TSTP Solution File: DAT239^1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : DAT239^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:39:50 EDT 2024
% Result : Theorem 12.23s 3.62s
% Output : Refutation 13.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 345
% Syntax : Number of formulae : 648 ( 196 unt; 44 typ; 0 def)
% Number of atoms : 1712 ( 514 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 6850 ( 130 ~; 44 |; 74 &;5946 @)
% ( 0 <=>; 656 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 4 con; 0-3 aty)
% Number of variables : 1266 ( 18 ^1194 !; 16 ?;1266 :)
% ( 38 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(num_type,type,
num: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(int_type,type,
int: $tType ).
thf(one_type,type,
one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_type,type,
zero:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(numeral_type,type,
numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(field_type,type,
field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(neg_numeral_type,type,
neg_numeral:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(preorder_type,type,
preorder:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(zero_less_one_type,type,
zero_less_one:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_div_type,type,
semiring_div:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(division_ring_type,type,
division_ring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semidom_divide_type,type,
semidom_divide:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_field_type,type,
linordered_field:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_div_parity_type,type,
semiring_div_parity:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(semiring_numeral_div_type,type,
semiring_numeral_div:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(linord1659791738miring_type,type,
linord1659791738miring:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : ( ( itself @ TA ) > $o ) ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(neg_numeral_dbl_type,type,
neg_numeral_dbl:
!>[TA: $tType] : ( TA > TA ) ).
thf(bit0_type,type,
bit0: num > num ).
thf(one2_type,type,
one2: num ).
thf(numeral_numeral_type,type,
numeral_numeral:
!>[TA: $tType] : ( num > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(type_type,type,
type:
!>[TA: $tType] : ( itself @ TA ) ).
thf(divide_divide_type,type,
divide_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(na_type,type,
na: nat ).
thf(193,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_measure__induct__rule) ).
thf(782,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(202,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_one__eq__numeral__iff) ).
thf(809,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ( one_one @ TA )
= ( numeral_numeral @ TA @ A ) )
= ( one2 = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(38,axiom,
! [TA: $tType] :
( ( one @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_one__reorient) ).
thf(365,plain,
! [TA: $tType] :
( ( one @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
= ( A
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
cancel1352612707id_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add) ).
thf(347,plain,
cancel1352612707id_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_add_Oleft__cancel) ).
thf(333,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(230,axiom,
one @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oone_21) ).
thf(893,plain,
one @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(100,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ one2 ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_divide__numeral__1) ).
thf(518,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ one2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(299,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_div__nonpos__pos__le0) ).
thf(1083,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(246,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_141_divide__less__0__iff) ).
thf(941,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[246]) ).
thf(151,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_94_frac__less) ).
thf(666,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[151]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_add__le__imp__le__right) ).
thf(352,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
=> ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(270,axiom,
zero_neq_one @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__neq__one_16) ).
thf(1005,plain,
zero_neq_one @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(157,axiom,
ab_semigroup_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_10) ).
thf(683,plain,
ab_semigroup_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(173,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( ord_less @ num @ one2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_one__less__numeral__iff) ).
thf(730,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( ord_less @ num @ one2 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(294,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_double__zero__sym) ).
thf(1068,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(72,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_not__less__zero) ).
thf(449,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_add__left__mono) ).
thf(379,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(68,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_75_divide__nonneg__nonpos) ).
thf(440,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[68]) ).
thf(286,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_86_divide__nonpos__pos) ).
thf(1041,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[286]) ).
thf(58,axiom,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_le__num__One__iff) ).
thf(408,plain,
! [A: num] :
( ( ord_less_eq @ num @ A @ one2 )
= ( A = one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(259,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_less__numeral__extra_I3_J) ).
thf(977,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(102,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_less__zeroE) ).
thf(523,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(186,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_div__neg__pos__less0) ).
thf(762,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(135,axiom,
! [A: nat] :
( ( divide_divide @ nat @ ( plus_plus @ nat @ A @ A ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_add__self__div__2) ).
thf(614,plain,
! [A: nat] :
( ( divide_divide @ nat @ ( plus_plus @ nat @ A @ A ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(155,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_less__add__same__cancel1) ).
thf(677,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(48,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_le__iff__add) ).
thf(384,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(93,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__imp__le__nat) ).
thf(500,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(81,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_less__numeral__extra_I4_J) ).
thf(472,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(162,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_42_divide__less__0__1__iff) ).
thf(698,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[162]) ).
thf(179,axiom,
semidom_divide @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemidom__divide_11) ).
thf(747,plain,
semidom_divide @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(292,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat__le__linear) ).
thf(1063,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(22,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_add__left__imp__eq) ).
thf(340,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_eq__imp__le) ).
thf(785,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_zero__less__numeral) ).
thf(504,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(239,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/sandbox/benchmark/theBenchmark.p',fact_175_div__pos__pos__trivial) ).
thf(917,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)],[239]) ).
thf(24,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ 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 @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_add__mono) ).
thf(344,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ 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 @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(108,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_not__one__less__zero) ).
thf(542,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(132,axiom,
! [TA: $tType] :
( ( semiring_div_parity @ TA @ ( type @ TA ) )
=> ( ( divide_divide @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_one__div__two__eq__zero) ).
thf(606,plain,
! [TA: $tType] :
( ( semiring_div_parity @ TA @ ( type @ TA ) )
=> ( ( divide_divide @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(275,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_144_divide__neg__pos) ).
thf(1013,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[275]) ).
thf(9,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_le__numeral__extra_I4_J) ).
thf(316,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(241,axiom,
! [A: num] :
~ ( ord_less @ num @ A @ one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_semiring__norm_I75_J) ).
thf(924,plain,
! [A: num] :
~ ( ord_less @ num @ A @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(183,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_numeral__plus__numeral) ).
thf(756,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(195,axiom,
semiring_char_0 @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_15) ).
thf(789,plain,
semiring_char_0 @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(12,axiom,
! [TA: $tType] :
( ( preorder @ TA @ ( type @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_order__refl) ).
thf(321,plain,
! [TA: $tType] :
( ( preorder @ TA @ ( type @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(138,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_9_divide__cancel__left) ).
thf(623,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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)],[138]) ).
thf(142,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_35_divide__le__0__1__iff) ).
