TSTP Solution File: NUN017_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUN017_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:46:06 EDT 2023
% Result : Theorem 6.89s 2.67s
% Output : Refutation 7.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 167
% Syntax : Number of formulae : 306 ( 128 unt; 30 typ; 0 def)
% Number of atoms : 642 ( 167 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2883 ( 42 ~; 3 |; 99 &;2475 @)
% ( 55 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 5 con; 0-3 aty)
% Number of variables : 350 ( 0 ^; 330 !; 0 ?; 350 :)
% ( 20 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[TA: $tType] : $o ).
thf(number_ring_type,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(linorder_type,type,
linorder:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_type,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_type,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(n_type,type,
n: nat ).
thf(v_type,type,
v: int ).
thf(w_type,type,
w: int ).
thf(100,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(461,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__int__code_I16_J) ).
thf(503,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(131,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__Bit0__Bit0) ).
thf(581,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(78,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(365,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(75,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_rel__simps_I29_J) ).
thf(347,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(103,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I46_J) ).
thf(468,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(76,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_sum__power2__le__zero__iff) ).
thf(352,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less_eq @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) )
=> ( ord_less_eq @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( ord_less @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
<=> ( ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ pls @ A ) )
& ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_less__nat__number__of) ).
thf(408,plain,
! [A: int,B: int] :
( ( ( ord_less @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
=> ( ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ pls @ A ) )
& ( ord_less @ int @ B @ A ) ) )
& ( ( ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ pls @ A ) )
& ( ord_less @ int @ B @ A ) )
=> ( ord_less @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_add__number__of__eq) ).
thf(217,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(63,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(308,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__eq__0__iff) ).
thf(449,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
( v
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
thf(379,plain,
( v
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(34,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__eq__int__code_I16_J) ).
thf(202,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(138,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(597,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(85,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_semiring__numeral__0__eq__0) ).
thf(384,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(118,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(533,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(5,axiom,
number @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(142,plain,
number @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(104,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I51_J) ).
thf(472,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ B )
= ( bit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit1 @ B )
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(16,axiom,
number_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(153,plain,
number_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(60,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rel__simps_I21_J) ).
thf(301,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_semiring__norm_I113_J) ).
thf(257,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(121,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_nat__number__of__Pls) ).
thf(542,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(20,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(157,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
<=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_less__int__def) ).
thf(416,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ A )
=> ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) ) )
& ( ( ( ord_less_eq @ int @ B @ A )
& ( B != A ) )
=> ( ord_less @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(69,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_add__number__of__left) ).
thf(325,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(15,axiom,
linorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(152,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(65,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
~ ( ord_less @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_not__sum__power2__lt__zero) ).
thf(316,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
~ ( ord_less @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(37,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(216,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I16_J) ).
thf(492,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(67,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(321,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(44,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I32_J) ).
thf(238,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(105,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_rel__simps_I38_J) ).
thf(480,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(10,axiom,
linorder @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(147,plain,
linorder @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zero__is__num__zero) ).
thf(243,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(62,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(307,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(57,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_power2__eq__imp__eq) ).
thf(292,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ B )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(47,axiom,
! [A: int] :
( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_eq__0__number__of) ).
thf(248,plain,
! [A: int] :
( ( ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( zero_zero @ nat )
= ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__int__code_I13_J) ).
thf(439,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(39,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__eq__power2) ).
thf(220,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(79,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I44_J) ).
thf(366,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_plus__numeral__code_I9_J) ).
thf(260,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(93,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I15_J) ).
thf(429,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(19,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(156,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less_eq @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_le__special_I3_J) ).
thf(188,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [A: int] :
( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_eq__number__of__0) ).
thf(388,plain,
! [A: int] :
( ( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(135,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(593,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(4,axiom,
ring_11004092258visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(141,plain,
ring_11004092258visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(70,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
<=> ( ( B
!= ( zero_zero @ TA ) )
| ( A
!= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_sum__power2__gt__zero__iff) ).
thf(328,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
=> ( ( B
!= ( zero_zero @ TA ) )
| ( A
!= ( zero_zero @ TA ) ) ) )
& ( ( ( B
!= ( zero_zero @ TA ) )
| ( A
!= ( zero_zero @ TA ) ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(125,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_number__of__Pls) ).
thf(554,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(116,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I34_J) ).
thf(526,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(134,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_Bit0__def) ).
thf(590,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(73,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_add__Pls__right) ).
thf(343,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(77,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I33_J) ).
thf(360,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(111,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_bin__less__0__simps_I1_J) ).
thf(508,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(59,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__Pls) ).
thf(298,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(92,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I50_J) ).
thf(425,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(113,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( zero_zero @ TA )
= ( number_number_of @ TA @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_semiring__norm_I112_J) ).
