TSTP Solution File: ITP131^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : ITP131^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:23:13 EDT 2024
% Result : Theorem 59.37s 21.24s
% Output : Refutation 60.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 309
% Syntax : Number of formulae : 607 ( 194 unt; 35 typ; 0 def)
% Number of atoms : 1513 ( 580 equ; 2 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 6002 ( 108 ~; 33 |; 44 &;5261 @)
% ( 0 <=>; 556 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 48 ( 48 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 34 usr; 5 con; 0-3 aty)
% Number of variables : 1594 ( 58 ^1489 !; 18 ?;1594 :)
% ( 29 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(nat_type,type,
nat: $tType ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(monoid_add_type,type,
monoid_add:
!>[TA: $tType] : $o ).
thf(ab_group_add_type,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(wellorder_type,type,
wellorder:
!>[TA: $tType] : $o ).
thf(semigroup_add_type,type,
semigroup_add:
!>[TA: $tType] : $o ).
thf(semigroup_mult_type,type,
semigroup_mult:
!>[TA: $tType] : $o ).
thf(comm_monoid_add_type,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_diff_type,type,
comm_monoid_diff:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_type,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(cancel1352612707id_add_type,type,
cancel1352612707id_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(ordere779506340up_add_type,type,
ordere779506340up_add:
!>[TA: $tType] : $o ).
thf(canoni770627133id_add_type,type,
canoni770627133id_add:
!>[TA: $tType] : $o ).
thf(ordere236663937imp_le_type,type,
ordere236663937imp_le:
!>[TA: $tType] : $o ).
thf(ordere223160158up_add_type,type,
ordere223160158up_add:
!>[TA: $tType] : $o ).
thf(ordere623563068d_diff_type,type,
ordere623563068d_diff:
!>[TA: $tType] : $o ).
thf(strict2144017051up_add_type,type,
strict2144017051up_add:
!>[TA: $tType] : $o ).
thf(ordere516151231imp_le_type,type,
ordere516151231imp_le:
!>[TA: $tType] : $o ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(number2016821345itions_type,type,
number2016821345itions: ( nat > nat ) > nat > $o ).
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(i_type,type,
i: nat ).
thf(k_type,type,
k: nat ).
thf(n_type,type,
n: nat ).
thf(p_type,type,
p: nat > nat ).
thf(130,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A )
= ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2) ).
thf(645,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A )
= ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(125,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_le__iff__diff__le__0) ).
thf(629,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(37,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_double__zero__sym) ).
thf(365,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(164,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_measure__induct__rule) ).
thf(760,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(31,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zero__eq__add__iff__both__eq__0) ).
thf(347,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ B ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(206,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_203_add__left__mono) ).
thf(893,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ 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)],[206]) ).
thf(169,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_add_Ocommute) ).
thf(775,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(776,plain,
! [TA: $tType] :
( ~ ( ab_semigroup_add @ TA )
| ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[775]) ).
thf(777,plain,
! [TA: $tType] :
( ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) )
| ~ ( ab_semigroup_add @ TA ) ),
inference(lifteq,[status(thm)],[776]) ).
thf(225,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_gr__implies__not0) ).
thf(962,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(72,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_69_double__add__le__zero__iff__single__add__le__zero) ).
thf(468,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[72]) ).
thf(143,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_diff__less__mono) ).
thf(683,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ A )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(276,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(268,axiom,
comm_monoid_diff @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__diff) ).
thf(1068,plain,
comm_monoid_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(18,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_nat__mult__less__cancel__disj) ).
thf(308,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(200,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_gr__zeroI) ).
thf(878,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(159,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D )
= ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( D
= ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_nat__eq__add__iff2) ).
thf(741,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D )
= ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( D
= ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(273,axiom,
wellorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder) ).
thf(1073,plain,
wellorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_diff__add__inverse) ).
thf(614,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_diff__less) ).
thf(677,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(100,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_diff__diff__add) ).
thf(550,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(152,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus @ nat @ B @ C ) )
= ( ~ ( ( ( ord_less @ nat @ B @ C )
& ~ ( A @ ( zero_zero @ nat ) ) )
| ? [D: nat] :
( ( B
= ( plus_plus @ nat @ C @ D ) )
& ~ ( A @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_nat__diff__split__asm) ).
thf(715,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus @ nat @ B @ C ) )
= ( ~ ( ( ( ord_less @ nat @ B @ C )
& ~ ( A @ ( zero_zero @ nat ) ) )
| ? [D: nat] :
( ( B
= ( plus_plus @ nat @ C @ D ) )
& ~ ( A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(181,axiom,
! [TA: $tType,A: TA > $o,B: TA > nat,C: TA] :
( ! [D: TA] :
( ~ ( A @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( B @ E ) @ ( B @ D ) )
& ~ ( A @ E ) ) )
=> ( A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_infinite__descent__measure) ).
thf(814,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)],[181]) ).
thf(213,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_comm__monoid__add__class_Oadd__0) ).
thf(913,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(263,axiom,
ordere779506340up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(1063,plain,
ordere779506340up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(220,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_add__mono__thms__linordered__field_I2_J) ).
thf(930,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( A = B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(50,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_add__diff__cancel__left_H) ).
thf(404,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(188,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_less__not__refl) ).
thf(841,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(203,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ( ( ord_less_eq @ TA )
= ( ^ [A: TA,B: TA] :
? [C: TA] :
( B
= ( plus_plus @ TA @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_le__iff__add) ).
thf(885,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ 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)],[203]) ).
thf(10,axiom,
i != k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062i_A_092_060noteq_062_Ak_092_060close_062) ).
thf(286,plain,
i != k,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(287,plain,
i != k,
inference(polarity_switch,[status(thm)],[286]) ).
thf(288,plain,
k != i,
inference(lifteq,[status(thm)],[287]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( minus_minus @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc) ).
thf(651,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( minus_minus @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(22,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_less__add__same__cancel1) ).
thf(320,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[22]) ).
thf(105,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_eq__diff__eq) ).
thf(565,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( A
= ( minus_minus @ TA @ B @ C ) )
= ( ( plus_plus @ TA @ A @ C )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(45,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__self) ).
thf(389,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(84,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Nat_Odiff__diff__right) ).
thf(504,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_diff__le__mono2) ).
thf(587,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(221,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__mono__thms__linordered__field_I5_J) ).
thf(934,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( ord_less @ TA @ C @ D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(259,axiom,
ordere623563068d_diff @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff) ).
thf(1059,plain,
ordere623563068d_diff @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(177,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_mult_Oleft__commute) ).
thf(802,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(30,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_27_add__le__cancel__left) ).
thf(344,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[30]) ).
thf(182,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_linorder__neqE__nat) ).
thf(817,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)],[182]) ).
thf(103,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_diff__diff__eq2) ).
thf(559,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(191,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
| ( ord_less_eq @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_nat__le__linear) ).
thf(853,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)],[191]) ).
