%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN004_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 : n015.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 08:18:30 AM UTC 2026
% Result : Theorem 8.82s 3.54s
% Output : Refutation 9.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 116
% Syntax : Number of formulae : 234 ( 116 unt; 0 typ; 0 def)
% Number of atoms : 500 ( 184 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 3455 ( 59 ~; 9 |; 61 &;3130 @)
% ( 30 <=>; 166 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 34 usr; 10 con; 0-3 aty)
% Number of variables : 342 ( 0 ^; 342 !; 0 ?; 342 :)
% 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(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(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_ring_decl,type,
linordered_ring:
!>[TA: $tType] : $o ).
thf(linord581940658strict_decl,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
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(zprime_decl,type,
zprime: int > $o ).
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(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(dvd_dvd_decl,type,
dvd_dvd:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(twoSqu1567020053sum2sq_decl,type,
twoSqu1567020053sum2sq: int > $o ).
thf(m_decl,type,
m: int ).
thf(m1_decl,type,
m1: int ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: int ).
thf(v_decl,type,
v: int ).
thf(w_decl,type,
w: int ).
thf(x_decl,type,
x: int ).
thf(y_decl,type,
y: int ).
thf(12,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_63_zero__less__power2) ).
thf(153,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)],[12]) ).
thf(97,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(448,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(64,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_61_zero__eq__power2) ).
thf(314,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)],[64]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_mult__nat__number__of) ).
thf(138,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(104,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I39_J) ).
thf(479,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(44,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I2_J) ).
thf(249,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_semiring__norm_I112_J) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ zero_zero )
= ( pls @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(114,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_37_left__distrib__number__of) ).
thf(523,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)],[114]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_zadd__power2) ).
thf(379,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(96,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I38_J) ).
thf(440,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(3,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(120,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(247,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(20,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_nat__mult__2__right) ).
thf(185,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(88,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_47_rel__simps_I16_J) ).
thf(417,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)],[88]) ).
thf(94,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(436,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(71,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(357,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(24,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(196,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(5,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(125,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(69,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_add__nat__number__of) ).
thf(344,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(31,axiom,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zprime__power__zdvd__cancel__right) ).
thf(216,plain,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(65,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(321,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)],[65]) ).
thf(4,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_40_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)],[4]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_one__power2) ).
thf(397,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(54,axiom,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_m1) ).
thf(280,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(57,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(293,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(86,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_33_mult__Bit0) ).
thf(411,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)],[86]) ).
thf(40,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_52_add__Bit0__Bit1) ).
thf(243,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)],[40]) ).
thf(63,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_not__sum__power2__lt__zero) ).
thf(312,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(27,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_41_mult__number__of__left) ).
thf(206,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)],[27]) ).
thf(43,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(248,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(116,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
<=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_zdvd__reduce) ).
thf(529,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( C @ ( int @ dvd_dvd ) ) )
=> ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) ) )
& ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( B @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_zadd__power3) ).
thf(366,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( B @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(67,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_n0) ).
thf(334,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(13,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(160,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(34,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_Bit0__Pls) ).
thf(229,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(25,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(197,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)],[25]) ).
thf(106,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_mult__Pls) ).
thf(493,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(21,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_5_power2__eq__square__number__of) ).
thf(188,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)],[21]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_power2__less__0) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
~ ( TA @ zero_zero @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(115,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_int__power) ).
thf(526,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(29,axiom,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14__0961_A_L_Aint_An_Advd_Av_A_094_A2_A_L_Aw_A_094_A2_096) ).
thf(212,plain,
pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
~ ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( A @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3__096_B_Bthesis_O_A_I_B_Bm1_O_Av_A_094_A2_A_L_Aw_A_094_A2_A_061_A_I1_A_L_Aint_An_J_A_K_Am1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(173,plain,
~ ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( A @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rel__simps_I4_J) ).
thf(129,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)],[7]) ).
thf(38,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_nat__1__add__1) ).
thf(237,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(48,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(266,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(59,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_semiring__norm_I113_J) ).
thf(298,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(91,axiom,
int @ linord581940658strict,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(430,plain,
int @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
! [A: nat,B: int,C: int] :
( ( C @ zprime )
=> ( ( A @ ( B @ ( int @ power_power ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_zprime__zdvd__power) ).