thf(646,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[142]) ).
thf(211,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_numeral__le__iff) ).
thf(834,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less_eq @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(201,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_division__ring__divide__zero) ).
thf(806,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(121,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_45_divide__le__eq__1__pos) ).
thf(574,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[121]) ).
thf(279,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_less__nat__zero__code) ).
thf(1020,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(27,axiom,
monoid_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Omonoid__add) ).
thf(348,plain,
monoid_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(235,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_neq0__conv) ).
thf(905,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(85,axiom,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_semiring__numeral__div__class_Odiv__less) ).
thf(480,plain,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less @ TA @ A @ B )
=> ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(188,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_le__add__same__cancel2) ).
thf(766,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(159,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__or__eq__imp__le) ).
thf(687,plain,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(54,axiom,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_div__0) ).
thf(396,plain,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(59,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_infinite__descent0__measure) ).
thf(411,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(223,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_142_divide__pos__pos) ).
thf(877,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[223]) ).
thf(160,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_dbl__simps_I5_J) ).
thf(692,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( neg_numeral_dbl @ TA @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(296,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_gr__zeroI) ).
thf(1074,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(74,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Divides_Odiv__positive) ).
thf(452,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(98,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_37_zero__less__divide__1__iff) ).
thf(512,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[98]) ).
thf(104,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( divide_divide @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Divides_Odiv__less) ).
thf(529,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)],[104]) ).
thf(185,axiom,
zero @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero_20) ).
thf(761,plain,
zero @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(45,axiom,
semiring_numeral_div @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Osemiring__numeral__div) ).
thf(381,plain,
semiring_numeral_div @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(168,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( divide_divide @ TA @ ( one_one @ TA ) @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_one__divide__eq__0__iff) ).
thf(714,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[168]) ).
thf(290,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_add_Oleft__neutral) ).
thf(1057,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(110,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_76_divide__nonneg__nonneg) ).
thf(546,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[110]) ).
thf(197,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_add__cancel__left__right) ).
thf(793,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(231,axiom,
semigroup_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_12) ).
thf(894,plain,
semigroup_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(208,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_le__zero__eq) ).
thf(825,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(192,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/sandbox/benchmark/theBenchmark.p',fact_174_div__neg__neg__trivial) ).
thf(778,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)],[192]) ).
thf(250,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zero__le__one) ).
thf(952,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_add__right__mono) ).
thf(349,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(129,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( one_one @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_int__div__less__self) ).
thf(598,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( one_one @ int ) @ B )
=> ( ord_less @ int @ ( divide_divide @ int @ A @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(116,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less @ num @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_numeral__less__iff) ).
thf(561,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( numeral_numeral @ TA @ B ) )
= ( ord_less @ num @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(283,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_zdiv__mono1) ).
thf(1032,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(34,axiom,
one @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oone) ).
thf(361,plain,
one @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(224,axiom,
numeral @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Num_Onumeral_19) ).
thf(879,plain,
numeral @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(17,axiom,
cancel_semigroup_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(329,plain,
cancel_semigroup_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(150,axiom,
linord1659791738miring @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3) ).
thf(665,plain,
linord1659791738miring @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(124,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_le__antisym) ).
thf(583,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(77,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_not__numeral__less__one) ).
thf(461,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(112,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_less__not__refl) ).
thf(551,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(215,axiom,
! [A: num] : ( ord_less @ num @ one2 @ ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_semiring__norm_I76_J) ).
thf(842,plain,
! [A: num] : ( ord_less @ num @ one2 @ ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(258,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_add__le__same__cancel1) ).
thf(974,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less_eq @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(217,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( divide_divide @ TA @ ( one_one @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_zero__eq__1__divide__iff) ).
thf(847,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[217]) ).
thf(118,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_84_le__divide__eq__1) ).
thf(566,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[118]) ).
thf(219,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_add__cancel__left__left) ).
thf(852,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(66,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_not__numeral__less__zero) ).
thf(435,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(222,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_not__gr__zero) ).
thf(874,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(277,axiom,
cancel_semigroup_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_7) ).
thf(1017,plain,
cancel_semigroup_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(56,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_half__gt__zero) ).
thf(403,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(271,axiom,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__one__le__zero) ).
thf(1006,plain,
! [TA: $tType] :
( ( linord1659791738miring @ TA @ ( type @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(61,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
| ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_divide__eq__0__iff) ).
thf(420,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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)],[61]) ).
thf(16,axiom,
group_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add) ).
thf(328,plain,
group_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(88,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_Suc__n__div__2__gt__zero) ).
thf(488,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ ( plus_plus @ nat @ A @ ( one_one @ nat ) ) @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(21,axiom,
linordered_idom @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__idom) ).
thf(339,plain,
linordered_idom @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(244,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_nat__less__induct) ).
thf(933,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(103,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_num_Oinject_I1_J) ).
thf(526,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(113,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le0) ).
thf(554,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(182,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_divide__zero__left) ).
thf(753,plain,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(212,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__numeral__extra_I3_J) ).
thf(837,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(163,axiom,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_semiring__norm_I71_J) ).
thf(701,plain,
! [A: num,B: num] :
( ( ord_less_eq @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_eq @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_add__less__cancel__left) ).
thf(515,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_78_divide__right__mono) ).
thf(738,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[176]) ).
thf(145,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_73_divide__nonpos__nonpos) ).
thf(654,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[145]) ).
thf(291,axiom,
! [A: int,B: int] :
( ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) )
= ( ( B
= ( zero_zero @ int ) )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ B ) )
| ( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
& ( ord_less @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_zdiv__eq__0__iff) ).
thf(1060,plain,
! [A: int,B: int] :
( ( ( divide_divide @ int @ A @ B )
= ( zero_zero @ int ) )
= ( ( B
= ( zero_zero @ int ) )
| ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
& ( ord_less @ int @ A @ B ) )
| ( ( ord_less_eq @ int @ A @ ( zero_zero @ int ) )
& ( ord_less @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(119,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_numeral__eq__one__iff) ).
thf(569,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ( numeral_numeral @ TA @ A )
= ( one_one @ TA ) )
= ( A = one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(40,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_add_Ocommute) ).
thf(371,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(262,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_numeral__One) ).
