TSTP Solution File: NUM971_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM971_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:43:55 EDT 2023
% Result : Theorem 15.60s 4.05s
% Output : Refutation 16.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 157
% Syntax : Number of formulae : 296 ( 116 unt; 32 typ; 0 def)
% Number of atoms : 618 ( 166 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2566 ( 51 ~; 9 |; 93 &;2167 @)
% ( 53 <=>; 193 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 29 usr; 6 con; 0-3 aty)
% Number of variables : 317 ( 0 ^; 296 !; 0 ?; 317 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $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_0_type,type,
semiring_0:
!>[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(ring_11004092258visors_type,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
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(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(pp_type,type,
pp: bool > $o ).
thf(s_type,type,
s: int ).
thf(t_type,type,
t: int ).
thf(57,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_54_eq__0__number__of) ).
thf(352,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)],[57]) ).
thf(12,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_le__special_I4_J) ).
thf(152,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less_eq @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less_eq @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less_eq @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(121,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(545,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(109,axiom,
semiring_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(533,plain,
semiring_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(125,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(549,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(550,plain,
~ ( pp @ fFalse ),
inference(polarity_switch,[status(thm)],[549]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A )
<=> ( ord_less @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add1__zle__eq) ).
thf(472,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A )
=> ( ord_less @ int @ B @ A ) )
& ( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(55,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I5_J) ).
thf(340,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)],[55]) ).
thf(114,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(538,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I51_J) ).
thf(185,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)],[20]) ).
thf(73,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_70_number__of__add) ).
thf(417,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)],[73]) ).
thf(78,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls) ).
thf(436,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,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_32_rel__simps_I31_J) ).
thf(257,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)],[35]) ).
thf(18,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_eq @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I27_J) ).
thf(174,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)],[18]) ).
thf(70,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_67_less__number__of__int__code) ).
thf(404,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)],[70]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
<=> ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_le__nat__number__of) ).
thf(320,plain,
! [A: int,B: int] :
( ( ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) )
=> ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) ) )
& ( ( ~ ( ord_less_eq @ int @ B @ A )
=> ( ord_less_eq @ int @ B @ pls ) )
=> ( ord_less_eq @ nat @ ( number_number_of @ nat @ B ) @ ( number_number_of @ nat @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(126,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(551,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(564,plain,
( ( pp @ fTrue )
!= ( pp @ fFalse ) ),
inference(paramod_ordered,[status(thm)],[551,550]) ).
thf(565,plain,
fTrue != fFalse,
inference(simp,[status(thm)],[564]) ).
thf(66,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_add__special_I3_J) ).
thf(389,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(94,axiom,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_bin__less__0__simps_I1_J) ).
thf(503,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(504,plain,
~ ( ord_less @ int @ pls @ ( zero_zero @ int ) ),
inference(polarity_switch,[status(thm)],[503]) ).
thf(118,axiom,
linorder @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(542,plain,
linorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(19,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_16_eq__number__of) ).
thf(179,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)],[19]) ).
thf(24,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I39_J) ).
thf(211,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(42,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_rel__simps_I12_J) ).
thf(280,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)],[42]) ).
thf(6,axiom,
( ( t
= ( zero_zero @ int ) )
=> ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096t_A_061_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_061_A0_096) ).
thf(132,plain,
( ( t
= ( zero_zero @ int ) )
=> ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(37,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_number__of__Pls) ).
thf(265,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(103,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(527,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(45,axiom,
! [A: int] :
( ( ord_less @ int @ ( bit0 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I10_J) ).
thf(292,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)],[45]) ).
thf(82,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_79_less__int__def) ).
thf(452,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)],[82]) ).
thf(63,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_one__add__one__is__two) ).
thf(380,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(79,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Bit0__def) ).
thf(439,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(105,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(529,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(122,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(546,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(22,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_19_double__eq__0__iff) ).
thf(201,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)],[22]) ).
thf(110,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(534,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(47,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nat__numeral__1__eq__1) ).
thf(302,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(67,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add__special_I2_J) ).
thf(392,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [A: int] :
( ( ord_less @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I4_J) ).
thf(297,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)],[46]) ).
thf(75,axiom,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zero__is__num__zero) ).
thf(429,plain,
( ( zero_zero @ int )
= ( number_number_of @ int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(8,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_one__power2) ).
