%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM925^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:18:17 AM UTC 2026
% Result : Theorem 5.72s 3.01s
% Output : Refutation 6.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 107
% Syntax : Number of formulae : 216 ( 206 unt; 0 typ; 0 def)
% Number of atoms : 400 ( 283 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 1081 ( 43 ~; 8 |; 14 &; 998 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 236 ( 0 ^; 236 !; 0 ?; 236 :)
% Comments :
%------------------------------------------------------------------------------
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(one_one_int_decl,type,
one_one_int: int ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_int_decl,type,
plus_plus_int: int > int > int ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > nat > nat ).
thf(zero_zero_int_decl,type,
zero_zero_int: int ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_int_decl,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > nat ).
thf(semiri1621563631at_int_decl,type,
semiri1621563631at_int: nat > int ).
thf(semiri984289939at_nat_decl,type,
semiri984289939at_nat: nat > nat ).
thf(ord_less_int_decl,type,
ord_less_int: int > int > $o ).
thf(ord_less_nat_decl,type,
ord_less_nat: nat > nat > $o ).
thf(power_power_int_decl,type,
power_power_int: int > nat > int ).
thf(power_power_nat_decl,type,
power_power_nat: nat > nat > nat ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: int ).
thf(88,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_rel__simps_I39_J) ).
thf(352,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(59,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__one__add__one__is__two) ).
thf(257,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(95,axiom,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zadd__0) ).
thf(372,plain,
! [A: int] :
( ( plus_plus_int @ zero_zero_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(4,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_eq__number__of) ).
thf(115,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,axiom,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_int__1) ).
thf(276,plain,
( ( semiri1621563631at_int @ one_one_nat )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(55,axiom,
! [A: nat] :
( ( number_number_of_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_number__of__int) ).
thf(247,plain,
! [A: nat] :
( ( number_number_of_int @ ( semiri1621563631at_int @ A ) )
= ( semiri1621563631at_int @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(37,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__int__code_I13_J) ).
thf(202,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(14,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_semiring__norm_I112_J) ).
thf(142,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(84,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_add__Bit0__Bit0) ).
thf(340,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( bit0 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(68,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_69_odd__less__0) ).
thf(284,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(108,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring__numeral__0__eq__0) ).
thf(416,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(18,axiom,
! [A: nat] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ A ) )
= ( semiri984289939at_nat @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_number__of__int) ).
thf(152,plain,
! [A: nat] :
( ( number_number_of_nat @ ( semiri1621563631at_int @ A ) )
= ( semiri984289939at_nat @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(43,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_nat__1__add__1) ).
thf(216,plain,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_Numeral1__eq1__nat) ).
thf(164,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(77,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_semiring__one__add__one__is__two) ).
thf(321,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(6,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_less__number__of__int__code) ).
thf(121,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I16_J) ).
thf(147,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(104,axiom,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_numeral__1__eq__1) ).
thf(397,plain,
( ( number_number_of_int @ ( bit1 @ pls ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(71,axiom,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_add__Pls) ).
thf(293,plain,
! [A: int] :
( ( plus_plus_int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(10,axiom,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_zero__power2) ).
thf(132,plain,
( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(62,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_less__special_I3_J) ).
thf(265,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(39,axiom,
ord_less_nat @ zero_zero_nat @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_n0) ).
thf(206,plain,
ord_less_nat @ zero_zero_nat @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(98,axiom,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(380,plain,
! [A: int] :
( ( ( plus_plus_int @ A @ A )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(45,axiom,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_power2__less__0) ).
thf(220,plain,
! [A: int] :
~ ( ord_less_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(93,axiom,
! [A: nat] :
( ( ( semiri1621563631at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_int__eq__0__conv) ).
thf(366,plain,
! [A: nat] :
( ( ( semiri1621563631at_int @ A )
= zero_zero_int )
= ( A = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_rel__simps_I48_J) ).
thf(334,plain,
! [A: int,B: int] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(74,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_power__0__left__number__of) ).
thf(302,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= one_one_nat ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ A ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(87,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_less__int__code_I15_J) ).
thf(349,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(33,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(192,plain,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zless__add1__eq) ).
thf(137,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
= ( ( ord_less_int @ A @ B )
| ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(48,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I14_J) ).
thf(229,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(35,axiom,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zadd__0__right) ).
thf(197,plain,
! [A: int] :
( ( plus_plus_int @ A @ zero_zero_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(91,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_one__add__one__is__two) ).
thf(361,plain,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_sum__power2__gt__zero__iff) ).
thf(188,plain,
! [A: int,B: int] :
( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( ( A != zero_zero_int )
| ( B != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(101,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_zadd__left__commute) ).