thf(55,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__nat__zero__code) ).
thf(419,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(420,plain,
~ ? [A: nat] : ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(miniscope,[status(thm)],[419]) ).
thf(421,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(cnf,[status(esa)],[420]) ).
thf(227,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_not__less0) ).
thf(969,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(11,axiom,
ord_less @ nat @ ( minus_minus @ nat @ n @ k ) @ i,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062n_A_N_Ak_A_060_Ai_092_060close_062) ).
thf(289,plain,
ord_less @ nat @ ( minus_minus @ nat @ n @ k ) @ i,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(242,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_less__add__eq__less) ).
thf(1013,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ D ) )
=> ( ord_less @ nat @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(8,axiom,
( ( p @ i )
!= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062p_Ai_A_092_060noteq_062_A0_092_060close_062) ).
thf(282,plain,
( ( p @ i )
!= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(283,plain,
( ( p @ i )
!= ( zero_zero @ nat ) ),
inference(polarity_switch,[status(thm)],[282]) ).
thf(284,plain,
( ( p @ i )
!= ( zero_zero @ nat ) ),
inference(lifteq,[status(thm)],[283]) ).
thf(201,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_198_add__le__imp__le__right) ).
thf(881,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[201]) ).
thf(54,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_bot__nat__0_Onot__eq__extremum) ).
thf(416,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(218,axiom,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__strict__mono) ).
thf(924,plain,
! [TA: $tType] :
( ( strict2144017051up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(80,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_diff__add__zero) ).
thf(492,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ A @ B ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(251,axiom,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_mult__0) ).
thf(1040,plain,
! [A: nat] :
( ( times_times @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
= ( minus_minus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_diff__mult__distrib2) ).
thf(623,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
= ( minus_minus @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(244,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_trans__less__add1) ).
thf(1020,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_add__le__mono1) ).
thf(1051,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_73_add__le__same__cancel1) ).
thf(480,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[76]) ).
thf(33,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_add__cancel__right__right) ).
thf(353,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ A @ B ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(226,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_less__zeroE) ).
thf(966,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(6,axiom,
ord_less @ nat @ n @ ( plus_plus @ nat @ ( times_times @ nat @ ( p @ i ) @ i ) @ ( times_times @ nat @ ( p @ k ) @ k ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_lower__bound) ).
thf(280,plain,
ord_less @ nat @ n @ ( plus_plus @ nat @ ( times_times @ nat @ ( p @ i ) @ i ) @ ( times_times @ nat @ ( p @ k ) @ k ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ( number2016821345itions @ A @ B )
=> ( ord_less_eq @ nat @ ( A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_partitions__bounds) ).
thf(293,plain,
! [A: nat > nat,B: nat,C: nat] :
( ( number2016821345itions @ A @ B )
=> ( ord_less_eq @ nat @ ( A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(135,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ C @ ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_le__add__diff) ).
thf(660,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ C @ ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(231,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_bot__nat__0_Oextremum__unique) ).
thf(981,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(166,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
=> ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_add__right__imp__eq) ).
thf(766,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[166]) ).
thf(272,axiom,
semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add) ).
thf(1072,plain,
semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_mult__is__0) ).
thf(453,plain,
! [A: nat,B: nat] :
( ( ( times_times @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(274,axiom,
monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Omonoid__add) ).
thf(1074,plain,
monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(216,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__strict__right__mono) ).
thf(920,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(42,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_diff__zero) ).
thf(380,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(86,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( plus_plus @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Nat_Oadd__diff__assoc) ).
thf(512,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( plus_plus @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(99,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= C )
=> ( A
= ( minus_minus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_add__implies__diff) ).
thf(546,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= C )
=> ( A
= ( minus_minus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(94,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_eq__iff__diff__eq__0) ).
thf(534,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ( ( (=) @ TA )
= ( ^ [A: TA,B: TA] :
( ( minus_minus @ TA @ A @ B )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(267,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(1067,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(257,axiom,
ordere516151231imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le) ).
thf(1057,plain,
ordere516151231imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(212,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_add_Ocomm__neutral) ).
thf(910,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(184,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ! [D: nat] :
( ( ord_less @ nat @ D @ C )
=> ( A @ D ) )
=> ( A @ C ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_nat__less__induct) ).
thf(825,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)],[184]) ).
thf(170,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_add_Oright__cancel) ).
thf(778,plain,
! [TA: $tType] :
( ( group_add @ 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)],[170]) ).
thf(16,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_mult__less__cancel2) ).
thf(302,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
& ( ord_less @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(194,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_le__trans) ).
thf(862,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)],[194]) ).
thf(183,axiom,
! [A: nat > $o,B: nat] :
( ! [C: nat] :
( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) )
=> ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_infinite__descent) ).
thf(820,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)],[183]) ).
thf(46,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_43_add__less__cancel__right) ).
thf(392,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[46]) ).
thf(59,axiom,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_Nat_Oadd__0__right) ).
thf(429,plain,
! [A: nat] :
( ( plus_plus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(156,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_nat__diff__add__eq1) ).
thf(729,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(51,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_add__diff__cancel__left) ).
thf(407,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ A @ C ) )
= ( minus_minus @ TA @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(146,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_less__diff__conv) ).
thf(693,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(214,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_211_add__less__imp__less__right) ).
thf(916,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[214]) ).
thf(190,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Nat_Oex__has__greatest__nat) ).
thf(847,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ B )
=> ( ! [D: nat] :
( ( A @ D )
=> ( ord_less_eq @ nat @ D @ C ) )
=> ? [D: nat] :
( ( A @ D )
& ! [E: nat] :
( ( A @ E )
=> ( ord_less_eq @ nat @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(248,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add__less__mono) ).
thf(1032,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ C @ D )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',fact_58_nat__add__left__cancel__less) ).
thf(435,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)],[61]) ).
thf(25,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ C @ B ) )
= ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_add__right__cancel) ).
thf(329,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[25]) ).
thf(137,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_le__diff__eq) ).
thf(665,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(163,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_zero__reorient) ).
thf(757,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',fact_65_nat__add__left__cancel__le) ).
thf(456,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)],[68]) ).
thf(9,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ ( p @ k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_assms_I2_J) ).
thf(285,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ ( p @ k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(89,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_diff__commute) ).
thf(522,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(185,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_less__irrefl__nat) ).
thf(830,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__less__same__cancel2) ).
thf(317,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[21]) ).
thf(243,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_trans__less__add2) ).
thf(1017,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(264,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(1064,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(178,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_mult_Ocommute) ).
thf(805,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(806,plain,
! [TA: $tType] :
( ~ ( ab_semigroup_mult @ TA )
| ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[805]) ).
thf(807,plain,
! [TA: $tType] :
( ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) )
| ~ ( ab_semigroup_mult @ TA ) ),
inference(lifteq,[status(thm)],[806]) ).