thf(137,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(89,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_86_le__number__of__eq__not__less) ).
thf(484,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)],[89]) ).
thf(100,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
= ( zero_zero @ int ) )
| ( A
= ( one_one @ int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_int__pos__lt__two__imp__zero__or__one) ).
thf(522,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ( ord_less @ int @ A @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) )
=> ( ( A
= ( zero_zero @ int ) )
| ( A
= ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(83,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_one__is__num__one) ).
thf(461,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(92,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_89_less__int__code_I15_J) ).
thf(493,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)],[92]) ).
thf(43,axiom,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_nat__number__of__Pls) ).
thf(285,plain,
( ( number_number_of @ nat @ pls )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(51,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_48_add__Bit0__Bit1) ).
thf(317,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)],[51]) ).
thf(17,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I21_J) ).
thf(169,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)],[17]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
<=> ( ( ord_less @ int @ B @ A )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_zless__add1__eq) ).
thf(420,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
=> ( ( ord_less @ int @ B @ A )
| ( B = A ) ) )
& ( ( ( ord_less @ int @ B @ A )
| ( B = A ) )
=> ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
ord_less_eq @ int @ pls @ pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I19_J) ).
thf(256,plain,
ord_less_eq @ int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(102,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(526,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(123,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(547,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I48_J) ).
thf(193,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)],[21]) ).
thf(113,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(537,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(3,axiom,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096_126_A1_A_060_061_At_096) ).
thf(128,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(129,plain,
~ ( ord_less_eq @ int @ ( one_one @ int ) @ t ),
inference(polarity_switch,[status(thm)],[128]) ).
thf(133,plain,
( ( t
!= ( zero_zero @ int ) )
| ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
( ( t
!= ( zero_zero @ int ) )
| ( ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) )
= ( zero_zero @ int ) ) ),
inference(lifteq,[status(thm)],[133]) ).
thf(31,axiom,
~ ( ord_less @ int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_rel__simps_I2_J) ).
thf(244,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(117,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(541,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(106,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(530,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(29,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Bit0__Pls) ).
thf(237,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(97,axiom,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_odd__nonzero) ).
thf(513,plain,
! [A: int] :
( ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A )
!= ( zero_zero @ int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(16,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(166,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( semiring_0 @ TA ) )
=> ! [A: int] :
( ( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ A ) )
= ( one_one @ TA ) ) )
& ( ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_power__0__left__number__of) ).
thf(161,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( semiring_0 @ TA ) )
=> ! [A: int] :
( ( ( ( number_number_of @ nat @ A )
= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ A ) )
= ( one_one @ TA ) ) )
& ( ( ( number_number_of @ nat @ A )
!= ( zero_zero @ nat ) )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ A ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_le__special_I2_J) ).
thf(149,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less_eq @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less_eq @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less_eq @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(93,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_90_bin__less__0__simps_I4_J) ).
thf(498,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)],[93]) ).
thf(54,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( bit1 @ A ) @ pls )
<=> ( ord_less @ int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I29_J) ).
thf(335,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)],[54]) ).
thf(116,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(540,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I49_J) ).
thf(219,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,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_37_add__number__of__left) ).
thf(274,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)],[40]) ).
thf(62,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_59_less__special_I1_J) ).
thf(377,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)],[62]) ).
thf(28,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_rel__simps_I38_J) ).
thf(230,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(245,plain,
~ ( ord_less @ int @ pls @ pls ),
inference(polarity_switch,[status(thm)],[244]) ).
thf(39,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_36_le__number__of) ).
thf(271,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)],[39]) ).
thf(88,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_85_number__of__reorient) ).
thf(477,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)],[88]) ).
thf(56,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_53_eq__number__of__0) ).
thf(345,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)],[56]) ).
thf(111,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(535,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(9,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_6_zero__power2) ).
thf(140,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)],[9]) ).
thf(99,axiom,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_le__imp__0__less) ).
thf(520,plain,
! [A: int] :
( ( ord_less_eq @ int @ ( zero_zero @ int ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( plus_plus @ int @ ( one_one @ int ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(33,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_30_rel__simps_I34_J) ).
thf(251,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)],[33]) ).
thf(13,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_10_le__special_I1_J) ).
thf(155,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)],[13]) ).
thf(4,axiom,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0960_A_060_061_As_A_094_A2_096) ).