thf(388,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(89,axiom,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_rel__simps_I4_J) ).
thf(356,plain,
! [A: int] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(24,axiom,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_rel__simps_I12_J) ).
thf(169,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zless__linear) ).
thf(124,plain,
! [A: int,B: int] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(58,axiom,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(256,plain,
ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(1,conjecture,
( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
!= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(80,axiom,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add__special_I2_J) ).
thf(328,plain,
! [A: int] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(11,axiom,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_quartic__square__square) ).
thf(134,plain,
! [A: int] :
( ( power_power_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,axiom,
ord_less_int @ zero_zero_int @ one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_int__0__less__1) ).
thf(205,plain,
ord_less_int @ zero_zero_int @ one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__simps_I10_J) ).
thf(343,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
= ( ord_less_int @ A @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(51,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_nat__numeral__1__eq__1) ).
thf(237,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__int__code_I16_J) ).
thf(166,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(72,axiom,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__numeral__0__right) ).
thf(296,plain,
! [A: int] :
( ( plus_plus_int @ A @ ( number_number_of_int @ pls ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(96,axiom,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__special_I4_J) ).
thf(375,plain,
! [A: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( ord_less_int @ A @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_number__of__reorient) ).
thf(118,plain,
! [A: int,B: int] :
( ( ( number_number_of_int @ A )
= B )
= ( B
= ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(67,axiom,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_number__of__reorient) ).
thf(281,plain,
! [A: int,B: nat] :
( ( ( number_number_of_nat @ A )
= B )
= ( B
= ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_number__of__add) ).
thf(259,plain,
! [A: int,B: int] :
( ( number_number_of_int @ ( plus_plus_int @ A @ B ) )
= ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(32,axiom,
ord_less_int @ one_one_int @ t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(191,plain,
ord_less_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_zadd__commute) ).
thf(402,plain,
! [A: int,B: int] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(102,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_less__special_I1_J) ).
thf(391,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ pls @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(76,axiom,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power__0__left__number__of) ).
thf(313,plain,
! [A: int] :
( ( ( ( number_number_of_nat @ A )
= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= one_one_int ) )
& ( ( ( number_number_of_nat @ A )
!= zero_zero_nat )
=> ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ A ) )
= zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(15,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_add__number__of__left) ).
thf(144,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( plus_plus_int @ ( number_number_of_int @ B ) @ C ) )
= ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(28,axiom,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__number__of__Pls) ).
thf(181,plain,
( ( number_number_of_nat @ pls )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__special_I3_J) ).
thf(172,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(54,axiom,
pls = zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Pls__def) ).
thf(245,plain,
pls = zero_zero_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(78,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_Bit1__def) ).
thf(323,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(13,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I2_J) ).
thf(140,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_zpower__int) ).
thf(213,plain,
! [A: nat,B: nat] :
( ( power_power_int @ ( semiri1621563631at_int @ A ) @ B )
= ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(19,axiom,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_zero__eq__power2) ).
thf(155,plain,
! [A: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int )
= ( A = zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_one__is__num__one) ).
thf(130,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_zadd__int) ).
thf(399,plain,
! [A: nat,B: nat] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( semiri1621563631at_int @ B ) )
= ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(66,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_63_bin__less__0__simps_I3_J) ).
thf(278,plain,
! [A: int] :
( ( ord_less_int @ ( bit0 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(46,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_rel__simps_I38_J) ).
thf(223,plain,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
= ( pls = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_int__int__eq) ).
thf(394,plain,
! [A: nat,B: nat] :
( ( ( semiri1621563631at_int @ A )
= ( semiri1621563631at_int @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(73,axiom,
! [A: nat,B: nat,C: int] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_zadd__int__left) ).
thf(299,plain,
! [A: nat,B: nat,C: int] :
( ( plus_plus_int @ ( semiri1621563631at_int @ A ) @ ( plus_plus_int @ ( semiri1621563631at_int @ B ) @ C ) )
= ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ A @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(47,axiom,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(226,plain,
! [A: int,B: int] :
( ( ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( B = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_one__power2) ).
thf(162,plain,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(3,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_less__number__of) ).
thf(112,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(34,axiom,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_int__less__0__conv) ).
thf(194,plain,
! [A: nat] :
~ ( ord_less_int @ ( semiri1621563631at_int @ A ) @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,axiom,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_semiring__norm_I113_J) ).
thf(150,plain,
( zero_zero_nat
= ( number_number_of_nat @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(75,axiom,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_int__power) ).
thf(310,plain,
! [A: nat,B: nat] :
( ( semiri1621563631at_int @ ( power_power_nat @ A @ B ) )
= ( power_power_int @ ( semiri1621563631at_int @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(81,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add__Bit1__Bit0) ).