thf(1110,plain,
! [TA: $tType] :
( ( ( times_times @ TA )
= ( ^ [A: TA,B: TA] : ( times_times @ TA @ B @ A ) ) )
| ( ( ab_semigroup_mult @ nat )
!= ( ab_semigroup_mult @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[1067,807]) ).
thf(1111,plain,
( ( times_times @ nat )
= ( ^ [A: nat,B: nat] : ( times_times @ nat @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1110:[bind_type(TA,$thf( nat ))]]) ).
thf(155,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( minus_minus @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_nat__diff__add__eq2) ).
thf(725,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( minus_minus @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(34,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add__cancel__right__left) ).
thf(356,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( A
= ( plus_plus @ TA @ B @ A ) )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(197,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_zero__less__iff__neq__zero) ).
thf(869,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
= ( A
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(234,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_add__eq__self__zero) ).
thf(989,plain,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= A )
=> ( B
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(88,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_diff__eq__diff__eq) ).
thf(519,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( A = B )
= ( C = D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_diffs0__imp__equal) ).
thf(578,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( zero_zero @ nat ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(73,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_70_le__add__same__cancel2) ).
thf(471,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[73]) ).
thf(269,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(1069,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(1081,plain,
! [TA: $tType] :
( ( ( plus_plus @ TA )
= ( ^ [A: TA,B: TA] : ( plus_plus @ TA @ B @ A ) ) )
| ( ( ab_semigroup_add @ nat )
!= ( ab_semigroup_add @ TA ) ) ),
inference(paramod_ordered,[status(thm)],[1069,777]) ).
thf(1082,plain,
( ( plus_plus @ nat )
= ( ^ [A: nat,B: nat] : ( plus_plus @ nat @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[1081:[bind_type(TA,$thf( nat ))]]) ).
thf(162,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_nat__less__add__iff1) ).
thf(753,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(95,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_diff__strict__right__mono) ).
thf(537,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(129,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right) ).
thf(642,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( minus_minus @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_diff__gt__0__iff__gt) ).
thf(489,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(113,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_le__diff__iff_H) ).
thf(590,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ B )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ B @ C ) )
= ( ord_less_eq @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__diff__iff) ).
thf(686,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(275,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ozero) ).
thf(1075,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(187,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_less__not__refl2) ).
thf(837,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(1097,plain,
! [A: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( p @ k ) )
!= ( ord_less @ nat @ A @ ( zero_zero @ nat ) ) ),
inference(paramod_ordered,[status(thm)],[285,421]) ).
thf(1098,plain,
! [A: nat] :
( ( ( zero_zero @ nat )
!= A )
| ( ( p @ k )
!= ( zero_zero @ nat ) ) ),
inference(simp,[status(thm)],[1097]) ).
thf(1099,plain,
( ( p @ k )
!= ( zero_zero @ nat ) ),
inference(simp,[status(thm)],[1098]) ).
thf(133,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc) ).
thf(654,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(260,axiom,
ordere223160158up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(1060,plain,
ordere223160158up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(232,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_le__0__eq) ).
thf(984,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(154,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ C )
= ( ord_less @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_less__diff__conv2) ).
thf(721,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( minus_minus @ nat @ B @ A ) @ C )
= ( ord_less @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(238,axiom,
! [A: nat,B: nat] :
( ( ( ord_less @ nat @ A @ B )
| ( A = B ) )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_less__or__eq__imp__le) ).
thf(1002,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)],[238]) ).
thf(39,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add_Oright__neutral) ).
thf(371,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( plus_plus @ nat @ ( minus_minus @ nat @ B @ A ) @ C )
= ( minus_minus @ nat @ ( plus_plus @ nat @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Nat_Oadd__diff__assoc2) ).
thf(508,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( plus_plus @ nat @ ( minus_minus @ nat @ B @ A ) @ C )
= ( minus_minus @ nat @ ( plus_plus @ nat @ B @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(19,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/sandbox2/benchmark/theBenchmark.p',fact_16_add__gr__0) ).
thf(311,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)],[19]) ).
thf(97,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_diff__eq__diff__less) ).
thf(541,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less @ TA @ A @ B )
= ( ord_less @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(134,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2) ).
thf(657,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ ( minus_minus @ TA @ B @ A ) )
= ( ord_less_eq @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(256,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_add__le__mono) ).
thf(1054,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ D )
=> ( ord_less_eq @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(271,axiom,
semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__mult) ).
thf(1071,plain,
semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(140,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( ord_less @ TA @ A @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_diff__less__eq) ).
thf(674,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( ord_less @ TA @ A @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(246,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_not__add__less2) ).
thf(1026,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_diff__left__mono) ).
thf(530,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(219,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_add__mono__thms__linordered__field_I1_J) ).
thf(926,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(48,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__diff__cancel__right_H) ).
thf(398,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(249,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_add__lessD1) ).
thf(1035,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ C )
=> ( ord_less @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(136,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_ordered__cancel__comm__monoid__diff__class_Odiff__add) ).
thf(662,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(153,axiom,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus @ nat @ B @ C ) )
= ( ( ( ord_less @ nat @ B @ C )
=> ( A @ ( zero_zero @ nat ) ) )
& ! [D: nat] :
( ( B
= ( plus_plus @ nat @ C @ D ) )
=> ( A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_nat__diff__split) ).
thf(718,plain,
! [A: nat > $o,B: nat,C: nat] :
( ( A @ ( minus_minus @ nat @ B @ C ) )
= ( ( ( ord_less @ nat @ B @ C )
=> ( A @ ( zero_zero @ nat ) ) )
& ! [D: nat] :
( ( B
= ( plus_plus @ nat @ C @ D ) )
=> ( A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(204,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_201_add__right__mono) ).
thf(888,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ 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)],[204]) ).
thf(57,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_bot__nat__0_Oextremum) ).
thf(425,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D )
= E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_nat__eq__add__iff1) ).
thf(745,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D )
= ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D )
= E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(5,axiom,
ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( p @ i ) @ i ) @ ( times_times @ nat @ ( p @ k ) @ k ) ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_upper__bound) ).
thf(279,plain,
ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( p @ i ) @ i ) @ ( times_times @ nat @ ( p @ k ) @ k ) ) @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_mult__le__cancel2) ).
thf(296,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ C @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ B )
=> ( ord_less_eq @ nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(64,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_mult__cancel2) ).
thf(444,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ C @ B ) )
= ( ( A = C )
| ( B
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(157,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( ord_less_eq @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_nat__le__add__iff2) ).
thf(733,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( ord_less_eq @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_diff__less__mono2) ).
thf(584,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ( ord_less @ nat @ A @ C )
=> ( ord_less @ nat @ ( minus_minus @ nat @ C @ B ) @ ( minus_minus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(239,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_le__eq__less__or__eq) ).
thf(1007,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(168,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_165_add_Oleft__commute) ).
thf(772,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(198,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_gr__implies__not__zero) ).
