%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ITP095^2 : TPTP v9.3.1. Released v7.5.0.
% 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 : n026.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 08:06:44 AM UTC 2026
% Result : Theorem 67.74s 15.40s
% Output : Refutation 59.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 347
% Syntax : Number of formulae : 713 ( 201 unt; 0 typ; 2 def)
% Number of atoms : 2212 ( 594 equ; 4 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 7869 ( 123 ~; 55 |; 88 &;6749 @)
% ( 0 <=>; 854 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 61 usr; 14 con; 0-3 aty)
% Number of variables : 1437 ( 29 ^;1390 !; 16 ?;1437 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(real_type,type,
real: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(idom_decl,type,
idom:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(ring_1_decl,type,
ring_1:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(comm_ring_decl,type,
comm_ring:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(comm_ring_1_decl,type,
comm_ring_1:
!>[TA: $tType] : $o ).
thf(idom_divide_decl,type,
idom_divide:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(field_char_0_decl,type,
field_char_0:
!>[TA: $tType] : $o ).
thf(division_ring_decl,type,
division_ring:
!>[TA: $tType] : $o ).
thf(field_abs_sgn_decl,type,
field_abs_sgn:
!>[TA: $tType] : $o ).
thf(comm_semiring_0_decl,type,
comm_semiring_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_decl,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_decl,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere142940540dd_abs_decl,type,
ordere142940540dd_abs:
!>[TA: $tType] : $o ).
thf(semiri1193490041visors_decl,type,
semiri1193490041visors:
!>[TA: $tType] : $o ).
thf(semiri134348788visors_decl,type,
semiri134348788visors:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_decl,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(abs_abs_decl,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ring_1_Ints_decl,type,
ring_1_Ints:
!>[TA: $tType] : ( set @ TA ) ).
thf(ring_1_of_int_decl,type,
ring_1_of_int:
!>[TA: $tType] : ( int > TA ) ).
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(algebraic_decl,type,
algebraic:
!>[TA: $tType] : ( TA > $o ) ).
thf(degree_decl,type,
degree:
!>[TA: $tType] : ( ( poly @ TA ) > nat ) ).
thf(poly2_decl,type,
poly2:
!>[TA: $tType] : ( ( poly @ TA ) > TA > TA ) ).
thf(coeff_decl,type,
coeff:
!>[TA: $tType] : ( ( poly @ TA ) > nat > TA ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(field_char_0_Rats_decl,type,
field_char_0_Rats:
!>[TA: $tType] : ( set @ TA ) ).
thf(divide_divide_decl,type,
divide_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( TA > $o ) > ( set @ TA ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( set @ TA ) > $o ) ).
thf(a_decl,type,
a: real ).
thf(m_decl,type,
m: real ).
thf(a2_decl,type,
a2: int ).
thf(b_decl,type,
b: int ).
thf(n_decl,type,
n: nat ).
thf(p_decl,type,
p: poly @ real ).
thf(roots_decl,type,
roots: set @ real ).
thf(thesis_decl,type,
thesis: $o ).
thf(x_decl,type,
x: real ).
thf(sk1_decl,type,
sk1:
!>[TA: $tType] : ( ( TA > $o ) > ( TA > $o ) > TA ) ).
thf(sk9_decl,type,
sk9: poly @ real ).
thf(sk1_def,definition,
( sk1
= ( ^ [TA: $tType,A: TA > $o,B: TA > $o] :
@+[C: TA] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( @+[A: poly @ real] :
~ ( ! [B: nat] : ( member @ real @ ( coeff @ real @ A @ B ) @ ( ring_1_Ints @ real ) )
=> ( ( A
!= ( zero_zero @ ( poly @ real ) ) )
=> ( ( poly2 @ real @ A @ x )
!= ( zero_zero @ real ) ) ) ) ) ) ).
thf(239,axiom,
field_abs_sgn @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield__abs__sgn) ).
thf(892,plain,
field_abs_sgn @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(137,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_frac__less) ).
thf(629,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(292,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ord_less_eq @ nat @ ( degree @ TA @ A ) @ B )
=> ( ( ( coeff @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ ( poly @ TA ) ) )
| ( ord_less @ nat @ ( degree @ TA @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_eq__zero__or__degree__less) ).
thf(1024,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ord_less_eq @ nat @ ( degree @ TA @ A ) @ B )
=> ( ( ( coeff @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( ( A
= ( zero_zero @ ( poly @ TA ) ) )
| ( ord_less @ nat @ ( degree @ TA @ A ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(12,axiom,
comm_ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__ring__1) ).
thf(365,plain,
comm_ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(73,axiom,
ring_n68954251visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__no__zero__divisors) ).
thf(479,plain,
ring_n68954251visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1,conjecture,
ord_less_eq @ real @ ( divide_divide @ real @ ( one_one @ real ) @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ ( degree @ real @ p ) ) ) @ ( abs_abs @ real @ ( poly2 @ real @ p @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less_eq @ real @ ( divide_divide @ real @ ( one_one @ real ) @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ ( degree @ real @ p ) ) ) @ ( abs_abs @ real @ ( poly2 @ real @ p @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(347,plain,
~ ( ord_less_eq @ real @ ( divide_divide @ real @ ( one_one @ real ) @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ ( degree @ real @ p ) ) ) @ ( abs_abs @ real @ ( poly2 @ real @ p @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(240,axiom,
ord_less_eq @ real @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ) @ ( divide_divide @ real @ a @ ( one_one @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81__092_060open_062A_A_P_Areal__of__int_Ab_A_094_An_A_092_060le_062_AA_A_P_A1_092_060close_062) ).
thf(893,plain,
ord_less_eq @ real @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ) @ ( divide_divide @ real @ a @ ( one_one @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(4,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere142940540dd_abs @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add__abs_41) ).
thf(351,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordere142940540dd_abs @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(352,plain,
! [TA: $tType] :
( ~ ( linordered_idom @ TA )
| ( ordere142940540dd_abs @ ( poly @ TA ) ) ),
inference(cnf,[status(esa)],[351]) ).
thf(247,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_one__less__power) ).
thf(909,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(295,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_div__pos__pos__trivial) ).
thf(1031,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ B )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(267,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( one_one @ ( poly @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_poly__1) ).
thf(962,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( one_one @ ( poly @ TA ) ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(66,axiom,
comm_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__ring) ).
thf(468,plain,
comm_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(272,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_of__int__eq__iff) ).
thf(977,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( ring_1_of_int @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(184,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ( divide_divide @ TA @ ( one_one @ TA ) @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_one__divide__eq__0__iff) ).
thf(762,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ( divide_divide @ TA @ ( one_one @ TA ) @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(284,axiom,
! [TA: $tType] :
( ( field_abs_sgn @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( divide_divide @ TA @ A @ B ) )
= ( divide_divide @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_abs__divide) ).
thf(1005,plain,
! [TA: $tType] :
( ( field_abs_sgn @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( divide_divide @ TA @ A @ B ) )
= ( divide_divide @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(21,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( coeff @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) )
= ( ^ [C: nat] : ( minus_minus @ TA @ ( coeff @ TA @ A @ C ) @ ( coeff @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_minus__poly_Orep__eq) ).
thf(379,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( coeff @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) )
= ( ^ [C: nat] : ( minus_minus @ TA @ ( coeff @ TA @ A @ C ) @ ( coeff @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(132,axiom,
! [A: poly @ real,B: int,C: int] :
( ! [D: nat] : ( member @ real @ ( coeff @ real @ A @ D ) @ ( ring_1_Ints @ real ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ( poly2 @ real @ A @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ B ) ) )
!= ( zero_zero @ real ) )
=> ( ord_less_eq @ real @ ( divide_divide @ real @ ( one_one @ real ) @ ( power_power @ real @ ( ring_1_of_int @ real @ B ) @ ( degree @ real @ A ) ) ) @ ( abs_abs @ real @ ( poly2 @ real @ A @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_int__poly__rat__no__root__ge) ).
thf(614,plain,
! [A: poly @ real,B: int,C: int] :
( ! [D: nat] : ( member @ real @ ( coeff @ real @ A @ D ) @ ( ring_1_Ints @ real ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ( poly2 @ real @ A @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ B ) ) )
!= ( zero_zero @ real ) )
=> ( ord_less_eq @ real @ ( divide_divide @ real @ ( one_one @ real ) @ ( power_power @ real @ ( ring_1_of_int @ real @ B ) @ ( degree @ real @ A ) ) ) @ ( abs_abs @ real @ ( poly2 @ real @ A @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(179,axiom,
~ ( member @ real @ x @ ( field_char_0_Rats @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_irrationsl) ).
thf(741,plain,
~ ( member @ real @ x @ ( field_char_0_Rats @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(311,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_of__int__le__0__iff) ).
thf(1073,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ int @ A @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(230,axiom,
idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oidom_1) ).
thf(873,plain,
idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(56,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( coeff @ TA @ A )
= ( coeff @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_coeff__inject) ).
thf(449,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( coeff @ TA @ A )
= ( coeff @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(148,axiom,
field_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield__char__0) ).
thf(655,plain,
field_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(92,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_diff__eq__diff__eq) ).
thf(511,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(298,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_divide__nonneg__pos) ).
thf(1041,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(225,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ 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_106_power__eq__0__iff) ).
thf(861,plain,
! [TA: $tType] :
( ( semiri134348788visors @ 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)],[225]) ).
thf(23,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ! [C: nat] :
( ( coeff @ TA @ A @ C )
= ( coeff @ TA @ B @ C ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_poly__eqI) ).