thf(130,plain,
ord_less_eq @ int @ ( zero_zero @ int ) @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_rel__simps_I44_J) ).
thf(223,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4__096t_A_060_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_060_A0_096) ).
thf(135,plain,
( ( ord_less @ int @ t @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( plus_plus @ int @ ( power_power @ int @ s @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( one_one @ int ) ) @ ( zero_zero @ int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(95,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_92_bin__less__0__simps_I3_J) ).
thf(505,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)],[95]) ).
thf(76,axiom,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_semiring__norm_I113_J) ).
thf(431,plain,
( ( zero_zero @ nat )
= ( number_number_of @ nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(91,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_88_add__numeral__0__right) ).
thf(490,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)],[91]) ).
thf(107,axiom,
linorder @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(531,plain,
linorder @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(124,axiom,
linorder @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(548,plain,
linorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(61,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_58_less__special_I3_J) ).
thf(374,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)],[61]) ).
thf(90,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_87_add__numeral__0) ).
thf(487,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)],[90]) ).
thf(101,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(525,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(5,axiom,
ord_less @ int @ t @ ( one_one @ int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096t_A_060_A1_096) ).
thf(131,plain,
ord_less @ int @ t @ ( one_one @ int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(555,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
!= ( ord_less @ int @ pls @ pls ) ),
inference(paramod_ordered,[status(thm)],[131,245]) ).
thf(557,plain,
( ( t != pls )
| ( pls
!= ( one_one @ int ) ) ),
inference(simp,[status(thm)],[555]) ).
thf(72,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_69_even__less__0__iff) ).
thf(414,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)],[72]) ).
thf(53,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_50_power__eq__0__iff__number__of) ).
thf(327,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)],[53]) ).
thf(71,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_68_less__eq__number__of__int__code) ).
thf(409,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)],[71]) ).
thf(84,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Numeral1__eq1__nat) ).
thf(463,plain,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(1,conjecture,
$false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ $false,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(127,plain,
~ $false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_zless__imp__add1__zle) ).
thf(470,plain,
! [A: int,B: int] :
( ( ord_less @ int @ B @ A )
=> ( ord_less_eq @ int @ ( plus_plus @ int @ B @ ( one_one @ int ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(58,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_55_rel__simps_I33_J) ).
thf(359,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)],[58]) ).
thf(120,axiom,
semiring_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(544,plain,
semiring_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(65,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
<=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__special_I2_J) ).
thf(386,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
=> ( ord_less @ int @ ( bit1 @ pls ) @ A ) )
& ( ( ord_less @ int @ ( bit1 @ pls ) @ A )
=> ( ord_less @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(50,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_47_add__Bit1__Bit0) ).
thf(314,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)],[50]) ).
thf(10,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_7_zero__eq__power2) ).
thf(143,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)],[10]) ).
thf(85,axiom,
! [A: int] :
( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
<=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_odd__less__0__iff) ).
thf(465,plain,
! [A: int] :
( ( ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) )
=> ( ord_less @ int @ A @ ( zero_zero @ int ) ) )
& ( ( ord_less @ int @ A @ ( zero_zero @ int ) )
=> ( ord_less @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) @ ( zero_zero @ int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(554,plain,
( ( ord_less @ int @ t @ ( one_one @ int ) )
!= ( ord_less @ int @ pls @ ( zero_zero @ int ) ) ),
inference(paramod_ordered,[status(thm)],[131,504]) ).
thf(556,plain,
( ( t != pls )
| ( ( one_one @ int )
!= ( zero_zero @ int ) ) ),
inference(simp,[status(thm)],[554]) ).
thf(115,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(539,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(98,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_95_semiring__add__number__of) ).
thf(517,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)],[98]) ).
thf(48,axiom,
! [A: int] :
( ( ord_less_eq @ int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq @ int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_rel__simps_I22_J) ).
thf(304,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)],[48]) ).
thf(14,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_11_le__special_I3_J) ).
thf(158,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)],[14]) ).
thf(69,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_66_plus__numeral__code_I9_J) ).
thf(401,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)],[69]) ).
thf(32,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_29_rel__simps_I14_J) ).
thf(246,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)],[32]) ).
thf(23,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I46_J) ).
thf(207,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(64,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
<=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__special_I4_J) ).