thf(872,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ B )
=> ( B
!= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(873,plain,
! [TA: $tType,B: TA,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ B )
| ( B
!= ( zero_zero @ TA ) ) ),
inference(cnf,[status(esa)],[872]) ).
thf(874,plain,
! [TA: $tType,B: TA,A: TA] :
( ( B
!= ( zero_zero @ TA ) )
| ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ B ) ),
inference(lifteq,[status(thm)],[873]) ).
thf(875,plain,
! [TA: $tType,A: TA] :
( ~ ( canoni770627133id_add @ TA )
| ~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(simp,[status(thm)],[874]) ).
thf(7,axiom,
ord_less_eq @ nat @ k @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__092_060open_062k_A_092_060le_062_An_092_060close_062) ).
thf(281,plain,
ord_less_eq @ nat @ k @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_add__diff__cancel) ).
thf(413,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(104,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add__diff__eq) ).
thf(562,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(229,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_gr0I) ).
thf(975,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(222,axiom,
! [TA: $tType,A: TA > nat,B: TA > $o,C: TA] :
( ! [D: TA] :
( ( ( A @ D )
= ( zero_zero @ nat ) )
=> ( B @ D ) )
=> ( ! [D: TA] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( A @ D ) )
=> ( ~ ( B @ D )
=> ? [E: TA] :
( ( ord_less @ nat @ ( A @ E ) @ ( A @ D ) )
& ~ ( B @ E ) ) ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_infinite__descent0__measure) ).
thf(936,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)],[222]) ).
thf(82,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_diff__is__0__eq_H) ).
thf(498,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(258,axiom,
strict2144017051up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add) ).
thf(1058,plain,
strict2144017051up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(27,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_le__zero__eq) ).
thf(335,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ord_less_eq @ TA @ A @ ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(149,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( minus_minus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_Nat_Odiff__add__assoc) ).
thf(704,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( minus_minus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(32,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__eq__0__iff__both__eq__0) ).
thf(350,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( zero_zero @ TA ) )
= ( ( A
= ( zero_zero @ TA ) )
& ( B
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_diff__add__inverse2) ).
thf(611,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(173,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_group__cancel_Oadd2) ).
thf(787,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ D @ A )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ D @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(172,axiom,
! [TA: $tType] :
( ( semigroup_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_169_add_Oassoc) ).
thf(784,plain,
! [TA: $tType] :
( ( semigroup_add @ 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)],[172]) ).
thf(254,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_trans__le__add1) ).
thf(1048,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(41,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_cancel__comm__monoid__add__class_Odiff__cancel) ).
thf(377,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(36,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add__cancel__left__left) ).
thf(362,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= B )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(158,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_nat__le__add__iff1) ).
thf(737,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ E ) )
= ( ord_less_eq @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ D ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(252,axiom,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_nat__le__iff__add) ).
thf(1043,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_Nat_Odiff__diff__eq) ).
thf(599,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( minus_minus @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( minus_minus @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(241,axiom,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_nat__less__le) ).
thf(1011,plain,
( ( ord_less @ nat )
= ( ^ [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
& ( A != B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(205,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_less__eqE) ).
thf(890,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ~ ! [C: TA] :
( B
!= ( plus_plus @ TA @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(75,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_72_add__le__same__cancel2) ).
thf(477,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[75]) ).
thf(180,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(811,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(193,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_eq__imp__le) ).
thf(858,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(23,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ A @ ( plus_plus @ TA @ B @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_less__add__same__cancel2) ).
thf(323,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[23]) ).
thf(114,axiom,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_diff__le__self) ).
thf(594,plain,
! [A: nat,B: nat] : ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(176,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_173_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(799,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ 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)],[176]) ).
thf(77,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_diff__ge__0__iff__ge) ).
thf(483,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( minus_minus @ TA @ A @ B ) )
= ( ord_less_eq @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(148,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ B @ C ) @ A )
= ( plus_plus @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Nat_Odiff__add__assoc2) ).
thf(700,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ ( plus_plus @ nat @ B @ C ) @ A )
= ( plus_plus @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(124,axiom,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_diff__mult__distrib) ).
thf(626,plain,
! [A: nat,B: nat,C: nat] :
( ( times_times @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ ( times_times @ nat @ A @ C ) @ ( times_times @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(167,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_add__left__imp__eq) ).
thf(769,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[167]) ).
thf(223,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_bot__nat__0_Oextremum__strict) ).
thf(943,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(138,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_diff__le__eq) ).
thf(668,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( ord_less_eq @ TA @ A @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(247,axiom,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_not__add__less1) ).
thf(1029,plain,
! [A: nat,B: nat] :
~ ( ord_less @ nat @ ( plus_plus @ nat @ A @ B ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(207,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_add__mono) ).
thf(895,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(70,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_diff__diff__left) ).
thf(462,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( minus_minus @ nat @ A @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(261,axiom,
ordere236663937imp_le @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1061,plain,
ordere236663937imp_le @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(1044,plain,
( ( ord_less_eq @ nat )
= ( ^ [A: nat,B: nat] :
? [C: nat] :
( B
= ( plus_plus @ nat @ A @ C ) ) ) ),
inference(lifteq,[status(thm)],[1043]) ).
thf(202,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_199_add__le__imp__le__left) ).
thf(883,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[202]) ).
thf(15,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less_eq @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_nat__mult__le__cancel__disj) ).
thf(299,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( times_times @ nat @ A @ B ) @ ( times_times @ nat @ A @ C ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less_eq @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_diff__self__eq__0) ).
thf(438,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(217,axiom,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add__strict__left__mono) ).
thf(922,plain,
! [TA: $tType] :
( ( ordere223160158up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( plus_plus @ TA @ C @ A ) @ ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(266,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(1066,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(4,axiom,
number2016821345itions @ p @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I1_J) ).
thf(278,plain,
number2016821345itions @ p @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(40,axiom,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_add_Oleft__neutral) ).
thf(374,plain,
! [TA: $tType] :
( ( monoid_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2) ).
thf(648,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ ( minus_minus @ TA @ B @ A ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ B @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( ord_less @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_nat__less__add__iff2) ).
thf(749,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less @ nat @ ( plus_plus @ nat @ ( times_times @ nat @ A @ C ) @ D ) @ ( plus_plus @ nat @ ( times_times @ nat @ B @ C ) @ E ) )
= ( ord_less @ nat @ D @ ( plus_plus @ nat @ ( times_times @ nat @ ( minus_minus @ nat @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(101,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_diff__add__eq__diff__diff__swap) ).
thf(553,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ A @ ( plus_plus @ TA @ B @ C ) )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(175,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_172_add__mono__thms__linordered__semiring_I4_J) ).
thf(795,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ 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)],[175]) ).
thf(142,axiom,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( plus_plus @ nat @ A @ B ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_diff__add__0) ).
thf(680,plain,
! [A: nat,B: nat] :
( ( minus_minus @ nat @ A @ ( plus_plus @ nat @ A @ B ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ C @ B ) )
= ( minus_minus @ nat @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_diff__cancel2) ).