thf(331,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(8,axiom,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_zadd__assoc) ).
thf(127,plain,
! [A: int,B: int,C: int] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_int__0) ).
thf(359,plain,
( ( semiri1621563631at_int @ zero_zero_nat )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(26,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_61_bin__less__0__simps_I4_J) ).
thf(175,plain,
! [A: int] :
( ( ord_less_int @ ( bit1 @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(100,axiom,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zadd__strict__right__mono) ).
thf(386,plain,
! [A: int,B: int,C: int] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(56,axiom,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_rel__simps_I50_J) ).
thf(250,plain,
! [A: int,B: int] :
( ( bit1 @ A )
!= ( bit0 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(92,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Bit0__def) ).
thf(363,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(44,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_number__of__Pls) ).
thf(218,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(20,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_100_odd__nonzero) ).
thf(158,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)],[20]) ).
thf(30,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_Bit0__Pls) ).
thf(186,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
~ ( ord_less_int @ pls @ zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_bin__less__0__simps_I1_J) ).
thf(235,plain,
~ ( ord_less_int @ pls @ zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(40,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I44_J) ).
thf(207,plain,
! [A: int] :
( ( ( bit0 @ A )
= pls )
= ( A = pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rel__simps_I49_J) ).
thf(272,plain,
! [A: int,B: int] :
( ( bit0 @ A )
!= ( bit1 @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(99,axiom,
zero_zero_int != one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_int__0__neq__1) ).
thf(383,plain,
zero_zero_int != one_one_int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rel__simps_I17_J) ).
thf(346,plain,
! [A: int,B: int] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
= ( ord_less_int @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zero__less__power2) ).
thf(287,plain,
! [A: int] :
( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( A != zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(70,axiom,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__numeral__0) ).
thf(290,plain,
! [A: int] :
( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(97,axiom,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_semiring__norm_I110_J) ).
thf(378,plain,
( one_one_int
= ( number_number_of_int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(61,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_add__number__of__eq) ).
thf(262,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(107,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_40_add__nat__number__of) ).
thf(405,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)],[107]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_add__Bit0__Bit1) ).
thf(183,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
= ( bit1 @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(41,axiom,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_rel__simps_I51_J) ).
thf(210,plain,
! [A: int,B: int] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(79,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zero__is__num__zero) ).
thf(326,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(63,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I46_J) ).
thf(268,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_plus__numeral__code_I9_J) ).
thf(239,plain,
! [A: int,B: int] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
= ( number_number_of_int @ ( plus_plus_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_power__eq__0__iff__number__of) ).
thf(242,plain,
! [A: int,B: int] :
( ( ( power_power_int @ A @ ( number_number_of_nat @ B ) )
= zero_zero_int )
= ( ( A = zero_zero_int )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(36,axiom,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__power2) ).
thf(200,plain,
( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(27,axiom,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_power__eq__0__iff__number__of) ).
thf(178,plain,
! [A: nat,B: int] :
( ( ( power_power_nat @ A @ ( number_number_of_nat @ B ) )
= zero_zero_nat )
= ( ( A = zero_zero_nat )
& ( ( number_number_of_nat @ B )
!= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(94,axiom,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_even__less__0__iff) ).
thf(369,plain,
! [A: int] :
( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
= ( ord_less_int @ A @ zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(57,axiom,
( ( number_number_of_int @ pls )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_semiring__numeral__0__eq__0) ).
thf(254,plain,
( ( number_number_of_int @ pls )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(83,axiom,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add__Pls__right) ).
thf(337,plain,
! [A: int] :
( ( plus_plus_int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(49,axiom,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__special_I2_J) ).
thf(232,plain,
! [A: int] :
( ( ord_less_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( ord_less_int @ ( bit1 @ pls ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(422,plain,
$false,
inference(e,[status(thm)],[352,257,372,115,276,247,202,142,340,284,416,152,216,164,321,121,147,397,293,132,265,206,380,220,366,334,302,349,192,137,229,197,361,188,388,356,169,124,256,109,328,134,205,343,237,166,296,375,118,281,259,191,402,391,313,144,181,172,245,323,140,213,155,130,399,278,223,394,299,226,162,112,194,150,310,331,127,359,175,386,250,363,218,158,186,235,207,272,383,346,287,290,378,262,405,183,210,326,268,239,242,200,178,369,254,337,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.22 % Computer : n019.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.23 % CPULimit : 300
% 0.11/0.23 % WCLimit : 300
% 0.11/0.23 % DateTime : Tue Sep 29 13:05:48 UTC 2026
% 0.11/0.23 % CPUTime :
% 0.11/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.00/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.10 % [INFO] Parsing done (289ms).
% 1.43/1.12 % [INFO] Running in sequential loop mode.