thf(984,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ( ( numeral_numeral @ TA @ one2 )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(237,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_double__add__less__zero__iff__single__add__less__zero) ).
thf(911,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(23,axiom,
preorder @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder) ).
thf(343,plain,
preorder @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(240,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( ( divide_divide @ TA @ B @ A )
= ( one_one @ TA ) )
= ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_right__inverse__eq) ).
thf(921,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ 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)],[240]) ).
thf(147,axiom,
semiring_numeral_div @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Osemiring__numeral__div_6) ).
thf(657,plain,
semiring_numeral_div @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(187,axiom,
preorder @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_17) ).
thf(765,plain,
preorder @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(284,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_one__add__one) ).
thf(1035,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(281,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ C @ B ) @ ( divide_divide @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_div__le__mono2) ).
thf(1026,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( divide_divide @ nat @ C @ B ) @ ( divide_divide @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(125,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_le__0__eq) ).
thf(586,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(149,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_eq__divide__eq__1) ).
thf(662,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[149]) ).
thf(300,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_less__not__refl2) ).
thf(1086,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(245,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_39_less__divide__eq__1__neg) ).
thf(938,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[245]) ).
thf(115,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_38_less__divide__eq__1__pos) ).
thf(558,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[115]) ).
thf(295,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/sandbox/benchmark/theBenchmark.p',fact_69_div__le__mono) ).
thf(1071,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)],[295]) ).
thf(181,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_linorder__neqE__linordered__idom) ).
thf(750,plain,
! [TA: $tType] :
( ( linordered_idom @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A != B )
=> ( ~ ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(64,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_add__gr__0) ).
thf(430,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( plus_plus @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
| ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_40_divide__less__eq__1__pos) ).
thf(444,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[70]) ).
thf(130,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_44_le__divide__eq__1__neg) ).
thf(601,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[130]) ).
thf(42,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_dbl__def) ).
thf(375,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA )
= ( ^ [A: TA] : ( plus_plus @ TA @ A @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(174,axiom,
~ ( ord_less_eq @ nat @ na @ ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False) ).
thf(733,plain,
~ ( ord_less_eq @ nat @ na @ ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(205,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_divide__self) ).
thf(819,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(62,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_neg__imp__zdiv__neg__iff) ).
thf(423,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(190,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_not__less0) ).
thf(772,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(253,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_add__less__same__cancel2) ).
thf(958,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(122,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) )
= ( ( ord_less_eq @ int @ B @ A )
& ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_nonneg1__imp__zdiv__pos__iff) ).
thf(577,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) )
= ( ( ord_less_eq @ int @ B @ A )
& ( ord_less @ int @ ( zero_zero @ int ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(167,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( one_one @ TA )
= ( divide_divide @ TA @ A @ B ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_one__eq__divide__iff) ).
thf(711,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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)],[167]) ).
thf(51,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_add__le__cancel__right) ).
thf(391,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less_eq @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(46,axiom,
linord219039673up_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(382,plain,
linord219039673up_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(120,axiom,
! [TA: $tType] :
( ( zero_less_one @ TA @ ( type @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_zero__less__one) ).
thf(572,plain,
! [TA: $tType] :
( ( zero_less_one @ TA @ ( type @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(7,axiom,
ordere236663937imp_le @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(313,plain,
ordere236663937imp_le @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_Divides_Otransfer__nat__int__function__closures_I1_J) ).
thf(466,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ B )
=> ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(301,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_zero__le__double__add__iff__zero__le__single__add) ).
thf(1090,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(164,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_measure__induct) ).
thf(704,plain,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(248,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_divide__eq__eq__1) ).
thf(947,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[248]) ).
thf(210,axiom,
! [A: num,B: num] :
( ( divide_divide @ int @ ( numeral_numeral @ int @ ( bit0 @ A ) ) @ ( numeral_numeral @ int @ ( bit0 @ B ) ) )
= ( divide_divide @ int @ ( numeral_numeral @ int @ A ) @ ( numeral_numeral @ int @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_zdiv__numeral__Bit0) ).
thf(831,plain,
! [A: num,B: num] :
( ( divide_divide @ int @ ( numeral_numeral @ int @ ( bit0 @ A ) ) @ ( numeral_numeral @ int @ ( bit0 @ B ) ) )
= ( divide_divide @ int @ ( numeral_numeral @ int @ A ) @ ( numeral_numeral @ int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(10,axiom,
semiring_div_parity @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Osemiring__div__parity) ).
thf(318,plain,
semiring_div_parity @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ na @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ na @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(303,plain,
~ ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ na @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(260,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_Nat_Oadd__0__right) ).
thf(979,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(131,axiom,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_semiring__numeral__div__class_Odiv__positive) ).
thf(604,plain,
! [TA: $tType] :
( ( semiring_numeral_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(264,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_43_le__divide__eq__1__pos) ).
thf(990,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[264]) ).
thf(267,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_pos__imp__zdiv__nonneg__iff) ).
thf(996,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ ( zero_zero @ int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(35,axiom,
semiring_char_0 @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0) ).
thf(362,plain,
semiring_char_0 @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(73,axiom,
canoni770627133id_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(451,plain,
canoni770627133id_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_85_divide__le__eq__1) ).
thf(509,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[97]) ).
thf(225,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_zero__neq__numeral) ).
thf(880,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(143,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_not__gr0) ).
thf(649,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(287,axiom,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_27_divide__self__if) ).
thf(1043,plain,
! [TA: $tType] :
( ( division_ring @ TA @ ( type @ 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)],[287]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_add__is__0) ).
thf(890,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(83,axiom,
zero_less_one @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Ozero__less__one_14) ).
thf(477,plain,
zero_less_one @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(49,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_add__left__cancel) ).
thf(387,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(221,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_infinite__descent0) ).
thf(858,plain,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ( ( divide_divide @ nat @ A @ B )
= A )
= ( B
= ( one_one @ nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_div__eq__dividend__iff) ).
thf(535,plain,
! [A: nat,B: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ( ( divide_divide @ nat @ A @ B )
= A )
= ( B
= ( one_one @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(133,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_infinite__descent__measure) ).
thf(609,plain,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(13,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_add__le__cancel__left) ).
thf(323,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_34_zero__le__divide__1__iff) ).
thf(483,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[86]) ).
