%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM924_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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:10:20 AM UTC 2026
% Result : Theorem 7.47s 3.42s
% Output : Refutation 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 107
% Syntax : Number of formulae : 216 ( 102 unt; 0 typ; 0 def)
% Number of atoms : 463 ( 172 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1982 ( 34 ~; 9 |; 62 &;1701 @)
% ( 43 <=>; 133 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 9 con; 0-2 aty)
% Number of variables : 320 ( 0 ^; 320 !; 0 ?; 320 :)
% 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(times_times_int_decl,type,
times_times_int: int > int > int ).
thf(times_times_nat_decl,type,
times_times_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(zprime_decl,type,
zprime: int > $o ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_int_decl,type,
number_number_of_int: int > int ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > 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(ord_less_eq_int_decl,type,
ord_less_eq_int: int > int > $o ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_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(twoSqu1431725154sum2sq_decl,type,
twoSqu1431725154sum2sq: int > $o ).
thf(m_decl,type,
m: int ).
thf(s_decl,type,
s: int ).
thf(t_decl,type,
t: int ).
thf(58,axiom,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_le__imp__0__less) ).
thf(347,plain,
! [A: int] :
( ( A @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( one_one_int @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sum__power2__gt__zero__iff) ).
thf(335,plain,
! [A: int,B: int] :
( ( ( ( B != zero_zero_int )
| ( A != zero_zero_int ) )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( ( B != zero_zero_int )
| ( A != zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(78,axiom,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
thf(438,plain,
! [A: int] :
( ( A @ ( pls @ times_times_int ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(29,axiom,
! [A: int,B: int] :
( ( ( A @ bit1 )
= ( B @ bit1 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_rel__simps_I51_J) ).
thf(217,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ bit1 )
= ( B @ bit1 ) ) )
& ( ( ( A @ bit1 )
= ( B @ bit1 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(50,axiom,
! [A: int,B: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_not__sum__power2__lt__zero) ).
thf(308,plain,
! [A: int,B: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(93,axiom,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
<=> ( A = zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_zero__eq__power2) ).
thf(511,plain,
! [A: int] :
( ( ( A = zero_zero_int )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) )
= zero_zero_int )
=> ( A = zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(40,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_add__special_I2_J) ).
thf(269,plain,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ plus_plus_int ) )
= ( A @ ( pls @ bit1 @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(67,axiom,
! [A: int] :
( ( zero_zero_nat
= ( A @ number_number_of_nat ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_eq__0__number__of) ).
thf(385,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( zero_zero_nat
= ( A @ number_number_of_nat ) ) )
& ( ( zero_zero_nat
= ( A @ number_number_of_nat ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(66,axiom,
t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ twoSqu1431725154sum2sq,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_qf1pt) ).
thf(384,plain,
t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ twoSqu1431725154sum2sq,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(19,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_zpower__zadd__distrib) ).
thf(174,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ power_power_int ) )
= ( C @ ( A @ power_power_int ) @ ( B @ ( A @ power_power_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(46,axiom,
! [A: int] :
( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_le__special_I3_J) ).
thf(288,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( zero_zero_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(77,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zero__power2) ).
thf(436,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_int @ power_power_int ) )
= zero_zero_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(3,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_le__number__of) ).
thf(110,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_eq_int ) )
=> ( A @ ( B @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_zle__trans) ).
thf(125,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( ( A @ ( C @ ord_less_eq_int ) )
=> ( A @ ( B @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(84,axiom,
! [A: int,B: nat] :
( ( ( A @ number_number_of_nat )
= B )
<=> ( B
= ( A @ number_number_of_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_number__of__reorient) ).
thf(460,plain,
! [A: int,B: nat] :
( ( ( B
= ( A @ number_number_of_nat ) )
=> ( ( A @ number_number_of_nat )
= B ) )
& ( ( ( A @ number_number_of_nat )
= B )
=> ( B
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(23,axiom,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ ord_less_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zadd__zless__mono) ).