thf(383,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( linordered_idom @ TA ) )
=> ! [A: int] :
( ( ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
=> ( ord_less @ int @ A @ ( bit1 @ pls ) ) )
& ( ( ord_less @ int @ A @ ( bit1 @ pls ) )
=> ( ord_less @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(536,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(44,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_41_rel__simps_I16_J) ).
thf(287,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)],[44]) ).
thf(77,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__Pls__right) ).
thf(433,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(96,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_Bit1__def) ).
thf(510,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(81,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_78_less__int__code_I13_J) ).
thf(447,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)],[81]) ).
thf(36,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_33_add__Bit0__Bit0) ).
thf(262,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)],[36]) ).
thf(30,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_27_rel__simps_I17_J) ).
thf(239,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)],[30]) ).
thf(38,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_35_less__number__of) ).
thf(268,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)],[38]) ).
thf(108,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(532,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(68,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_65_zero__less__power2) ).
thf(395,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)],[68]) ).
thf(104,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(528,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(41,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_38_add__number__of__eq) ).
thf(277,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)],[41]) ).
thf(80,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_77_less__int__code_I16_J) ).
thf(442,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)],[80]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
<=> ( ord_less_eq @ int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zle__add1__eq__le) ).
thf(369,plain,
! [A: int,B: int] :
( ( ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) )
=> ( ord_less_eq @ int @ B @ A ) )
& ( ( ord_less_eq @ int @ B @ A )
=> ( ord_less @ int @ B @ ( plus_plus @ int @ A @ ( one_one @ int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(49,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_46_rel__simps_I32_J) ).
thf(309,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)],[49]) ).
thf(119,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(543,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I50_J) ).
thf(215,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(59,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_56_rel__simps_I15_J) ).
thf(364,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)],[59]) ).
thf(1969,plain,
$false,
inference(cvc4,[status(thm)],[352,152,545,533,550,472,340,538,185,417,436,257,174,404,320,565,389,504,542,179,211,280,132,265,527,292,452,380,439,529,546,201,534,302,392,297,429,137,484,522,461,493,551,285,317,169,420,256,526,547,193,537,129,503,134,244,541,530,128,237,513,166,161,149,498,335,540,219,274,377,230,245,271,477,345,535,140,520,251,155,130,223,135,505,431,490,531,548,374,487,525,557,414,327,409,463,127,470,359,544,386,314,143,465,556,539,517,304,158,401,246,207,383,549,536,287,433,510,447,262,239,268,532,395,528,131,277,442,369,309,543,215,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : NUM971_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n008.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Thu May 18 16:41:10 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.93/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.01 % [INFO] Parsing done (176ms).
% 1.29/1.02 % [INFO] Running in sequential loop mode.
% 1.98/1.23 % [INFO] eprover registered as external prover.
% 1.98/1.23 % [INFO] cvc4 registered as external prover.
% 1.98/1.24 % [INFO] Scanning for conjecture ...
% 2.09/1.32 % [INFO] Found a conjecture and 124 axioms. Running axiom selection ...
% 2.29/1.34 % [INFO] Axiom selection finished. Selected 124 axioms (removed 0 axioms).
% 2.71/1.46 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.77/1.48 % [INFO] Type checking passed.
% 2.77/1.48 % [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 ...
% 15.60/4.05 % External prover 'cvc4' found a proof!
% 15.60/4.05 % [INFO] Killing All external provers ...