thf(255,axiom,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_div__by__0) ).
thf(964,plain,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(139,axiom,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_ex__least__nat__le) ).
thf(626,plain,
! [A: nat > $o,B: nat] :
( ~ ( A @ ( zero_zero @ nat ) )
=> ( ( A @ B )
=> ? [C: nat] :
( ( ord_less_eq @ nat @ C @ B )
& ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ~ ( A @ D ) )
& ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(189,axiom,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_semiring__norm_I69_J) ).
thf(769,plain,
! [A: num] :
~ ( ord_less_eq @ num @ ( bit0 @ A ) @ one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(152,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_divide__zero) ).
thf(668,plain,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(18,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_add__right__cancel) ).
thf(330,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(91,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_half__gt__zero__iff) ).
thf(494,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( divide_divide @ TA @ A @ ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(298,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_nat__add__left__cancel__le) ).
thf(1080,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less_eq @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(282,axiom,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_div__by__1) ).
thf(1029,plain,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(232,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_less__not__refl3) ).
thf(895,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(101,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_linordered__field__no__ub) ).
thf(521,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(55,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_pos__imp__zdiv__pos__iff) ).
thf(399,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(161,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_zero__less__iff__neq__zero) ).
thf(695,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(276,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_87_divide__nonpos__neg) ).
thf(1015,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[276]) ).
thf(268,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_gr0I) ).
thf(1000,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(148,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_num_Odistinct_I1_J) ).
thf(658,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(75,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_div__self) ).
thf(455,plain,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ A @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(226,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_div__nonneg__neg__le0) ).
thf(883,plain,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ B @ ( zero_zero @ int ) )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(52,axiom,
semiring_div @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Divides_Osemiring__div) ).
thf(394,plain,
semiring_div @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_add__mono__thms__linordered__semiring_I4_J) ).
thf(306,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( C = D ) )
=> ( ( plus_plus @ TA @ A @ C )
= ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(89,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(490,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(126,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ C @ ( zero_zero @ int ) )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ B @ C ) @ ( divide_divide @ int @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_zdiv__mono1__neg) ).
thf(589,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ A @ B )
=> ( ( ord_less @ int @ C @ ( zero_zero @ int ) )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ B @ C ) @ ( divide_divide @ int @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(247,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_numeral__eq__iff) ).
thf(944,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA @ ( type @ TA ) )
=> ! [A: num,B: num] :
( ( ( numeral_numeral @ TA @ A )
= ( numeral_numeral @ TA @ B ) )
= ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(156,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_less__add__same__cancel2) ).
thf(680,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(111,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_41_divide__less__eq__1__neg) ).
thf(548,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[111]) ).
thf(203,axiom,
linordered_semidom @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Olinordered__semidom_9) ).
thf(812,plain,
linordered_semidom @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(136,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_77_zero__le__divide__iff) ).
thf(617,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[136]) ).
thf(278,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_138_divide__strict__right__mono) ).
thf(1018,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[278]) ).
thf(32,axiom,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_add_Oright__cancel) ).
thf(355,plain,
! [TA: $tType] :
( ( group_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(288,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_le__trans) ).
thf(1049,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(242,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le__numeral__extra_I1_J) ).
thf(927,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(41,axiom,
semidom_divide @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemidom__divide) ).
thf(374,plain,
semidom_divide @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(76,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_79_divide__le__0__iff) ).
thf(458,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[76]) ).
thf(207,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_le__numeral__extra_I2_J) ).
thf(823,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(269,axiom,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_semiring__norm_I68_J) ).
thf(1003,plain,
! [A: num] : ( ord_less_eq @ num @ one2 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(220,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_add__numeral__left) ).
thf(855,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num,B: num,C: TA] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( plus_plus @ TA @ ( numeral_numeral @ TA @ B ) @ C ) )
= ( plus_plus @ TA @ ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ B ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(140,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_numeral__le__one__iff) ).
thf(640,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( ord_less_eq @ num @ A @ one2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(165,axiom,
ordere779506340up_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_4) ).
thf(707,plain,
ordere779506340up_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(228,axiom,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( divide_divide @ int @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_zdiv__mono2__neg) ).
thf(887,plain,
! [A: int,B: int,C: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ B ) @ ( divide_divide @ int @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(257,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_one__plus__numeral) ).
thf(971,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ one2 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(15,axiom,
ab_semigroup_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add) ).
thf(327,plain,
ab_semigroup_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(251,axiom,
cancel1352612707id_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_5) ).
thf(954,plain,
cancel1352612707id_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(6,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_add__right__imp__eq) ).
thf(310,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(265,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_88_divide__nonneg__pos) ).
thf(993,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[265]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_gr__implies__not0) ).
thf(673,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(285,axiom,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_add_Oright__neutral) ).
thf(1038,plain,
! [TA: $tType] :
( ( monoid_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(169,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_10_divide__cancel__right) ).
thf(717,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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)],[169]) ).
thf(94,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_not__numeral__le__zero) ).
thf(502,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] :
~ ( ord_less_eq @ TA @ ( numeral_numeral @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(214,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_137_divide__strict__right__mono__neg) ).
thf(840,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[214]) ).
thf(78,axiom,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_semiring__norm_I87_J) ).
thf(463,plain,
! [A: num,B: num] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(141,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_double__zero) ).
thf(643,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(109,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_div__le__dividend) ).
thf(544,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( divide_divide @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(178,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_91_divide__le__cancel) ).
thf(744,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[178]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_add_Oleft__commute) ).
thf(336,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(289,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_infinite__descent) ).
thf(1052,plain,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(172,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_dbl__simps_I2_J) ).
thf(727,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(272,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(1008,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( numeral_numeral @ int @ ( bit0 @ one2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(8,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_add__le__imp__le__left) ).
thf(314,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
=> ( ord_less_eq @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_add__le__same__cancel2) ).
thf(595,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(134,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_nat__less__le) ).
thf(612,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_nat__neq__iff) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(146,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(656,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( zero_zero @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(280,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_add__less__same__cancel1) ).
thf(1023,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(107,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/sandbox/benchmark/theBenchmark.p',fact_147_div__eq__0__iff) ).
thf(539,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)],[107]) ).
thf(153,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_145_divide__neg__neg) ).