thf(513,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( zero_zero @ TA )
= ( number_number_of @ TA @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(23,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I10_J) ).
thf(166,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
zero_neq_one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(148,plain,
zero_neq_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I14_J) ).
thf(161,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(129,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_even__less__0__iff) ).
thf(573,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( plus_plus @ TA @ A @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(96,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I5_J) ).
thf(444,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(12,axiom,
mult_zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(149,plain,
mult_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(132,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(584,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(127,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Bit0__Pls) ).
thf(562,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(29,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_le__number__of__eq__not__less) ).
thf(191,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( linorder @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) ) )
& ( ~ ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ B ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(55,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(286,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(50,axiom,
ord_less @ int @ ( zero_zero @ int ) @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0960_A_060_Av_A_094_A2_096) ).
thf(259,plain,
ord_less @ int @ ( zero_zero @ int ) @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_power2__less__imp__less) ).
thf(382,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(7,axiom,
linordered_semidom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(144,plain,
linordered_semidom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(109,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_bin__less__0__simps_I3_J) ).
thf(498,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit0 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(120,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_power2__less__0) ).
thf(540,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
~ ( ord_less @ TA @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(27,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(187,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__eq__int__code_I15_J) ).
thf(230,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(46,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__numeral__0__right) ).
thf(245,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(66,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ int @ A @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_less__special_I3_J) ).
thf(318,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_less__int__code_I14_J) ).
thf(434,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(86,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(387,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(124,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zero__le__power2) ).
thf(552,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(18,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(155,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_power2__le__imp__le) ).
thf(198,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: TA,B: TA] :
( ( ord_less_eq @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less_eq @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(101,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(462,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(136,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__0960_A_060_061_Aw_A_094_A2_096) ).
thf(594,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(3,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(140,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(115,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I31_J) ).
thf(521,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_sum__power2__eq__zero__iff) ).
thf(278,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) )
=> ( ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(98,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__add) ).
thf(455,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(61,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(306,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(40,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(226,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(117,axiom,
( pls
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_Pls__def) ).
thf(531,plain,
( pls
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(81,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I39_J) ).
thf(374,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(48,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sum__power2__ge__zero) ).
thf(255,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] : ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(106,axiom,
! [A: int] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_less__0__number__of) ).
thf(487,plain,
! [A: int] :
( ( ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(114,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__eq__int__code_I14_J) ).
thf(516,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(72,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I19_J) ).
thf(342,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_add__Bit1__Bit0) ).
thf(458,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(30,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(194,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(8,axiom,
number_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(145,plain,
number_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(126,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I17_J) ).
thf(557,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(58,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_semiring__add__number__of) ).
thf(295,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: int,B: int] :
( ( ord_less_eq @ int @ pls @ B )
=> ( ( ord_less_eq @ int @ pls @ A )
=> ( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(13,axiom,
no_zero_divisors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(150,plain,
no_zero_divisors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_add__nat__number__of) ).
thf(263,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ A ) ) )
& ( ~ ( ord_less @ int @ B @ pls )
=> ( ( ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ B ) ) )
& ( ~ ( ord_less @ int @ A @ pls )
=> ( ( plus_plus @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
= ( number_number_of @ nat @ ( plus_plus @ int @ B @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(133,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__eq__int__code_I13_J) ).
thf(585,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( bit0 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(102,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_rel__simps_I27_J) ).
thf(463,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
=> ( ord_less_eq @ int @ A @ pls ) )
& ( ( ord_less_eq @ int @ A @ pls )
=> ( ord_less_eq @ int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(130,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_less__number__of__int__code) ).
thf(576,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(122,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_rel__simps_I12_J) ).
thf(544,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ pls )
=> ( ord_less @ int @ A @ pls ) )
& ( ( ord_less @ int @ A @ pls )
=> ( ord_less @ int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_less__int__code_I15_J) ).
thf(177,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ int @ ( bit1 @ B ) @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__eq__number__of__int__code) ).
thf(182,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_eq__number__of) ).
thf(336,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(17,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(154,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(137,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I2_J) ).
thf(595,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(6,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(143,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(108,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(497,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_le__special_I1_J) ).
thf(158,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( A
!= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__less__power2) ).
thf(171,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( A
!= ( zero_zero @ TA ) ) )
& ( ( A
!= ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,conjecture,
ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(139,plain,
~ ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(82,axiom,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_n0) ).
thf(378,plain,
ord_less @ nat @ ( zero_zero @ nat ) @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(43,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_number__of__Bit0) ).
thf(235,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit0 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(112,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_add__Bit0__Bit1) ).
thf(510,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: int,B: TA] :
( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_power__eq__0__iff__number__of) ).