% 15.60/4.05 % Time passed: 3548ms (effective reasoning time: 3024ms)
% 15.60/4.05 % 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)>
% 15.60/4.05 % Axioms used in derivation (124): fact_51_rel__simps_I29_J, fact_76_Bit0__def, fact_73_semiring__norm_I113_J, fact_57_zle__add1__eq__le, fact_52_rel__simps_I5_J, fact_86_le__number__of__eq__not__less, fact_60_one__add__one__is__two, fact_75_add__Pls, fact_19_double__eq__0__iff, fact_13_numeral__1__eq__1, fact_67_less__number__of__int__code, fact_88_add__numeral__0__right, arity_Int_Oint___Rings_Olinordered__idom, fact_15_rel__simps_I27_J, arity_Nat_Onat___Rings_Osemiring__1, arity_Int_Oint___Int_Oring__char__0, fact_17_rel__simps_I51_J, fact_45_rel__simps_I22_J, fact_63_add__special_I3_J, fact_3__096t_A_061_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_061_A0_096, fact_41_rel__simps_I16_J, fact_71_zless__add1__eq, fact_54_eq__0__number__of, fact_65_zero__less__power2, fact_26_Bit0__Pls, fact_50_power__eq__0__iff__number__of, fact_85_number__of__reorient, fact_6_zero__power2, fact_23_rel__simps_I49_J, arity_Nat_Onat___Int_Onumber__semiring, fact_7_zero__eq__power2, arity_Nat_Onat___Power_Opower, fact_97_int__pos__lt__two__imp__zero__or__one, fact_25_rel__simps_I38_J, arity_Int_Oint___Rings_Ono__zero__divisors, fact_10_le__special_I1_J, fact_28_rel__simps_I2_J, fact_55_rel__simps_I33_J, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, fact_29_rel__simps_I14_J, fact_58_less__special_I3_J, fact_49_le__nat__number__of, fact_68_less__eq__number__of__int__code, arity_Int_Oint___Int_Onumber__semiring, fact_61_less__special_I4_J, fact_9_le__special_I4_J, arity_Int_Oint___Int_Onumber__ring, fact_48_add__Bit0__Bit1, arity_Int_Oint___Rings_Osemiring__1, fact_44_nat__numeral__1__eq__1, arity_HOL_Obool___Orderings_Olinorder, arity_Nat_Onat___Rings_Omult__zero, fact_70_number__of__add, fact_32_rel__simps_I31_J, fact_36_le__number__of, fact_2__096t_A_060_A1_096, fact_69_even__less__0__iff, fact_66_plus__numeral__code_I9_J, fact_47_add__Bit1__Bit0, fact_64_add__special_I2_J, fact_42_rel__simps_I10_J, fact_5_one__power2, fact_81_Numeral1__eq1__nat, arity_Nat_Onat___Orderings_Olinorder, fact_84_add1__zle__eq, fact_14_rel__simps_I21_J, fact_93_Bit1__def, fact_89_less__int__code_I15_J, arity_Nat_Onat___Rings_Osemiring__0, fact_87_add__numeral__0, fact_77_less__int__code_I16_J, fact_30_rel__simps_I34_J, fact_95_semiring__add__number__of, fact_74_add__Pls__right, fact_33_add__Bit0__Bit0, fact_90_bin__less__0__simps_I4_J, fact_78_less__int__code_I13_J, arity_Int_Oint___Orderings_Olinorder, fact_11_le__special_I3_J, fact_96_le__imp__0__less, fact_79_less__int__def, fact_16_eq__number__of, fact_24_rel__simps_I44_J, fact_12_power__0__left__number__of, fact_39_rel__simps_I12_J, fact_27_rel__simps_I17_J, fact_59_less__special_I1_J, fact_72_zero__is__num__zero, fact_22_rel__simps_I50_J, fact_83_zless__imp__add1__zle, fact_56_rel__simps_I15_J, fact_80_one__is__num__one, arity_Int_Oint___Power_Opower, fact_94_odd__nonzero, fact_38_add__number__of__eq, fact_21_rel__simps_I39_J, fact_18_rel__simps_I48_J, arity_Int_Oint___Rings_Osemiring__0, fact_91_bin__less__0__simps_I1_J, arity_Nat_Onat___Int_Onumber, fact_34_number__of__Pls, fact_46_rel__simps_I32_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_92_bin__less__0__simps_I3_J, fact_0__096_126_A1_A_060_061_At_096, fact_8_le__special_I2_J, fact_1__0960_A_060_061_As_A_094_A2_096, fact_53_eq__number__of__0, fact_4__096t_A_060_A0_A_061_061_062_As_A_094_A2_A_L_A1_A_060_A0_096, help_pp_1_1_U, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_40_nat__number__of__Pls, fact_82_odd__less__0__iff, fact_31_rel__simps_I19_J, fact_43_rel__simps_I4_J, arity_Int_Oint___Int_Onumber, fact_35_less__number__of, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Int_Oint___Rings_Omult__zero, fact_20_rel__simps_I46_J, help_pp_2_1_U, arity_Nat_Onat___Rings_Ozero__neq__one, fact_62_less__special_I2_J, fact_37_add__number__of__left
% 15.60/4.05 % No. of inferences in proof: 264
% 15.60/4.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3548 ms resp. 3024 ms w/o parsing
% 16.17/4.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.17/4.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------