%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : DAT159^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 07:48:03 AM UTC 2026
% Result : Theorem 40.20s 21.73s
% Output : Refutation 40.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 323
% Syntax : Number of formulae : 648 ( 213 unt; 0 typ; 0 def)
% Number of atoms : 1937 ( 418 equ; 2 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 7137 ( 208 ~; 43 |; 92 &;5756 @)
% ( 0 <=>;1038 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 162 ( 162 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 5 con; 0-4 aty)
% Number of variables : 1691 ( 48 ^;1547 !; 96 ?;1691 :)
% Comments :
%------------------------------------------------------------------------------
thf(code_natural_type,type,
code_natural: $tType ).
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(field_decl,type,
field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(order_decl,type,
order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_bot_decl,type,
no_bot:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(no_top_decl,type,
no_top:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(wellorder_decl,type,
wellorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(division_ring_decl,type,
division_ring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_order_decl,type,
dense_order:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(dense_linorder_decl,type,
dense_linorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiri134348788visors_decl,type,
semiri134348788visors:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(archim1804426504_field_decl,type,
archim1804426504_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1656338222tinuum_decl,type,
condit1656338222tinuum:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(condit1037483654norder_decl,type,
condit1037483654norder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(code_case_natural_decl,type,
code_case_natural:
!>[TA: $tType] : ( TA > ( code_natural > TA ) > code_natural > TA ) ).
thf(code_size_natural_decl,type,
code_size_natural: code_natural > nat ).
thf(inverse_inverse_decl,type,
inverse_inverse:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(hammin1195055315smooth_decl,type,
hammin1195055315smooth: nat > $o ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( $o > TA > TA > TA ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(type2_decl,type,
type2:
!>[TA: $tType] : ( itself @ TA ) ).
thf(zero_neq_one_of_bool_decl,type,
zero_neq_one_of_bool:
!>[TA: $tType] : ( $o > TA ) ).
thf(n_decl,type,
n: nat ).
thf(186,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_less__not__refl) ).
thf(809,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(125,axiom,
semiring_1 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_11) ).
thf(629,plain,
semiring_1 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(198,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_zero__power) ).
thf(846,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_le__funI) ).
thf(333,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB] :
( ! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) )
=> ( ord_less_eq @ ( TA > TB ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(93,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_neq0__conv) ).
thf(518,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(15,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_of__nat__eq__iff) ).
thf(352,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( semiring_1_of_nat @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(132,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_dual__order_Ostrict__implies__not__eq) ).
thf(645,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(212,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_zero__le) ).
thf(892,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_less__imp__of__nat__less) ).
thf(1083,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_le__funD) ).
thf(468,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(140,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_less__or__eq__imp__le) ).
thf(666,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(324,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_not__less) ).
thf(1295,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(39,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_order__refl) ).
thf(408,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(207,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_nonneg__int__cases) ).
thf(873,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(202,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_order_Oasym) ).
thf(861,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(278,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_dual__order_Ostrict__iff__order) ).
thf(1142,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(26,axiom,
dense_linorder @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Odense__linorder) ).
thf(379,plain,
dense_linorder @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(30,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_le__cases) ).
thf(385,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(276,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__eq__int__code_I1_J) ).
thf(1137,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_less__fun__def) ).
thf(533,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
& ~ ( ord_less_eq @ ( TA > TB ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(284,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_minf_I1_J) ).
thf(1164,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(156,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_inverse__le__iff__le) ).
thf(715,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(220,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_ord__less__eq__trans) ).
thf(913,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(229,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_of__nat__0__eq__iff) ).
thf(945,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ( zero_zero @ TA )
= ( semiring_1_of_nat @ TA @ A ) )
= ( ( zero_zero @ nat )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(10,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord) ).
thf(340,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ( ord @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(101,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_le__refl) ).
thf(538,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(302,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_dense__ge__bounded) ).
thf(1222,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ C @ D ) ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(269,axiom,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_natural_Osize_I1_J) ).
thf(1095,plain,
( ( code_size_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(292,axiom,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_gt__ex) ).
thf(1196,plain,
! [TA: $tType] :
( ( no_top @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(180,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ~ ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_less__le__not__le) ).
thf(782,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ 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)],[180]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_le__trans) ).
thf(709,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)],[154]) ).
thf(134,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_inverse__positive__imp__positive) ).
thf(651,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(196,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_le__zero__eq) ).
thf(841,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(44,axiom,
linorder @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder) ).
thf(417,plain,
linorder @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(159,axiom,
! [A: int > $o] :
( ( ? [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( A @ B ) ) )
= ( ? [B: nat] : ( A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_transfer__int__nat__quantifiers_I2_J) ).
thf(724,plain,
! [A: int > $o] :
( ( ? [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& ( A @ B ) ) )
= ( ? [B: nat] : ( A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(321,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ C @ B )
=> ( A = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_minf_I11_J) ).
thf(1287,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(181,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_gr__zeroI) ).
thf(785,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(87,axiom,
zero_neq_one @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ozero__neq__one_25) ).
thf(504,plain,
zero_neq_one @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(314,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_power__not__zero) ).
thf(1264,plain,
! [TA: $tType] :
( ( semiri134348788visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ B )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(195,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( power_power @ nat @ A @ B ) )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_of__nat__power) ).
thf(838,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( semiring_1_of_nat @ TA @ ( power_power @ nat @ A @ B ) )
= ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(221,axiom,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(917,plain,
! [A: nat] : ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(318,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_neq__iff) ).
thf(1279,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
= ( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(274,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_of__nat__0) ).
thf(1132,plain,
! [TA: $tType] :
( ( semiring_1 @ TA @ ( type2 @ TA ) )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(225,axiom,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_ex__gt__or__lt) ).
thf(934,plain,
! [TA: $tType] :
( ( condit1656338222tinuum @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
( ( ord_less @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(18,axiom,
no_top @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__top) ).
thf(357,plain,
no_top @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(289,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1191,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_le__imp__inverse__le) ).
thf(1147,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(308,axiom,
! [A: int > $o] :
( ( ! [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( A @ B ) ) )
= ( ! [B: nat] : ( A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_transfer__int__nat__quantifiers_I1_J) ).
thf(1247,plain,
! [A: int > $o] :
( ( ! [B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( A @ B ) ) )
= ( ! [B: nat] : ( A @ ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(48,axiom,
semiring_1 @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__1_38) ).
thf(421,plain,
semiring_1 @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(236,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_minf_I2_J) ).
thf(969,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(43,axiom,
preorder @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_1) ).
