%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM970_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:33 AM UTC 2026
% Result : Theorem 8.40s 3.70s
% Output : Refutation 8.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 139
% Syntax : Number of formulae : 280 ( 134 unt; 0 typ; 0 def)
% Number of atoms : 688 ( 171 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2504 ( 39 ~; 16 |; 95 &;2070 @)
% ( 45 <=>; 239 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 33 usr; 6 con; 0-4 aty)
% Number of variables : 383 ( 0 ^; 383 !; 0 ?; 383 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(ord_decl,type,
ord:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(order_decl,type,
order:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(preorder_decl,type,
preorder:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(pp_decl,type,
pp: bool > $o ).
thf(s_decl,type,
s: int ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_power2__eq__imp__eq) ).
thf(357,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) ) )
=> ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_linorder__le__cases) ).
thf(373,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ~ ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(136,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_rel__simps_I46_J) ).
thf(629,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(135,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(628,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(101,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_rel__simps_I51_J) ).
thf(468,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(58,axiom,
int @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(308,plain,
int @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(28,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(202,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_le__special_I1_J) ).
thf(597,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(117,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_le__refl) ).
thf(550,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(3,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(142,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(153,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ order )
=> ( TA @ ( TB @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(19,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_mult__Pls) ).
thf(174,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(24,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_order__eq__iff) ).
thf(185,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
& ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(88,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__funD) ).
thf(417,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(257,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(10,axiom,
bool @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(152,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_zero__le__power) ).
thf(261,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__less__power2) ).
thf(443,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A
!= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_le__funE) ).
thf(321,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TA,B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(42,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(253,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(147,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ preorder )
=> ( TA @ ( TB @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,axiom,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_number__of2) ).
thf(221,plain,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(57,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(307,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_rel__simps_I48_J) ).
thf(292,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(94,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
<=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__fun__def) ).
thf(439,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ord )
=> ! [A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ( ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( TB @ ( TA @ fun ) @ ord_less_eq ) ) )
=> ! [C: TA] : ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( TB @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(77,axiom,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(381,plain,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(37,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Bit0__Pls) ).
thf(233,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(98,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_rel__simps_I50_J) ).
thf(452,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(334,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(54,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(302,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(68,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(349,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(81,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_rel__simps_I2_J) ).
thf(392,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_power__mono) ).
thf(407,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(51,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
<=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_imp__le__cong) ).
thf(275,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) ) )
& ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ pp ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ pp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(16,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_less__number__of) ).
thf(165,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(26,axiom,
pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(197,plain,
pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__zero__less__power__iff) ).
thf(361,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(134,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_mult__0) ).
thf(625,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(126,axiom,
! [A: int] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_power2__ge__self) ).
thf(583,plain,
! [A: int] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_rel__simps_I17_J) ).
thf(456,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(33,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(229,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(122,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_less__zeroE) ).
thf(566,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_linorder__linear) ).
thf(519,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA] :
( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
| ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_less__eq__number__of__int__code) ).
thf(156,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(85,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_le__special_I3_J) ).
thf(403,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_order__refl) ).
thf(169,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA] : ( A @ ( A @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(141,plain,
~ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(104,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(488,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_power__eq__0__iff) ).
thf(339,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(120,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_less__eq__int__code_I13_J) ).
thf(554,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_order__trans) ).
thf(642,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(105,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_rel__simps_I27_J) ).
thf(489,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(123,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_le__0__eq) ).
thf(569,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_zero__le__power2) ).
thf(371,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] : ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(49,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_neq0__conv) ).
thf(266,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(108,axiom,
! [A: int] :
( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_eq__number__of__0) ).
thf(508,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(137,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_number__of__is__id) ).
thf(633,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(72,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(360,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_zero__eq__power2) ).
thf(618,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(90,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(425,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(8,axiom,
bool @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(149,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(76,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_rel__simps_I22_J) ).
thf(375,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(131,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I38_J) ).
thf(601,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_rel__simps_I14_J) ).
thf(286,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(124,axiom,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_order__eq__refl) ).
thf(577,plain,
! [TA: $tType] :
( ( TA @ preorder )
=> ! [A: TA,B: TA] :
( ( B = A )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_rel__simps_I49_J) ).
thf(545,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(80,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(391,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(5,axiom,
bool @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(144,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(335,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(39,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( A @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_number__of1) ).
thf(236,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ bit1 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
& ( A @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(181,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_ord__eq__le__trans) ).
thf(350,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( C = B )
=> ( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(50,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(274,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I31_J) ).
thf(419,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(34,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(230,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(97,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(451,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_semiring__norm_I112_J) ).
thf(434,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(55,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(303,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(118,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(552,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_power__eq__0__iff__number__of) ).
thf(609,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(62,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_le__number__of) ).
thf(323,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(40,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_le__trans) ).
thf(240,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(12,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(155,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_ord__le__eq__trans) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ ord )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( B = A )
=> ( A @ ( C @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(100,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_less__eq__int__code_I16_J) ).
thf(462,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_order__antisym__conv) ).
thf(521,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( ( A = B )
=> ( B @ ( A @ ( TA @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(138,axiom,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_eq__imp__le) ).