thf(671,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[153]) ).
thf(234,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_one__le__numeral) ).
thf(903,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_72_divide__right__mono__neg) ).
thf(581,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[123]) ).
thf(184,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_le__refl) ).
thf(759,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(274,axiom,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_divide__1) ).
thf(1010,plain,
! [TA: $tType] :
( ( semidom_divide @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( divide_divide @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(36,axiom,
ordere516151231imp_le @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(363,plain,
ordere516151231imp_le @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(114,axiom,
! [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_div__2__gt__zero) ).
thf(556,plain,
! [A: nat] :
( ( ord_less @ nat @ ( one_one @ nat ) @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( divide_divide @ nat @ A @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(39,axiom,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_add_Oassoc) ).
thf(368,plain,
! [TA: $tType] :
( ( semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(216,axiom,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_less__one) ).
thf(844,plain,
! [A: nat] :
( ( ord_less @ nat @ A @ ( one_one @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ 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 @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_add__mono__thms__linordered__semiring_I1_J) ).
thf(319,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA @ ( type @ 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 @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(180,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_le__eq__less__or__eq) ).
thf(748,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(3,axiom,
linordered_semidom @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__semidom) ).
thf(304,plain,
linordered_semidom @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(50,axiom,
preorder @ $o @ ( type @ $o ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_23) ).
thf(390,plain,
preorder @ $o @ ( type @ $o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(60,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zero__le__numeral) ).
thf(418,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ! [A: num] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( numeral_numeral @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(266,axiom,
semiring_div_parity @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Osemiring__div__parity_8) ).
thf(995,plain,
semiring_div_parity @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(254,axiom,
! [TA: $tType] :
( ( zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_zero__reorient) ).
thf(961,plain,
! [TA: $tType] :
( ( zero @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(204,axiom,
~ ( ( na
= ( zero_zero @ nat ) )
| ( na
= ( one_one @ nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ns) ).
thf(813,plain,
~ ( ( na
= ( zero_zero @ nat ) )
| ( na
= ( one_one @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(144,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_143_divide__pos__neg) ).
thf(652,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[144]) ).
thf(29,axiom,
numeral @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Onumeral) ).
thf(351,plain,
numeral @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_89_divide__nonneg__neg) ).
thf(433,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[65]) ).
thf(243,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_neg__imp__zdiv__nonneg__iff) ).
thf(929,plain,
! [A: int,B: int] :
( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ( ord_less_eq @ int @ ( zero_zero @ int ) @ ( divide_divide @ int @ B @ A ) )
= ( ord_less_eq @ int @ B @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(47,axiom,
ordere779506340up_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(383,plain,
ordere779506340up_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(233,axiom,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_semiring__norm_I85_J) ).
thf(899,plain,
! [A: num] :
( ( bit0 @ A )
!= one2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(158,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_zero__less__double__add__iff__zero__less__single__add) ).
thf(684,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(25,axiom,
zero @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ozero) ).
thf(346,plain,
zero @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(199,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_add__cancel__right__left) ).
thf(800,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(238,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_122_divide__less__eq__1) ).
thf(914,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[238]) ).
thf(43,axiom,
zero_less_one @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__less__one) ).
thf(378,plain,
zero_less_one @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(297,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_46_divide__le__eq__1__neg) ).
thf(1077,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[297]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_frac__le) ).
thf(478,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less @ TA @ ( zero_zero @ TA ) @ C )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( divide_divide @ TA @ A @ D ) @ ( divide_divide @ TA @ B @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(137,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_nat__add__left__cancel__less) ).
thf(620,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( ord_less @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(71,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_less__eq__nat_Osimps_I1_J) ).
thf(447,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(256,axiom,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_semiring__norm_I83_J) ).
thf(967,plain,
! [A: num] :
( one2
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(249,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_less__numeral__extra_I1_J) ).
thf(950,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(57,axiom,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( plus_plus @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_div__add__self2) ).
thf(405,plain,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( plus_plus @ TA @ B @ A ) @ A )
= ( plus_plus @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(196,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_139_zero__less__divide__iff) ).
thf(790,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[196]) ).
thf(175,axiom,
! [TA: $tType] :
( ( semiring_div_parity @ TA @ ( type @ TA ) )
=> ( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_zero__not__eq__two) ).
thf(735,plain,
! [TA: $tType] :
( ( semiring_div_parity @ TA @ ( type @ TA ) )
=> ( ( zero_zero @ TA )
!= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(117,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_less__numeral__extra_I2_J) ).
thf(564,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA @ ( type @ TA ) )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(4,axiom,
linord1659791738miring @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Olinordered__nonzero__semiring) ).
thf(305,plain,
linord1659791738miring @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(14,axiom,
preorder @ num @ ( type @ num ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Num_Onum___Orderings_Opreorder_22) ).
thf(326,plain,
preorder @ num @ ( type @ num ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__neq__implies__less) ).
thf(506,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(33,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(358,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ A @ B ) @ C )
= ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(67,axiom,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( plus_plus @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_div__add__self1) ).
thf(437,plain,
! [TA: $tType] :
( ( semiring_div @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ( divide_divide @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( plus_plus @ TA @ ( divide_divide @ TA @ B @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(82,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_add__less__cancel__right) ).
thf(474,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( ord_less @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(209,axiom,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_numeral__plus__one) ).
thf(828,plain,
! [TA: $tType] :
( ( numeral @ TA @ ( type @ TA ) )
=> ! [A: num] :
( ( plus_plus @ TA @ ( numeral_numeral @ TA @ A ) @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( plus_plus @ num @ A @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(170,axiom,
! [A: num,B: num] :
( ( ord_less @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less @ num @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_semiring__norm_I78_J) ).
thf(720,plain,
! [A: num,B: num] :
( ( ord_less @ num @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less @ num @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(252,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/sandbox/benchmark/theBenchmark.p',fact_123_div__less__dividend) ).
thf(955,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)],[252]) ).
thf(198,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ B @ ( zero_zero @ int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_pos__imp__zdiv__neg__iff) ).
thf(796,plain,
! [A: int,B: int] :
( ( ord_less @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( divide_divide @ int @ B @ A ) @ ( zero_zero @ int ) )
= ( ord_less @ int @ B @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(227,axiom,
semiring_div @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Divides_Osemiring__div_13) ).