thf(416,plain,
preorder @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1,conjecture,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ n ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(325,plain,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(305,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_less__imp__inverse__less__neg) ).
thf(1232,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(248,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_less__not__refl2) ).
thf(1013,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_inverse__le__iff__le__neg) ).
thf(770,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(81,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_antisym__conv) ).
thf(492,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(183,axiom,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> C )
= ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_imp__le__cong) ).
thf(789,plain,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> C )
= ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(253,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_dense__ge) ).
thf(1040,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ A @ C )
=> ( ord_less_eq @ TA @ B @ C ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(24,axiom,
ord @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_3) ).
thf(376,plain,
ord @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(75,axiom,
semiring_1 @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(485,plain,
semiring_1 @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(250,axiom,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_ex__has__greatest__nat) ).
thf(1020,plain,
! [TA: $tType,A: TA > $o,B: TA,C: TA > nat,D: nat] :
( ( A @ B )
=> ( ! [E: TA] :
( ( A @ E )
=> ( ord_less @ nat @ ( C @ E ) @ D ) )
=> ? [E: TA] :
( ( A @ E )
& ! [F: TA] :
( ( A @ F )
=> ( ord_less_eq @ nat @ ( C @ F ) @ ( C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(238,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_le__eq__less__or__eq) ).
thf(981,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(147,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type2 @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_field__class_Ofield__inverse__zero) ).
thf(687,plain,
! [TA: $tType] :
( ( field @ TA @ ( type2 @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(128,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_of__nat__less__imp__less) ).
thf(634,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(162,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zero__le__imp__eq__int) ).
thf(734,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( A
= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(138,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( power_power @ TA @ B @ A )
= ( power_power @ TA @ C @ A ) )
= ( B = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_power__eq__iff__eq__base) ).
thf(660,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: TA,C: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ( power_power @ TA @ B @ A )
= ( power_power @ TA @ C @ A ) )
= ( B = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(294,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_not__less__zero) ).
thf(1201,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(199,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_power__mono) ).
thf(849,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(90,axiom,
ord @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_14) ).
thf(507,plain,
ord @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(96,axiom,
order @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_13) ).
thf(527,plain,
order @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(208,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ( power_power @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_power__eq__0__iff) ).
thf(877,plain,
! [TA: $tType] :
( ( semiri134348788visors @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ( power_power @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__linear) ).
thf(692,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(27,axiom,
zero @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_33) ).
thf(380,plain,
zero @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(227,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__not__sym) ).
thf(942,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(28,axiom,
preorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_16) ).
thf(381,plain,
preorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(282,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_dual__order_Oirrefl) ).
thf(1153,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(172,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_inverse__positive__iff__positive) ).
thf(761,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(255,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_not__less__iff__gr__or__eq) ).
thf(1047,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less @ TA @ A @ B ) )
= ( ( ord_less @ TA @ B @ A )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(184,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_measure__induct) ).
thf(798,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(213,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_gr0I) ).
thf(894,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_of__nat__0__le__iff) ).
thf(778,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(231,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_dual__order_Oasym) ).
thf(952,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(310,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_zero__le__power) ).
thf(1255,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(285,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_infinite__descent0__measure) ).
thf(1174,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(299,axiom,
( ( zero_zero @ int )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_zero__integer_Orsp) ).
thf(1217,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(191,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_pinf_I1_J) ).
thf(820,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
& ( C @ F ) )
= ( ( B @ F )
& ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(109,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_of__nat__le__0__iff) ).
thf(561,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(51,axiom,
zero_neq_one @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__neq__one) ).
thf(424,plain,
zero_neq_one @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(126,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__trans) ).
thf(630,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_int__int__eq) ).
thf(429,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(182,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA] :
? [B: TB] :
! [C: TB] :
( ( ord_less @ TB @ B @ C )
=> ( A = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_pinf_I11_J) ).
thf(788,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(72,axiom,
semiring_char_0 @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Osemiring__char__0_24) ).
thf(467,plain,
semiring_char_0 @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_inverse__eq__iff__eq) ).
thf(361,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(201,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_nat__less__induct) ).
thf(852,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(192,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_zero__reorient) ).
thf(830,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(69,axiom,
field @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield) ).
thf(461,plain,
field @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_pinf_I4_J) ).
thf(1210,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_leD) ).
thf(1079,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(323,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_order__less__le__subst2) ).
thf(1291,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_le__neq__implies__less) ).
thf(682,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(291,axiom,
semiri134348788visors @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_5) ).
thf(1195,plain,
semiri134348788visors @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(107,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_less__imp__inverse__less) ).
thf(551,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(272,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_less__imp__not__less) ).
thf(1128,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(114,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_dual__order_Ostrict__implies__order) ).
thf(578,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(306,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB ) > TA > TB > $o] :
( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
( ! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( A @ C @ E @ B )
= ( A @ D @ E @ B ) ) )
=> ( ! [B: TA,C: TA > TB] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ B )
=> ( A @ C @ D @ ( C @ D ) ) )
=> ? [D: TB] : ( A @ C @ B @ D ) )
=> ? [B: TA > TB] :
! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_dependent__wellorder__choice) ).
thf(1234,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: ( TA > TB ) > TA > TB > $o] :
( ! [B: TB,C: TA > TB,D: TA > TB,E: TA] :
( ! [F: TA] :
( ( ord_less @ TA @ F @ E )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ( ( A @ C @ E @ B )
= ( A @ D @ E @ B ) ) )
=> ( ! [B: TA,C: TA > TB] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ B )
=> ( A @ C @ D @ ( C @ D ) ) )
=> ? [D: TB] : ( A @ C @ B @ D ) )
=> ? [B: TA > TB] :
! [C: TA] : ( A @ B @ C @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(312,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_not__le) ).
thf(1259,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ~ ( ord_less_eq @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(230,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ 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 @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_order__less__le__subst1) ).
thf(948,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ 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 @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(249,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_antisym__conv2) ).
thf(1017,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ A @ B ) )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(303,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_inverse__negative__imp__negative) ).
thf(1227,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(37,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_order_Otrans) ).
thf(403,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(47,axiom,
order @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_18) ).
thf(420,plain,
order @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(241,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A = C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_power__eq__imp__eq__base) ).
thf(989,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat,C: TA] :
( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( A = C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(277,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_order__less__subst2) ).
thf(1138,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(17,axiom,
linorder @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Olinorder_27) ).
thf(356,plain,
linorder @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(4,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_inverse__inverse__eq) ).
thf(328,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(78,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_dual__order_Otrans) ).
thf(488,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(9,axiom,
ord @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_19) ).
thf(339,plain,
ord @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(298,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_not__gr0) ).