thf(617,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ C @ B ) )
= ( minus_minus @ nat @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(87,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_cancel__ab__semigroup__add__class_Odiff__right__commute) ).
thf(516,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( minus_minus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_diff__eq__diff__less__eq) ).
thf(525,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( minus_minus @ TA @ A @ B )
= ( minus_minus @ TA @ C @ D ) )
=> ( ( ord_less_eq @ TA @ A @ B )
= ( ord_less_eq @ TA @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(151,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_le__diff__conv) ).
thf(712,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ B ) @ C )
= ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_le__antisym) ).
thf(855,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)],[192]) ).
thf(145,axiom,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( plus_plus @ nat @ B @ ( minus_minus @ nat @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_add__diff__inverse__nat) ).
thf(690,plain,
! [A: nat,B: nat] :
( ~ ( ord_less @ nat @ A @ B )
=> ( ( plus_plus @ nat @ B @ ( minus_minus @ nat @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(270,axiom,
comm_monoid_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(1070,plain,
comm_monoid_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(174,axiom,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_group__cancel_Oadd1) ).
thf(791,plain,
! [TA: $tType] :
( ( comm_monoid_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( plus_plus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(63,axiom,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_diff__0__eq__0) ).
thf(441,plain,
! [A: nat] :
( ( minus_minus @ nat @ ( zero_zero @ nat ) @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(28,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_not__gr__zero) ).
thf(338,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
( ( ~ ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(179,axiom,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_mult_Oassoc) ).
thf(808,plain,
! [TA: $tType] :
( ( semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ A @ B ) @ C )
= ( times_times @ TA @ A @ ( times_times @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(35,axiom,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add__cancel__left__right) ).
thf(359,plain,
! [TA: $tType] :
( ( cancel1352612707id_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ A @ B )
= A )
= ( B
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_diff__strict__mono) ).
thf(544,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ( ord_less @ TA @ C @ D )
=> ( ord_less @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(211,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add_Ogroup__left__neutral) ).
thf(907,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( zero_zero @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_add__less__mono1) ).
thf(1023,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( plus_plus @ nat @ A @ C ) @ ( plus_plus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(1008,plain,
( ( ^ [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
| ( A = B ) ) )
= ( ord_less_eq @ nat ) ),
inference(lifteq,[status(thm)],[1007]) ).
thf(20,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ B ) @ A )
= ( ord_less @ TA @ B @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__less__same__cancel1) ).
thf(314,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[20]) ).
thf(107,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_group__cancel_Osub1) ).
thf(571,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( A
= ( plus_plus @ TA @ B @ C ) )
=> ( ( minus_minus @ TA @ A @ D )
= ( plus_plus @ TA @ B @ ( minus_minus @ TA @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(199,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_not__less__zero) ).
thf(876,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(230,axiom,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_bot__nat__0_Oextremum__uniqueI) ).
thf(978,plain,
! [A: nat] :
( ( ord_less_eq @ nat @ A @ ( zero_zero @ nat ) )
=> ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(44,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_diff__0__right) ).
thf(386,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ A @ ( zero_zero @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(71,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ 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/sandbox2/benchmark/theBenchmark.p',fact_68_zero__le__double__add__iff__zero__le__single__add) ).
thf(465,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[71]) ).
thf(66,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_mult__0__right) ).
thf(450,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_diff__add__eq) ).
thf(556,plain,
! [TA: $tType] :
( ( ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ C )
= ( minus_minus @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(96,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_diff__strict__left__mono) ).
thf(539,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ B )
=> ( ord_less @ TA @ ( minus_minus @ TA @ C @ B ) @ ( minus_minus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(139,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_less__diff__eq) ).
thf(671,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less @ TA @ A @ ( minus_minus @ TA @ B @ C ) )
= ( ord_less @ TA @ ( plus_plus @ TA @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(210,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add__mono__thms__linordered__semiring_I3_J) ).
thf(903,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( C = D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_less__imp__diff__less) ).
thf(581,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less @ nat @ ( minus_minus @ nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_zero__less__diff) ).
thf(495,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( minus_minus @ nat @ A @ B ) )
= ( ord_less @ nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(38,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_double__zero) ).
thf(368,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
= ( A
= ( zero_zero @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(189,axiom,
! [A: nat,B: nat] :
( ( A != B )
= ( ( ord_less @ nat @ A @ B )
| ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_nat__neq__iff) ).
thf(844,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)],[189]) ).
thf(262,axiom,
canoni770627133id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add) ).
thf(1062,plain,
canoni770627133id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(224,axiom,
! [A: nat > $o,B: nat] :
( ( A @ ( zero_zero @ nat ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( A @ C )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( A @ D ) ) ) )
=> ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_infinite__descent0) ).
thf(946,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)],[224]) ).
thf(126,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_less__iff__diff__less__0) ).
thf(632,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ( ( ord_less @ TA )
= ( ^ [A: TA,B: TA] : ( ord_less @ TA @ ( minus_minus @ TA @ A @ B ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(49,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__diff__cancel__right) ).
thf(401,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( minus_minus @ TA @ ( plus_plus @ TA @ A @ B ) @ ( plus_plus @ TA @ C @ B ) )
= ( minus_minus @ TA @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(171,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_add_Oleft__cancel) ).
thf(781,plain,
! [TA: $tType] :
( ( group_add @ 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)],[171]) ).
thf(236,axiom,
! [A: nat > nat,B: nat,C: nat] :
( ! [D: nat,E: nat] :
( ( ord_less @ nat @ D @ E )
=> ( ord_less @ nat @ ( A @ D ) @ ( A @ E ) ) )
=> ( ( ord_less_eq @ nat @ B @ C )
=> ( ord_less_eq @ nat @ ( A @ B ) @ ( A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_less__mono__imp__le__mono) ).
thf(995,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)],[236]) ).
thf(106,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_diff__eq__eq) ).
thf(568,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( minus_minus @ TA @ A @ B )
= C )
= ( A
= ( plus_plus @ TA @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(12,axiom,
! [A: nat > nat] :
( ( number2016821345itions @ A @ ( zero_zero @ nat ) )
= ( A
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_partitions__zero) ).
thf(290,plain,
! [A: nat > nat] :
( ( number2016821345itions @ A @ ( zero_zero @ nat ) )
= ( A
= ( ^ [B: nat] : ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(165,axiom,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_measure__induct) ).
thf(763,plain,
! [TA: $tType,TB: $tType] :
( ( wellorder @ TB )
=> ! [A: TA > TB,B: TA > $o,C: TA] :
( ! [D: TA] :
( ! [E: TA] :
( ( ord_less @ TB @ ( A @ E ) @ ( A @ D ) )
=> ( B @ E ) )
=> ( B @ D ) )
=> ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(43,axiom,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zero__diff) ).