thf(886,plain,
semiring_div @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(105,axiom,
! [TA: $tType] :
( ( field @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ( divide_divide @ TA @ A @ B )
= ( one_one @ TA ) )
= ( ( B
!= ( zero_zero @ TA ) )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_divide__eq__1__iff) ).
thf(532,plain,
! [TA: $tType] :
( ( field @ TA @ ( type @ 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)],[105]) ).
thf(293,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_140_divide__less__cancel) ).
thf(1065,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[293]) ).
thf(177,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_gr__implies__not__zero) ).
thf(740,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(263,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_linorder__neqE__nat) ).
thf(987,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(63,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type @ TA ) )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__neq__one) ).
thf(427,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA @ ( type @ TA ) )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(236,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_le__add__same__cancel1) ).
thf(908,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(171,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_less__mono__imp__le__mono) ).
thf(723,plain,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(206,axiom,
monoid_add @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add_18) ).
thf(822,plain,
monoid_add @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(218,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_linordered__field__no__lb) ).
thf(850,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ TA ) )
=> ! [A: TA] :
? [B: TA] : ( ord_less @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(261,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_74_divide__nonpos__nonneg) ).
thf(982,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[261]) ).
thf(69,axiom,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_numerals_I1_J) ).
thf(442,plain,
( ( numeral_numeral @ nat @ one2 )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(302,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_93_frac__less2) ).
thf(1093,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[302]) ).
thf(53,axiom,
zero_neq_one @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Ozero__neq__one) ).
thf(395,plain,
zero_neq_one @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(213,axiom,
ordere516151231imp_le @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_1) ).
thf(839,plain,
ordere516151231imp_le @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(87,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_zero__le) ).
thf(486,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA @ ( type @ TA ) )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(200,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_double__add__le__zero__iff__single__add__le__zero) ).
thf(803,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA @ ( type @ TA ) )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(80,axiom,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_dbl__simps_I3_J) ).
thf(469,plain,
! [TA: $tType] :
( ( neg_numeral @ TA @ ( type @ TA ) )
=> ( ( neg_numeral_dbl @ TA @ ( one_one @ TA ) )
= ( numeral_numeral @ TA @ ( bit0 @ one2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(31,axiom,
semigroup_add @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add) ).
thf(354,plain,
semigroup_add @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(273,axiom,
ordere236663937imp_le @ nat @ ( type @ nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_2) ).
thf(1009,plain,
ordere236663937imp_le @ nat @ ( type @ nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(191,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_add__cancel__right__right) ).
thf(775,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA @ ( type @ TA ) )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(90,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__irrefl__nat) ).
thf(491,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(127,axiom,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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/sandbox/benchmark/theBenchmark.p',fact_121_less__divide__eq__1) ).
thf(592,plain,
! [TA: $tType] :
( ( linordered_field @ TA @ ( type @ 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)],[127]) ).
thf(37,axiom,
neg_numeral @ int @ ( type @ int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Int_Oint___Num_Oneg__numeral) ).
thf(364,plain,
neg_numeral @ int @ ( type @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(166,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_zdiv__mono2) ).
thf(708,plain,
! [A: int,B: int,C: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ ( zero_zero @ int ) @ B )
=> ( ( ord_less_eq @ int @ B @ C )
=> ( ord_less_eq @ int @ ( divide_divide @ int @ A @ C ) @ ( divide_divide @ int @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(1095,plain,
$false,
inference(e,[status(thm)],[782,809,365,347,333,893,518,1083,941,666,352,1005,683,730,1068,449,379,440,1041,408,977,523,762,614,677,384,500,472,698,747,1063,340,785,504,917,344,542,606,1013,316,924,756,789,321,623,646,834,806,574,1020,348,905,480,766,687,396,411,877,692,1074,452,512,529,761,381,714,1057,546,793,894,825,778,952,349,598,561,1032,361,879,329,665,583,461,551,842,974,847,566,852,435,874,1017,403,1006,420,328,488,339,933,526,554,753,837,701,515,738,654,1060,569,371,984,911,343,921,657,765,1035,1026,586,662,1086,938,558,1071,750,430,444,601,375,733,819,423,772,958,577,711,391,382,572,313,466,1090,704,947,831,318,303,979,604,990,996,362,451,509,880,649,1043,890,477,387,858,535,609,323,483,964,626,769,668,330,494,1080,1029,895,521,399,695,1015,1000,658,455,883,394,306,490,589,944,680,548,812,617,1018,355,1049,927,374,458,823,1003,855,640,707,887,971,327,954,310,993,673,1038,717,502,840,463,643,544,744,336,1052,727,1008,314,595,612,497,656,1023,539,671,903,581,759,1010,363,556,368,844,319,748,304,390,418,995,961,813,652,351,433,929,383,899,684,346,800,914,378,1077,478,620,447,967,950,405,790,735,564,305,326,506,358,437,474,828,720,955,796,886,532,1065,740,987,427,908,723,822,850,982,442,1093,395,839,486,803,469,354,1009,775,491,592,364,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT239^1 : TPTP v8.1.2. Released v7.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n011.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 11:37:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.89/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.83/1.08 % [INFO] Parsing done (241ms).
% 1.83/1.09 % [INFO] Running in sequential loop mode.
% 2.50/1.30 % [INFO] eprover registered as external prover.
% 2.50/1.30 % [INFO] cvc4 registered as external prover.
% 2.50/1.31 % [INFO] Scanning for conjecture ...
% 2.75/1.40 % [INFO] Found a conjecture and 300 axioms. Running axiom selection ...
% 3.06/1.50 % [INFO] Axiom selection finished. Selected 300 axioms (removed 0 axioms).
% 3.76/1.66 % [INFO] Problem is higher-order (TPTP THF).
% 3.76/1.68 % [INFO] Type checking passed.
% 3.76/1.68 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 12.23/3.61 % External prover 'e' found a proof!
% 12.23/3.61 % [INFO] Killing All external provers ...
