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_strict_mono @ TA @ TB @ A )
=> ( ( ( A @ B )
= ( A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(181,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_neg__0__le__iff__le) ).
thf(940,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( uminus_uminus @ TA @ A ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(17,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(354,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA )
=> ( order @ ( TB > TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(210,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_antimono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_antimonoD) ).
thf(1037,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA )
& ( order @ TB ) )
=> ! [A: TA > TB,B: TA,C: TA] :
( ( order_antimono @ TA @ TB @ A )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(151,axiom,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
= ( ? [B: real] :
( A
= ( extended_ereal2 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_not__infty__ereal) ).
thf(676,plain,
! [A: extended_ereal] :
( ( ( abs_abs @ extended_ereal @ A )
!= ( extend1396239628finity @ extended_ereal ) )
= ( ? [B: real] :
( A
= ( extended_ereal2 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(228,axiom,
( ( numeral_numeral @ extended_ereal )
= ( ^ [A: num] : ( extended_ereal2 @ ( numeral_numeral @ real @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_numeral__eq__ereal) ).
thf(1088,plain,
( ( numeral_numeral @ extended_ereal )
= ( ^ [A: num] : ( extended_ereal2 @ ( numeral_numeral @ real @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(268,axiom,
! [A: extended_ereal] :
( ! [B: real] : ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ B ) @ A )
=> ( A
= ( extend1396239628finity @ extended_ereal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_ereal__top) ).
thf(1204,plain,
! [A: extended_ereal] :
( ! [B: real] : ( ord_less_eq @ extended_ereal @ ( extended_ereal2 @ B ) @ A )
=> ( A
= ( extend1396239628finity @ extended_ereal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_abs__le__D2) ).
thf(592,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ B )
=> ( ord_less_eq @ TA @ ( uminus_uminus @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(68,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Olinordered__ab__group__add) ).
thf(454,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(22,axiom,
order @ $o,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_14) ).
thf(364,plain,
order @ $o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(187,axiom,
( ( '?' @ extended_ereal )
= ( ^ [A: extended_ereal > $o] :
( ( A @ ( extend1396239628finity @ extended_ereal ) )
| ? [B: real] : ( A @ ( extended_ereal2 @ B ) )
| ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_ereal__ex__split) ).
thf(972,plain,
( ( '?' @ extended_ereal )
= ( ^ [A: extended_ereal > $o] :
( ( A @ ( extend1396239628finity @ extended_ereal ) )
| ? [B: real] : ( A @ ( extended_ereal2 @ B ) )
| ( A @ ( uminus_uminus @ extended_ereal @ ( extend1396239628finity @ extended_ereal ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1411,plain,
$false,
inference(cvc4,[status(thm)],[1105,893,1083,555,666,1110,365,1190,333,1031,481,352,1005,1290,1068,449,1142,440,614,408,977,523,582,500,1164,472,913,1354,670,1222,930,1196,898,1001,1243,1046,1359,565,436,389,1055,1287,570,1298,372,504,619,542,902,559,1147,606,1013,416,448,1232,1319,421,475,1302,1334,485,353,1283,905,348,574,602,1169,1215,453,396,1351,988,507,527,428,1201,439,661,925,1153,381,910,957,1343,1042,1217,424,407,1370,1238,862,349,484,889,1079,682,974,916,467,1159,461,493,1210,551,1128,519,650,1121,980,1096,1118,499,1138,356,471,1329,1028,1361,339,933,1182,489,547,901,476,1016,1207,679,1039,622,393,1099,515,1131,1192,1060,647,1263,1086,360,921,1167,1185,513,1219,856,1301,444,375,1135,412,562,1007,402,579,1256,1226,545,641,382,1312,611,498,1058,1332,1090,1258,947,350,672,445,936,1271,1371,406,419,1349,1043,1175,990,996,494,1339,535,594,1162,1325,895,943,1177,330,462,1112,345,552,1293,668,1198,399,1213,868,455,608,563,1250,1102,431,658,394,986,1034,490,1304,531,1277,342,1049,473,1076,1203,589,927,374,617,516,1145,1018,525,1003,1025,1070,1156,887,971,327,954,1267,409,993,1188,441,585,1235,576,359,1336,336,656,600,1052,386,859,1240,991,465,450,1180,1321,891,1126,1010,368,1108,363,556,1253,1062,351,390,418,568,378,510,1308,478,383,684,536,346,1309,1116,1133,999,1280,432,410,1229,854,865,373,564,326,918,664,1346,415,1363,1314,474,1410,532,1065,1261,1268,427,528,644,1357,908,501,369,486,940,354,1037,676,1088,1204,592,454,364,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP114^2 : TPTP v8.2.0. Released v7.5.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n029.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sat May 18 17:28:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.75/1.10 % [INFO] Parsing done (229ms).