thf(383,plain,
! [TA: $tType] :
( ( comm_monoid_diff @ TA )
=> ! [A: TA] :
( ( minus_minus @ TA @ ( zero_zero @ TA ) @ A )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(209,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: 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/sandbox2/benchmark/theBenchmark.p',fact_206_add__mono__thms__linordered__semiring_I2_J) ).
thf(899,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: 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)],[209]) ).
thf(253,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_trans__le__add2) ).
thf(1045,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ ( plus_plus @ nat @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__cancel1) ).
thf(447,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( B = C )
| ( A
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( ( plus_plus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ( A
= ( zero_zero @ nat ) )
& ( B
= ( zero_zero @ nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_add__is__0) ).
thf(432,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)],[60]) ).
thf(56,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_neq0__conv) ).
thf(422,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
= ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(196,axiom,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_zero__le) ).
thf(867,plain,
! [TA: $tType] :
( ( canoni770627133id_add @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(195,axiom,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_le__refl) ).
thf(865,plain,
! [A: nat] : ( ord_less_eq @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(117,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_le__diff__iff) ).
thf(603,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ord_less_eq @ nat @ ( minus_minus @ nat @ B @ A ) @ ( minus_minus @ nat @ C @ A ) )
= ( ord_less_eq @ nat @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( A != B )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_le__neq__implies__less) ).
thf(999,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)],[237]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( minus_minus @ nat @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Nat_Odiff__cancel) ).
thf(620,plain,
! [A: nat,B: nat,C: nat] :
( ( minus_minus @ nat @ ( plus_plus @ nat @ A @ B ) @ ( plus_plus @ nat @ A @ C ) )
= ( minus_minus @ nat @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(186,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_less__not__refl3) ).
thf(833,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(52,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_diff__add__cancel) ).
thf(410,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ ( minus_minus @ TA @ A @ B ) @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ nat @ A @ B ) )
= ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
& ( ord_less @ nat @ ( zero_zero @ nat ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_nat__0__less__mult__iff) ).
thf(305,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( times_times @ 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)],[17]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
= ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_double__add__less__zero__iff__single__add__less__zero) ).
thf(326,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[24]) ).
thf(215,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_212_add__less__imp__less__left) ).
thf(918,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[215]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_26_add__le__cancel__right) ).
thf(341,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[29]) ).
thf(127,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ( minus_minus @ TA @ B @ A )
= C )
= ( B
= ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add) ).
thf(635,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ A @ B )
=> ( ( ( minus_minus @ TA @ B @ A )
= C )
= ( B
= ( plus_plus @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(147,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( minus_minus @ nat @ B @ A )
= C )
= ( B
= ( plus_plus @ nat @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Nat_Ole__imp__diff__is__add) ).
thf(696,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ( minus_minus @ nat @ B @ A )
= C )
= ( B
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(208,axiom,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_add__mono__thms__linordered__semiring_I1_J) ).
thf(897,plain,
! [TA: $tType] :
( ( ordere779506340up_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ord_less_eq @ TA @ A @ B )
& ( ord_less_eq @ TA @ C @ D ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ A @ C ) @ ( plus_plus @ TA @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(74,axiom,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_71_le__add__same__cancel1) ).
thf(474,plain,
! [TA: $tType] :
( ( ordere516151231imp_le @ 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)],[74]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__mono) ).
thf(532,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( ord_less_eq @ TA @ C @ D )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ D ) @ ( minus_minus @ TA @ B @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(265,axiom,
cancel1352612707id_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add) ).
thf(1065,plain,
cancel1352612707id_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(47,axiom,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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/sandbox2/benchmark/theBenchmark.p',fact_44_add__less__cancel__left) ).
thf(395,plain,
! [TA: $tType] :
( ( ordere236663937imp_le @ 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)],[47]) ).
thf(233,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_less__eq__nat_Osimps_I1_J) ).
thf(987,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(26,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ A @ B )
= ( plus_plus @ TA @ A @ C ) )
= ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_add__left__cancel) ).
thf(332,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ 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)],[26]) ).
thf(108,axiom,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_minus__nat_Odiff__0) ).
thf(575,plain,
! [A: nat] :
( ( minus_minus @ nat @ A @ ( zero_zero @ nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(58,axiom,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_le0) ).
thf(427,plain,
! [A: nat] : ( ord_less_eq @ nat @ ( zero_zero @ nat ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_diff__le__mono) ).
thf(596,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ord_less_eq @ nat @ ( minus_minus @ nat @ A @ C ) @ ( minus_minus @ nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(91,axiom,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_diff__right__mono) ).
thf(528,plain,
! [TA: $tType] :
( ( ordered_ab_group_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ord_less_eq @ TA @ ( minus_minus @ TA @ A @ C ) @ ( minus_minus @ TA @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_diff__diff__cancel) ).
thf(459,plain,
! [A: nat,B: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( minus_minus @ nat @ B @ ( minus_minus @ nat @ B @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(235,axiom,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_plus__nat_Oadd__0) ).
thf(992,plain,
! [A: nat] :
( ( plus_plus @ nat @ ( zero_zero @ nat ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(3,axiom,
ord_less_eq @ nat @ i @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__092_060open_062i_A_092_060le_062_An_092_060close_062) ).
thf(277,plain,
ord_less_eq @ nat @ i @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,axiom,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_diff__is__0__eq) ).
thf(501,plain,
! [A: nat,B: nat] :
( ( ( minus_minus @ nat @ A @ B )
= ( zero_zero @ nat ) )
= ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_eq__diff__iff) ).
thf(607,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ A @ C )
=> ( ( ( minus_minus @ nat @ B @ A )
= ( minus_minus @ nat @ C @ A ) )
= ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(78,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ A @ A ) )
= ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_zero__less__double__add__iff__zero__less__single__add) ).
thf(486,plain,
! [TA: $tType] :
( ( linord219039673up_add @ 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)],[78]) ).
thf(240,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_less__imp__le__nat) ).
thf(1009,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ A @ B )
=> ( ord_less_eq @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(128,axiom,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ A ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse) ).
thf(639,plain,
! [TA: $tType] :
( ( ordere623563068d_diff @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ A @ B )
=> ( ( plus_plus @ TA @ A @ ( minus_minus @ TA @ B @ A ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Nat_Ole__diff__conv2) ).
thf(708,plain,
! [A: nat,B: nat,C: nat] :
( ( ord_less_eq @ nat @ A @ B )
=> ( ( ord_less_eq @ nat @ C @ ( minus_minus @ nat @ B @ A ) )
= ( ord_less_eq @ nat @ ( plus_plus @ nat @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(228,axiom,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_not__gr0) ).
thf(972,plain,
! [A: nat] :
( ( ~ ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
= ( A
= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(250,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_nat__mult__eq__cancel__disj) ).