thf(1214,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(296,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__0__eq) ).
thf(1207,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(143,axiom,
wellorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(679,plain,
wellorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_inverse__less__iff__less) ).
thf(706,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(283,axiom,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ C )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_int__if__cong) ).
thf(1155,plain,
! [A: $o,B: nat,C: nat] :
( ( A
=> ( ( semiring_1_of_nat @ int @ B )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) )
& ( ~ A
=> ( ( semiring_1_of_nat @ int @ C )
= ( semiring_1_of_nat @ int @ ( if @ nat @ A @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(105,axiom,
( ( zero_zero @ nat )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_zero__natural_Orsp) ).
thf(547,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(244,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_pinf_I2_J) ).
thf(997,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA > $o,C: TA > $o,D: TA > $o] :
( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( A @ F )
= ( B @ F ) ) )
=> ( ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( C @ F )
= ( D @ F ) ) )
=> ? [E: TA] :
! [F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ( ( A @ F )
| ( C @ F ) )
= ( ( B @ F )
| ( D @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(654,plain,
! [A: nat,B: nat] :
( ( power_power @ int @ ( semiring_1_of_nat @ int @ A ) @ B )
= ( semiring_1_of_nat @ int @ ( power_power @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(290,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_inverse__nonpositive__iff__nonpositive) ).
thf(1192,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(219,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_minf_I7_J) ).
thf(911,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(259,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_less__asym_H) ).
thf(1060,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_le__antisym) ).
thf(1050,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)],[256]) ).
thf(67,axiom,
zero @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(457,plain,
zero @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(86,axiom,
no_bot @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Ono__bot_30) ).
thf(503,plain,
no_bot @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(121,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_ord__eq__less__trans) ).
thf(605,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(12,axiom,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder) ).
thf(343,plain,
! [TA: $tType,TB: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( order @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
semiri134348788visors @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Osemiring__1__no__zero__divisors_34) ).
thf(360,plain,
semiri134348788visors @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(91,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ord__less__eq__subst) ).
thf(508,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less @ TB @ E @ F )
=> ( ord_less @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(136,axiom,
hammin1195055315smooth @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(657,plain,
hammin1195055315smooth @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_antisym__conv3) ).
thf(773,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ~ ( ord_less @ TA @ B @ A ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(157,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_pinf_I8_J) ).
thf(718,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(320,axiom,
linordered_semidom @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_6) ).
thf(1286,plain,
linordered_semidom @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(251,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_minf_I6_J) ).
thf(1035,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(217,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_dual__order_Ostrict__trans1) ).
thf(906,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(52,axiom,
semiri134348788visors @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_21) ).
thf(425,plain,
semiri134348788visors @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(167,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_order_Onot__eq__order__implies__strict) ).
thf(745,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(60,axiom,
dense_order @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Odense__order) ).
thf(444,plain,
dense_order @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(275,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_nat__le__linear) ).
thf(1135,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)],[275]) ).
thf(41,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_antisym) ).
thf(412,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(50,axiom,
zero_neq_one @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_35) ).
thf(423,plain,
zero_neq_one @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_pinf_I7_J) ).
thf(1007,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(36,axiom,
semiring_1 @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1_28) ).
thf(402,plain,
semiring_1 @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(166,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_order_Ostrict__trans1) ).
thf(743,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(29,axiom,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_transfer__int__nat__relations_I1_J) ).
thf(382,plain,
! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ int @ A )
= ( semiring_1_of_nat @ int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(316,axiom,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__induct) ).
thf(1271,plain,
! [TA: $tType] :
( ( wellorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > $o,B: TA] :
( ! [C: TA] :
( ! [D: TA] :
( ( ord_less @ TA @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(123,axiom,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_ex__least__nat__le) ).
thf(611,plain,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_ord__eq__le__trans) ).
thf(498,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( A = B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(7,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_inverse__eq__imp__eq) ).
thf(335,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(266,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_inverse__less__imp__less) ).
thf(1090,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(102,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_less__irrefl__nat) ).
thf(540,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(141,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_nonneg__eq__int) ).
thf(672,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ~ ! [B: nat] :
( A
!= ( semiring_1_of_nat @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(61,axiom,
! [A: $o] :
( ( A = $true )
| ( A = $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(445,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(226,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_measure__induct__rule) ).
thf(936,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(71,axiom,
ord @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Oord_40) ).
thf(466,plain,
ord @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(267,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_linordered__field__no__ub) ).
thf(1092,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(222,axiom,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& C )
= ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_conj__le__cong) ).
thf(919,plain,
! [A: int,B: int,C: $o,D: $o] :
( ( A = B )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( C = D ) )
=> ( ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& C )
= ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
& D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(185,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_less__mono__imp__le__mono) ).
thf(804,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(215,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_less__zeroE) ).
thf(900,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(319,axiom,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_dense) ).
thf(1282,plain,
! [TA: $tType] :
( ( dense_order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ? [C: TA] :
( ( ord_less @ TA @ A @ C )
& ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(25,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_le__funE) ).
thf(377,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ! [A: TA > TB,B: TA > TB,C: TA] :
( ( ord_less_eq @ ( TA > TB ) @ A @ B )
=> ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_le__fun__def) ).
thf(451,plain,
! [TA: $tType,TB: $tType] :
( ( ord @ TB @ ( type2 @ TB ) )
=> ( ( ord_less_eq @ ( TA > TB ) )
= ( ^ [A: TA > TB,B: TA > TB] :
! [C: TA] : ( ord_less_eq @ TB @ ( A @ C ) @ ( B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(163,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_linordered__field__no__lb) ).
thf(737,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(203,axiom,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_natural_Osize_I3_J) ).
thf(863,plain,
( ( size_size @ code_natural @ ( zero_zero @ code_natural ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(173,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_linorder__neqE__nat) ).
thf(764,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(237,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_less__int__code_I1_J) ).
thf(979,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(247,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_less__imp__le__nat) ).
thf(1011,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(46,axiom,
preorder @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Opreorder_26) ).
thf(419,plain,
preorder @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(209,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_infinite__descent__measure) ).
thf(880,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(133,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_pinf_I5_J) ).
thf(649,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(57,axiom,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ord__le__eq__trans) ).
thf(434,plain,
! [TA: $tType] :
( ( ord @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( B = C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_power__strict__mono) ).
thf(890,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ord__le__eq__subst) ).
thf(387,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ( C @ B )
= D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(171,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_of__nat__eq__0__iff) ).
thf(758,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ( semiring_1_of_nat @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(13,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_linorder__wlog) ).