thf(161,plain,
! [A: nat,B: int,C: int] :
( ( C @ zprime )
=> ( ( A @ ( B @ ( int @ power_power ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I50_J) ).
thf(423,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(1,conjecture,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) )
!= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(118,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) )
!= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( w @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( v @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_semiring__numeral__0__eq__0) ).
thf(191,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(84,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_67_less__int__code_I13_J) ).
thf(402,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)],[84]) ).
thf(78,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(382,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)],[78]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_sum__squares__gt__zero__iff) ).
thf(335,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) )
=> ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(52,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( D @ ( E @ ( int @ dvd_dvd ) ) )
=> ( ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
<=> ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zdvd__period) ).
thf(274,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( D @ ( E @ ( int @ dvd_dvd ) ) )
=> ( ( ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) )
& ( ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
=> ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(109,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_t1) ).
thf(509,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(61,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_66_less__int__code_I16_J) ).
thf(303,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)],[61]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_number__of__Pls) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(73,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(362,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(98,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_8_add__special_I3_J) ).
thf(451,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)],[98]) ).
thf(117,axiom,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_xy) ).
thf(535,plain,
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( y @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( x @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(30,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_38_right__distrib__number__of) ).
thf(213,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)],[30]) ).
thf(105,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(483,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)],[105]) ).
thf(45,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_43_add__number__of__left) ).
thf(251,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)],[45]) ).
thf(113,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_nat__numeral__1__eq__1) ).
thf(521,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( B @ twoSqu1567020053sum2sq )
=> ( ( A @ twoSqu1567020053sum2sq )
=> ( A @ ( B @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_is__mult__sum2sq) ).
thf(278,plain,
! [A: int,B: int] :
( ( B @ twoSqu1567020053sum2sq )
=> ( ( A @ twoSqu1567020053sum2sq )
=> ( A @ ( B @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_less__number__of__int__code) ).
thf(223,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(81,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_34_add__Bit0__Bit0) ).
thf(394,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)],[81]) ).
thf(8,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(135,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,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_35_mn) ).
thf(267,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)],[49]) ).
thf(92,axiom,
int @ linordered_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(431,plain,
int @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zpower__int) ).
thf(209,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(111,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(516,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_not__sum__squares__lt__zero) ).
thf(355,plain,
! [TA: $tType] :
( ( TA @ linordered_ring )
=> ! [A: TA,B: TA] :
~ ( TA @ zero_zero @ ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_rel__simps_I12_J) ).
thf(458,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)],[100]) ).
thf(23,axiom,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_nQ1) ).
thf(194,plain,
~ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(55,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I44_J) ).
thf(282,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(87,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(414,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)],[87]) ).
thf(47,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_84_zadd__int__left) ).
thf(263,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)],[47]) ).
thf(19,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_42_arith__simps_I32_J) ).
thf(182,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)],[19]) ).
thf(66,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_44_add__number__of__eq) ).
thf(331,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)],[66]) ).
thf(108,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(502,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)],[108]) ).
thf(74,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_85_zadd__int) ).
thf(363,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)],[74]) ).
thf(26,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit0 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_number__of__Bit0) ).
thf(203,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit0 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(32,axiom,
~ ! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_A_I1_A_L_Aint_An_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(218,plain,
~ ! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [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 @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_sum__power2__gt__zero__iff) ).
thf(465,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) )
=> ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A
!= ( TA @ zero_zero ) )
| ( B
!= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(35,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(231,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(112,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_57_less__special_I1_J) ).
thf(517,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)],[112]) ).
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_59_less__special_I4_J) ).
thf(390,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(16,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_int__1) ).
thf(171,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(56,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_9_one__add__one__is__two) ).
thf(290,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)],[56]) ).
thf(110,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_rel__simps_I10_J) ).
thf(510,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)],[110]) ).
thf(37,axiom,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zprime__power__zdvd__cancel__left) ).
thf(235,plain,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(41,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(246,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(60,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_51_add__Bit1__Bit0) ).
thf(300,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)],[60]) ).
thf(93,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_rel__simps_I46_J) ).
thf(432,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(11,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(146,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)],[11]) ).
thf(39,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_60_less__special_I2_J) ).
thf(239,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)],[39]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zmult__int) ).
thf(268,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(72,axiom,
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
& ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_IH) ).