thf(385,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ! [C: nat] :
( ( coeff @ TA @ A @ C )
= ( coeff @ TA @ B @ C ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_abs__le__zero__iff) ).
thf(533,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_diff__strict__left__mono) ).
thf(500,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(344,axiom,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_p_I2_J) ).
thf(1164,plain,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(68,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(472,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(207,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_power__less__imp__less__exp) ).
thf(814,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
=> ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(307,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_one__reorient) ).
thf(1063,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(104,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_diff__left__mono) ).
thf(538,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(154,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_divide__less__cancel) ).
thf(670,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ C @ A ) )
& ( B
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(193,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__1_26) ).
thf(782,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(169,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ A @ C ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_power__inject__exp) ).
thf(709,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ( power_power @ TA @ A @ B )
= ( power_power @ TA @ A @ C ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_linordered__field__no__lb) ).
thf(417,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(300,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_of__int__pos) ).
thf(1046,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(114,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( poly2 @ TA @ A @ ( zero_zero @ TA ) )
= ( coeff @ TA @ A @ ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_poly__0__coeff__0) ).
thf(565,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: poly @ TA] :
( ( poly2 @ TA @ A @ ( zero_zero @ TA ) )
= ( coeff @ TA @ A @ ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(171,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_divide__le__0__1__iff) ).
thf(719,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(18,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(372,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(250,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_diff__right__mono) ).
thf(917,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(201,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_183_power__strict__mono) ).
thf(802,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[201]) ).
thf(262,axiom,
cancel1352612707id_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_21) ).
thf(949,plain,
cancel1352612707id_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(7,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_not__gr__zero) ).
thf(355,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(356,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(cnf,[status(esa)],[355]) ).
thf(357,plain,
! [TA: $tType,A: TA] :
( ( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) )
| ~ ( canoni770627133id_add @ TA ) ),
inference(lifteq,[status(thm)],[356]) ).
thf(1183,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
| ( A
!= ( zero_zero @ TA ) ) ),
inference(bool_ext,[status(thm)],[357]) ).
thf(1188,plain,
! [TA: $tType,A: TA] :
( ( A
!= ( zero_zero @ TA ) )
| ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(lifteq,[status(thm)],[1183]) ).
thf(1190,plain,
! [TA: $tType,A: TA] :
( ( A
!= ( zero_zero @ TA ) )
| ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(cnf,[status(esa)],[1188]) ).
thf(1191,plain,
! [TA: $tType] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(simp,[status(thm)],[1190]) ).
thf(209,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less_eq @ TA @ A @ ( power_power @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_self__le__power) ).
thf(817,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less_eq @ TA @ A @ ( power_power @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ C ) @ ( divide_divide @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_div__le__mono) ).
thf(559,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ C ) @ ( divide_divide @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(316,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__idom_25) ).
thf(1087,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(339,axiom,
! [A: int] :
( ( ord_less @ int @ ( abs_abs @ int @ A ) @ ( one_one @ int ) )
= ( A
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zabs__less__one__iff) ).
thf(1147,plain,
! [A: int] :
( ( ord_less @ int @ ( abs_abs @ int @ A ) @ ( one_one @ int ) )
= ( A
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(187,axiom,
ab_group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oab__group__add_2) ).
thf(770,plain,
ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(37,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Power_Opower_14) ).
thf(416,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(321,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_power__le__imp__le__exp) ).
thf(1100,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
=> ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(141,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_div__le__dividend) ).
thf(638,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(221,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_divide__le__0__iff) ).
thf(853,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(40,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_16) ).
thf(421,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(229,axiom,
! [TA: $tType] :
( ( semiri134348788visors @ 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_141_power__not__zero) ).
thf(870,plain,
! [TA: $tType] :
( ( semiri134348788visors @ 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)],[229]) ).
thf(181,axiom,
~ ! [A: poly @ real] :
( ! [B: nat] : ( member @ real @ ( coeff @ real @ A @ B ) @ ( ring_1_Ints @ real ) )
=> ( ( A
!= ( zero_zero @ ( poly @ real ) ) )
=> ( ( poly2 @ real @ A @ x )
!= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062) ).
thf(750,plain,
~ ! [A: poly @ real] :
( ! [B: nat] : ( member @ real @ ( coeff @ real @ A @ B ) @ ( ring_1_Ints @ real ) )
=> ( ( A
!= ( zero_zero @ ( poly @ real ) ) )
=> ( ( poly2 @ real @ A @ x )
!= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(751,plain,
~ ! [A: poly @ real] :
( ! [B: nat] : ( member @ real @ ( coeff @ real @ A @ B ) @ ( ring_1_Ints @ real ) )
=> ( ( A
!= ( zero_zero @ ( poly @ real ) ) )
=> ( ( poly2 @ real @ A @ x )
!= ( zero_zero @ real ) ) ) ),
inference(polarity_switch,[status(thm)],[750]) ).
thf(752,plain,
! [A: nat] :
( ( member @ real @ ( coeff @ real @ sk9 @ A ) @ ( ring_1_Ints @ real ) )
& ( sk9
!= ( zero_zero @ ( poly @ real ) ) )
& ( ( poly2 @ real @ sk9 @ x )
= ( zero_zero @ real ) ) ),
inference(cnf,[status(esa)],[751]) ).
thf(754,plain,
( sk9
!= ( zero_zero @ ( poly @ real ) ) ),
inference(cnfConj,[status(thm)],[752]) ).
thf(756,plain,
( sk9
!= ( zero_zero @ ( poly @ real ) ) ),
inference(lifteq,[status(thm)],[754]) ).
thf(198,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: TA] :
( ( algebraic @ TA @ A )
=> ~ ! [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( ring_1_Ints @ TA ) )
=> ( ( B
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( poly2 @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_algebraicE) ).
thf(789,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: TA] :
( ( algebraic @ TA @ A )
=> ~ ! [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( ring_1_Ints @ TA ) )
=> ( ( B
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( poly2 @ TA @ B @ A )
!= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(134,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_power__strict__increasing) ).
thf(623,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(144,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: poly @ TA,B: poly @ TA,C: TA] :
( ( poly2 @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) @ C )
= ( minus_minus @ TA @ ( poly2 @ TA @ A @ C ) @ ( poly2 @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_poly__diff) ).
thf(646,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ! [A: poly @ TA,B: poly @ TA,C: TA] :
( ( poly2 @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) @ C )
= ( minus_minus @ TA @ ( poly2 @ TA @ A @ C ) @ ( poly2 @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(93,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Oring__char__0) ).
thf(514,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(5,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(353,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(74,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ogroup__add_54) ).
thf(480,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( ab_group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oab__group__add) ).
thf(485,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ( ab_group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(335,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_of__int__power__eq__of__int__cancel__iff) ).
thf(1136,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ( ring_1_of_int @ TA @ A )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( A
= ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(215,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_one__eq__divide__iff) ).
thf(834,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(290,axiom,
ordered_ab_group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add_23) ).
thf(1020,plain,
ordered_ab_group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(3,axiom,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong) ).
thf(348,plain,
! [TA: $tType,A: TA > $o,B: TA > $o] :
( ! [C: TA] :
( ( A @ C )
= ( B @ C ) )
=> ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( ! [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_poly__all__0__iff__0) ).
thf(602,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA] :
( ( ! [B: TA] :
( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(28,axiom,
! [TA: $tType] :
( ( idom_divide @ TA )
=> ( idom_divide @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oidom__divide_51) ).
thf(397,plain,
! [TA: $tType] :
( ( idom_divide @ TA )
=> ( idom_divide @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(139,axiom,
ord_less @ int @ ( zero_zero @ int ) @ b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_b) ).
thf(634,plain,
ord_less @ int @ ( zero_zero @ int ) @ b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(232,axiom,
! [A: real,B: nat] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ! [C: int,D: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ord_less @ real @ ( divide_divide @ real @ A @ ( power_power @ real @ ( ring_1_of_int @ real @ D ) @ B ) ) @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ D ) ) ) ) ) )
=> thesis ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_that) ).
thf(877,plain,
! [A: real,B: nat] :
( ( ord_less @ real @ ( zero_zero @ real ) @ A )
=> ( ! [C: int,D: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ D )
=> ( ord_less @ real @ ( divide_divide @ real @ A @ ( power_power @ real @ ( ring_1_of_int @ real @ D ) @ B ) ) @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ C ) @ ( ring_1_of_int @ real @ D ) ) ) ) ) )
=> thesis ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_divide__nonpos__nonpos) ).
thf(734,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(265,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_89_nat__zero__less__power__iff) ).
thf(956,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)],[265]) ).
thf(58,axiom,
group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(453,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(327,axiom,
cancel146912293up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_20) ).
thf(1119,plain,
cancel146912293up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(27,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_not__less__zero) ).
thf(395,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(396,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[395]) ).
thf(150,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_divide__neg__pos) ).
thf(660,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(44,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(428,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(323,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_power__0__left) ).
thf(1104,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ! [A: nat] :
( ( ( A
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( one_one @ TA ) ) )
& ( ( A
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(89,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring__1_57) ).
thf(507,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_8) ).
thf(411,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(276,axiom,
~ ( member @ real @ x @ roots ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22__092_060open_062x_A_092_060notin_062_Aroots_092_060close_062) ).
thf(988,plain,
~ ( member @ real @ x @ roots ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(57,axiom,
semiri1193490041visors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_6) ).
thf(452,plain,
semiri1193490041visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(259,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Omonoid__mult_28) ).
thf(942,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(107,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA,B: nat,C: TA] :
( ( poly2 @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ C )
= ( power_power @ TA @ ( poly2 @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_poly__power) ).