thf(1037,plain,
! [A: nat,B: nat,C: nat] :
( ( ( times_times @ nat @ A @ B )
= ( times_times @ nat @ A @ C ) )
= ( ( A
= ( zero_zero @ nat ) )
| ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(60209,plain,
$false,
inference(cvc4,[status(thm)],[645,629,365,760,347,893,777,962,468,683,276,1068,308,878,741,1073,614,677,550,715,814,913,1063,930,404,841,885,288,651,320,565,389,504,587,934,1059,802,344,817,559,853,421,969,289,1013,284,881,416,924,492,1040,623,1020,1051,480,353,966,280,293,660,981,766,1072,453,1074,920,380,512,546,534,1067,1057,910,825,778,302,862,820,392,429,729,407,693,916,847,1032,435,329,665,757,456,285,522,830,317,1017,1064,1111,725,356,869,989,519,578,471,1082,753,537,642,489,590,686,1075,837,1099,654,1060,984,721,1002,371,805,508,311,541,657,1054,1071,674,1026,530,926,398,1035,662,718,888,425,745,279,296,444,733,584,1007,772,286,875,281,413,562,975,936,498,1058,335,704,350,611,787,784,1048,377,362,737,1043,599,1011,419,890,477,811,858,323,594,799,483,700,626,769,943,668,1029,895,462,1061,1044,883,299,438,922,1066,278,374,648,749,553,795,680,617,516,525,712,855,690,282,1070,872,791,441,338,808,359,544,907,1023,1008,314,571,876,978,386,465,450,556,539,671,903,581,495,368,844,1062,946,632,401,781,995,568,290,763,383,899,1045,447,432,422,867,865,603,999,620,833,410,305,326,918,341,807,635,696,897,474,532,1065,395,987,332,575,427,596,528,459,992,277,501,607,486,1009,639,1069,708,972,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP131^2 : TPTP v8.2.0. Released v7.5.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n016.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Sat May 18 17:04:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.98/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.11 % [INFO] Parsing done (223ms).
% 1.73/1.11 % [INFO] Running in sequential loop mode.
% 2.33/1.33 % [INFO] eprover registered as external prover.
% 2.61/1.33 % [INFO] cvc4 registered as external prover.
% 2.61/1.34 % [INFO] Scanning for conjecture ...
% 2.78/1.42 % [INFO] Found a conjecture (or negated_conjecture) and 273 axioms. Running axiom selection ...
% 2.78/1.44 % [INFO] Axiom selection finished. Selected 273 axioms (removed 0 axioms).
% 3.21/1.61 % [INFO] Problem is higher-order (TPTP THF).
% 3.21/1.63 % [INFO] Type checking passed.
% 3.21/1.63 % [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 ...
% 59.37/21.24 % External prover 'cvc4' found a proof!
% 59.37/21.24 % [INFO] Killing All external provers ...
% 59.37/21.24 % Time passed: 20700ms (effective reasoning time: 20122ms)
% 59.37/21.24 % 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)>
% 59.37/21.24 % Axioms used in derivation (273): fact_33_add__cancel__left__left, fact_152_nat__diff__add__eq2, fact_252_add__le__mono1, fact_222_gr__implies__not0, fact_168_add_Oleft__cancel, fact_207_add__mono__thms__linordered__semiring_I3_J, fact_239_less__add__eq__less, fact_50_add__diff__cancel, fact_169_add_Oassoc, fact_122_le__iff__diff__le__0, fact_85_diff__eq__diff__eq, fact_21_double__add__less__zero__iff__single__add__less__zero, fact_212_add__less__imp__less__left, fact_107_less__imp__diff__less, fact_27_add__le__cancel__left, fact_200_le__iff__add, fact_155_nat__le__add__iff1, fact_82_Nat_Oadd__diff__assoc2, fact_143_less__diff__conv, fact_86_diff__commute, fact_162_measure__induct, fact_10_partitions__bounds, fact_225_not__gr0, fact_3_lower__bound, fact_156_nat__eq__add__iff2, fact_202_less__eqE, fact_83_Nat_Oadd__diff__assoc, fact_62_mult__cancel1, fact_79_diff__is__0__eq_H, fact_11_mult__le__cancel2, fact_213_add__strict__right__mono, fact_56_Nat_Oadd__0__right, tcon_Nat_Onat___Groups_Ocomm__monoid__diff, fact_91_eq__iff__diff__eq__0, fact_175_mult_Ocommute, fact_206_add__mono__thms__linordered__semiring_I2_J, fact_34_double__zero__sym, fact_159_nat__less__add__iff1, fact_35_double__zero, fact_54_bot__nat__0_Oextremum, fact_211_add__less__imp__less__right, fact_31_add__cancel__right__left, fact_192_le__refl, fact_181_nat__less__induct, fact_48_add__diff__cancel__left, fact_15_nat__mult__less__cancel__disj, fact_218_add__mono__thms__linordered__field_I5_J, tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add, fact_106_diffs0__imp__equal, fact_215_add__strict__mono, fact_145_Nat_Odiff__add__assoc2, fact_65_nat__add__left__cancel__le, fact_4__092_060open_062k_A_092_060le_062_An_092_060close_062, fact_14_nat__0__less__mult__iff, fact_160_zero__reorient, fact_140_diff__less__mono, fact_59_diff__self__eq__0, fact_165_add_Oleft__commute, fact_128_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__monoid__add__imp__le, fact_74_diff__ge__0__iff__ge, fact_63_mult__0__right, fact_53_neq0__conv, fact_238_nat__less__le, fact_229_le__0__eq, fact_147_Nat_Ole__diff__conv2, fact_78_zero__less__diff, fact_98_diff__add__eq__diff__diff__swap, fact_227_bot__nat__0_Oextremum__uniqueI, fact_157_nat__eq__add__iff1, fact_109_diff__le__mono2, fact_66_diff__diff__cancel, fact_49_diff__add__cancel, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_28_zero__eq__add__iff__both__eq__0, fact_131_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2, fact_1_assms_I1_J, fact_199_add__le__imp__le__left, fact_64_mult__is__0, fact_176_mult_Oassoc, fact_73_add__le__same__cancel1, fact_76_diff__gt__0__iff__gt, fact_81_Nat_Odiff__diff__right, tcon_Nat_Onat___Groups_Ocomm__monoid__add, fact_43_add__less__cancel__right, fact_205_add__mono__thms__linordered__semiring_I1_J, fact_12_nat__mult__le__cancel__disj, fact_36_add_Oright__neutral, fact_135_diff__le__eq, fact_241_trans__less__add1, fact_226_gr0I, fact_25_not__gr__zero, fact_246_add__lessD1, fact_51_bot__nat__0_Onot__eq__extremum, fact_69_double__add__le__zero__iff__single__add__le__zero, fact_89_diff__left__mono, fact_46_add__diff__cancel__right, tcon_Nat_Onat___Groups_Ocancel__semigroup__add, fact_60_diff__0__eq__0, fact_171_group__cancel_Oadd1, tcon_Nat_Onat___Groups_Oordered__cancel__comm__monoid__diff, fact_234_le__neq__implies__less