% 1.75/1.11 % [INFO] Running in sequential loop mode.
% 2.43/1.32 % [INFO] eprover registered as external prover.
% 2.43/1.32 % [INFO] cvc4 registered as external prover.
% 2.43/1.32 % [INFO] Scanning for conjecture ...
% 2.78/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 324 axioms. Running axiom selection ...
% 3.02/1.50 % [INFO] Axiom selection finished. Selected 323 axioms (removed 1 axioms).
% 3.71/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 3.71/1.67 % [INFO] Type checking passed.
% 3.71/1.67 % [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 ...
% 63.66/25.04 % External prover 'cvc4' found a proof!
% 63.66/25.05 % [INFO] Killing All external provers ...
% 63.66/25.05 % Time passed: 24516ms (effective reasoning time: 23937ms)
% 63.66/25.05 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 63.66/25.05 % Axioms used in derivation (323): fact_5_le__funD, fact_169_numeral__eq__ereal, fact_83_ereal__uminus__zero, tcon_Nat_Onat___Topological__Spaces_Otopological__space_1, fact_43_antimonoD, tcon_Extended__Real_Oereal___Topological__Spaces_Otopological__space_39, fact_177_zero__ereal__def, tcon_Extended__Nat_Oenat___Topological__Spaces_Otopological__space_29, fact_247_abs__minus__le__zero, fact_6_le__funE, tcon_HOL_Obool___Orderings_Oorder_14, tfree_0, fact_171_ereal__eq__0_I2_J, fact_105_equation__minus__iff, fact_153_ereal__uminus__uminus, fact_35_Greatest__equality, fact_81_verit__minus__simplify_I4_J, tcon_Nat_Onat___Orderings_Olinorder, tcon_HOL_Obool___Lattices_Oboolean__algebra_11, fact_29_eq__refl, fact_217_abs__minus__cancel, fact_158_compl__le__swap1, fact_129_real__of__ereal__positive__mono, fact_234_abs__eq__infinity__cases, tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs, fact_151_compl__eq__compl__iff, fact_63_not__numeral__le__zero, fact_137_GreatestI__nat, fact_20_order__trans, fact_47_decseq__def, tcon_HOL_Obool___Orderings_Opreorder_12, fact_100_neg__less__eq__nonneg, tcon_Extended__Nat_Oenat___Orderings_Oorder_35, tcon_HOL_Obool___Topological__Spaces_Otopological__space_9, fact_238_abs__ge__zero, fact_134_le__trans, fact_42_antimonoE, fact_65_ile0__eq, fact_53_ereal__of__enat__zero, tcon_Extended__Nat_Oenat___Orderings_Opreorder_33, fact_204_uminus__ereal_Oinduct, fact_150_double__compl, fact_225_abs__neg__numeral, fact_123_neg__numeral__le__numeral, fact_31_antisym, fact_132_not__MInfty__nonneg, fact_212_abs__idempotent, fact_131_not__zero__le__neg__numeral, fact_172_ereal__less__eq_I3_J, fact_186_ereal__all__split, tcon_fun___Orderings_Oord, tcon_Extended__Real_Oereal___Groups_Ozero_47, fact_18_linorder__wlog, fact_251_divide__le__0__abs__iff, fact_148_the__enat_Osimps, tcon_Real_Oreal___Topological__Spaces_Oorder__topology_18, fact_89_equal__neg__zero, tcon_Real_Oreal___Topological__Spaces_Otopological__space_17, fact_146_less__eq__nat_Osimps_I1_J, fact_85_enat_Oinject, fact_138_nat__le__linear, tcon_fun___Topological