thf(546,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA,B: nat,C: TA] :
( ( poly2 @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ C )
= ( power_power @ TA @ ( poly2 @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(253,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( abs_abs @ TA @ ( divide_divide @ TA @ B @ A ) )
= ( divide_divide @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_nonzero__abs__divide) ).
thf(925,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( abs_abs @ TA @ ( divide_divide @ TA @ B @ A ) )
= ( divide_divide @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(341,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ A ) )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ B ) @ ( zero_zero @ real ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_poly__IVT__neg) ).
thf(1153,plain,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ A ) )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ B ) @ ( zero_zero @ real ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_diff__strict__mono) ).
thf(366,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(309,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_of__int__power__le__of__int__cancel__iff) ).
thf(1067,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less_eq @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(305,axiom,
! [A: real] :
( ( A != x )
=> ( ( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) )
=> ( ord_less @ real @ a @ ( abs_abs @ real @ ( minus_minus @ real @ A @ x ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_A__less_I3_J) ).
thf(1057,plain,
! [A: real] :
( ( A != x )
=> ( ( ( poly2 @ real @ p @ A )
= ( zero_zero @ real ) )
=> ( ord_less @ real @ a @ ( abs_abs @ real @ ( minus_minus @ real @ A @ x ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(241,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_of__int__nonneg) ).
thf(894,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(318,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_of__int__0__less__iff) ).
thf(1091,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(212,axiom,
( ( poly2 @ real @ p @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) )
!= ( zero_zero @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_no__root) ).
thf(825,plain,
( ( poly2 @ real @ p @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) )
!= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(291,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) )
= ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_zero__le__divide__abs__iff) ).
thf(1021,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) )
= ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(329,axiom,
ord_less @ real @ ( zero_zero @ real ) @ m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_M__pos) ).
thf(1123,plain,
ord_less @ real @ ( zero_zero @ real ) @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(163,axiom,
comm_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__ring_33) ).
thf(693,plain,
comm_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(45,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_7) ).
thf(429,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq) ).
thf(361,plain,
! [TA: $tType,A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( collect @ TA @ B ) )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(135,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_abs__triangle__ineq2) ).
thf(625,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(49,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_less__iff__diff__less__0) ).
thf(435,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(152,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_divide__neg__neg) ).
thf(665,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(236,axiom,
ordere142940540dd_abs @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs_19) ).
thf(889,plain,
ordere142940540dd_abs @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(80,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Omonoid__mult_50) ).
thf(493,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( monoid_mult @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(159,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: int] :
( ( degree @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_degree__of__int) ).
thf(682,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: int] :
( ( degree @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(109,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( coeff @ TA @ A @ ( degree @ TA @ A ) )
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_leading__coeff__neq__0) ).
thf(551,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( coeff @ TA @ A @ ( degree @ TA @ A ) )
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(271,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ A @ B )
= C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_of__int__eq__of__int__power__cancel__iff) ).
thf(974,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B )
= ( ring_1_of_int @ TA @ C ) )
= ( ( power_power @ int @ A @ B )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(313,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_power__divide) ).
thf(1079,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ A @ B ) @ C )
= ( divide_divide @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(293,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_power__one__right) ).
thf(1027,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(60,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel1352612707id_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add_43) ).
thf(456,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel1352612707id_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ int @ A @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_of__int__less__0__iff) ).
thf(842,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ int @ A @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(165,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_power__one) ).
thf(697,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(231,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_le__divide__eq__1__pos) ).
thf(874,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(289,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_zero__le__divide__1__iff) ).
thf(1017,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(324,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_abs__triangle__ineq2__sym) ).
thf(1111,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_divide__less__0__iff) ).
thf(725,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__semidom_46) ).
thf(388,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_semidom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(125,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ( coeff @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ord_less_eq @ nat @ B @ ( degree @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__degree) ).
thf(593,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ( coeff @ TA @ A @ B )
!= ( zero_zero @ TA ) )
=> ( ord_less_eq @ nat @ B @ ( degree @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(194,axiom,
algebraic @ real @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I2_J) ).
thf(783,plain,
algebraic @ real @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(85,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(499,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(989,plain,
~ ( member @ real @ x @ roots ),
inference(polarity_switch,[status(thm)],[988]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) )
= ( ( A
!= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__less__power__abs__iff) ).
thf(857,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) )
= ( ( A
!= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(96,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Osemiring__1_53) ).
thf(519,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(742,plain,
~ ( member @ real @ x @ ( field_char_0_Rats @ real ) ),
inference(polarity_switch,[status(thm)],[741]) ).
thf(119,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] : ( member @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_Ints @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_Ints__of__int) ).
thf(578,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int] : ( member @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_Ints @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(273,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_divide__nonneg__nonpos) ).
thf(980,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(31,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( (=) @ ( poly @ TA ) )
= ( ^ [A: poly @ TA,B: poly @ TA] :
! [C: nat] :
( ( coeff @ TA @ A @ C )
= ( coeff @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_poly__eq__iff) ).
thf(403,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( (=) @ ( poly @ TA ) )
= ( ^ [A: poly @ TA,B: poly @ TA] :
! [C: nat] :
( ( coeff @ TA @ A @ C )
= ( coeff @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(234,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_divide__pos__pos) ).
thf(884,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(342,axiom,
semiri1193490041visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_18) ).
thf(1160,plain,
semiri1193490041visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(314,axiom,
! [A: nat,B: nat] :
( ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( ord_less @ nat @ A @ B )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Euclidean__Division_Odiv__eq__0__iff) ).
thf(1082,plain,
! [A: nat,B: nat] :
( ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( ord_less @ nat @ A @ B )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(256,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_division__ring__divide__zero) ).
thf(933,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(110,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_abs__zero) ).
thf(554,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ( ( abs_abs @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_linordered__field__no__ub) ).
thf(489,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zero__eq__1__divide__iff) ).
thf(590,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(168,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( coeff @ TA @ ( one_one @ ( poly @ TA ) ) @ ( degree @ TA @ ( one_one @ ( poly @ TA ) ) ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_lead__coeff__1) ).
thf(706,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( coeff @ TA @ ( one_one @ ( poly @ TA ) ) @ ( degree @ TA @ ( one_one @ ( poly @ TA ) ) ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(244,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( abs_abs @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_abs__0__eq) ).
thf(901,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( abs_abs @ TA @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(71,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_44) ).
thf(476,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( ring_n68954251visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(158,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_less__divide__eq__1__neg) ).
thf(679,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(269,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_power__increasing) ).
thf(970,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(216,axiom,
! [A: real] :
( ( member @ real @ A @ ( field_char_0_Rats @ real ) )
=> ~ ! [B: int,C: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( A
!= ( divide_divide @ real @ ( ring_1_of_int @ real @ B ) @ ( ring_1_of_int @ real @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_Liouville__Numbers__Misc_ORats__cases_H) ).
thf(837,plain,
! [A: real] :
( ( member @ real @ A @ ( field_char_0_Rats @ real ) )
=> ~ ! [B: int,C: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( A
!= ( divide_divide @ real @ ( ring_1_of_int @ real @ B ) @ ( ring_1_of_int @ real @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(26,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ozero_59) ).
thf(393,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( zero @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(281,axiom,
! [TA: $tType] :
( ( semiring_1 @ 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_126_zero__power) ).
thf(997,plain,
! [TA: $tType] :
( ( semiring_1 @ 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)],[281]) ).
thf(275,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( divide_divide @ TA @ ( abs_abs @ TA @ B ) @ A )
= ( abs_abs @ TA @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_abs__div__pos) ).
thf(985,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( divide_divide @ TA @ ( abs_abs @ TA @ B ) @ A )
= ( abs_abs @ TA @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(248,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_le__iff__diff__le__0) ).
thf(911,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(283,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_abs__idempotent) ).
thf(1002,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(192,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ B )
= ( divide_divide @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_power__one__over) ).
thf(779,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: nat] :
( ( power_power @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ B )
= ( divide_divide @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(17,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__1_10) ).
thf(371,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( abs_abs @ TA @ A )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_abs__of__nonneg) ).
thf(605,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( abs_abs @ TA @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(94,axiom,
ab_group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__group__add_4) ).
thf(515,plain,
ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(340,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ord_less @ TA @ ( abs_abs @ TA @ A ) @ ( one_one @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_Ints__nonzero__abs__less1) ).
thf(1150,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( ord_less @ TA @ ( abs_abs @ TA @ A ) @ ( one_one @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(306,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less_eq @ TA @ A @ B ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ A ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_divide__le__eq__1) ).
thf(1060,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less_eq @ TA @ A @ B ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ A ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(302,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: nat] :
( ( ring_1_of_int @ TA @ ( power_power @ int @ A @ B ) )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_of__int__power) ).
thf(1050,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: nat] :
( ( ring_1_of_int @ TA @ ( power_power @ int @ A @ B ) )
= ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(9,axiom,
idom_divide @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oidom__divide) ).
thf(360,plain,
idom_divide @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(203,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_divide__nonpos__neg) ).
thf(805,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(185,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_165_zero__less__power) ).
thf(765,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[185]) ).
thf(346,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_eq__divide__eq__1) ).
thf(1170,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(296,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_Ints__cases) ).
thf(1035,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ~ ! [B: int] :
( A
!= ( ring_1_of_int @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(156,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_one__le__power) ).
thf(674,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( power_power @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(345,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_128_power__eq__iff__eq__base) ).
thf(1167,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[345]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_zero__less__divide__1__iff) ).
thf(953,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(151,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_of__int__0__eq__iff) ).