, fact_243_not__add__less2, fact_240_trans__less__add2, fact_88_diff__right__mono, tcon_Nat_Onat___Groups_Oab__semigroup__mult, fact_80_diff__is__0__eq, fact_55_le0, fact_37_add_Oleft__neutral, tcon_Nat_Onat___Groups_Omonoid__add, fact_146_Nat_Odiff__add__assoc, fact_101_add__diff__eq, fact_8__092_060open_062n_A_N_Ak_A_060_Ai_092_060close_062, fact_142_add__diff__inverse__nat, fact_245_add__less__mono, fact_163_add__right__imp__eq, fact_26_add__le__cancel__right, fact_136_less__diff__eq, fact_190_eq__imp__le, fact_114_le__diff__iff, fact_221_infinite__descent0, fact_203_add__left__mono, fact_105_minus__nat_Odiff__0, fact_95_diff__strict__mono, fact_41_diff__0__right, fact_129_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc, fact_19_less__add__same__cancel1, fact_195_gr__implies__not__zero, fact_223_less__zeroE, fact_166_add_Ocommute, fact_97_diff__diff__add, fact_39_diff__zero, fact_208_add_Ogroup__left__neutral, fact_149_nat__diff__split__asm, fact_138_diff__less, fact_42_diff__self, tcon_Nat_Onat___Orderings_Owellorder, tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_57_add__is__0, tcon_Nat_Onat___Groups_Ozero, fact_154_nat__le__add__iff2, fact_133_ordered__cancel__comm__monoid__diff__class_Odiff__add, fact_113_Nat_Odiff__diff__eq, fact_197_gr__zeroI, fact_178_infinite__descent__measure, fact_52_less__nat__zero__code, fact_61_mult__cancel2, fact_184_less__not__refl2, fact_177_ab__semigroup__mult__class_Omult__ac_I1_J, fact_100_diff__diff__eq2, fact_18_add__less__same__cancel2, fact_244_not__add__less1, fact_231_add__eq__self__zero, fact_121_diff__mult__distrib, fact_191_le__trans, fact_182_less__irrefl__nat, fact_45_add__diff__cancel__right_H, fact_209_add_Ocomm__neutral, fact_174_mult_Oleft__commute, fact_126_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right, fact_148_le__diff__conv, fact_249_nat__le__iff__add, fact_67_diff__diff__left, fact_16_add__gr__0, fact_132_le__add__diff, fact_139_diff__add__0, fact_228_bot__nat__0_Oextremum__unique, fact_32_add__cancel__left__right, fact_68_zero__le__double__add__iff__zero__le__single__add, fact_112_diff__le__mono, fact_118_diff__cancel2, fact_125_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse, fact_72_add__le__same__cancel2, tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_188_nat__le__linear, fact_235_less__or__eq__imp__le, fact_115_eq__diff__iff, fact_214_add__strict__left__mono, fact_217_add__mono__thms__linordered__field_I2_J, fact_0__092_060open_062i_A_092_060le_062_An_092_060close_062, fact_194_zero__less__iff__neq__zero, fact_161_measure__induct__rule, fact_44_add__less__cancel__left, fact_144_Nat_Ole__imp__diff__is__add, fact_116_diff__add__inverse2, fact_164_add__left__imp__eq, fact_248_mult__0, fact_153_nat__diff__add__eq1, fact_96_add__implies__diff, fact_93_diff__strict__left__mono, fact_22_add__right__cancel, fact_196_not__less__zero, fact_224_not__less0, fact_20_less__add__same__cancel2, fact_119_Nat_Odiff__cancel, fact_185_less__not__refl, fact_6_assms_I2_J, fact_2_upper__bound, fact_167_add_Oright__cancel, fact_70_le__add__same__cancel2, fact_150_nat__diff__split, fact_71_le__add__same__cancel1, fact_180_infinite__descent, fact_237_less__imp__le__nat, tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_111_diff__le__self, fact_210_comm__monoid__add__class_Oadd__0, fact_134_le__diff__eq, fact_251_trans__le__add1, fact_247_nat__mult__eq__cancel__disj, fact_99_diff__add__eq, fact_17_add__less__same__cancel1, fact_9_partitions__zero, fact_232_plus__nat_Oadd__0, fact_102_eq__diff__eq, fact_130_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc, fact_90_diff__mono, fact_183_less__not__refl3, fact_193_zero__le, fact_29_add__eq__0__iff__both__eq__0, fact_189_le__antisym, fact_198_add__le__imp__le__right, fact_242_add__less__mono1, fact_127_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2, fact_24_le__zero__eq, fact_38_cancel__comm__monoid__add__class_Odiff__cancel, fact_173_ab__semigroup__add__class_Oadd__ac_I1_J, fact_87_diff__eq__diff__less__eq, fact_187_Nat_Oex__has__greatest__nat, fact_236_le__eq__less__or__eq, fact_104_group__cancel_Osub1, fact_47_add__diff__cancel__left_H, fact_186_nat__neq__iff, tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add, tcon_Nat_Onat___Groups_Osemigroup__add, fact_94_diff__eq__diff__less, fact_170_group__cancel_Oadd2, tcon_Nat_Onat___Groups_Osemigroup__mult, fact_13_mult__less__cancel2, fact_219_infinite__descent0__measure, tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add, fact_216_add__mono__thms__linordered__field_I1_J, fact_141_less__diff__iff, fact_123_less__iff__diff__less__0, fact_58_nat__add__left__cancel__less, fact_137_diff__less__eq, fact_110_le__diff__iff_H, fact_117_diff__add__inverse, fact_103_diff__eq__eq, fact_92_diff__strict__right__mono, fact_77_diff__add__zero, fact_40_zero__diff, fact_158_nat__less__add__iff2, tcon_Nat_Onat___Groups_Oab__semigroup__add, fact_204_add__mono, fact_230_less__eq__nat_Osimps_I1_J, fact_233_less__mono__imp__le__mono, fact_151_less__diff__conv2, fact_120_diff__mult__distrib2, fact_5__092_060open_062p_Ai_A_092_060noteq_062_A0_092_060close_062, fact_23_add__left__cancel, fact_30_add__cancel__right__right, fact_201_add__right__mono, fact_108_diff__less__mono2, fact_7__092_060open_062i_A_092_060noteq_062_Ak_092_060close_062, fact_172_add__mono__thms__linordered__semiring_I4_J, fact_179_linorder__neqE__nat, fact_253_add__le__mono, fact_84_cancel__ab__semigroup__add__class_Odiff__right__commute, fact_250_trans__le__add2, fact_75_zero__less__double__add__iff__zero__less__single__add, fact_124_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add, fact_220_bot__nat__0_Oextremum__strict
% 59.37/21.24 % No. of inferences in proof: 572
% 59.37/21.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 20700 ms resp. 20122 ms w/o parsing
% 60.01/21.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 60.01/21.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------