thf(345,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA > TA > $o,B: TA,C: TA] :
( ! [D: TA,E: TA] :
( ( ord_less_eq @ TA @ D @ E )
=> ( A @ D @ E ) )
=> ( ! [D: TA,E: TA] :
( ( A @ E @ D )
=> ( A @ D @ E ) )
=> ( A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(189,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__irrefl) ).
thf(816,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(122,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_le__less__trans) ).
thf(609,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(118,axiom,
zero_neq_one @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one_8) ).
thf(594,plain,
zero_neq_one @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(281,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_pinf_I3_J) ).
thf(1149,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_natural_Osimps_I4_J) ).
thf(626,plain,
! [TA: $tType,A: TA,B: code_natural > TA] :
( ( code_case_natural @ TA @ A @ B @ ( zero_zero @ code_natural ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(70,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_order__subst1) ).
thf(462,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(239,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_eq__imp__le) ).
thf(983,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(293,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ A )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_nonzero__imp__inverse__nonzero) ).
thf(1198,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ A )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(33,axiom,
linordered_semidom @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semidom_22) ).
thf(399,plain,
linordered_semidom @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(233,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_less__not__refl3) ).
thf(959,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(205,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_not__gr__zero) ).
thf(868,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(179,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_inverse__less__imp__less__neg) ).
thf(780,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(309,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_dense__le__bounded) ).
thf(1250,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ! [D: TA] :
( ( ord_less @ TA @ A @ D )
=> ( ( ord_less @ TA @ D @ B )
=> ( ord_less_eq @ TA @ D @ C ) ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(200,axiom,
condit1037483654norder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_4) ).
thf(851,plain,
condit1037483654norder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(137,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_le__less__linear) ).
thf(658,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(146,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_reals__Archimedean2) ).
thf(685,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(94,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_dual__order_Oorder__iff__strict) ).
thf(521,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(150,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__imp__not__eq) ).
thf(695,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(129,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_minf_I4_J) ).
thf(636,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(254,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_nat__zero__less__power__iff) ).
thf(1044,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( power_power @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(88,axiom,
condit1037483654norder @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_20) ).
thf(505,plain,
condit1037483654norder @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(58,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( power_power @ TA @ ( inverse_inverse @ TA @ A ) @ B )
= ( inverse_inverse @ TA @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_power__inverse) ).
thf(438,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( power_power @ TA @ ( inverse_inverse @ TA @ A ) @ B )
= ( inverse_inverse @ TA @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(79,axiom,
order @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oorder_31) ).
thf(490,plain,
order @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(426,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $false @ A @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(144,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_minf_I5_J) ).
thf(680,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( ord_less @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(317,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_le__imp__inverse__le__neg) ).
thf(1277,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ B ) @ ( inverse_inverse @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(77,axiom,
linordered_field @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(487,plain,
linordered_field @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(187,axiom,
linorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder_10) ).
thf(812,plain,
linorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(262,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_order_Ostrict__implies__order) ).
thf(1081,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(92,axiom,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_transfer__int__nat__numerals_I1_J) ).
thf(516,plain,
( ( zero_zero @ int )
= ( semiring_1_of_nat @ int @ ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(11,axiom,
no_top @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Ono__top_29) ).
thf(342,plain,
no_top @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(279,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__asym) ).
thf(1145,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ~ ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(16,axiom,
no_bot @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__bot) ).
thf(355,plain,
no_bot @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_ord__eq__less__subst) ).
thf(553,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(458,plain,
! [TA: $tType,A: TA,B: TA] :
( ( if @ TA @ $true @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(194,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_minf_I8_J) ).
thf(836,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(295,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__imp__neq) ).
thf(1203,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(116,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_nonzero__inverse__inverse__eq) ).
thf(589,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( inverse_inverse @ TA @ ( inverse_inverse @ TA @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(98,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_inverse__le__imp__le) ).
thf(531,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(228,axiom,
semiring_char_0 @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_7) ).
thf(944,plain,
semiring_char_0 @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(139,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_inverse__less__iff__less__neg) ).
thf(663,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
= ( ord_less @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(106,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_nat__power__less__imp__less) ).
thf(548,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( power_power @ nat @ A @ B ) @ ( power_power @ nat @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(177,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_less__imp__le) ).
thf(776,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(155,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_inverse__zero__imp__zero) ).
thf(712,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(115,axiom,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_realpow__pos__nth__unique) ).
thf(580,plain,
! [A: nat,B: real] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ B )
=> ? [C: real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ C )
& ( ( power_power @ real @ C @ A )
= B )
& ! [D: real] :
( ( ( ord_less @ real @ ( zero_zero @ real ) @ D )
& ( ( power_power @ real @ D @ A )
= B ) )
=> ( D = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(148,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_order_Ostrict__trans) ).
thf(690,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_inverse__negative__iff__negative) ).
thf(640,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(232,axiom,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zero__less__imp__eq__int) ).
thf(954,plain,
! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( A
= ( semiring_1_of_nat @ int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(164,axiom,
zero @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_15) ).
thf(739,plain,
zero @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(315,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_gr__implies__not0) ).
thf(1267,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(304,axiom,
~ ( hammin1195055315smooth @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_smooth__0) ).
thf(1230,plain,
~ ( hammin1195055315smooth @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(257,axiom,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(1053,plain,
! [A: int,B: nat] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(59,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_order__class_Oorder_Oantisym) ).
thf(441,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(85,axiom,
condit1037483654norder @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder) ).
thf(502,plain,
condit1037483654norder @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(313,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_inverse__le__imp__le__neg) ).
thf(1262,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( inverse_inverse @ TA @ A ) @ ( inverse_inverse @ TA @ B ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(8,axiom,
archim1804426504_field @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field) ).
thf(338,plain,
archim1804426504_field @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(273,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_of__nat__less__0__iff) ).
thf(1130,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(300,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_dual__order_Ostrict__trans) ).
thf(1218,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(131,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_nat__less__le) ).
thf(643,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(301,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_dual__order_Ostrict__trans2) ).
thf(1220,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ A )
=> ( ord_less @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(104,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_order_Ostrict__iff__order) ).
thf(544,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(5,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_dual__order_Orefl) ).
thf(331,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(288,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_linorder__neqE__linordered__idom) ).
thf(1188,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(287,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_less__le__trans) ).
thf(1186,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_of__nat__zero__less__power__iff) ).
thf(1085,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( semiring_1_of_nat @ TA @ A ) @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( B
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(74,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_le__cases3) ).