thf(662,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( zero_zero @ TA )
= ( ring_1_of_int @ TA @ A ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Nat_Oring__char__0_56) ).
thf(412,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA ) )
=> ( ring_char_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(133,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: poly @ TA] :
( ( ord_less @ nat @ A @ ( degree @ TA @ B ) )
=> ? [C: nat] :
( ( ord_less @ nat @ A @ C )
& ( ( coeff @ TA @ B @ C )
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_less__degree__imp) ).
thf(618,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: poly @ TA] :
( ( ord_less @ nat @ A @ ( degree @ TA @ B ) )
=> ? [C: nat] :
( ( ord_less @ nat @ A @ C )
& ( ( coeff @ TA @ B @ C )
!= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(42,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel146912293up_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add_42) ).
thf(425,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ( cancel146912293up_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__mult_12) ).
thf(430,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(222,axiom,
division_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Odivision__ring) ).
thf(856,plain,
division_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(53,axiom,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Oidom) ).
thf(444,plain,
! [TA: $tType] :
( ( idom @ TA )
=> ( idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(19,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_gr__zeroI) ).
thf(375,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(268,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: poly @ TA] :
( ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( ( coeff @ TA @ B @ C )
= ( zero_zero @ TA ) ) )
=> ( ord_less_eq @ nat @ ( degree @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_degree__le) ).
thf(965,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat,B: poly @ TA] :
( ! [C: nat] :
( ( ord_less @ nat @ A @ C )
=> ( ( coeff @ TA @ B @ C )
= ( zero_zero @ TA ) ) )
=> ( ord_less_eq @ nat @ ( degree @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(121,axiom,
ord_less @ real @ a @ ( divide_divide @ real @ ( one_one @ real ) @ m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_A__less_I2_J) ).
thf(584,plain,
ord_less @ real @ a @ ( divide_divide @ real @ ( one_one @ real ) @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(210,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_divide__cancel__right) ).
thf(819,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ C @ B ) )
= ( ( B
= ( zero_zero @ TA ) )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(164,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_of__int__le__iff) ).
thf(694,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(189,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_divide__eq__1__iff) ).
thf(772,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(180,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_divide__self__if) ).
thf(743,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( ( A
= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(330,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_divide__right__mono__neg) ).
thf(1124,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(113,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_divide__eq__eq__1) ).
thf(562,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(245,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_poly__0) ).
thf(904,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ! [A: TA] :
( ( poly2 @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(336,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_divide__right__mono) ).
thf(1139,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(257,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ord_less @ nat @ ( degree @ TA @ A ) @ B )
=> ( ( coeff @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_coeff__eq__0) ).
thf(936,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( ord_less @ nat @ ( degree @ TA @ A ) @ B )
=> ( ( coeff @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(22,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_diff__gt__0__iff__gt) ).
thf(382,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(84,axiom,
ring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oring__1) ).
thf(498,plain,
ring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(349,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( ( A @ ( sk1 @ TA @ B @ A ) )
!= ( B @ ( sk1 @ TA @ B @ A ) ) )
| ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(cnf,[status(esa)],[348]) ).
thf(350,plain,
! [TA: $tType,B: TA > $o,A: TA > $o] :
( ( ( A @ ( sk1 @ TA @ B @ A ) )
!= ( B @ ( sk1 @ TA @ B @ A ) ) )
| ( ( collect @ TA @ A )
= ( collect @ TA @ B ) ) ),
inference(lifteq,[status(thm)],[349]) ).
thf(105,axiom,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_power__0) ).
thf(540,plain,
! [TA: $tType] :
( ( power @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( zero_zero @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(131,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_divide__self) ).
thf(611,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(197,axiom,
! [A: nat] : ( member @ real @ ( coeff @ real @ p @ A ) @ ( ring_1_Ints @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_p_I1_J) ).
thf(787,plain,
! [A: nat] : ( member @ real @ ( coeff @ real @ p @ A ) @ ( ring_1_Ints @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(251,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less @ int @ A @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_of__int__less__1__iff) ).
thf(919,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less @ int @ A @ ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(202,axiom,
ord_less @ real @ ( zero_zero @ real ) @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_A__pos) ).
thf(804,plain,
ord_less @ real @ ( zero_zero @ real ) @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(32,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( coeff @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_coeff__0) ).
thf(406,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: nat] :
( ( coeff @ TA @ ( zero_zero @ ( poly @ TA ) ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(214,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_divide__less__0__1__iff) ).
thf(831,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ ( one_one @ TA ) @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(195,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ D ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_frac__le) ).
thf(784,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ B @ A )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ D ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(277,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_154_power__mono) ).
thf(990,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[277]) ).
thf(338,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_le__divide__eq__1__neg) ).
thf(1144,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( abs_abs @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_Ints__nonzero__abs__ge1) ).
thf(599,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( abs_abs @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(287,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_divide__cancel__left) ).
thf(1011,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( divide_divide @ TA @ A @ C ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(39,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( power @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Power_Opower_58) ).
thf(419,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( power @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(301,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ ( one_one @ TA ) )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_power__le__one) ).
thf(1048,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ ( one_one @ TA ) )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(177,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_zero__less__abs__iff) ).
thf(736,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( abs_abs @ TA @ A ) )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(90,axiom,
comm_semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ocomm__semiring__0_11) ).
thf(509,plain,
comm_semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(145,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: int] :
( ( ring_1_of_int @ TA @ ( minus_minus @ int @ A @ B ) )
= ( minus_minus @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_of__int__diff) ).
thf(649,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: int,B: int] :
( ( ring_1_of_int @ TA @ ( minus_minus @ int @ A @ B ) )
= ( minus_minus @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(299,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_less__divide__eq__1__pos) ).
thf(1043,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ B @ A ) )
= ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(237,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1_31) ).
thf(890,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(206,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ B @ A )
= ( one_one @ TA ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_right__inverse__eq) ).
thf(811,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ B @ A )
= ( one_one @ TA ) )
= ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(138,axiom,
! [TA: $tType] :
( ( idom_divide @ TA )
=> ! [A: poly @ TA] :
( ( divide_divide @ ( poly @ TA ) @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_divide__poly__0) ).
thf(631,plain,
! [TA: $tType] :
( ( idom_divide @ TA )
=> ! [A: poly @ TA] :
( ( divide_divide @ ( poly @ TA ) @ A @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ ( poly @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(182,axiom,
idom_divide @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oidom__divide_29) ).
thf(758,plain,
idom_divide @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(208,axiom,
power @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Power_Opower_36) ).
thf(816,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(200,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: TA] :
( ( ord_less @ TA @ ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) @ B )
=> ( ( A
= ( zero_zero @ int ) )
| ( ord_less @ TA @ ( one_one @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_of__int__lessD) ).
thf(799,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: TA] :
( ( ord_less @ TA @ ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) @ B )
=> ( ( A
= ( zero_zero @ int ) )
| ( ord_less @ TA @ ( one_one @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(260,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( divide_divide @ nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_div__less__dividend) ).
thf(943,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( divide_divide @ nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(63,axiom,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_49) ).
thf(462,plain,
! [TA: $tType] :
( ( comm_semiring_0 @ TA )
=> ( comm_semiring_0 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(219,axiom,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_diff__divide__distrib) ).
thf(848,plain,
! [TA: $tType] :
( ( division_ring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( divide_divide @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(166,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less @ nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_power__strict__decreasing__iff) ).
thf(700,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less @ nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(29,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add_45) ).
thf(399,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( ordered_ab_group_add @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(266,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_129_power__eq__imp__eq__base) ).
thf(959,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[266]) ).
thf(130,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_int__one__le__iff__zero__less) ).
thf(608,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( one_one @ int ) @ A )
= ( ord_less @ int @ ( zero_zero @ int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(325,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less_eq @ TA @ B @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_le__divide__eq__1) ).
thf(1113,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less_eq @ TA @ B @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(282,axiom,
( ( poly2 @ real @ p @ x )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_p_I3_J) ).
thf(1000,plain,
( ( poly2 @ real @ p @ x )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(47,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_13) ).
thf(431,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(147,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_divide__nonpos__nonneg) ).
thf(653,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(252,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ring_1_of_int @ TA @ ( abs_abs @ int @ A ) )
= ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_of__int__abs) ).
thf(922,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ring_1_of_int @ TA @ ( abs_abs @ int @ A ) )
= ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(160,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
= ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_divide__le__0__abs__iff) ).
thf(685,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ ( abs_abs @ TA @ B ) ) @ ( zero_zero @ TA ) )
= ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(97,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_diff__zero) ).
thf(521,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(308,axiom,
ring_n68954251visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__no__zero__divisors_22) ).
thf(1066,plain,
ring_n68954251visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(228,axiom,
( n
= ( degree @ real @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_n__def) ).
thf(868,plain,
( n
= ( degree @ real @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(220,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_frac__less2) ).
thf(851,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(322,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ ( one_one @ TA ) )
=> ( ord_less @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_power__strict__decreasing) ).
thf(1102,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less @ TA @ C @ ( one_one @ TA ) )
=> ( ord_less @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(88,axiom,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ( semiri1193490041visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_40) ).
thf(505,plain,
! [TA: $tType] :
( ( ( comm_semiring_0 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ( semiri1193490041visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_zero__reorient) ).
thf(438,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(172,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ B ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ A ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_divide__less__eq__1) ).
thf(722,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( one_one @ TA ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ A @ B ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ A ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(1165,plain,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
inference(polarity_switch,[status(thm)],[1164]) ).