thf(189,plain,
! [A: int,B: int,C: int,D: int] :
( ( D @ ( C @ ord_less_int ) )
=> ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ ( D @ plus_plus_int ) @ ( A @ ( C @ plus_plus_int ) @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_less__eq__number__of__int__code) ).
thf(152,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(28,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_le__special_I1_J) ).
thf(211,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) ) )
& ( ( A @ number_number_of_int @ ( zero_zero_int @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [A: int] :
( ( ( A @ number_number_of_nat )
= zero_zero_nat )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_eq__number__of__0) ).
thf(480,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat )
= zero_zero_nat ) )
& ( ( ( A @ number_number_of_nat )
= zero_zero_nat )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(4,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_number__of__mult) ).
thf(116,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) @ number_number_of_int )
= ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_one__power2) ).
thf(312,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_nat @ power_power_nat ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(37,axiom,
! [A: int] :
( ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) )
<=> ( A @ ( pls @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__0__number__of) ).
thf(248,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_int ) )
=> ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) ) )
& ( ( A @ number_number_of_nat @ ( zero_zero_nat @ ord_less_nat ) )
=> ( A @ ( pls @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(63,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_one__power2) ).
thf(366,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( one_one_int @ power_power_int ) )
= one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(97,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( A @ number_number_of_int @ times_times_int ) @ ( B @ ( A @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_right__distrib__number__of) ).
thf(534,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( A @ number_number_of_int @ times_times_int ) @ ( B @ ( A @ number_number_of_int @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(49,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I22_J) ).
thf(302,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit1 @ ( pls @ ord_less_eq_int ) ) )
& ( ( A @ bit1 @ ( pls @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(59,axiom,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Numeral1__eq1__nat) ).
thf(349,plain,
( one_one_nat
= ( pls @ bit1 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(74,axiom,
pls @ ( pls @ ord_less_eq_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_rel__simps_I19_J) ).
thf(429,plain,
pls @ ( pls @ ord_less_eq_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(25,axiom,
zero_zero_int @ ( t @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096t_A_060_A0_096) ).
thf(197,plain,
zero_zero_int @ ( t @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(56,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ord_less_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_rel__simps_I5_J) ).
thf(329,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit1 @ ( pls @ ord_less_int ) ) )
& ( ( A @ bit1 @ ( pls @ ord_less_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(95,axiom,
! [A: int] :
( ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) )
<=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_le__special_I2_J) ).
thf(522,plain,
! [A: int] :
( ( ( A @ ( pls @ bit1 @ ord_less_eq_int ) )
=> ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) ) )
& ( ( A @ number_number_of_int @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( pls @ bit1 @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(101,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ times_times_int ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_semiring__mult__number__of) ).
thf(551,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ times_times_int ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(82,axiom,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_zmult__1) ).
thf(456,plain,
! [A: int] :
( ( A @ ( one_one_int @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(31,axiom,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_semiring__norm_I113_J) ).
thf(229,plain,
( zero_zero_nat
= ( pls @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(106,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( t @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_t__l__p) ).
thf(566,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( t @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_plus__numeral__code_I9_J) ).
thf(519,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( B @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(54,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rel__simps_I15_J) ).
thf(317,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(69,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring__add__number__of) ).
thf(403,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_int @ ( B @ number_number_of_int @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) )
<=> ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_less__nat__number__of) ).
thf(420,plain,
! [A: int,B: int] :
( ( ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) )
=> ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_nat ) )
=> ( ( B @ ( A @ ord_less_int ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( pls @ ord_less_int ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(1,conjecture,
zero_zero_int @ ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( zero_zero_int @ ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(109,plain,
~ ( zero_zero_int @ ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(88,axiom,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_nat__1__add__1) ).
thf(488,plain,
( ( one_one_nat @ ( one_one_nat @ plus_plus_nat ) )
= ( pls @ bit1 @ bit0 @ number_number_of_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(102,axiom,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_zero__power2) ).
thf(554,plain,
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( zero_zero_nat @ power_power_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(98,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__number__of__int__code) ).
thf(537,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__squares__eq__zero__iff) ).
thf(393,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(9,axiom,
! [A: int] : ( A @ ( A @ ord_less_eq_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zle__refl) ).