thf(207,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: int,B: TA] :
( ( ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ TA @ B @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(74,axiom,
linorder @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(346,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(123,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__number__of) ).
thf(549,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I49_J) ).
thf(536,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_bin__less__0__simps_I4_J) ).
thf(287,plain,
! [A: int] :
( ( ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( bit1 @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(14,axiom,
power @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(151,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(146,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(53,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I4_J) ).
thf(273,plain,
! [A: int] :
( ( ( ord_less @ int @ pls @ ( bit0 @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(373,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(128,axiom,
! [A: real,B: real] :
( ( ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
<=> ( ( B
= ( zero_zero @ real ) )
& ( A
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_realpow__two__sum__zero__iff) ).
thf(564,plain,
! [A: real,B: real] :
( ( ( ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) )
=> ( ( B
= ( zero_zero @ real ) )
& ( A
= ( zero_zero @ real ) ) ) )
& ( ( ( B
= ( zero_zero @ real ) )
& ( A
= ( zero_zero @ real ) ) )
=> ( ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(31,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ pls @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_less__special_I1_J) ).
thf(195,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ pls @ A ) )
& ( ( ord_less @ int @ pls @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I48_J) ).
thf(400,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ B )
= ( bit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit0 @ B )
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(88,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I22_J) ).
thf(395,plain,
! [A: int] :
( ( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq @ int @ pls @ A ) )
& ( ( ord_less_eq @ int @ pls @ A )
=> ( ord_less_eq @ int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(33,axiom,
( ( plus_plus @ int @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096v_A_094_A2_A_L_Aw_A_094_A2_A_061_A0_096) ).
thf(200,plain,
( ( plus_plus @ int @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(41,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__numeral__0) ).
thf(227,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_le__number__of) ).
thf(322,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int,B: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(64,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_number__of__reorient) ).
thf(309,plain,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( ( number_number_of @ TA @ B )
= A )
=> ( A
= ( number_number_of @ TA @ B ) ) )
& ( ( A
= ( number_number_of @ TA @ B ) )
=> ( ( number_number_of @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(215,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(598,plain,
$false,
inference(e,[status(thm)],[461,503,581,365,347,468,352,408,217,308,449,379,202,597,384,533,142,472,153,301,257,542,157,416,325,152,316,216,492,321,238,480,147,243,307,292,248,439,220,366,260,429,156,188,388,593,141,328,554,526,590,343,360,508,298,425,513,166,148,161,573,444,149,584,562,191,286,259,382,144,498,540,187,230,245,318,434,387,552,155,198,462,594,140,521,278,455,306,226,531,374,255,487,516,342,458,194,145,557,295,150,263,585,463,576,544,177,182,336,154,595,143,497,158,171,139,378,235,510,207,346,549,536,287,151,146,273,373,564,195,400,395,200,227,322,309,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUN017_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n004.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 21:03:10 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.84/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/0.98 % [INFO] Parsing done (177ms).
% 1.37/0.99 % [INFO] Running in sequential loop mode.
% 1.86/1.19 % [INFO] eprover registered as external prover.
% 1.86/1.20 % [INFO] cvc4 registered as external prover.
% 1.86/1.20 % [INFO] Scanning for conjecture ...
% 2.02/1.30 % [INFO] Found a conjecture and 138 axioms. Running axiom selection ...
% 2.31/1.38 % [INFO] Axiom selection finished. Selected 136 axioms (removed 2 axioms).
% 2.81/1.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.81/1.50 % [INFO] Type checking passed.
% 2.81/1.50 % [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 ...
% 6.89/2.67 % External prover 'e' found a proof!
% 6.89/2.67 % [INFO] Killing All external provers ...