thf(1166,plain,
( p
!= ( zero_zero @ ( poly @ real ) ) ),
inference(lifteq,[status(thm)],[1165]) ).
thf(101,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_zero__le) ).
thf(531,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( minus_minus @ TA @ A @ B ) @ ( ring_1_Ints @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_Ints__diff) ).
thf(487,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( minus_minus @ TA @ A @ B ) @ ( ring_1_Ints @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(95,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_eq__iff__diff__eq__0) ).
thf(516,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(258,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_divide__less__eq__1__neg) ).
thf(939,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(61,axiom,
idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Oidom_3) ).
thf(458,plain,
idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(69,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(473,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(312,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( ( A = B )
= ( ord_less @ TA @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) @ ( one_one @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_Ints__eq__abs__less1) ).
thf(1076,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ( member @ TA @ B @ ( ring_1_Ints @ TA ) )
=> ( ( A = B )
= ( ord_less @ TA @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) @ ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(191,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_diff__ge__0__iff__ge) ).
thf(776,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_diff__eq__diff__less__eq) ).
thf(525,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(120,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ A )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_div__neg__neg__trivial) ).
thf(580,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ B @ A )
=> ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(162,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_power__increasing__iff) ).
thf(690,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(142,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ B @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_less__divide__eq__1) ).
thf(640,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
& ( ord_less @ TA @ B @ A ) )
| ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(310,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_of__int__eq__1__iff) ).
thf(1070,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( one_one @ TA ) )
= ( A
= ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(36,axiom,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_less__int__code_I1_J) ).
thf(414,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( abs_abs @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_abs__triangle__ineq3) ).
thf(739,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( abs_abs @ TA @ ( minus_minus @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ B ) ) ) @ ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( ring_1_Ints @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_Ints__0) ).
thf(409,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( zero_zero @ TA ) @ ( ring_1_Ints @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(279,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ ( one_one @ TA ) )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_power__decreasing) ).
thf(993,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ ( one_one @ TA ) )
=> ( ord_less_eq @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(170,axiom,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ A ) @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ B ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_poly__IVT__pos) ).
thf(712,plain,
! [A: real,B: real,C: poly @ real] :
( ( ord_less @ real @ A @ B )
=> ( ( ord_less @ real @ ( poly2 @ real @ C @ A ) @ ( zero_zero @ real ) )
=> ( ( ord_less @ real @ ( zero_zero @ real ) @ ( poly2 @ real @ C @ B ) )
=> ? [D: real] :
( ( ord_less @ real @ A @ D )
& ( ord_less @ real @ D @ B )
& ( ( poly2 @ real @ C @ D )
= ( zero_zero @ real ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(111,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_divide__strict__right__mono) ).
thf(557,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ C ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(303,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_zero__less__divide__iff) ).
thf(1053,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(155,axiom,
comm_ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__ring__1_30) ).
thf(673,plain,
comm_ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(51,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_15) ).
thf(441,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(87,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_diff__0__right) ).
thf(502,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(205,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_le__zero__eq) ).
thf(808,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(333,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_divide__le__eq__1__neg) ).
thf(1130,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(143,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( abs_abs @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_abs__eq__0) ).
thf(643,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ( abs_abs @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(246,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_divide__nonpos__pos) ).
thf(907,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(297,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( abs_abs @ TA @ ( minus_minus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_abs__minus__commute) ).
thf(1038,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( minus_minus @ TA @ A @ B ) )
= ( abs_abs @ TA @ ( minus_minus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(122,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( coeff @ TA @ A @ ( degree @ TA @ A ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_leading__coeff__0__iff) ).
thf(585,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: poly @ TA] :
( ( ( coeff @ TA @ A @ ( degree @ TA @ A ) )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(16,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(370,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(315,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_divide__pos__neg) ).
thf(1085,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(118,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_diff__mono) ).
thf(576,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(167,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( degree @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_degree__0) ).
thf(703,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( degree @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(337,axiom,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_of__int__eq__0__iff) ).
thf(1141,plain,
! [TA: $tType] :
( ( ring_char_0 @ TA )
=> ! [A: int] :
( ( ( ring_1_of_int @ TA @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( divide_divide @ nat @ A @ B )
= A )
= ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_div__eq__dividend__iff) ).
thf(656,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ( divide_divide @ nat @ A @ B )
= A )
= ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(226,axiom,
ring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Oring__1_35) ).
thf(864,plain,
ring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(319,axiom,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: poly @ TA,B: nat] :
( ( coeff @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ ( degree @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) ) )
= ( power_power @ TA @ ( coeff @ TA @ A @ ( degree @ TA @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_lead__coeff__power) ).
thf(1094,plain,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri1193490041visors @ TA ) )
=> ! [A: poly @ TA,B: nat] :
( ( coeff @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ ( degree @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) ) )
= ( power_power @ TA @ ( coeff @ TA @ A @ ( degree @ TA @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(285,axiom,
semiri134348788visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_17) ).
thf(1008,plain,
semiri134348788visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(83,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(497,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(54,axiom,
semiri1193490041visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__no__zero__divisors) ).
thf(446,plain,
semiri1193490041visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(116,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ! [C: int] : ( B @ ( ring_1_of_int @ TA @ C ) )
=> ( B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_Ints__induct) ).
thf(571,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: TA > $o] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( ! [C: int] : ( B @ ( ring_1_of_int @ TA @ C ) )
=> ( B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(218,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) @ B )
=> ( ( A
= ( zero_zero @ int ) )
| ( ord_less_eq @ TA @ ( one_one @ TA ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_of__int__leD) ).
thf(845,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ ( ring_1_of_int @ TA @ A ) ) @ B )
=> ( ( A
= ( zero_zero @ int ) )
| ( ord_less_eq @ TA @ ( one_one @ TA ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(65,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: poly @ TA,B: poly @ TA,C: nat] :
( ( coeff @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) @ C )
= ( minus_minus @ TA @ ( coeff @ TA @ A @ C ) @ ( coeff @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_coeff__diff) ).
thf(465,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: poly @ TA,B: poly @ TA,C: nat] :
( ( coeff @ TA @ ( minus_minus @ ( poly @ TA ) @ A @ B ) @ C )
= ( minus_minus @ TA @ ( coeff @ TA @ A @ C ) @ ( coeff @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(136,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_divide__nonneg__nonneg) ).
thf(627,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(255,axiom,
! [A: poly @ real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( coeff @ real @ A @ ( degree @ real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( coeff @ real @ A @ ( degree @ real @ A ) ) @ ( poly2 @ real @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_poly__pinfty__gt__lc) ).
thf(931,plain,
! [A: poly @ real] :
( ( ord_less @ real @ ( zero_zero @ real ) @ ( coeff @ real @ A @ ( degree @ real @ A ) ) )
=> ? [B: real] :
! [C: real] :
( ( ord_less_eq @ real @ B @ C )
=> ( ord_less_eq @ real @ ( coeff @ real @ A @ ( degree @ real @ A ) ) @ ( poly2 @ real @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(75,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_diff__eq__diff__less) ).
thf(482,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(161,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( one_one @ TA ) @ ( ring_1_Ints @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_Ints__1) ).
thf(688,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( member @ TA @ ( one_one @ TA ) @ ( ring_1_Ints @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(98,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Nat_Oring__char__0_34) ).
thf(524,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(81,axiom,
cancel1352612707id_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(495,plain,
cancel1352612707id_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(183,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_of__int__1__less__iff) ).
thf(759,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(238,axiom,
ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_ab_H) ).
thf(891,plain,
ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(331,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_power__strict__increasing__iff) ).
thf(1126,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( one_one @ TA ) @ A )
=> ( ( ord_less @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(14,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(368,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(188,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_less__eq__int__code_I1_J) ).
thf(771,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(123,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: nat] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( power_power @ TA @ A @ B ) @ ( ring_1_Ints @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_Ints__power) ).
thf(588,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ! [A: TA,B: nat] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( power_power @ TA @ A @ B ) @ ( ring_1_Ints @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(242,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ord_less @ nat @ ( degree @ TA @ A ) @ ( degree @ TA @ B ) )
=> ( ( divide_divide @ ( poly @ TA ) @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_div__poly__less) ).
thf(896,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ord_less @ nat @ ( degree @ TA @ A ) @ ( degree @ TA @ B ) )
=> ( ( divide_divide @ ( poly @ TA ) @ A @ B )
= ( zero_zero @ ( poly @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(261,axiom,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_divide__eq__0__iff) ).
thf(946,plain,
! [TA: $tType] :
( ( field @ TA )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(25,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_zero__diff) ).
thf(390,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_diff__strict__right__mono) ).
thf(401,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(280,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_182_power__less__imp__less__base) ).
thf(995,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[280]) ).
thf(146,axiom,
one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Oone_38) ).
thf(652,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(175,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_of__int__0__le__iff) ).
thf(731,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(196,axiom,
group_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ogroup__add_32) ).
thf(786,plain,
group_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(294,axiom,
linordered_field @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Olinordered__field) ).
thf(1030,plain,
linordered_field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(115,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_of__int__less__of__int__power__cancel__iff) ).
thf(568,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(91,axiom,
ordered_ab_group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add) ).
thf(510,plain,
ordered_ab_group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] :
( ( abs_abs @ TA @ ( power_power @ TA @ A @ B ) )
= ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_power__abs) ).
thf(667,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] :
( ( abs_abs @ TA @ ( power_power @ TA @ A @ B ) )
= ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(72,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1) ).
thf(478,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(243,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( abs_abs @ TA @ A ) @ ( ring_1_Ints @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Ints__abs) ).