thf(470,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
=> ~ ( ord_less_eq @ TA @ B @ C ) )
=> ( ( ( ord_less_eq @ TA @ B @ A )
=> ~ ( ord_less_eq @ TA @ A @ C ) )
=> ( ( ( ord_less_eq @ TA @ A @ C )
=> ~ ( ord_less_eq @ TA @ C @ B ) )
=> ( ( ( ord_less_eq @ TA @ C @ B )
=> ~ ( ord_less_eq @ TA @ B @ A ) )
=> ( ( ( ord_less_eq @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) )
=> ~ ( ( ord_less_eq @ TA @ C @ A )
=> ~ ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(311,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_less__numeral__extra_I3_J) ).
thf(1257,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(152,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_of__nat__le__iff) ).
thf(703,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less_eq @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(160,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_less__imp__not__eq2) ).
thf(727,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(268,axiom,
preorder @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_9) ).
thf(1094,plain,
preorder @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(119,axiom,
no_top @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top_12) ).
thf(595,plain,
no_top @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(83,axiom,
linorder @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Olinorder_37) ).
thf(497,plain,
linorder @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(62,axiom,
linordered_semidom @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(446,plain,
linordered_semidom @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(112,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_gr__implies__not__zero) ).
thf(571,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(64,axiom,
linordered_idom @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(450,plain,
linordered_idom @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(224,axiom,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_transfer__int__nat__relations_I2_J) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( ord_less @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(216,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_nat__neq__iff) ).
thf(903,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_antisym__conv1) ).
thf(524,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(82,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_linear) ).
thf(495,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
| ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(271,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_negative__imp__inverse__negative) ).
thf(1126,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( inverse_inverse @ TA @ A ) @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(23,axiom,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_ord__eq__le__subst) ).
thf(368,plain,
! [TA: $tType,TB: $tType] :
( ( ( ord @ TA @ ( type2 @ TA ) )
& ( ord @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( A
= ( B @ C ) )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less_eq @ TA @ E @ F )
=> ( ord_less_eq @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less_eq @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(197,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_not__le__imp__less) ).
thf(844,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(151,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_ex__inverse__of__nat__less) ).
thf(699,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ? [B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ TA @ ( inverse_inverse @ TA @ ( semiring_1_of_nat @ TA @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(188,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_inverse__nonzero__iff__nonzero) ).
thf(813,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(234,axiom,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_dense__le) ).
thf(963,plain,
! [TA: $tType] :
( ( dense_linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ! [C: TA] :
( ( ord_less @ TA @ C @ A )
=> ( ord_less_eq @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(168,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_minf_I3_J) ).
thf(748,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ C @ B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(260,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_infinite__descent0) ).
thf(1062,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(14,axiom,
zero @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Groups_Ozero_41) ).
thf(351,plain,
zero @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(127,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le0) ).
thf(632,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(35,axiom,
order @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Oorder_39) ).
thf(401,plain,
order @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(307,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_of__nat__0__less__iff) ).
thf(1244,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(243,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_leI) ).
thf(995,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(161,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_of__nat__less__iff) ).
thf(731,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( semiring_1_of_nat @ TA @ B ) )
= ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(45,axiom,
condit1656338222tinuum @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum) ).
thf(418,plain,
condit1656338222tinuum @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(111,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_le__neq__trans) ).
thf(568,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(56,axiom,
linordered_idom @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_23) ).
thf(433,plain,
linordered_idom @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(100,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_le__numeral__extra_I3_J) ).
thf(536,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_linorder__cases) ).
thf(752,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ~ ( ord_less @ TA @ A @ B )
=> ( ( A != B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(63,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ! [A: $o,B: $o] :
( ( ( zero_neq_one_of_bool @ TA @ A )
= ( zero_neq_one_of_bool @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_of__bool__eq__iff) ).
thf(447,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ! [A: $o,B: $o] :
( ( ( zero_neq_one_of_bool @ TA @ A )
= ( zero_neq_one_of_bool @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(55,axiom,
order @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_2) ).
thf(432,plain,
order @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(270,axiom,
! [TA: $tType] :
( ( condit1037483654norder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_complete__interval) ).
thf(1097,plain,
! [TA: $tType] :
( ( condit1037483654norder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA > $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( C @ A )
=> ( ~ ( C @ B )
=> ? [D: TA] :
( ( ord_less_eq @ TA @ A @ D )
& ( ord_less_eq @ TA @ D @ B )
& ! [E: TA] :
( ( ( ord_less_eq @ TA @ A @ E )
& ( ord_less @ TA @ E @ D ) )
=> ( C @ E ) )
& ! [E: TA] :
( ! [F: TA] :
( ( ( ord_less_eq @ TA @ A @ F )
& ( ord_less @ TA @ F @ E ) )
=> ( C @ F ) )
=> ( ord_less_eq @ TA @ E @ D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(190,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__imp__triv) ).
thf(818,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: $o] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ B @ A )
=> C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(38,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_eq__iff) ).
thf(405,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
division_ring @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Odivision__ring) ).
thf(422,plain,
division_ring @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(204,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_inverse__nonnegative__iff__nonnegative) ).
thf(865,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(193,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_le__less) ).
thf(833,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(40,axiom,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_real__arch__simple) ).
thf(410,plain,
! [TA: $tType] :
( ( archim1804426504_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: nat] : ( ord_less_eq @ TA @ A @ ( semiring_1_of_nat @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(235,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_zero__less__power) ).
thf(967,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(110,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_order__le__less__subst1) ).
thf(564,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less_eq @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(3,axiom,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder) ).
thf(326,plain,
! [TA: $tType,TB: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ( preorder @ ( TB > TA ) @ ( type2 @ ( TB > TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(89,axiom,
ord @ real @ ( type2 @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Orderings_Oord_32) ).
thf(506,plain,
ord @ real @ ( type2 @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(19,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_order__trans) ).
thf(358,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less_eq @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(258,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_order__less__subst1) ).
thf(1056,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TA > TB,C: TA,D: TA] :
( ( ord_less @ TB @ A @ ( B @ C ) )
=> ( ( ord_less @ TA @ C @ D )
=> ( ! [E: TA,F: TA] :
( ( ord_less @ TA @ E @ F )
=> ( ord_less @ TB @ ( B @ E ) @ ( B @ F ) ) )
=> ( ord_less @ TB @ A @ ( B @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(158,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_order__le__less__subst2) ).
thf(720,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(214,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_not__less0) ).
thf(897,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(174,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_less__nat__zero__code) ).
thf(767,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(322,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_zle__int) ).
thf(1288,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(34,axiom,
preorder @ code_natural @ ( type2 @ code_natural ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Code__Numeral_Onatural___Orderings_Opreorder_36) ).