thf(636,plain,
! [A: nat,B: nat] :
( ( B = A )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(82,axiom,
int @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(394,plain,
int @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_number__of__reorient) ).
thf(426,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(44,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Pls__def) ).
thf(255,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(109,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_quartic__square__square) ).
thf(516,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(119,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(553,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(6,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(145,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ ord )
=> ( TA @ ( TB @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(162,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(113,axiom,
! [A: int,B: int] :
( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
<=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_le__nat__number__of) ).
thf(531,plain,
! [A: int,B: int] :
( ( ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq ) ) )
=> ( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(139,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_nat__le__linear) ).
thf(640,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
| ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(9,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(150,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult__less__cancel1) ).
thf(327,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( B @ ( nat @ ord_less ) ) )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I44_J) ).
thf(409,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(48,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_mult__0__right) ).
thf(263,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(60,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_mult__cancel2) ).
thf(310,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_semiring__numeral__0__eq__0) ).
thf(585,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(20,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(177,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(23,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_power2__eq__square__number__of) ).
thf(182,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(66,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_zero__power2) ).
thf(336,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(4,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(143,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(107,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_mult__is__0) ).
thf(497,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(35,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(231,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(96,axiom,
nat @ order,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(450,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(114,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_rel__simps_I32_J) ).
thf(539,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_power2__le__imp__le) ).
thf(581,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(106,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_less__eq__nat_Osimps_I1_J) ).
thf(495,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_less__eq__int__code_I14_J) ).
thf(482,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
<=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_mult__cancel1) ).
thf(203,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(128,axiom,
! [A: int] :
( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_eq__0__number__of) ).
thf(588,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) ) )
& ( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(56,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult__Bit0) ).
thf(304,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_order__antisym) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ order )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(79,axiom,
int @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(390,plain,
int @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_nat__number__of__Pls) ).
thf(401,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_field__power__not__zero) ).
thf(171,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(38,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(235,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(102,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_rel__simps_I39_J) ).
thf(478,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mult__less__cancel2) ).
thf(383,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( C @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) ) )
& ( ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(116,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I19_J) ).
thf(549,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__0__less__mult__iff) ).
thf(214,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(41,axiom,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( B @ pp )
<=> ( A @ pp ) ) )
=> ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
<=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_conj__le__cong) ).
thf(242,plain,
! [A: bool,B: bool,C: int] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( ( A @ pp )
=> ( B @ pp ) )
& ( ( B @ pp )
=> ( A @ pp ) ) ) )
=> ( ( ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) )
& ( ( ( B @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ( ( A @ pp )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(25,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zero__is__num__zero) ).
thf(195,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(93,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_semiring__norm_I113_J) ).
thf(437,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(83,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_rel__simps_I21_J) ).
thf(395,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(129,axiom,
int @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(596,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(112,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_le__antisym) ).
thf(528,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(15,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_le0) ).
thf(163,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_less__nat__zero__code) ).
thf(178,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(43,axiom,
nat @ preorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(254,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_number__of__Pls) ).
thf(354,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(59,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(309,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(121,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I34_J) ).
thf(560,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(32,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_eq__number__of) ).
thf(222,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(36,axiom,
nat @ ord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(232,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(644,plain,
$false,
inference(e,[status(thm)],[357,373,629,628,468,308,202,597,550,142,153,174,185,417,257,152,261,443,321,253,147,221,307,292,439,381,233,452,334,302,349,392,407,275,165,197,361,625,583,456,229,566,519,156,403,169,141,488,339,554,642,489,569,371,266,508,633,360,618,425,149,375,601,286,577,545,391,144,335,236,181,350,274,419,230,451,434,303,552,609,323,240,155,198,462,521,636,394,426,255,516,553,145,162,531,640,150,327,409,263,310,585,177,182,336,143,497,231,450,539,581,495,482,203,588,304,258,390,401,171,235,478,383,549,214,242,195,437,395,596,528,163,178,254,354,309,560,222,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM970_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.16/0.40 % Computer : n001.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Sat Sep 26 04:29:26 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.82/1.30 % [INFO] Parsing done (313ms).
% 1.82/1.32 % [INFO] Running in sequential loop mode.
% 2.72/1.71 % [INFO] eprover registered as external prover.
% 2.72/1.72 % [INFO] Scanning for conjecture ...
% 2.90/1.87 % [INFO] Found a conjecture (or negated_conjecture) and 138 axioms. Running axiom selection ...
% 3.09/1.98 % [INFO] Axiom selection finished. Selected 138 axioms (removed 0 axioms).
% 3.74/2.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.74/2.18 % [INFO] Type checking passed.
% 3.74/2.19 % [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 ...
% 8.03/3.70 % External prover 'e' found a proof!
% 8.03/3.70 % [INFO] Killing All external provers ...