thf(899,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( member @ TA @ A @ ( ring_1_Ints @ TA ) )
=> ( member @ TA @ ( abs_abs @ TA @ A ) @ ( ring_1_Ints @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_zero__le__power__abs) ).
thf(549,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: nat] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ ( abs_abs @ TA @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(103,axiom,
! [TA: $tType] :
( ( linordered_semidom @ 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_155_zero__le__power) ).
thf(536,plain,
! [TA: $tType] :
( ( linordered_semidom @ 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)],[103]) ).
thf(343,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_abs__le__self__iff) ).
thf(1161,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( abs_abs @ TA @ A ) @ A )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(249,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_122_nat__power__less__imp__less) ).
thf(914,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)],[249]) ).
thf(20,axiom,
ordere142940540dd_abs @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
thf(378,plain,
ordere142940540dd_abs @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(326,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: poly @ TA,B: TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ A @ C ) @ ( ring_1_Ints @ TA ) )
=> ( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( algebraic @ TA @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_algebraicI) ).
thf(1116,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ! [A: poly @ TA,B: TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ A @ C ) @ ( ring_1_Ints @ TA ) )
=> ( ( A
!= ( zero_zero @ ( poly @ TA ) ) )
=> ( ( ( poly2 @ TA @ A @ B )
= ( zero_zero @ TA ) )
=> ( algebraic @ TA @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(334,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_power__mono__iff) ).
thf(1133,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA,C: nat] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ C ) @ ( power_power @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(55,axiom,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( comm_ring @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__ring_55) ).
thf(447,plain,
! [TA: $tType] :
( ( comm_ring @ TA )
=> ( comm_ring @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(48,axiom,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq) ).
thf(432,plain,
! [TA: $tType,A: set @ TA] :
( ( collect @ TA
@ ^ [B: TA] : ( member @ TA @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( coeff @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( ^ [A: nat] : ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zero__poly_Orep__eq) ).
thf(422,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ( ( coeff @ TA @ ( zero_zero @ ( poly @ TA ) ) )
= ( ^ [A: nat] : ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(227,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less_eq @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_of__int__le__of__int__power__cancel__iff) ).
thf(865,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: nat,C: int] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ ( ring_1_of_int @ TA @ A ) @ B ) @ ( ring_1_of_int @ TA @ C ) )
= ( ord_less_eq @ int @ ( power_power @ int @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(263,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_divide__less__eq__1__pos) ).
thf(950,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(320,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_divide__le__cancel) ).
thf(1097,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( divide_divide @ TA @ C @ B ) )
= ( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ B )
=> ( ord_less_eq @ TA @ A @ C ) )
& ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(304,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Olinordered__semidom_24) ).
thf(1056,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(213,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_of__int__power__less__of__int__cancel__iff) ).
thf(828,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int,C: nat] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( power_power @ TA @ ( ring_1_of_int @ TA @ B ) @ C ) )
= ( ord_less @ int @ A @ ( power_power @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(140,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: int] :
( ( coeff @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) @ ( degree @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) ) )
= ( ring_1_of_int @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_lead__coeff__of__int) ).
thf(635,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ! [A: int] :
( ( coeff @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) @ ( degree @ TA @ ( ring_1_of_int @ ( poly @ TA ) @ A ) ) )
= ( ring_1_of_int @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(199,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( one_one @ int ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_of__int__1) ).
thf(796,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( one_one @ int ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(8,axiom,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri134348788visors @ TA ) )
=> ( semiri134348788visors @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Osemiring__1__no__zero__divisors_39) ).
thf(358,plain,
! [TA: $tType] :
( ( ( comm_semiring_1 @ TA )
& ( semiri134348788visors @ TA ) )
=> ( semiri134348788visors @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(204,axiom,
comm_semiring_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Rings_Ocomm__semiring__0_27) ).
thf(807,plain,
comm_semiring_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Olinordered__idom_47) ).
thf(474,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ( linordered_idom @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(186,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( coeff @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ ( zero_zero @ nat ) )
= ( power_power @ TA @ ( coeff @ TA @ A @ ( zero_zero @ nat ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_coeff__0__power) ).
thf(767,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: poly @ TA,B: nat] :
( ( coeff @ TA @ ( power_power @ ( poly @ TA ) @ A @ B ) @ ( zero_zero @ nat ) )
= ( power_power @ TA @ ( coeff @ TA @ A @ ( zero_zero @ nat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(235,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ( algebraic @ TA )
= ( ^ [A: TA] :
? [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( ring_1_Ints @ TA ) )
& ( B
!= ( zero_zero @ ( poly @ TA ) ) )
& ( ( poly2 @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_algebraic__def) ).
thf(886,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ( algebraic @ TA )
= ( ^ [A: TA] :
? [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( ring_1_Ints @ TA ) )
& ( B
!= ( zero_zero @ ( poly @ TA ) ) )
& ( ( poly2 @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(254,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_of__int__less__iff) ).
thf(928,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( ring_1_of_int @ TA @ A ) @ ( ring_1_of_int @ TA @ B ) )
= ( ord_less @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(415,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ) ),
inference(polarity_switch,[status(thm)],[414]) ).
thf(174,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less_eq @ nat @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_power__decreasing__iff) ).
thf(728,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: nat,C: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ ( one_one @ TA ) )
=> ( ( ord_less_eq @ TA @ ( power_power @ TA @ A @ B ) @ ( power_power @ TA @ A @ C ) )
= ( ord_less_eq @ nat @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(64,axiom,
comm_semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ocomm__semiring__0) ).
thf(464,plain,
comm_semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(332,axiom,
ord_less_eq @ real @ a @ ( one_one @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87__092_060open_062A_A_092_060le_062_A1_092_060close_062) ).
thf(1129,plain,
ord_less_eq @ real @ a @ ( one_one @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(117,axiom,
ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_ab) ).
thf(575,plain,
ord_less_eq @ real @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(43,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_9) ).
thf(427,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(224,axiom,
field @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Fields_Ofield) ).
thf(860,plain,
field @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(126,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ int @ A @ ( one_one @ int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_of__int__le__1__iff) ).
thf(596,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( ring_1_of_int @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ int @ A @ ( one_one @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(100,axiom,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= ( poly2 @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_poly__eq__poly__eq__iff) ).
thf(528,plain,
! [TA: $tType] :
( ( ( ring_char_0 @ TA )
& ( comm_ring_1 @ TA )
& ( ring_n68954251visors @ TA ) )
=> ! [A: poly @ TA,B: poly @ TA] :
( ( ( poly2 @ TA @ A )
= ( poly2 @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(62,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_diff__self) ).
thf(459,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(278,axiom,
ord_less @ real @ a @ ( one_one @ real ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_A__less_I1_J) ).
thf(992,plain,
ord_less @ real @ a @ ( one_one @ real ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(211,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_div__less) ).
thf(822,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(274,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_zero__le__divide__iff) ).
thf(982,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ B ) )
= ( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
& ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) )
| ( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
& ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(52,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_48) ).
thf(442,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( comm_semiring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(328,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_divide__le__eq__1__pos) ).
thf(1120,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(15,axiom,
semiri134348788visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors) ).
thf(369,plain,
semiri134348788visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(67,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(469,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(6,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Power_Opower) ).
thf(354,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(286,axiom,
~ ( ord_less @ real @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ) @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121__092_060open_062_092_060not_062_AA_A_P_Areal__of__int_Ab_A_094_An_A_060_A_092_060bar_062x_A_N_Areal__of__int_Aa_A_P_Areal__of__int_Ab_092_060bar_062_092_060close_062) ).
thf(1009,plain,
~ ( ord_less @ real @ ( divide_divide @ real @ a @ ( power_power @ real @ ( ring_1_of_int @ real @ b ) @ n ) ) @ ( abs_abs @ real @ ( minus_minus @ real @ x @ ( divide_divide @ real @ ( ring_1_of_int @ real @ a2 ) @ ( ring_1_of_int @ real @ b ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(106,axiom,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ( algebraic @ TA )
= ( ^ [A: TA] :
? [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( field_char_0_Rats @ TA ) )
& ( B
!= ( zero_zero @ ( poly @ TA ) ) )
& ( ( poly2 @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_algebraic__altdef) ).
thf(543,plain,
! [TA: $tType] :
( ( field_char_0 @ TA )
=> ( ( algebraic @ TA )
= ( ^ [A: TA] :
? [B: poly @ TA] :
( ! [C: nat] : ( member @ TA @ ( coeff @ TA @ B @ C ) @ ( field_char_0_Rats @ TA ) )
& ( B
!= ( zero_zero @ ( poly @ TA ) ) )
& ( ( poly2 @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(190,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Real_Oreal___Groups_Ozero_37) ).
thf(775,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(157,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( degree @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_degree__1) ).
thf(676,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( ( degree @ TA @ ( one_one @ ( poly @ TA ) ) )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(11,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__mult) ).
thf(364,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(233,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_divide__strict__right__mono__neg) ).
thf(882,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( divide_divide @ TA @ B @ C ) @ ( divide_divide @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(79,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Groups_Oone_60) ).
thf(491,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ( one @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(317,axiom,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_of__int__0) ).
thf(1088,plain,
! [TA: $tType] :
( ( ring_1 @ TA )
=> ( ( ring_1_of_int @ TA @ ( zero_zero @ int ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(82,axiom,
semiri134348788visors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_5) ).
thf(496,plain,
semiri134348788visors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(59,axiom,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_52) ).
thf(454,plain,
! [TA: $tType] :
( ( comm_ring_1 @ TA )
=> ( comm_ring_1 @ ( poly @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(288,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_of__int__1__le__iff) ).