thf(400,plain,
preorder @ code_natural @ ( type2 @ code_natural ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(210,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_order_Ostrict__implies__not__eq) ).
thf(886,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(223,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_order_Oorder__iff__strict) ).
thf(928,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(42,axiom,
semiri134348788visors @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors) ).
thf(415,plain,
semiri134348788visors @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_order__subst2) ).
thf(395,plain,
! [TA: $tType,TB: $tType] :
( ( ( order @ TA @ ( type2 @ TA ) )
& ( order @ TB @ ( type2 @ TB ) ) )
=> ! [A: TB,B: TB,C: TB > TA,D: TA] :
( ( ord_less_eq @ TB @ A @ B )
=> ( ( ord_less_eq @ TA @ ( C @ B ) @ D )
=> ( ! [E: TB,F: TB] :
( ( ord_less_eq @ TB @ E @ F )
=> ( ord_less_eq @ TA @ ( C @ E ) @ ( C @ F ) ) )
=> ( ord_less_eq @ TA @ ( C @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(165,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_inverse__zero) ).
thf(740,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ( ( inverse_inverse @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(240,axiom,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_lt__ex) ).
thf(987,plain,
! [TA: $tType] :
( ( no_bot @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(113,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zero__less__iff__neq__zero) ).
thf(575,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(120,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_infinite__descent) ).
thf(596,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_neqE) ).
thf(528,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(206,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_positive__imp__inverse__positive) ).
thf(871,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( inverse_inverse @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(218,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_less__le) ).
thf(908,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
& ( A != B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(242,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_le__imp__less__or__eq) ).
thf(992,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(76,axiom,
linorder @ $o @ ( type2 @ $o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_17) ).
thf(486,plain,
linorder @ $o @ ( type2 @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(246,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_less__eq__nat_Osimps_I1_J) ).
thf(1009,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(286,axiom,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_pinf_I6_J) ).
thf(1184,plain,
! [TA: $tType] :
( ( linorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA] :
? [B: TA] :
! [C: TA] :
( ( ord_less @ TA @ B @ C )
=> ~ ( ord_less_eq @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(103,axiom,
canoni770627133id_add @ nat @ ( type2 @ nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(543,plain,
canoni770627133id_add @ nat @ ( type2 @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(252,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_nonzero__inverse__eq__imp__eq) ).
thf(1037,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( inverse_inverse @ TA @ A )
= ( inverse_inverse @ TA @ B ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ( B
!= ( zero_zero @ TA ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_power__less__imp__less__base) ).
thf(592,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: nat,C: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ C @ B ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(66,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_dual__order_Oantisym) ).
thf(454,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(22,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_eq__refl) ).
thf(364,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA] :
( ( A = B )
=> ( ord_less_eq @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(170,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ( ( zero_neq_one_of_bool @ TA @ $false )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_of__bool__eq_I1_J) ).
thf(755,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type2 @ TA ) )
=> ( ( zero_neq_one_of_bool @ TA @ $false )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_transfer__int__nat__relations_I3_J) ).
thf(676,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ int @ ( semiring_1_of_nat @ int @ A ) @ ( semiring_1_of_nat @ int @ B ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(80,axiom,
semiring_char_0 @ int @ ( type2 @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(491,plain,
semiring_char_0 @ int @ ( type2 @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(265,axiom,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_order_Ostrict__trans2) ).
thf(1088,plain,
! [TA: $tType] :
( ( order @ TA @ ( type2 @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ B @ C )
=> ( ord_less @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1298,plain,
$false,
inference(e,[status(thm)],[809,629,846,333,518,352,645,892,1083,468,666,1295,408,873,861,1142,379,385,1137,533,1164,715,913,945,340,538,1222,1095,1196,782,709,651,841,417,724,1287,785,504,1264,838,917,1279,1132,934,357,1191,1147,1247,421,969,416,325,1232,1013,770,492,789,1040,376,485,1020,981,687,634,734,660,1201,849,507,527,877,692,380,942,381,1153,761,1047,798,894,778,952,1255,1174,1217,820,561,424,630,429,788,467,361,852,830,461,1210,1079,1291,682,1195,551,1128,578,1234,1259,948,1017,1227,403,420,989,1138,356,328,488,339,1214,1207,679,706,1155,547,997,654,1192,911,1060,1050,457,503,605,343,360,508,657,773,718,1286,1035,906,425,745,444,1135,412,423,1007,402,743,382,1271,611,498,335,1090,540,672,445,936,466,1092,919,804,900,1282,377,451,737,863,764,979,1011,419,880,649,434,890,387,758,345,816,609,594,1149,626,462,983,1198,399,959,868,780,1250,851,658,685,521,695,636,1044,505,438,490,426,680,1277,487,812,1081,516,342,1145,355,553,458,836,1203,589,531,944,663,548,776,712,580,690,640,954,739,1267,1230,1053,441,502,1262,338,1130,1218,643,1220,544,331,1188,1186,1085,470,1257,703,727,1094,595,497,446,571,450,931,903,524,495,1126,368,844,699,813,963,748,1062,351,632,401,1244,995,731,418,568,433,536,752,447,432,1097,818,405,422,865,833,410,967,564,326,506,358,1056,720,897,767,1288,400,886,928,415,395,740,987,575,596,528,871,908,992,486,1009,1184,543,1037,592,454,364,755,676,491,1088]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT159^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.20 % Computer : n013.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 18:02:51 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.42/1.20 % [INFO] Parsing done (425ms).
% 2.42/1.22 % [INFO] Running in sequential loop mode.
% 3.56/1.61 % [INFO] eprover registered as external prover.
% 3.56/1.62 % [INFO] Scanning for conjecture ...
% 3.74/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 322 axioms. Running axiom selection ...
% 4.31/1.92 % [INFO] Axiom selection finished. Selected 322 axioms (removed 0 axioms).
% 5.30/2.22 % [INFO] Problem is higher-order (TPTP THF).
% 5.30/2.25 % [INFO] Type checking passed.
% 5.30/2.26 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 40.20/21.72 % External prover 'e' found a proof!
% 40.20/21.72 % [INFO] Killing All external provers ...
