%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM992_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 : n014.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 08:10:35 AM UTC 2026
% Result : Theorem 32.64s 7.41s
% Output : Refutation 29.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 224 ( 90 unt; 0 typ; 0 def)
% Number of atoms : 525 ( 129 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2667 ( 20 ~; 0 |; 86 &;2346 @)
% ( 51 <=>; 164 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 23 usr; 5 con; 0-3 aty)
% Number of variables : 337 ( 0 ^; 334 !; 3 ?; 337 :)
% 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(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[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(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
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(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > 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(m1_decl,type,
m1: int ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: int ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_number__of__Pls) ).
thf(257,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(42,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__imp__0__less) ).
thf(260,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(95,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_80_less__eq__int__code_I14_J) ).
thf(479,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)],[95]) ).
thf(64,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_less__special_I2_J) ).
thf(333,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(35,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__int__def) ).
thf(234,plain,
! [A: int,B: int] :
( ( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(68,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_int__0) ).
thf(352,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(4,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(115,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I19_J) ).
thf(276,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(9,axiom,
int @ zero_zero @ ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096) ).
thf(120,plain,
int @ zero_zero @ ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
<=> ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zle__iff__zadd) ).
thf(379,plain,
! [A: int,B: int] :
( ( ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_diff__bin__simps_I7_J) ).
thf(472,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zless__int) ).
thf(340,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(101,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_rel__simps_I29_J) ).
thf(504,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(11,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(125,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_double__eq__0__iff) ).
thf(152,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I49_J) ).
thf(289,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(88,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_31_rel__simps_I14_J) ).
thf(448,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)],[88]) ).
thf(60,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_int__1) ).
thf(316,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(94,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_69_le__special_I1_J) ).
thf(475,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)],[94]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_add__Bit0__Bit0) ).
thf(376,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(39,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_t1) ).
thf(253,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(96,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_zero__less__int__conv) ).
thf(485,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(10,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_45_less__number__of) ).
thf(121,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)],[10]) ).
thf(103,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_36_mult__Bit0) ).
thf(514,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)],[103]) ).
thf(77,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_95_number__of__reorient) ).
thf(397,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)],[77]) ).
thf(53,axiom,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zadd__int__left) ).
thf(293,plain,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_zless__imp__add1__zle) ).
thf(132,plain,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit0__Bit1) ).
thf(411,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(5,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(116,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__number__of__eq) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_le__number__of__eq__not__less) ).
thf(312,plain,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( 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 ) ) )
=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(37,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Bit0__Pls) ).
thf(248,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(6,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(117,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(439,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(107,axiom,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(534,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_right__diff__distrib__number__of) ).
thf(197,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(71,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_mult__Pls) ).
thf(361,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(112,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_18_eq__number__of) ).
thf(551,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)],[112]) ).
thf(62,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zadd__int) ).
thf(324,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__int__code_I14_J) ).
thf(225,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(106,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_int__int__eq) ).
thf(526,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(14,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_29_rel__simps_I17_J) ).
thf(134,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)],[14]) ).
thf(36,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I50_J) ).
thf(244,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(109,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I46_J) ).
thf(541,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zle__diff1__eq) ).
thf(161,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_diff__bin__simps_I10_J) ).
thf(296,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(26,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_right__distrib__number__of) ).
thf(191,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096) ).
thf(118,plain,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(110,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_diff__bin__simps_I3_J) ).
thf(545,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(99,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_less__special_I1_J) ).
thf(498,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(92,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_75_less__eq__number__of__int__code) ).
thf(466,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)],[92]) ).
thf(18,axiom,
! [A: nat,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zmult__zless__mono2__lemma) ).
thf(159,plain,
! [A: nat,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__special_I3_J) ).
thf(187,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,conjecture,
int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(32,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_rel__simps_I5_J) ).
thf(219,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(61,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_rel__simps_I15_J) ).
thf(318,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(30,axiom,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_tpos) ).
thf(208,plain,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I48_J) ).
thf(387,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)],[76]) ).
thf(108,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I27_J) ).
thf(535,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)],[108]) ).
thf(15,axiom,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_int__one__le__iff__zero__less) ).
thf(140,plain,
! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(462,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_mult__number__of__left) ).