thf(1014,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( ring_1_of_int @ TA @ A ) )
= ( ord_less_eq @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(270,axiom,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_divide__nonneg__neg) ).
thf(972,plain,
! [TA: $tType] :
( ( linordered_field @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ B @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(4788,plain,
$false,
inference(e,[status(thm)],[892,629,1024,365,479,347,893,352,909,1031,962,468,977,762,1005,379,614,741,1073,873,449,655,511,1041,861,385,533,500,1164,472,814,1063,538,670,782,709,417,1046,565,719,372,917,802,949,357,1191,817,559,1087,1147,770,416,1100,638,853,421,870,756,789,623,646,514,353,480,485,1136,834,1020,348,602,397,634,877,734,956,453,1119,396,660,428,1104,507,411,988,452,942,546,925,1153,366,1067,1057,894,1091,825,1021,1123,693,429,361,625,435,665,889,493,682,551,974,1079,1027,456,842,697,874,1017,1111,725,388,593,783,499,989,857,519,742,578,980,403,884,1160,1082,933,554,489,590,706,901,476,679,970,837,393,997,985,911,1002,779,371,605,515,1150,1060,1050,360,805,765,1170,1035,674,1167,953,662,412,618,425,430,856,444,375,965,750,584,819,694,772,743,1124,562,904,1139,936,382,498,350,540,611,787,919,804,406,831,784,990,1144,599,1011,419,1048,736,509,649,1043,890,811,631,758,816,799,943,462,848,700,399,959,608,1113,1000,431,653,922,685,521,1066,868,851,1102,505,438,722,1166,531,487,516,939,355,458,473,1076,776,525,580,690,640,1070,414,739,409,993,712,557,1053,673,441,502,808,1130,643,907,1038,585,370,1085,576,703,1141,656,864,1094,1008,497,446,571,845,465,627,931,482,688,524,495,759,891,1126,368,771,588,896,946,390,401,995,652,351,731,786,1030,568,510,667,478,899,549,536,1161,914,378,1116,1133,447,432,422,865,950,1097,1056,828,635,796,358,807,474,767,886,928,415,395,728,464,1129,575,427,860,596,528,459,992,822,982,442,1120,369,469,354,1009,543,775,676,364,882,491,1088,496,454,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP095^2 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:55:42 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.91/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.39/1.20 % [INFO] Parsing done (401ms).
% 2.39/1.21 % [INFO] Running in sequential loop mode.
% 3.70/1.60 % [INFO] eprover registered as external prover.
% 3.70/1.61 % [INFO] Scanning for conjecture ...
% 3.90/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 345 axioms. Running axiom selection ...
% 4.49/1.95 % [INFO] Axiom selection finished. Selected 344 axioms (removed 1 axioms).
% 5.54/2.25 % [INFO] Problem is higher-order (TPTP THF).
% 5.54/2.28 % [INFO] Type checking passed.
% 5.54/2.28 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 67.74/15.39 % External prover 'e' found a proof!
% 67.74/15.39 % [INFO] Killing All external provers ...
% 67.74/15.39 % Time passed: 15035ms (effective reasoning time: 14168ms)
% 67.74/15.39 % 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)>
% 67.74/15.40 % Axioms used in derivation (344): fact_156_divide__neg__neg, fact_248_div__le__dividend, fact_42_less__int__code_I1_J, fact_98_divide__self, tcon_Real_Oreal___Groups_Oone_38, fact_68_Ints__nonzero__abs__less1, fact_87__092_060open_062A_A_092_060le_062_A1_092_060close_062, fact_29_poly__0, tcon_Nat_Onat___Groups_Oone_16, fact_2_p_I1_J, fact_38_of__int__less__1__iff, tcon_Real_Oreal___Rings_Olinordered__semidom_24, tcon_Int_Oint___Rings_Olinordered__semidom, fact_214_coeff__diff, fact_189_power__le__imp__le__exp, fact_116_less__divide__eq__1__pos, fact_11_poly__power, fact_60_leading__coeff__neq__0, fact_0_assms_I2_J, fact_5_no__root, fact_141_power__not__zero, fact_136_less__degree__imp, fact_3_b, tcon_Polynomial_Opoly___Groups_Oab__group__add, fact_70_lead__coeff__power, fact_245_div__eq__dividend__iff, fact_109_degree__of__int, fact_239_Ints__diff, fact_72_poly__eq__poly__eq__iff, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_226_diff__left__mono, fact_138_Liouville__Numbers__Misc_ORats__cases_H, fact_39_of__int__1__less__iff, tcon_Real_Oreal___Rings_Ocomm__semiring__1_26, tcon_Polynomial_Opoly___Rings_Osemiring__1__no__zero__divisors_39, tcon_Polynomial_Opoly___Rings_Olinordered__idom_47, fact_66_Ints__induct, fact_83_zero__le__divide__abs__iff, tcon_Int_Oint___Groups_Ozero, fact_88_power__one__right, fact_27_of__int__less__iff, fact_191_abs__div__pos, fact_174_frac__le, tcon_Real_Oreal___Fields_Ofield__char__0, fact_74_of__int__leD, fact_58_algebraicE, fact_236_diff__divide__distrib, fact_117_zero__less__divide__1__iff, fact_127_power__0, fact_114_divide__less__eq__1__pos, fact_150_divide__nonneg__nonpos, tcon_Int_Oint___Rings_Oidom__divide, fact_56_algebraic__def, tcon_Int_Oint___Nat_Oring__char__0, fact_206_zero__diff, fact_168_one__le__power, fact_37_of__int__0__less__iff, fact_243_zero__reorient, tcon_Int_Oint___Groups_Oordered__ab__group__add, tcon_Int_Oint___Rings_Oring__1, fact_170_power__less__imp__less__exp, tcon_Nat_Onat___Power_Opower_14, fact_113_divide__less__eq__1__neg, fact_188_power__strict__decreasing, fact_107_degree__0, tcon_Real_Oreal___Rings_Ocomm__ring__1_30, fact_207_diff__0__right, tcon_Int_Oint___Groups_Omonoid__mult, tcon_Polynomial_Opoly___Rings_Ocomm__ring_55, fact_53_coeff__inject, tcon_Polynomial_Opoly___Rings_Oidom, fact_173_nonzero__abs__divide, fact_234_diff__eq__diff__eq, tcon_Polynomial_Opoly___Rings_Oring__no__zero__divisors_44, fact_171_power__strict__increasing, fact_153_divide__right__mono__neg, tcon_Polynomial_Opoly___Rings_Ocomm__semiring__0_49, fact_44_poly__eqI, fact_33_lead__coeff__1, fact_203_not__gr__zero, fact_22__092_060open_062x_A_092_060notin_062_Aroots_092_060close_062, fact_52_int__one__le__iff__zero__less, tcon_Polynomial_Opoly___Groups_Ocancel__comm__monoid__add_43, fact_30_lead__coeff__of__int, tcon_Real_Oreal___Groups_Oab__group__add_2, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_8, fact_219_abs__le__zero__iff, fact_77_le__divide__eq__1__pos, fact_172_power__one__over, fact_200_M__pos, fact_6_n__def, tcon_Polynomial_Opoly___Groups_Ogroup__add_54, fact_61_poly__all__0__iff__0, fact_106_power__eq__0__iff, tcon_Real_Oreal___Rings_Oring__no__zero__divisors_22, fact_253_not__less__zero, fact_160_divide__less__0__iff, fact_177_divide__le__cancel, tcon_Polynomial_Opoly___Rings_Osemiring__no__zero__divisors_40, fact_155_zero__le__power, fact_65_Ints__of__int, tcon_Real_Oreal___Rings_Oring__1_35, fact_41_of__int__less__of__int__power__cancel__iff, fact_112_divide__less__0__1__iff, fact_31_leading__coeff__0__iff, fact_166_right__inverse__eq, fact_46_Collect__mem__eq, fact_104_power__inject__exp, fact_241_abs__triangle__ineq3, tcon_Int_Oint___Rings_Ocomm__ring__1, tcon_Real_Oreal___Rings_Oidom_1, fact_204_cancel__comm__monoid__add__class_Odiff__cancel, fact_161_divide__less__cancel, fact_209_abs__zero, fact_51_zero__poly_Orep__eq, fact_32_zabs__less__one__iff, fact_198_div__neg__neg__trivial, tcon_Int_Oint___Rings_Ocomm__ring, fact_140_eq__zero__or__degree__less, fact_81__092_060open_062A_A_P_Areal__of__int_Ab_A_094_An_A_092_060le_062_AA_A_P_A1_092_060close_062, fact_208_diff__self, tcon_Nat_Onat___Rings_Osemiring__1__no__zero__divisors_5, fact_169_power__increasing, fact_182_power__less__imp__less__base, fact_164_divide__strict__right__mono__neg, fact_99_divide__self__if, fact_211_abs__0__eq, fact_157_divide__neg__pos, fact_235_cancel__ab__semigroup__add__class_Odiff__right__commute, tcon_Real_Oreal___Groups_Omonoid__mult_28, fact_210_abs__eq__0, fact_63_Ints__power, fact_9_of__int__1__le__iff, fact_222_that, fact_93_division__ring__divide__zero, fact_73_of__int__lessD, tcon_Real_Oreal___Rings