% 12.23/3.62 % Time passed: 3085ms (effective reasoning time: 2527ms)
% 12.23/3.62 % 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)>
% 12.23/3.62 % Axioms used in derivation (300): tcon_Nat_Onat___Groups_Omonoid__add_18, fact_83_div__by__1, fact_186_gr__zeroI, fact_248_add__left__mono, tcon_Int_Oint___Divides_Osemiring__div, fact_102_measure__induct__rule, tcon_Int_Oint___Rings_Olinordered__semidom, fact_120_div__eq__dividend__iff, tcon_Nat_Onat___Num_Onumeral_19, tcon_Nat_Onat___Divides_Osemiring__numeral__div_6, fact_63_le__neq__implies__less, fact_196_add__le__cancel__left, fact_127_infinite__descent0__measure, fact_121_less__divide__eq__1, fact_112_not__one__less__zero, fact_166_zdiv__mono2, fact_105_nat__less__induct, fact_130_gr__implies__not0, fact_21_one__eq__numeral__iff, fact_243_ab__semigroup__add__class_Oadd__ac_I1_J, fact_153_not__gr__zero, fact_154_le__zero__eq, fact_122_divide__less__eq__1, tcon_Int_Oint___Groups_Ozero, fact_66_less__imp__le__nat, fact_241_add_Oassoc, fact_27_divide__self__if, fact_9_divide__cancel__left, fact_11_divide__zero, fact_191_order__refl, fact_12_divide__zero__left, fact_235_add__right__imp__eq, fact_137_divide__strict__right__mono__neg, fact_33_numeral__le__one__iff, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le_2, fact_1_False, fact_34_zero__le__divide__1__iff, fact_155_dbl__simps_I3_J, fact_25_eq__divide__eq__1, fact_107_measure__induct, fact_30_div__self, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le_1, fact_79_divide__le__0__iff, fact_96_Divides_Odiv__positive, fact_164_Divides_Otransfer__nat__int__function__closures_I1_J, fact_10_divide__cancel__right, fact_115_less__numeral__extra_I2_J, fact_169_zdiv__mono2__neg, fact_74_divide__nonpos__nonneg, fact_158_semiring__norm_I87_J, tcon_Nat_Onat___Groups_Ozero_20, fact_199_double__zero, fact_6_div__0, fact_47_one__div__two__eq__zero, fact_157_semiring__norm_I78_J, fact_132_not__less0, fact_214_add__le__same__cancel2, fact_146_divide__numeral__1, fact_72_divide__right__mono__neg, tcon_HOL_Obool___Orderings_Opreorder_23, fact_211_nat__add__left__cancel__less, fact_220_double__add__less__zero__iff__single__add__less__zero, fact_40_divide__less__eq__1__pos, fact_152_semiring__norm_I85_J, fact_167_zdiv__eq__0__iff, fact_53_nat__le__linear, fact_129_infinite__descent0, fact_100_linordered__field__no__lb, tcon_Nat_Onat___Orderings_Opreorder_17, fact_71_zero__le__numeral, fact_246_le__iff__add, fact_228_div__add__self2, fact_215_le__add__same__cancel1, fact_19_divide__1, fact_250_add__mono__thms__linordered__semiring_I1_J, fact_242_add__mono__thms__linordered__semiring_I4_J, fact_43_le__divide__eq__1__pos, fact_133_not__gr0, fact_77_zero__le__divide__iff, fact_150_semiring__norm_I76_J, fact_82_less__numeral__extra_I4_J, tcon_Nat_Onat___Groups_Oone_21, fact_151_semiring__norm_I83_J, fact_55_zero__le__one, tcon_Int_Oint___Groups_Ocancel__semigroup__add, fact_42_divide__less__0__1__iff, fact_116_not__numeral__less__one, fact_194_add__left__cancel, fact_14_num_Oinject_I1_J, fact_210_Nat_Oadd__0__right, fact_204_add__cancel__right__right, tcon_Int_Oint___Groups_Omonoid__add, fact_5_neq0__conv, fact_36_one__less__numeral__iff, tcon_Int_Oint___Groups_Oab__semigroup__add, fact_219_zero__less__double__add__iff__zero__less__single__add, tcon_Int_Oint___Groups_Osemigroup__add, fact_207_numeral__plus__numeral, fact_139_zero__less__divide__iff, fact_7_divide__eq__0__iff, fact_197_add_Oleft__neutral, fact_212_nat__add__left__cancel__le, fact_46_divide__le__eq__1__neg, fact_145_divide__neg__neg, fact_92_semiring__numeral__div__class_Odiv__less, fact_237_add_Oleft__commute, fact_94_frac__less, fact_56_le__numeral__extra_I1_J, fact_187_not__less__zero, fact_193_add__right__cancel, tcon_Nat_Onat___Divides_Osemiring__div__parity_8, tcon_Int_Oint___Num_Onumeral, fact_24_one__divide__eq__0__iff, fact_61_less__eq__nat_Osimps_I1_J, fact_159_semiring__norm_I71_J, fact_136_zero__less__numeral, fact_231_add__self__div__2, fact_227_one__plus__numeral, fact_114_less__numeral__extra_I1_J, tcon_Nat_Onat___Groups_Ocancel__semigroup__add_7, tcon_Int_Oint___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_91_divide__le__cancel, fact_3_half__gt__zero, fact_249_add__mono, fact_222_less__add__same__cancel1, tcon_Nat_Onat___Groups_Osemigroup__add_12, fact_126_num_Odistinct_I1_J, tcon_Int_Oint___Groups_Ocancel__comm__monoid__add, fact_147_div__eq__0__iff, tcon_Int_Oint___Rings_Osemidom__divide, tcon_Int_Oint___Orderings_Opreorder, fact_135_not__numeral__less__zero, fact_171_int__div__less__self, fact_125_zero__neq__numeral, fact_217_double__add__le__zero__iff__single__add__le__zero, fact_200_double__zero__sym, tcon_Int_Oint___Rings_Olinordered__idom, tcon_Nat_Onat___Groups_Oab__semigroup__add_10, fact_244_add__le__imp__le__right, fact_185_zero__le, fact_67_nat__less__le, tcon_Int_Oint___Rings_Ozero__less__one, fact_205_add__less__cancel__left, fact_37_zero__less__divide__1__iff, fact_236_add__left__imp__eq, fact_149_zero__not__eq__two, fact_178_pos__imp__zdiv__pos__iff, fact_117_numeral__One, fact_142_divide__pos__pos, fact_13_zdiv__numeral__Bit0, fact_213_add__le__same