thf(306,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(55,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_73_less__eq__int__code_I13_J) ).
thf(299,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)],[55]) ).
thf(84,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_34_rel__simps_I31_J) ).
thf(431,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)],[84]) ).
thf(20,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(167,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(82,axiom,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096) ).
thf(426,plain,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_mult__Bit1) ).
thf(548,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_rel__simps_I51_J) ).
thf(209,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)],[31]) ).
thf(70,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_32_rel__simps_I34_J) ).
thf(355,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)],[70]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__special_I2_J) ).
thf(194,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(105,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(525,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__special_I4_J) ).
thf(414,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_less__eq__int__code_I15_J) ).
thf(327,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(44,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I2_J) ).
thf(263,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(23,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I10_J) ).
thf(177,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I33_J) ).
thf(370,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(100,axiom,
~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_126_Am1_A_060_A1_A_L_Aint_An_096) ).
thf(502,plain,
~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(98,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_left__diff__distrib__number__of) ).
thf(495,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(38,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_number__of__is__id) ).
thf(250,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(91,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(465,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__special_I3_J) ).
thf(231,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(104,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_int__eq__0__conv) ).
thf(517,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(3,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(114,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I22_J) ).
thf(171,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)],[22]) ).
thf(81,axiom,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_int__le__0__conv) ).
thf(418,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(8,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(119,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(102,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_68_le__special_I3_J) ).
thf(510,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)],[102]) ).
thf(47,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(272,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(67,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(346,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(16,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_72_less__eq__int__code_I16_J) ).
thf(146,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)],[16]) ).
thf(78,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_56_rel__simps_I32_J) ).
thf(405,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)],[78]) ).
thf(24,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__special_I4_J) ).
thf(183,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_arith__simps_I32_J) ).
thf(273,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_left__distrib__number__of) ).
thf(168,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(43,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(262,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(56,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_n0) ).
thf(305,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(12,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I4_J) ).
thf(126,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(46,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_46_le__number__of) ).
thf(268,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)],[46]) ).
thf(85,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zero__zle__int) ).
thf(437,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_zle__add1__eq__le) ).
thf(283,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(83,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__special_I2_J) ).
thf(427,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(29,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I44_J) ).
thf(200,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I21_J) ).
thf(277,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)],[50]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I16_J) ).
thf(442,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__number__of__left) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_add__Bit1__Bit0) ).
thf(337,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(69,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(354,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(58,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_diff__bin__simps_I9_J) ).
thf(309,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(97,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I39_J) ).
thf(491,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(89,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I38_J) ).
thf(454,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_add1__zle__eq) ).
thf(364,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(4170,plain,
$false,
inference(e,[status(thm)],[257,260,479,333,234,352,115,276,120,379,472,340,504,125,152,289,448,316,475,376,253,485,121,514,397,293,132,411,116,265,312,248,117,439,534,197,361,551,324,225,526,134,244,541,161,296,191,118,545,498,466,159,187,113,219,318,208,387,535,140,462,306,299,431,167,426,548,209,355,194,525,414,327,263,177,370,502,495,250,465,231,517,114,171,418,119,510,272,346,146,405,183,273,168,262,305,126,268,437,283,427,200,277,442,254,337,354,309,491,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM992_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
% 0.14/0.41 % Computer : n014.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 04:24:47 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/1.29 % [INFO] Parsing done (295ms).
% 1.49/1.30 % [INFO] Running in sequential loop mode.
% 2.64/1.71 % [INFO] eprover registered as external prover.
% 2.64/1.72 % [INFO] Scanning for conjecture ...
% 2.84/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ...
% 3.05/2.00 % [INFO] Axiom selection finished. Selected 110 axioms (removed 2 axioms).
% 3.71/2.16 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.71/2.18 % [INFO] Type checking passed.
% 3.71/2.18 % [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 ...
% 32.08/7.40 % External prover 'e' found a proof!
% 32.64/7.40 % [INFO] Killing All external provers ...