% 6.89/2.67 % Time passed: 2171ms (effective reasoning time: 1677ms)
% 6.89/2.67 % 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)>
% 6.89/2.67 % Axioms used in derivation (136): fact_61_semiring__norm_I113_J, fact_39_add__number__of__left, fact_6_zero__eq__power2, fact_79_semiring__norm_I112_J, fact_54_add__nat__number__of, fact_11_add__Bit0__Bit1, fact_13_rel__simps_I4_J, fact_35_add__Bit0__Bit0, fact_46_less__0__number__of, arity_Int_Oint___Rings_Olinordered__idom, fact_43_rel__simps_I32_J, arity_Nat_Onat___Rings_Osemiring__1, fact_93_number__of__Bit0, arity_Int_Oint___Int_Oring__char__0, fact_69_less__int__code_I14_J, fact_86_bin__less__0__simps_I3_J, fact_27_Bit0__Pls, fact_63_less__eq__int__code_I13_J, fact_31_rel__simps_I34_J, fact_36_number__of__Pls, fact_68_less__eq__int__code_I15_J, fact_38_le__number__of, fact_62_less__eq__int__code_I16_J, fact_80_add__numeral__0, fact_45_rel__simps_I21_J, arity_RealDef_Oreal___Int_Onumber__semiring, fact_34_rel__simps_I31_J, arity_Nat_Onat___Int_Onumber__semiring, fact_22_rel__simps_I39_J, arity_Nat_Onat___Power_Opower, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_66_le__number__of__eq__not__less, fact_32_nat__number__of__Pls, fact_65_number__of__reorient, fact_15_rel__simps_I16_J, fact_74_add__Pls, fact_1__0960_A_060_Av_A_094_A2_096, fact_64_less__int__def, fact_2__0960_A_060_061_Aw_A_094_A2_096, fact_78_semiring__numeral__0__eq__0, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Int_Onumber__ring, fact_42_rel__simps_I22_J, fact_95_sum__power2__eq__zero__iff, arity_HOL_Obool___Orderings_Olinorder, fact_59_plus__numeral__code_I9_J, fact_16_n0, arity_Int_Oint___Rings_Osemiring__1, arity_Nat_Onat___Rings_Omult__zero, fact_33_rel__simps_I19_J, fact_28_rel__simps_I17_J, fact_90_power2__less__imp__less, fact_57_less__eq__number__of__int__code, fact_40_add__number__of__eq, fact_12_add__Bit1__Bit0, fact_47_less__nat__number__of, arity_Nat_Onat___Orderings_Olinorder, fact_75_Bit0__def, fact_24_rel__simps_I49_J, arity_RealDef_Oreal___Rings_Osemiring__1, fact_18_rel__simps_I51_J, fact_3__096v_A_094_A2_A_L_Aw_A_094_A2_A_061_A0_096, fact_96_realpow__two__sum__zero__iff, arity_RealDef_Oreal___Int_Onumber__ring, fact_29_rel__simps_I2_J, fact_21_rel__simps_I46_J, fact_94_power2__less__0, fact_92_sum__power2__ge__zero, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_70_Pls__def, arity_Int_Oint___Orderings_Olinorder, fact_23_rel__simps_I50_J, arity_Nat_Onat___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_73_add__Pls__right, fact_72_less__int__code_I13_J, fact_10_sum__power2__gt__zero__iff, fact_60_zero__is__num__zero, arity_RealDef_Oreal___Rings_Omult__zero, arity_RealDef_Oreal___Int_Oring__char__0, fact_88_power2__le__imp__le, fact_76_semiring__add__number__of, fact_51_rel__simps_I5_J, fact_53_rel__simps_I15_J, fact_85_bin__less__0__simps_I1_J, fact_0__096v_A_126_061_A0_096, fact_52_rel__simps_I33_J, arity_RealDef_Oreal___Rings_Ono__zero__divisors, fact_49_eq__0__number__of, arity_Int_Oint___Power_Opower, fact_91_sum__power2__le__zero__iff, fact_25_rel__simps_I44_J, fact_67_less__eq__int__code_I14_J, fact_58_less__number__of__int__code, arity_RealDef_Oreal___Orderings_Olinorder, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, fact_56_le__special_I1_J, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_37_less__number__of, fact_44_rel__simps_I27_J, fact_82_number__of__add, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_7_less__special_I1_J, fact_5_zero__power2, fact_20_double__eq__0__iff, arity_Int_Oint___Rings_Ozero__neq__one, fact_9_not__sum__power2__lt__zero, fact_4_zero__less__power2, fact_8_less__special_I3_J, fact_83_less__int__code_I15_J, fact_26_rel__simps_I38_J, fact_97_power__eq__0__iff__number__of, fact_14_rel__simps_I10_J, fact_71_less__int__code_I16_J, fact_77_even__less__0__iff, fact_50_rel__simps_I29_J, fact_81_add__numeral__0__right, arity_RealDef_Oreal___Power_Opower, fact_17_eq__number__of, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Int_Onumber, fact_87_power2__eq__imp__eq, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_19_rel__simps_I48_J, fact_84_bin__less__0__simps_I4_J, fact_55_le__special_I3_J, arity_Int_Oint___Rings_Omult__zero, fact_89_zero__le__power2, fact_30_rel__simps_I14_J, arity_Int_Oint___Rings_Olinordered__semidom, fact_48_eq__number__of__0, arity_Nat_Onat___Rings_Ozero__neq__one, fact_41_rel__simps_I12_J
% 6.89/2.67 % No. of inferences in proof: 276
% 6.89/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2171 ms resp. 1677 ms w/o parsing
% 7.25/2.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.25/2.76 % [INFO] Killing All external provers ...
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