% 8.40/3.70 % Time passed: 3153ms (effective reasoning time: 2375ms)
% 8.40/3.70 % 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)>
% 8.40/3.70 % Axioms used in derivation (138): fact_83_mult__0, fact_57_less__eq__nat_Osimps_I1_J, fact_75_nat__le__linear, arity_HOL_Obool___Orderings_Oorder, arity_Nat_Onat___Groups_Omonoid__mult, fact_3_le__special_I3_J, fact_56_le__0__eq, fact_11_zero__le__power2, fact_41_power__eq__0__iff, arity_HOL_Obool___Orderings_Oord, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Orderings_Oorder, fact_30_zero__is__num__zero, arity_Int_Oint___Int_Oring__char__0, fact_89_nat__0__less__mult__iff, fact_35_less__eq__int__code_I13_J, arity_Int_Oint___Rings_Olinordered__idom, arity_HOL_Obool___Orderings_Opreorder, fact_53_conj__le__cong, fact_10_number__of__Pls, fact_4_rel__simps_I21_J, fact_28_eq__0__number__of, arity_fun___Orderings_Oord, arity_Int_Oint___Orderings_Oord, fact_63_order__antisym, fact_93_mult__Pls, fact_48_number__of2, fact_32_number__of__reorient, fact_95_mult__Bit0, fact_21_Bit0__Pls, fact_16_rel__simps_I39_J, arity_Int_Oint___Orderings_Opreorder, arity_Nat_Onat___Int_Onumber__semiring, arity_Nat_Onat___Orderings_Opreorder, arity_Nat_Onat___Power_Opower, fact_61_le__funE, fact_5_rel__simps_I27_J, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_59_order__refl, arity_Int_Oint___Rings_Ono__zero__divisors, arity_Int_Oint___Int_Onumber__semiring, fact_8_power__eq__0__iff__number__of, fact_6_rel__simps_I32_J, fact_0_zero__power2, arity_Int_Oint___Int_Onumber__ring, fact_34_less__eq__int__code_I16_J, fact_71_le__fun__def, fact_65_ord__eq__le__trans, fact_96_less__number__of, arity_Int_Oint___Rings_Osemiring__1, arity_HOL_Obool___Orderings_Olinorder, fact_22_rel__simps_I34_J, fact_79_mult__cancel2, fact_81_mult__is__0, fact_90_nat__zero__less__power__iff, fact_54_imp__le__cong, arity_Nat_Onat___Rings_Omult__zero, fact_78_zero__less__power2, fact_40_power2__le__imp__le, fact_80_mult__cancel1, fact_15_rel__simps_I46_J, fact_72_le__antisym, fact_7_rel__simps_I22_J, fact_76_le__refl, fact_60_linorder__le__cases, fact_49_power__mono, fact_77_power2__eq__square__number__of, fact_44_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_Nat_Onat___Orderings_Olinorder, fact_9_le__number__of, fact_17_rel__simps_I50_J, arity_fun___Orderings_Oorder, fact_50_number__of__is__id, arity_fun___Orderings_Opreorder, fact_84_less__zeroE, fact_27_eq__number__of__0, fact_19_rel__simps_I44_J, fact_26_le__nat__number__of, arity_Int_Oint___Groups_Omonoid__mult, fact_2_le__special_I1_J, fact_25_nat__number__of__Pls, fact_55_zero__le__power, fact_46_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, arity_Int_Oint___Orderings_Olinorder, fact_74_eq__imp__le, arity_Nat_Onat___Rings_Olinordered__semidom, fact_43_quartic__square__square, fact_92_rel__simps_I2_J, fact_31_semiring__norm_I113_J, fact_88_mult__less__cancel1, fact_33_Pls__def, fact_62_order__trans, arity_Nat_Onat___Groups_Ozero, fact_86_neq0__conv, fact_85_less__nat__zero__code, arity_Nat_Onat___Orderings_Oord, fact_29_less__eq__number__of__int__code, fact_13_rel__simps_I51_J, fact_45_number__of1, fact_38_less__eq__int__code_I14_J, fact_66_order__antisym__conv, arity_Int_Oint___Power_Opower, fact_67_le__funD, fact_1_zero__eq__power2, fact_12_eq__number__of, fact_37_semiring__norm_I112_J, arity_Nat_Onat___Int_Onumber, fact_14_rel__simps_I48_J, fact_52_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_24_rel__simps_I31_J, fact_68_order__eq__refl, fact_91_rel__simps_I17_J, fact_87_mult__less__cancel2, arity_Nat_Onat___Orderings_Oorder, fact_18_rel__simps_I49_J, fact_51_field__power__not__zero, fact_70_linorder__linear, fact_39_power2__eq__imp__eq, fact_23_rel__simps_I19_J, fact_94_rel__simps_I14_J, help_pp_1_1_U, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_82_mult__0__right, arity_Int_Oint___Int_Onumber, fact_73_le__trans, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_58_le0, arity_Nat_Onat___Rings_Ozero__neq__one, fact_47_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_36_semiring__numeral__0__eq__0, fact_69_order__eq__iff, fact_42_power2__ge__self, fact_64_ord__le__eq__trans, fact_20_rel__simps_I38_J
% 8.40/3.70 % No. of inferences in proof: 280
% 8.40/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3153 ms resp. 2375 ms w/o parsing
% 8.75/3.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.75/3.84 % [INFO] Killing All external provers ...
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