__Spaces_Otopological__space, fact_162_dbl__simps_I1_J, fact_62_zero__le__numeral, tcon_HOL_Obool___Orderings_Oord_15, tcon_Extended__Nat_Oenat___Groups_Ocanonically__ordered__monoid__add_28, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring, fact_214_abs__eq__0, fact_221_ereal__divide__zero__left, fact_194_uminus__ereal_Osimps_I1_J, fact_229_ereal__divide__Infty_I2_J, fact_168_ereal_Oinject, tcon_Real_Oreal___Nat_Oring__char__0, fact_115_enat__0__iff_I1_J, fact_152_enat_Osimps_I4_J, tcon_Extended__Real_Oereal___Orderings_Oord_44, fact_199_uminus__ereal_Oelims, fact_87_neg__le__iff__le, fact_8_le__fun__def, fact_104_minus__equation__iff, fact_51_ereal__infty__less__eq_I1_J, fact_68_zero__reorient, fact_37_le__rel__bool__arg__iff, fact_118_MInfty__neq__PInfty_I1_J, subcl_Real__Vector__Spaces_Ometric__space___Topological__Spaces_Otopological__space, fact_160_real__eq__0__iff__le__ge__0, fact_116_enat__0__iff_I2_J, fact_210_ereal__divide__ereal, fact_174_real__of__ereal_Osimps_I1_J, fact_7_le__funI, fact_60_numeral__le__iff, fact_197_ereal_Osize__gen_I3_J, fact_41_antimonoI, fact_23_ord__eq__le__trans, fact_188_ereal__ex__split, tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_32, fact_170_ereal__eq__0_I1_J, fact_92_add_Oinverse__neutral, fact_59_ereal__less__eq_I1_J, fact_149_uminus__apply, fact_93_neg__numeral__eq__iff, fact_15_dual__order_Oantisym, fact_201_ereal_Osize__gen_I2_J, fact_139_Greatest__le__nat, fact_196_real__of__ereal_Oelims, tcon_Real_Oreal___Num_Onumeral_26, fact_109_le__imp__neg__le, fact_112_numeral__neq__neg__numeral, subcl_Real__Vector__Spaces_Ometric__space___HOL_Otype, fact_113_neg__numeral__neq__numeral, fact_195_ereal__bot, fact_154_ereal__uminus__eq__iff, fact_233_ereal__infinity__cases, fact_215_abs__0__eq, fact_44_lsc__def, tcon_Num_Onum___Orderings_Oorder_7, fact_88_neg__equal__zero, fact_4_ereal__complete__Sup, fact_50_numeral__le__ereal__of__enat__iff, fact_16_dual__order_Oeq__iff, tcon_Real_Oreal___Groups_Oordered__ab__group__add, tcon_Real_Oreal___Real__Vector__Spaces_Ometric__space, fact_79_neg__equal__iff__equal, fact_144_bot__nat__0_Oextremum__unique, fact_230_not__infty__ereal, fact_73_le0, fact_126_Infty__neq__0_I3_J, fact_157_compl__le__swap2, tcon_HOL_Obool___Groups_Ouminus_16, tcon_Real_Oreal___Orderings_Oord_24, fact_17_dual__order_Otrans, fact_57_neq__PInf__trans, fact_36_GreatestI2__order, fact_111_le__minus__iff, fact_110_minus__le__iff, fact_216_abs__numeral, fact_103_real__of__ereal_Osimps_I3_J, fact_13_ord__le__eq__subst, fact_236_abs__ereal__pos, fact_97_neg__0__le__iff__le, fact_9_order__subst1, fact_80_add_Oinverse__inverse, fact_231_abs__neq__infinity__cases, fact_142_strict__mono__imp__increasing, fact_226_abs__ereal__ge0, fact_26_le__cases3, fact_155_ereal__uminus__eq__reorder, fact_190_ereal2__cases, fact_107_real__of__ereal__eq__0, fact_70_le__numeral__extra_I3_J, fact_90_neg__equal__0__iff__equal, fact_240_abs__le__D2, fact_40_antimono__def, fact_237_zero__le__divide__ereal, tcon_Nat_Onat___Groups_Ozero, tcon_Extended__Real_Oereal___Orderings_Olinorder_42, fact_175_ereal__le__real, fact_213_abs__zero, fact_211_ereal__le__real__iff, fact_39_ereal__of__enat__le__iff, fact_193_ereal__top, fact_64_numeral__eq__iff, fact_98_neg__le__0__iff__le, fact_192_MInfty__neq__ereal_I1_J, fact_71_zero__neq__numeral, fact_128_ereal__less__eq_I2_J, fact_38_lsc__lsc__hull, fact_28_le__cases, fact_140_GreatestI__ex__nat, fact_120_enat__ile, fact_66_i0__lb, fact_232_abs__ereal_Osimps_I2_J, fact_33_lsc__hull__iff__greatest, fact_125_zero__neq__neg__numeral, fact_14_lsc__hull__le, fact_21_order__class_Oorder_Oantisym, fact_76_sub__non__positive, fact_145_le__0__eq, fact_235_ereal__abs__leI, fact_82_ereal__uminus__zero__iff, fact_191_ereal__cases, fact_69_zero__le, tcon_Extended__Real_Oereal___Topological__Spaces_Oorder__topology_40, fact_176_PInfty__neq__ereal_I1_J, fact_121_numeral__eq__enat, tcon_Extended__Real_Oereal___Orderings_Opreorder_41, fact_198_ereal_Osize__gen_I1_J, fact_136_le__antisym, fact_34_lsc__hull__greatest, tcon_Nat_Onat___Orderings_Opreorder_2, fact_78_real__of__ereal__le__0, fact_141_Nat_Oex__has__greatest__nat, fact_182_times__ereal_Oinduct, fact_1_calculation, fact_209_uminus__ereal_Osimps_I3_J, fact_135_eq__imp__le, fact_179_ereal__le__le, fact_12_ord__eq__le__subst, fact_227_ereal__divide__Infty_I1_J, fact_202_infinity__ereal__def, fact_77_sub__non__negative, tcon_Extended__Nat_Oenat___Topological__Spaces_Oorder__topology_30, fact_91_neg__0__equal__iff__equal, tcon_Extended__Real_Oereal___Orderings_Oorder_43, tcon_Real_Oreal___Orderings_Opreorder_21, tcon_Extended__Real_Oereal___Groups_Ouminus_45, fact_52_strict__mono__less__eq, tcon_Real_Oreal___Nat_Osemiring__char__0_20, fact_95_ereal__uminus__le__0__iff, tcon_HOL_Obool___Orderings_Olinorder_13, fact_241_abs__le__iff, fact_117_lsc__at__MInfty, tcon_fun___Lattices_Oboolean__algebra, fact_181_real__of__ereal_Ocases, fact_246_abs__le__D1, fact_178_le__ereal__le, fact_48_ereal__of__enat__nonneg, fact_3_ereal__complete__Inf, tcon_Real_Oreal___Groups_Ogroup__add, fact_30_linear, fact_24_order__class_Oorder_Oeq__iff, fact_203_ereal_Odistinct_I5_J, fact_206_ereal_Oexhaust, fact_224_abs__le__zero__iff, tcon_Nat_Onat___Num_Onumeral, fact_161_enat_Osimps_I6_J, tcon_Extended__Nat_Oenat___Orderings_Olinorder_34, fact_25_antisym__conv, fact_75_numeral__le__enat__iff, tcon_Nat_Onat___Orderings_Oorder_3, tcon_Real_Oreal___Groups_Ozero_27, fact_2_order__refl, fact_167_ereal__cong, tcon_Extended__Nat_Oenat___Groups_Ozero_38, tcon_fun___Orderings_Opreorder, tcon_Extended__Real_Oereal___Num_Onumeral_46, tcon_Num_Onum___Orderings_Opreorder_5, fact_11_verit__la__disequality, fact_101_real__of__ereal__0, tcon_Real_Oreal___Fields_Olinordered__field, tcon_Real_Oreal___Rings_Olinordered__idom, fact_250_real__le__ereal__iff, fact_165_ereal__less__eq_I4_J, fact_108_real__of__ereal_Osimps_I2_J, fact_156_fun__Compl__def, fact_46_decseqD, fact_243_ereal__divide__eq__0__iff, fact_114_zero__enat__def, fact_249_ereal__real, tcon_Extended__Nat_Oenat___Rings_Olinordered__nonzero__semiring_31, fact_58_ereal__infty__less__eq2_I1_J, fact_102_enat__ord__simps_I1_J, fact_220_ereal__uminus__divide, fact_61_le__zero__eq, fact_67_enat__ord__number_I1_J, fact_99_less__eq__neg__nonpos, fact_72_bot__nat__0_Oextremum, fact_133_le__refl, tcon_Extended__Nat_Oenat___Orderings_Oord_36, fact_218_abs__ereal__uminus, tcon_Nat_Onat___Topological__Spaces_Oorder__topology, fact_96_ereal__0__le__uminus__iff, tcon_HOL_Obool___Topological__Spaces_Oorder__topology_10, tcon_Num_Onum___Orderings_Olinorder_6, tcon_Real_Oreal___Num_Oneg__numeral, fact_74_neg__numeral__le__iff, tcon_Real_Oreal___Orderings_Olinorder_22, tcon_fun___Orderings_Oorder, fact_147_compl__le__compl__iff, fact_22_ord__le__eq__trans, fact_180_real__of__ereal_Oinduct, fact_84_ereal__minus__le__minus, fact_222_abs__of__nonneg, fact_208_uminus__ereal_Osimps_I2_J, tcon_Real_Oreal___Groups_Olinordered__ab__group__add, tcon_Real_Oreal___Orderings_Oorder_23, fact_119_ereal__uminus__le__reorder, fact_106_verit__negate__coefficient_I3_J, fact_228_abs__of__nonpos, fact_207_ereal_Oinduct, fact_223_abs__le__self__iff, fact_242_abs__ge__minus__self, fact_205_uminus__ereal_Ocases, tcon_Nat_Onat___Orderings_Oord_4, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, tcon_fun___Groups_Ouminus, fact_163_dbl__simps_I2_J, tcon_Real_Oreal___Rings_Olinordered__nonzero__semiring_19, fact_184_less__ereal_Oinduct, fact_55_Infty__neq__0_I1_J, fact_86_real__of__ereal, fact_245_abs__ge__self, tcon_Real_Oreal___Groups_Ouminus_25, fact_189_ereal3__cases, fact_248_ereal__real_H, fact_0_assms, fact_94_ereal__infty__less__eq_I2_J, fact_164_ereal__less__eq_I5_J, fact_166_MInfty__eq__minfinity, fact_187_abs__ereal_Ocases, fact_54_strict__mono__eq, fact_219_abs__ereal__zero, fact_49_ereal__of__enat__ge__zero__cancel__iff, tcon_Nat_Onat___Nat_Osemiring__char__0, fact_239_abs__leI, fact_10_order__subst2, fact_122_real__of__ereal__pos, fact_56_strict__mono__leD, fact_124_not__numeral__le__neg__numeral, tcon_Num_Onum___Orderings_Oord_8, fact_183_plus__ereal_Oinduct, fact_27_order_Otrans, fact_244_abs__ereal_Osimps_I3_J, fact_19_dual__order_Orefl, fact_130_neg__numeral__le__zero, fact_159_compl__mono, fact_143_bot__nat__0_Oextremum__uniqueI, fact_185_abs__ereal_Oinduct, fact_200_ereal_Odistinct_I1_J, fact_127_ereal__infty__less__eq2_I2_J, fact_173_ereal_Odistinct_I3_J, tcon_Extended__Nat_Oenat___Num_Onumeral_37, fact_32_eq__iff
% 63.66/25.05 % No. of inferences in proof: 650
% 63.66/25.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 24516 ms resp. 23937 ms w/o parsing
% 64.10/25.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 64.10/25.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------