% 40.20/21.72 % Time passed: 21388ms (effective reasoning time: 20495ms)
% 40.20/21.72 % 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)>
% 40.20/21.73 % Axioms used in derivation (322): fact_3_gr0I, tcon_Code__Numeral_Onatural___Orderings_Opreorder_36, tcon_Real_Oreal___Orderings_Opreorder_26, fact_251_pinf_I6_J, fact_4_not__gr0, fact_12_zero__reorient, fact_177_le__less__trans, fact_76_zero__less__imp__eq__int, tcon_Code__Numeral_Onatural___Rings_Osemiring__1__no__zero__divisors_34, fact_214_transfer__int__nat__relations_I2_J, tcon_Int_Oint___Rings_Olinordered__semidom, fact_227_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, tcon_Real_Oreal___Rings_Olinordered__idom_23, fact_121_le__cases, tcon_Code__Numeral_Onatural___Rings_Ozero__neq__one_35, fact_10_infinite__descent0__measure, fact_62_less__irrefl, tcon_Nat_Onat___Rings_Ozero__neq__one_8, fact_16_infinite__descent, fact_96_inverse__positive__iff__positive, fact_211_zero__power, fact_82_of__bool__eq_I1_J, fact_237_pinf_I4_J, fact_77_reals__Archimedean2, fact_206_inverse__negative__imp__negative, fact_189_le__less, fact_247_minf_I11_J, fact_15_linorder__neqE__nat, fact_129_order__subst1, fact_185_order__less__le__subst1, tcon_Nat_Onat___Orderings_Oord_14, fact_67_less__not__sym, fact_213_ex__least__nat__le, fact_124_antisym, fact_119_real__arch__simple, fact_170_not__le__imp__less, tcon_Int_Oint___Orderings_Oorder_2, fact_38_dual__order_Ostrict__trans, fact_186_order__le__less__subst2, fact_91_inverse__zero, fact_122_eq__refl, tcon_Int_Oint___Groups_Ozero, fact_79_of__nat__zero__less__power__iff, fact_63_ord__eq__less__trans, fact_157_order_Onot__eq__order__implies__strict, fact_149_nonzero__inverse__eq__imp__eq, fact_224_le__trans, tcon_Real_Oreal___Orderings_Oord_32, fact_246_minf_I7_J, fact_24_zero__less__iff__neq__zero, fact_81_natural_Osize_I3_J, fact_47_ord__eq__less__subst, fact_33_linordered__field__no__ub, fact_137_power__less__imp__less__base, fact_200_zero__less__power, fact_26_not__less__zero, fact_70_less__imp__not__eq2, tcon_HOL_Obool___Orderings_Oord_19, fact_209_less__imp__inverse__less, fact_190_leI, tcon_fun___Orderings_Oord, tcon_Nat_Onat___Rings_Osemiring__1_11, fact_160_dual__order_Oorder__iff__strict, fact_245_minf_I5_J, fact_87_inverse__eq__iff__eq, tcon_Real_Oreal___Orderings_Ono__top_29, fact_144_inverse__le__imp__le__neg, fact_123_linear, fact_99_inverse__less__iff__less, fact_232_imp__le__cong, fact_8_infinite__descent0, tcon_Code__Numeral_Onatural___Orderings_Olinorder_37, fact_2_not__gr__zero, fact_100_inverse__le__iff__le__neg, fact_253_realpow__pos__nth__unique, fact_175_dense__ge, fact_43_of__nat__less__iff, fact_243_minf_I3_J, tcon_HOL_Obool___Orderings_Oorder_18, fact_9_less__nat__zero__code, fact_205_inverse__positive__imp__positive, fact_42_of__nat__eq__0__iff, fact_74_order_Ostrict__trans, fact_172_le__imp__less__or__eq, fact_156_complete__interval, fact_216_natural_Osimps_I4_J, fact_34_linordered__field__no__lb, fact_7_gr__implies__not0, tcon_Nat_Onat___Orderings_Oorder_13, fact_57_less__imp__neq, fact_50_order__less__subst2, fact_141_less__eq__int__code_I1_J, fact_196_less__or__eq__imp__le, fact_199_nat__less__le, fact_18_less__irrefl__nat, fact_187_order__le__less__subst1, fact_184_order__less__le__subst2, fact_220_less__fun__def, fact_194_less__mono__imp__le__mono, tcon_HOL_Obool___Orderings_Opreorder_16, fact_95_inverse__nonpositive__iff__nonpositive, fact_111_linorder__wlog, tcon_Int_Oint___Orderings_Opreorder_1, fact_132_le__funE, fact_134_int__int__eq, fact_212_of__nat__0__le__iff, fact_150_inverse__zero__imp__zero, fact_88_le__zero__eq, fact_75_less__imp__not__less, fact_249_minf_I6_J, fact_52_gt__ex, fact_115_ord__le__eq__trans, tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_5, fact_14_measure__induct__rule, fact_41_of__nat__0__eq__iff, fact_114_order__class_Oorder_Oantisym, fact_53_neqE, fact_210_inverse__less__imp__less, tcon_Nat_Onat___Orderings_Olinorder_10, fact_250_pinf_I8_J, fact_147_nonzero__imp__inverse__nonzero, fact_61_less__linear, fact_133_le__funD, fact_188_less__le, fact_230_transfer__int__nat__relations_I1_J, fact_155_le__numeral__extra_I3_J, tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder, help_If_1_1_T, fact_164_dual__order_Ostrict__trans2, fact_169_order_Ostrict__trans1, fact_223_eq__imp__le, fact_126_ord__le__eq__subst, fact_163_dense__ge__bounded, fact_92_nat__zero__less__power__iff, fact_202_power__strict__mono, fact_176_less__le__trans, fact_45_less__imp__of__nat__less, fact_89_of__nat__le__iff, fact_94_inverse__nonnegative__iff__nonnegative, fact_27_gr__zeroI, fact_218_transfer__int__nat__quantifiers_I1_J, tcon_Nat_Onat___Orderings_Ono__top_12, fact_120_order_Otrans, fact_84_order__refl, fact_46_of__nat__less__imp__less, tcon_Int_Oint___Rings_Olinordered__idom, fact_108_dual__order_Oantisym, fact_166_order_Ostrict__iff__order, tcon_Int_Oint___Orderings_Olinorder, fact_93_of__nat__power, fact_73_dual__order_Oirrefl, fact_106_zero__integer_Orsp, fact_248_minf_I8_J, fact_143_le__imp__inverse__le__neg, tcon_Real_Oreal___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_20, fact_31_linorder__neqE__linordered__idom, fact_192_le__0__eq, tcon_Nat_Onat___Orderings_Owellorder, fact_48_ord__less__eq__subst, tcon_Real_Oreal___Rings_Olinordered__semidom_22, fact_98_inverse__less__iff__less__neg, fact_30_ex__gt__or__lt, fact_107_inverse__eq__imp__eq, fact_83_ex__inverse__of__nat__less, fact_217_transfer__int__nat__quantifiers_I2_J, fact_17_nat__less__induct, fact_68_less__induct, fact_49_order__less__subst1, tcon_Real_Oreal___Orderings_Olinorder_27, fact_28_of__nat__0__less__iff, fact_201_nat__power__less__imp__less, fact_226_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_85_le0, tcon_Nat_Onat___Nat_Osemiring__char__0_7, fact_97_inverse__negative__iff__negative, fact_102_power__eq__0__iff, tcon_Real_Oreal___Conditionally__Complete__Lattices_Olinear__continuum, fact_51_lt__ex, fact_182_not__less, fact_235_pinf_I2_J, tcon_Real_Oreal___Nat_Osemiring__char__0_24, fact_208_inverse__less__imp__less__neg, fact_65_dual__order_Oasym, fact_90_inverse__nonzero__iff__nonzero, fact_66_less__imp__not__eq, fact_37_not__less__iff__gr__or__eq, fact_168_order_Ostrict__trans2, tcon_Int_Oint___Rings_Osemiring__1, fact_158_dual__order_Ostrict__implies__order, tcon_Real_Oreal___Orderings_Odense__order, fact_36_dependent__wellorder__choice, tcon_Real_Oreal___Orderings_Odense__linorder, fact_219_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_231_int__if__cong, tcon_Int_Oint___Rings_Ozero__neq__one, fact_54_neq__iff, fact_242_minf_I2_J, fact_56_dense, fact_13_infinite__descent__measure, fact_25_gr__implies__not__zero, fact_128_order__subst2, fact_136_power__not__zero, fact_135_zle__int, fact_222_le__antisym, fact_69_antisym__conv3, fact_195_le__neq__implies__less, fact_215_transfer__int__nat__numerals_I1_J, fact_112_dual__order_Orefl, tcon_Nat_Onat___Rings_Olinordered__semidom_6, fact_183_not__le, tcon_Real_Oreal___Orderings_Oorder_31, fact_139_zero__le__power, fact_238_pinf_I5_J, help_If_3_1_T, fact_151_field__class_Ofield__inverse__zero, fact_20_less__not__refl3, fact_72_linorder__cases, help_If_2_1_T, fact_240_pinf_I11_J, fact_244_minf_I4_J, fact_252_ex__has__greatest__nat, tcon_Code__Numeral_Onatural___Orderings_Oord_40, fact_207_less__imp__inverse__less__neg, fact_64_ord__less__eq__trans, fact_130_le__fun__def, fact_153_power__eq__iff__eq__base, fact_203_positive__imp__inverse__positive, fact_80_of__nat__le__0__iff, fact_11_less__numeral__extra_I3_J, fact_198_less__imp__le__nat, fact_78_natural_Osize_I1_J, fact_179_antisym__conv1, fact_103_nonneg__eq__int, fact_39_of__nat__eq__iff, fact_19_measure__induct, fact_145_le__imp__inverse__le, fact_125_eq__iff, fact_113_order__trans, fact_161_order_Ostrict__implies__order, fact_32_dual__order_Ostrict__implies__not__eq, fact_110_dual__order_Otrans, tcon_fun___Orderings_Opreorder, fact_138_power__inverse, fact_146_inverse__le__imp__le, fact_142_less__int__code_I1_J, fact_116_ord__eq__le__trans, fact_35_order_Ostrict__implies__not__eq, fact_118_le__cases3, tcon_Real_Oreal___Fields_Olinordered__field, fact_241_minf_I1_J, fact_233_conj__le__cong, fact_204_negative__imp__inverse__negative, fact_197_le__eq__less__or__eq, fact_221_nat__le__linear, fact_22_less__not__refl, fact_55_order_Oasym, tcon_Code__Numeral_Onatural___Groups_Ozero_41, tcon_Code__Numeral_Onatural___Rings_Osemiring__1_38, fact_58_less__asym, fact_191_leD, fact_21_less__not__refl2, fact_178_antisym__conv2, fact_5_not__less0, tcon_Nat_Onat___Groups_Ozero_15, tcon_Int_Oint___Nat_Osemiring__char__0, tcon_Real_Oreal___Groups_Ozero_33, tcon_Code__Numeral_Onatural___Orderings_Oorder_39, fact_174_dense__le, fact_239_pinf_I7_J, fact_193_less__eq__nat_Osimps_I1_J, fact_105_zero__le__imp__eq__int, fact_152_power__eq__imp__eq__base, tcon_Real_Oreal___Rings_Osemiring__1_28, fact_162_dense__le__bounded, fact_1_neq0__conv, fact_0_smooth__0, tcon_Int_Oint___Orderings_Ono__bot, fact_236_pinf_I3_J, tcon_fun___Orderings_Oorder, tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_21, fact_59_less__asym_H, fact_167_order_Oorder__iff__strict, tcon_Nat_Onat___Conditionally__Complete__Lattices_Oconditionally__complete__linorder_4, tcon_Real_Oreal___Rings_Ozero__neq__one_25, tcon_Int_Oint___Orderings_Ono__top, fact_101_inverse__le__iff__le, fact_127_ord__eq__le__subst, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, tcon_Nat_Onat___Orderings_Opreorder_9, fact_228_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_109_of__bool__eq__iff, fact_86_inverse__inverse__eq, fact_234_pinf_I1_J, fact_171_less__le__not__le, fact_23_nat__neq__iff, tcon_Real_Oreal___Archimedean__Field_Oarchimedean__field, tcon_Int_Oint___Orderings_Oord_3, conj_0, fact_229_transfer__int__nat__relations_I3_J, fact_117_antisym__conv, tcon_Real_Oreal___Orderings_Ono__bot_30, fact_154_zero__le, fact_225_le__refl, tcon_Real_Oreal___Fields_Ofield, tcon_HOL_Obool___Orderings_Olinorder_17, fact_140_power__mono, fact_60_less__trans, fact_104_nonneg__int__cases, fact_165_dual__order_Ostrict__trans1, fact_40_of__nat__0, fact_180_less__imp__le, fact_44_of__nat__less__0__iff, fact_29_zero__natural_Orsp, tcon_Real_Oreal___Fields_Odivision__ring, tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors, fact_148_nonzero__inverse__inverse__eq, fact_131_le__funI, fact_71_less__imp__triv, fact_6_less__zeroE, fact_173_le__less__linear, fact_181_le__neq__trans, fact_159_dual__order_Ostrict__iff__order
% 40.20/21.73 % No. of inferences in proof: 648
% 40.20/21.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21388 ms resp. 20495 ms w/o parsing
% 40.90/21.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.90/21.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------