thf(358,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq )
& ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(95,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_62_zero__power2) ).
thf(437,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)],[95]) ).
thf(103,axiom,
~ ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
=> ~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_smaller_I2_J) ).
thf(474,plain,
~ ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
=> ~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ twoSqu1567020053sum2sq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(83,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat__number__of__Pls) ).
thf(400,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(58,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_56_less__special_I3_J) ).
thf(294,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)],[58]) ).
thf(6,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_7_add__special_I2_J) ).
thf(126,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)],[6]) ).
thf(9,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Numeral1__eq1__nat) ).
thf(136,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(101,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(464,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_int__mult) ).
thf(427,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(15,axiom,
! [A: nat,B: int,C: int] :
( ( ~ ( pls @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( C @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) ) ) )
& ( ( pls @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( C @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_nat__number__of__mult__left) ).
thf(163,plain,
! [A: nat,B: int,C: int] :
( ( ~ ( pls @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( C @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) ) ) )
& ( ( pls @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( C @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_even__less__0__iff) ).
thf(178,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( A @ ( TA @ plus_plus ) ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B = A )
| ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_zless__add1__eq) ).
thf(369,plain,
! [A: int,B: int] :
( ( ( ( B = A )
| ( A @ ( B @ ( int @ ord_less ) ) ) )
=> ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
=> ( ( B = A )
| ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_sum__squares__eq__zero__iff) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ linord581940658strict )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ times_times ) ) @ ( B @ ( B @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(62,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_nat__mult__2) ).
thf(309,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(36,axiom,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_zpower__zpower) ).
thf(232,plain,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(107,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_77_less__int__code_I15_J) ).
thf(496,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)],[107]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I49_J) ).
thf(454,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(539,plain,
$false,
inference(e,[status(thm)],[153,448,314,138,479,249,408,523,379,440,120,247,185,417,436,357,196,125,344,216,321,121,397,280,293,411,243,312,206,248,529,366,334,160,229,197,493,188,388,526,212,173,129,237,266,298,430,161,423,118,191,402,382,335,274,509,303,271,362,451,535,213,483,251,521,278,223,394,135,267,431,209,516,355,458,194,282,414,263,182,331,502,363,203,218,465,231,517,390,171,290,510,235,246,300,432,146,239,268,358,437,474,400,294,126,136,464,427,163,178,369,254,309,232,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN004_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.12/0.56 % Computer : n015.cluster.edu
% 0.12/0.56 % Model : x86_64 x86_64
% 0.12/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.56 % Memory : 8046.5625MB
% 0.12/0.56 % OS : Linux 6.8.0-71-generic
% 0.12/0.56 % CPULimit : 300
% 0.12/0.56 % WCLimit : 300
% 0.12/0.56 % DateTime : Sat Sep 26 04:28:43 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 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
% 0.16/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.67/1.20 % [INFO] Parsing done (318ms).
% 1.67/1.22 % [INFO] Running in sequential loop mode.
% 2.51/1.60 % [INFO] eprover registered as external prover.
% 2.51/1.61 % [INFO] Scanning for conjecture ...
% 2.92/1.80 % [INFO] Found a conjecture (or negated_conjecture) and 117 axioms. Running axiom selection ...
% 3.25/1.93 % [INFO] Axiom selection finished. Selected 115 axioms (removed 2 axioms).
% 3.71/2.11 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.71/2.13 % [INFO] Type checking passed.
% 3.71/2.14 % [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 ...
% 8.82/3.54 % External prover 'e' found a proof!
% 8.82/3.54 % [INFO] Killing All external provers ...