__cancel1, fact_192_Suc__n__div__2__gt__zero, fact_31_divide__eq__1__iff, fact_29_one__eq__divide__iff, fact_168_zdiv__mono1__neg, fact_223_add__less__same__cancel2, fact_118_right__inverse__eq, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add, fact_95_frac__le, fact_44_le__divide__eq__1__neg, fact_98_linorder__neqE__linordered__idom, fact_234_dbl__def, fact_239_add_Oright__cancel, fact_32_less__one, fact_156_semiring__norm_I75_J, tcon_Nat_Onat___Divides_Osemiring__div_13, fact_4_half__gt__zero__iff, fact_247_add__right__mono, fact_18_division__ring__divide__zero, fact_233_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, tcon_Int_Oint___Rings_Ozero__neq__one, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_5, fact_140_divide__less__cancel, fact_182_le__num__One__iff, fact_230_one__add__one, fact_173_div__nonpos__pos__le0, fact_174_div__neg__neg__trivial, tcon_Nat_Onat___Rings_Osemidom__divide_11, fact_106_less__irrefl__nat, fact_41_divide__less__eq__1__neg, fact_59_le__numeral__extra_I3_J, fact_87_divide__nonpos__neg, fact_101_infinite__descent__measure, tcon_Nat_Onat___Rings_Olinordered__nonzero__semiring_3, tcon_Int_Oint___Groups_Ogroup__add, fact_84_le__divide__eq__1, fact_38_less__divide__eq__1__pos, fact_119_numerals_I1_J, tcon_Int_Oint___Num_Oneg__numeral, fact_54_not__one__le__zero, fact_201_add__cancel__left__left, fact_224_add__less__same__cancel1, fact_35_divide__le__0__1__iff, fact_216_le__add__same__cancel2, fact_209_add__is__0, fact_8_div__by__0, fact_50_le__trans, tcon_Int_Oint___Groups_Olinordered__ab__group__add, fact_180_pos__imp__zdiv__nonneg__iff, tcon_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_20_le0, fact_62_less__mono__imp__le__mono, fact_240_add_Oleft__cancel, fact_177_pos__imp__zdiv__neg__iff, tcon_Int_Oint___Divides_Osemiring__div__parity, fact_245_add__le__imp__le__left, fact_70_not__numeral__le__zero, fact_109_less__not__refl2, fact_16_numeral__le__iff, fact_85_divide__le__eq__1, fact_161_dbl__simps_I2_J, tcon_Nat_Onat___Rings_Olinordered__semidom_9, fact_123_div__less__dividend, fact_195_add__le__cancel__right, fact_226_numeral__plus__one, fact_0_ns, fact_65_le__eq__less__or__eq, fact_51_eq__imp__le, tcon_Num_Onum___Orderings_Opreorder_22, fact_90_semiring__numeral__div__class_Odiv__positive, fact_78_divide__right__mono, fact_225_add__gr__0, fact_76_divide__nonneg__nonneg, fact_15_numeral__eq__iff, fact_22_numeral__eq__one__iff, tcon_Int_Oint___Nat_Osemiring__char__0, fact_108_less__not__refl3, fact_64_less__or__eq__imp__le, fact_111_nat__neq__iff, fact_75_divide__nonneg__nonpos, fact_58_one__le__numeral, fact_190_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, fact_93_frac__less2, fact_124_less__numeral__extra_I3_J, fact_202_add__cancel__left__right, fact_134_gr0I, fact_184_one__reorient, fact_188_gr__implies__not__zero, fact_73_divide__nonpos__nonpos, fact_113_zero__less__one, fact_97_div__le__mono2, fact_144_divide__neg__pos, fact_17_numeral__less__iff, fact_148_div__2__gt__zero, fact_49_le__refl, fact_110_less__not__refl, fact_203_add__cancel__right__left, fact_221_less__add__same__cancel2, fact_57_le__numeral__extra_I2_J, fact_232_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_86_divide__nonpos__pos, tcon_Nat_Onat___Nat_Osemiring__char__0_15, fact_163_dbl__simps_I5_J, fact_80_ex__least__nat__le, fact_45_divide__le__eq__1__pos, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_175_div__pos__pos__trivial, fact_238_add_Ocommute, tcon_Nat_Onat___Rings_Ozero__less__one_14, fact_141_divide__less__0__iff, fact_198_add_Oright__neutral, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_4, fact_206_add__less__cancel__right, fact_60_le__0__eq, fact_69_div__le__mono, fact_99_linordered__field__no__ub, tcon_Nat_Onat___Rings_Ozero__neq__one_16, fact_160_semiring__norm_I68_J, fact_26_divide__eq__eq__1, tcon_Int_Oint___Divides_Osemiring__numeral__div, fact_52_le__antisym, fact_104_infinite__descent, fact_218_zero__le__double__add__iff__zero__le__single__add, fact_88_divide__nonneg__pos, fact_81_zero__neq__one, fact_162_semiring__norm_I69_J, fact_23_zero__eq__1__divide__iff, fact_138_divide__strict__right__mono, fact_229_div__add__self1, fact_68_div__le__dividend, fact_172_div__nonneg__neg__le0, tcon_Int_Oint___Rings_Olinordered__nonzero__semiring, tcon_Int_Oint___Groups_Oone, fact_128_less__nat__zero__code, fact_89_divide__nonneg__neg, fact_189_zero__less__iff__neq__zero, fact_170_div__neg__pos__less0, fact_143_divide__pos__neg, fact_2_Divides_Odiv__less, fact_28_divide__self, fact_208_add__numeral__left, fact_103_linorder__neqE__nat, fact_165_zdiv__mono1, fact_131_less__zeroE, fact_176_neg__imp__zdiv__neg__iff, fact_39_less__divide__eq__1__neg, fact_48_le__numeral__extra_I4_J, fact_179_neg__imp__zdiv__nonneg__iff, fact_181_nonneg1__imp__zdiv__pos__iff, fact_183_zero__reorient
% 12.23/3.62 % No. of inferences in proof: 604
% 12.23/3.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3085 ms resp. 2527 ms w/o parsing
% 13.09/3.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.09/3.80 % [INFO] Killing All external provers ...
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