% 2.42/1.50 % [INFO] eprover registered as external prover.
% 2.42/1.51 % [INFO] Scanning for conjecture ...
% 2.60/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 2.79/1.72 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 3.05/1.84 % [INFO] Problem is higher-order (TPTP THF).
% 3.05/1.86 % [INFO] Type checking passed.
% 3.05/1.86 % [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 ...
% 5.72/3.00 % External prover 'e' found a proof!
% 5.72/3.00 % [INFO] Killing All external provers ...
% 5.72/3.00 % Time passed: 2622ms (effective reasoning time: 1877ms)
% 5.72/3.00 % 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)>
% 5.72/3.00 % Axioms used in derivation (106): fact_59_rel__simps_I10_J, fact_81_add__Pls, fact_82_add__Bit0__Bit0, fact_2_sum__power2__eq__zero__iff, fact_33_nat__1__add__1, fact_57_less__int__code_I15_J, fact_28_int__1, fact_36_rel__simps_I2_J, fact_70_double__eq__0__iff, fact_92_power__eq__0__iff__number__of, fact_49_even__less__0__iff, fact_91_add__numeral__0__right, fact_25_int__power, fact_37_less__int__code_I13_J, fact_4_one__power2, fact_58_rel__simps_I16_J, fact_95_add__number__of__eq, fact_31_int__eq__0__conv, fact_46_number__of__reorient, fact_19_zless__linear, fact_53_int__int__eq, fact_80_add__Pls__right, fact_54_less__special_I3_J, fact_7_zero__eq__power2, fact_11_semiring__one__add__one__is__two, fact_6_zero__power2, fact_68_less__special_I2_J, fact_61_bin__less__0__simps_I4_J, fact_29_nat__number__of__Pls, fact_50_zadd__assoc, fact_8_add__special_I2_J, fact_101_number__of__int, fact_17_numeral__1__eq__1, fact_88_number__of__Pls, fact_71_rel__simps_I46_J, fact_73_rel__simps_I50_J, fact_42_nat__numeral__1__eq__1, fact_39_zadd__strict__right__mono, fact_62_bin__less__0__simps_I1_J, fact_99_Bit1__def, fact_16_semiring__norm_I110_J, fact_56_rel__simps_I12_J, fact_26_zadd__int__left, fact_63_bin__less__0__simps_I3_J, fact_102_number__of__int, fact_77_Bit0__Pls, fact_103_zero__less__power2, fact_27_zadd__int, fact_1_t1, fact_23_zero__is__num__zero, fact_86_semiring__numeral__0__eq__0, fact_87_semiring__numeral__0__eq__0, fact_47_rel__simps_I51_J, fact_75_rel__simps_I44_J, fact_20_less__number__of__int__code, fact_69_odd__less__0, fact_83_Bit0__def, fact_48_rel__simps_I48_J, fact_44_eq__number__of, fact_10_one__add__one__is__two, fact_105_sum__power2__gt__zero__iff, fact_9_add__special_I3_J, fact_65_zless__add1__eq, fact_104_power2__less__0, fact_89_semiring__norm_I112_J, fact_74_rel__simps_I49_J, fact_78_Pls__def, fact_38_rel__simps_I14_J, fact_84_zadd__0__right, fact_85_zadd__0, fact_93_power__eq__0__iff__number__of, fact_96_number__of__add, fact_14_power__0__left__number__of, fact_98_add__Bit0__Bit1, fact_52_zadd__commute, fact_72_rel__simps_I39_J, fact_41_one__is__num__one, fact_76_rel__simps_I38_J, fact_79_int__0__neq__1, fact_100_odd__nonzero, fact_66_int__less__0__conv, fact_97_add__Bit1__Bit0, fact_40_add__nat__number__of, fact_22_less__number__of, fact_5_zero__power2, fact_30_semiring__norm_I113_J, fact_51_zadd__left__commute, fact_60_rel__simps_I4_J, fact_12_semiring__one__add__one__is__two, fact_34_less__int__code_I16_J, fact_18_n0, fact_55_less__special_I1_J, fact_24_zpower__int, fact_0_n1pos, fact_90_add__numeral__0, fact_35_rel__simps_I17_J, fact_32_int__0, fact_67_less__special_I4_J, fact_13_quartic__square__square, fact_43_Numeral1__eq1__nat, fact_45_number__of__reorient, fact_3_one__power2, fact_21_plus__numeral__code_I9_J, fact_15_power__0__left__number__of, fact_94_add__number__of__left, fact_64_int__0__less__1
% 5.72/3.00 % No. of inferences in proof: 216
% 5.72/3.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2622 ms resp. 1877 ms w/o parsing
% 6.41/3.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.41/3.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------