thf(129,plain,
! [A: int] : ( A @ ( A @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_semiring__mult__number__of) ).
thf(237,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ times_times_nat ) )
= ( A @ ( B @ times_times_int ) @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(92,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_zadd__assoc) ).
thf(508,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ plus_plus_int ) )
= ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(51,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
thf(311,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(71,axiom,
~ ( t @ ( one_one_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
thf(412,plain,
~ ( t @ ( one_one_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_semiring__add__number__of) ).
thf(430,plain,
! [A: int,B: int] :
( ( B @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(21,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
<=> ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_le__number__of__eq__not__less) ).
thf(180,plain,
! [A: int,B: int] :
( ( ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) )
=> ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) ) )
& ( ( B @ number_number_of_nat @ ( A @ number_number_of_nat @ ord_less_eq_nat ) )
=> ~ ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ ord_less_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
thf(149,plain,
! [A: int] :
( ( A @ number_number_of_int )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(24,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_rel__simps_I27_J) ).
thf(191,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_eq_int ) )
=> ( pls @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( pls @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(45,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zless__imp__add1__zle) ).
thf(286,plain,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(108,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_rel__simps_I31_J) ).
thf(577,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(39,axiom,
! [A: int,B: int] :
( ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_sum__squares__le__zero__iff) ).
thf(259,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) ) )
& ( ( zero_zero_int @ ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(70,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( pls @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_rel__simps_I29_J) ).
thf(406,plain,
! [A: int] :
( ( ( pls @ ( A @ ord_less_int ) )
=> ( pls @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( pls @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( pls @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
! [A: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_power2__less__0) ).
thf(274,plain,
! [A: int] :
~ ( zero_zero_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ord_less_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( ( A @ bit0 )
= ( B @ bit0 ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_rel__simps_I48_J) ).
thf(567,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ bit0 )
= ( B @ bit0 ) ) )
& ( ( ( A @ bit0 )
= ( B @ bit0 ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(36,axiom,
! [A: int,B: int,C: int] :
( ( C @ number_number_of_int @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ number_number_of_int @ ( B @ times_times_int ) @ ( C @ number_number_of_int @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_left__distrib__number__of) ).
thf(245,plain,
! [A: int,B: int,C: int] :
( ( C @ number_number_of_int @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ number_number_of_int @ ( B @ times_times_int ) @ ( C @ number_number_of_int @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(55,axiom,
! [A: int] :
( ( A @ ( one_one_int @ ord_less_eq_int ) )
<=> ( A @ ( zero_zero_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__one__le__iff__zero__less) ).
thf(323,plain,
! [A: int] :
( ( ( A @ ( zero_zero_int @ ord_less_int ) )
=> ( A @ ( one_one_int @ ord_less_eq_int ) ) )
& ( ( A @ ( one_one_int @ ord_less_eq_int ) )
=> ( A @ ( zero_zero_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(11,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zmult__assoc) ).
thf(140,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ times_times_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( A @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,axiom,
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
thf(240,plain,
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_add__nat__number__of) ).
thf(198,plain,
! [A: int,B: int] :
( ( ~ ( pls @ ( B @ ord_less_int ) )
=> ( ( ~ ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ ( B @ plus_plus_int ) @ number_number_of_nat ) ) )
& ( ( pls @ ( A @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( B @ number_number_of_nat ) ) ) ) )
& ( ( pls @ ( B @ ord_less_int ) )
=> ( ( A @ number_number_of_nat @ ( B @ number_number_of_nat @ plus_plus_nat ) )
= ( A @ number_number_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_zle__add1__eq__le) ).
thf(490,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) ) )
& ( ( one_one_int @ ( B @ plus_plus_int ) @ ( A @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(27,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( C @ ( A @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_zadd__left__mono) ).
thf(209,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ord_less_eq_int ) )
=> ( C @ ( A @ plus_plus_int ) @ ( B @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(104,axiom,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_add__special_I3_J) ).
thf(557,plain,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ plus_plus_int ) )
= ( pls @ bit1 @ ( A @ plus_plus_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(72,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rel__simps_I34_J) ).