% 8.82/3.54 % Time passed: 2880ms (effective reasoning time: 2315ms)
% 8.82/3.54 % 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)>
% 8.82/3.54 % Axioms used in derivation (115): fact_62_zero__power2, fact_67_less__int__code_I13_J, fact_66_less__int__code_I16_J, fact_41_mult__number__of__left, fact_2__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_A_I1_A_L_Aint_An_J_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_Nat_Onat___Groups_Omonoid__mult, fact_40_less__number__of, fact_39_number__of__Pls, arity_Int_Oint___Rings_Olinordered__ring__strict, fact_13_numeral__1__eq__1, fact_0_m1, arity_Int_Oint___Rings_Olinordered__idom, arity_Nat_Onat___Rings_Osemiring__1, fact_93_number__of__Bit0, fact_72_zprime__power__zdvd__cancel__right, arity_Int_Oint___Int_Oring__char__0, fact_28_Bit0__Pls, fact_65_zprime__zdvd__power, fact_42_arith__simps_I32_J, fact_20_rel__simps_I48_J, fact_7_add__special_I2_J, fact_47_rel__simps_I16_J, fact_10_nQ1, arity_Int_Oint___Rings_Olinordered__ring, fact_33_mult__Bit0, fact_94_Numeral1__eq1__nat, fact_69_zpower__zpower, fact_52_add__Bit0__Bit1, fact_38_right__distrib__number__of, arity_Nat_Onat___Int_Onumber__semiring, fact_68_less__number__of__int__code, fact_53_IH, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_6_one__power2, fact_34_add__Bit0__Bit0, fact_46_nat__number__of__Pls, fact_44_add__number__of__eq, fact_58_mult__nat__number__of, arity_Int_Oint___Int_Onumber__semiring, fact_88_int__1, arity_Int_Oint___Int_Onumber__ring, fact_30_rel__simps_I2_J, fact_84_zadd__int__left, arity_Int_Oint___Rings_Osemiring__1, fact_8_add__special_I3_J, fact_18_eq__number__of, fact_11_smaller_I2_J, fact_97_is__mult__sum2sq, fact_16_zadd__power3, fact_25_rel__simps_I49_J, fact_5_power2__eq__square__number__of, fact_27_rel__simps_I38_J, fact_45_rel__simps_I12_J, fact_1_xy, fact_9_one__add__one__is__two, fact_17_t1, fact_71_not__sum__squares__lt__zero, fact_82_zpower__int, fact_79_semiring__numeral__0__eq__0, arity_Int_Oint___Groups_Omonoid__mult, fact_14__0961_A_L_Aint_An_Advd_Av_A_094_A2_A_L_Aw_A_094_A2_096, fact_19_rel__simps_I51_J, fact_23_rel__simps_I39_J, fact_74_nat__number__of__mult__left, fact_55_add__nat__number__of, fact_85_zadd__int, fact_32_mult__Pls, fact_43_add__number__of__left, arity_Int_Oint___Rings_Osemiring, fact_77_less__int__code_I15_J, fact_75_zdvd__period, fact_76_zdvd__reduce, fact_83_int__power, fact_61_zero__eq__power2, fact_80_semiring__norm_I112_J, fact_36_n0, fact_90_nat__mult__2, fact_48_rel__simps_I10_J, fact_29_rel__simps_I17_J, fact_51_add__Bit1__Bit0, fact_81_zless__add1__eq, fact_59_less__special_I4_J, fact_4_p, fact_50_nat__numeral__1__eq__1, arity_Nat_Onat___Int_Onumber, fact_15_zadd__power2, fact_86_zmult__int, fact_31_rel__simps_I14_J, fact_78_sum__squares__eq__zero__iff, fact_57_less__special_I1_J, fact_49_rel__simps_I4_J, fact_87_int__mult, fact_12_mult__Bit1, fact_89_semiring__norm_I113_J, arity_Nat_Onat___Rings_Osemiring, fact_22_rel__simps_I46_J, fact_54_nat__1__add__1, fact_35_mn, fact_56_less__special_I3_J, fact_64_even__less__0__iff, fact_63_zero__less__power2, fact_70_sum__squares__gt__zero__iff, fact_73_zprime__power__zdvd__cancel__left, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_91_nat__mult__2__right, fact_60_less__special_I2_J, fact_92_power2__less__0, fact_24_rel__simps_I50_J, fact_96_not__sum__power2__lt__zero, fact_21_double__eq__0__iff, fact_26_rel__simps_I44_J, fact_3__096_B_Bthesis_O_A_I_B_Bm1_O_Av_A_094_A2_A_L_Aw_A_094_A2_A_061_A_I1_A_L_Aint_An_J_A_K_Am1_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, fact_37_left__distrib__number__of, fact_95_sum__power2__gt__zero__iff
% 8.82/3.54 % No. of inferences in proof: 234
% 8.82/3.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2880 ms resp. 2315 ms w/o parsing
% 9.35/3.68 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.35/3.69 % [INFO] Killing All external provers ...
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