% 32.64/7.40 % Time passed: 6848ms (effective reasoning time: 6100ms)
% 32.64/7.41 % 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)>
% 32.64/7.41 % Axioms used in derivation (110): fact_37_add__Bit0__Bit0, fact_86_int__1, fact_17_tpos, fact_79_le__number__of__eq__not__less, fact_82_zadd__int__left, fact_36_mult__Bit0, fact_13_numeral__1__eq__1, fact_9_less__special_I1_J, fact_35_mult__Pls, fact_39__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096, arity_Int_Oint___Rings_Olinordered__idom, arity_Int_Oint___Int_Oring__char__0, fact_28_Bit0__Pls, fact_5_add__special_I3_J, fact_43_left__diff__distrib__number__of, fact_20_rel__simps_I48_J, fact_41_right__distrib__number__of, fact_63_rel__simps_I5_J, fact_97_int__int__eq, fact_76_int__le__0__conv, fact_93_add1__zle__eq, fact_65_rel__simps_I15_J, fact_14_diff__bin__simps_I3_J, fact_64_rel__simps_I33_J, fact_46_le__number__of, fact_34_rel__simps_I31_J, fact_92_zless__imp__add1__zle, fact_70_le__special_I4_J, arity_Int_Oint___Rings_Oring, fact_42_number__of__Pls, fact_2__096_126_Am1_A_060_A1_A_L_Aint_An_096, fact_55_rel__simps_I22_J, fact_6_less__special_I2_J, fact_57_rel__simps_I27_J, fact_80_less__eq__int__code_I14_J, arity_Int_Oint___Int_Onumber__ring, fact_11__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096, fact_30_rel__simps_I2_J, fact_16_n0, arity_HOL_Obool___Orderings_Olinorder, fact_33_rel__simps_I19_J, fact_77_zero__less__int__conv, fact_96_number__of__is__id, fact_74_less__int__def, fact_91_int__one__le__iff__zero__less, fact_60_add__Bit0__Bit1, fact_18_eq__number__of, fact_78_zmult__zless__mono2__lemma, fact_54_rel__simps_I4_J, fact_1_t1, fact_44_right__diff__distrib__number__of, fact_25_rel__simps_I49_J, fact_27_rel__simps_I38_J, fact_75_less__eq__number__of__int__code, arity_Nat_Onat___Orderings_Olinorder, fact_4_add__special_I2_J, fact_85_zle__iff__zadd, fact_87_int__eq__0__conv, fact_49_add__number__of__left, fact_84_zless__int, fact_19_rel__simps_I51_J, fact_66_zle__add1__eq__le, fact_52_rel__simps_I16_J, fact_23_rel__simps_I39_J, fact_32_rel__simps_I34_J, arity_Int_Oint___Orderings_Olinorder, fact_72_less__eq__int__code_I16_J, fact_61_diff__bin__simps_I10_J, fact_73_less__eq__int__code_I13_J, fact_88_int__0, fact_94_le__imp__0__less, fact_68_le__special_I3_J, arity_Int_Oint___Rings_Osemiring, fact_71_le__special_I2_J, fact_58_rel__simps_I21_J, fact_51_rel__simps_I12_J, fact_56_rel__simps_I32_J, fact_45_less__number__of, fact_81_zero__zle__int, fact_29_rel__simps_I17_J, fact_8_one__add__one__is__two, fact_95_number__of__reorient, arity_Nat_Onat___Int_Onumber, fact_31_rel__simps_I14_J, fact_47_mult__number__of__left, fact_50_add__number__of__eq, fact_7_less__special_I4_J, fact_59_add__Bit1__Bit0, arity_Nat_Onat___Rings_Osemiring, fact_22_rel__simps_I46_J, fact_62_rel__simps_I29_J, fact_48_arith__simps_I32_J, fact_12_mult__Bit1, fact_83_zadd__int, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_3__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096, fact_90_less__int__code_I14_J, fact_0_n1pos, fact_38_diff__bin__simps_I7_J, fact_24_rel__simps_I50_J, fact_53_rel__simps_I10_J, fact_21_double__eq__0__iff, fact_26_rel__simps_I44_J, fact_89_less__eq__int__code_I15_J, fact_67_zle__diff1__eq, fact_10_less__special_I3_J, fact_15_diff__bin__simps_I9_J, fact_40_left__distrib__number__of, fact_69_le__special_I1_J
% 32.64/7.41 % No. of inferences in proof: 224
% 32.64/7.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 6848 ms resp. 6100 ms w/o parsing
% 29.97/7.53 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.97/7.53 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------