_Oidom__divide_29, fact_115_less__divide__eq__1__neg, fact_89_nat__zero__less__power__iff, fact_95_abs__divide, fact_78_le__divide__eq__1__neg, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, tcon_Polynomial_Opoly___Rings_Osemiring__1_53, tcon_Polynomial_Opoly___Rings_Oidom__divide_51, fact_36_of__int__less__0__iff, fact_84_divide__le__0__abs__iff, fact_218_diff__gt__0__iff__gt, fact_20_of__int__eq__iff, fact_213_of__int__diff, tcon_Int_Oint___Rings_Ocomm__semiring__1, fact_216_A__less_I3_J, tcon_Int_Oint___Rings_Olinordered__idom, fact_212_div__less, fact_108_degree__1, fact_187_less__divide__eq__1, tcon_Nat_Onat___Rings_Ocomm__semiring__1_10, fact_34_of__int__le__0__iff, fact_199_zero__less__abs__iff, tcon_Real_Oreal___Groups_Ogroup__add_32, tcon_Polynomial_Opoly___Groups_Oone_60, fact_129_power__eq__imp__eq__base, tcon_Polynomial_Opoly___Groups_Ozero_59, fact_178_divide__nonneg__neg, tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add_45, fact_175_frac__less, fact_230_diff__strict__left__mono, fact_57_algebraicI, fact_195_ab, fact_45_mem__Collect__eq, fact_85_A__pos, fact_26_of__int__le__iff, tcon_Polynomial_Opoly___Rings_Oring__1_57, fact_21__092_060open_062_092_060And_062thesisa_O_A_I_092_060And_062p_O_A_092_060lbrakk_062_092_060And_062i_O_Acoeff_Ap_Ai_A_092_060in_062_A_092_060int_062_059_Ap_A_092_060noteq_062_A0_059_Apoly_Ap_Ax_A_061_A0_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesisa_J_A_092_060Longrightarrow_062_Athesisa_092_060close_062, fact_250_Ints__eq__abs__less1, tcon_Nat_Onat___Rings_Osemiring__no__zero__divisors_6, fact_221_abs__of__nonneg, fact_196_ab_H, fact_100_divide__eq__eq__1, fact_147_divide__right__mono, tcon_Int_Oint___Power_Opower, fact_192_divide__le__eq__1, fact_240_abs__triangle__ineq2__sym, fact_92_divide__cancel__right, fact_163_divide__strict__right__mono, fact_137_degree__le, fact_62_Ints__1, fact_50_Ints__0, fact_205_diff__zero, fact_223_minus__poly_Orep__eq, tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add, tcon_Real_Oreal___Nat_Oring__char__0_34, fact_101_eq__divide__eq__1, fact_246_div__less__dividend, tcon_Int_Oint___Rings_Osemiring__1, tcon_Real_Oreal___Rings_Osemiring__no__zero__divisors_18, fact_124_self__le__power, fact_76_power__decreasing__iff, fact_105_power__strict__increasing__iff, fact_144_power__abs, fact_132_poly__IVT__pos, fact_244_one__reorient, tcon_Real_Oreal___Groups_Oordered__ab__group__add_23, fact_7_of__int__le__of__int__power__cancel__iff, tcon_Int_Oint___Groups_Ogroup__add, tcon_Real_Oreal___Groups_Ocancel__comm__monoid__add_21, fact_152_divide__nonpos__nonpos, fact_133_linordered__field__no__ub, fact_197_div__pos__pos__trivial, fact_120_power__increasing__iff, fact_90_divide__eq__0__iff, fact_24_of__int__0__eq__iff, fact_47_Collect__cong, fact_202_le__zero__eq, fact_16_of__int__power__eq__of__int__cancel__iff, fact_232_diff__strict__mono, tcon_Real_Oreal___Rings_Olinordered__idom_25, fact_162_zero__less__divide__iff, fact_159_divide__pos__pos, fact_10_of__int__le__1__iff, fact_180_divide__nonpos__neg, fact_224_eq__iff__diff__eq__0, fact_167_power__0__left, fact_79_divide__le__eq__1__pos, fact_4_p_I3_J, fact_242_abs__triangle__ineq2, fact_86_A__less_I1_J, tcon_Nat_Onat___Rings_Ocomm__semiring__0_11, fact_49_poly__eq__iff, fact_215_poly__diff, tcon_Polynomial_Opoly___Rings_Ocomm__semiring__1_48, fact_149_divide__nonneg__nonneg, fact_25_of__int__0, fact_229_diff__strict__right__mono, fact_252_gr__zeroI, fact_131_poly__IVT__neg, fact_217_diff__ge__0__iff__ge, fact_145_algebraic__altdef, tcon_Nat_Onat___Rings_Olinordered__semidom_9, tcon_Int_Oint___Rings_Osemiring__no__zero__divisors, fact_91_divide__cancel__left, fact_103_zero__eq__1__divide__iff, tcon_Polynomial_Opoly___Rings_Ocomm__ring__1_52, tcon_Real_Oreal___Rings_Osemiring__1__no__zero__divisors_17, fact_185_power__decreasing, fact_154_power__mono, fact_128_power__eq__iff__eq__base, fact_97_one__eq__divide__iff, tcon_Nat_Onat___Rings_Osemiring__1_13, tcon_Int_Oint___Groups_Oab__group__add_4, fact_228_diff__eq__diff__less__eq, tcon_Int_Oint___Rings_Oring__no__zero__divisors, fact_18_of__int__eq__1__iff, fact_23_of__int__eq__0__iff, tcon_Int_Oint___Rings_Ocomm__semiring__0, tcon_Polynomial_Opoly___Groups_Ocancel__ab__semigroup__add_42, fact_102_one__divide__eq__0__iff, fact_151_divide__nonpos__nonneg, tcon_Real_Oreal___Fields_Olinordered__field, fact_220_abs__le__self__iff, fact_176_frac__less2, fact_82_zero__less__power__abs__iff, fact_125_divide__poly__0, fact_123_div__poly__less, fact_12_poly__1, tcon_Int_Oint___Groups_Oordered__ab__group__add__abs, fact_28_coeff__0, fact_130_one__less__power, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_7, fact_146_divide__le__0__iff, fact_35_of__int__0__le__iff, fact_231_diff__eq__diff__less, fact_121__092_060open_062_092_060not_062_AA_A_P_Areal__of__int_Ab_A_094_An_A_060_A_092_060bar_062x_A_N_Areal__of__int_Aa_A_P_Areal__of__int_Ab_092_060bar_062_092_060close_062, tcon_Nat_Onat___Groups_Ozero_15, tcon_Polynomial_Opoly___Groups_Omonoid__mult_50, fact_225_diff__mono, fact_134_linordered__field__no__lb, fact_158_divide__pos__neg, tcon_Int_Oint___Rings_Oidom_3, fact_181_divide__nonpos__pos, fact_249_div__le__mono, fact_184_power__le__one, fact_110_divide__le__0__1__iff, fact_119_power__mono__iff, fact_80_divide__le__eq__1__neg, fact_71_Ints__nonzero__abs__ge1, tcon_Real_Oreal___Rings_Ocomm__ring_33, fact_55_poly__0__coeff__0, tcon_Real_Oreal___Groups_Ocancel__ab__semigroup__add_20, fact_67_Ints__cases, fact_251_zero__le, fact_54_le__degree, fact_201_abs__idempotent, fact_69_of__int__nonneg, tcon_Polynomial_Opoly___Nat_Oring__char__0_56, fact_118_power__strict__decreasing__iff, fact_59_of__int__pos, fact_14_of__int__power, fact_19_irrationsl, tcon_Real_Oreal___Fields_Ofield__abs__sgn, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_75_int__poly__rat__no__root__ge, fact_247_Euclidean__Division_Odiv__eq__0__iff, fact_111_zero__le__divide__1__iff, fact_142_power__divide, fact_165_zero__less__power, fact_190_zero__le__power__abs, fact_1_p_I2_J, fact_148_zero__le__divide__iff, tcon_Polynomial_Opoly___Groups_Oordered__ab__group__add__abs_41, fact_238_less__iff__diff__less__0, fact_139_coeff__0__power, fact_126_zero__power, fact_193_le__divide__eq__1, fact_40_of__int__power__less__of__int__cancel__iff, fact_183_power__strict__mono, fact_94_power__one, tcon_Real_Oreal___Power_Opower_36, fact_233_abs__minus__commute, fact_122_nat__power__less__imp__less, fact_186_divide__less__eq__1, tcon_Nat_Onat___Groups_Omonoid__mult_12, tcon_Real_Oreal___Rings_Ocomm__semiring__0_27, fact_15_of__int__eq__of__int__power__cancel__iff, tcon_Real_Oreal___Fields_Ofield, fact_194_A__less_I2_J, fact_179_divide__nonneg__pos, tcon_Int_Oint___Groups_Oone, fact_13_of__int__abs, tcon_Polynomial_Opoly___Rings_Olinordered__semidom_46, fact_8_of__int__power__le__of__int__cancel__iff, tcon_Polynomial_Opoly___Power_Opower_58, fact_227_diff__right__mono, fact_135_coeff__eq__0, fact_237_le__iff__diff__le__0, fact_143_poly__pinfty__gt__lc, fact_96_divide__eq__1__iff, fact_64_Ints__abs, tcon_Real_Oreal___Rings_Osemiring__1_31, fact_43_less__eq__int__code_I1_J, tcon_Real_Oreal___Groups_Oordered__ab__group__add__abs_19, tcon_Real_Oreal___Fields_Odivision__ring, tcon_Int_Oint___Rings_Osemiring__1__no__zero__divisors, fact_17_of__int__1, tcon_Real_Oreal___Groups_Ozero_37
% 67.74/15.40 % No. of inferences in proof: 711
% 67.74/15.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15035 ms resp. 14168 ms w/o parsing
% 59.25/15.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 59.25/15.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------