thf(414,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(20,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_zless__linear) ).
thf(177,plain,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_int ) )
| ( A = B )
| ( B @ ( A @ ord_less_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(79,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_less__eq__int__code_I16_J) ).
thf(441,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(91,axiom,
! [A: int] :
( ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_le__special_I4_J) ).
thf(502,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( A @ ord_less_eq_int ) )
=> ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( one_one_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ( pls @ bit1 @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(8,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_eq_int ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_zle__linear) ).
thf(127,plain,
! [A: int,B: int] :
( ( A @ ( B @ ord_less_eq_int ) )
| ( B @ ( A @ ord_less_eq_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(86,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_int ) )
<=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zless__le) ).
thf(470,plain,
! [A: int,B: int] :
( ( ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) )
=> ( B @ ( A @ ord_less_int ) ) )
& ( ( B @ ( A @ ord_less_int ) )
=> ( ( A != B )
& ( B @ ( A @ ord_less_eq_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,axiom,
( ( t = zero_zero_int )
=> ( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_calculation_I2_J) ).
thf(314,plain,
( ( t = zero_zero_int )
=> ( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(12,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ times_times_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number_number_of_int @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mult__number__of__left) ).
thf(143,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ number_number_of_int @ times_times_int ) @ ( A @ number_number_of_int @ times_times_int ) )
= ( C @ ( B @ ( A @ times_times_int ) @ number_number_of_int @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(32,axiom,
! [A: int,B: int] :
( ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add1__zle__eq) ).
thf(231,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) ) )
& ( ( B @ ( one_one_int @ ( A @ plus_plus_int ) @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(81,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_less__int__code_I14_J) ).
thf(450,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
<=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_sum__power2__eq__zero__iff) ).
thf(368,plain,
! [A: int,B: int] :
( ( ( ( B = zero_zero_int )
& ( A = zero_zero_int ) )
=> ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int ) )
& ( ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( B @ power_power_int ) @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ plus_plus_int ) )
= zero_zero_int )
=> ( ( B = zero_zero_int )
& ( A = zero_zero_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(62,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_zadd__left__commute) ).
thf(363,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ plus_plus_int ) )
= ( C @ ( A @ plus_plus_int ) @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(103,axiom,
zero_zero_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(556,plain,
zero_zero_int @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ ( t @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(22,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_zadd__zmult__distrib) ).
thf(186,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ ( A @ plus_plus_int ) @ times_times_int ) )
= ( C @ ( B @ times_times_int ) @ ( C @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(18,axiom,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
thf(171,plain,
! [A: int,B: int] :
( ( B @ ( A @ plus_plus_int ) )
= ( A @ ( B @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_eq__number__of) ).
thf(158,plain,
! [A: int,B: int] :
( ( ( A = B )
=> ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) ) )
& ( ( ( A @ number_number_of_int )
= ( B @ number_number_of_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(60,axiom,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_zadd__zmult__distrib2) ).
thf(351,plain,
! [A: int,B: int,C: int] :
( ( C @ ( B @ plus_plus_int ) @ ( A @ times_times_int ) )
= ( C @ ( A @ times_times_int ) @ ( B @ ( A @ times_times_int ) @ plus_plus_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( B @ ( A @ bit0 @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_mult__Bit0) ).
thf(433,plain,
! [A: int,B: int] :
( ( B @ ( A @ bit0 @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(41,axiom,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
thf(272,plain,
( zero_zero_int
= ( pls @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(100,axiom,
! [A: int,B: int] : ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_sum__squares__ge__zero) ).
thf(549,plain,
! [A: int,B: int] : ( B @ ( B @ times_times_int ) @ ( A @ ( A @ times_times_int ) @ plus_plus_int ) @ ( zero_zero_int @ ord_less_eq_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(5,axiom,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_eq_int ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_zle__antisym) ).
thf(119,plain,
! [A: int,B: int] :
( ( B @ ( A @ ord_less_eq_int ) )
=> ( ( A @ ( B @ ord_less_eq_int ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_rel__simps_I32_J) ).
thf(378,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(48,axiom,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__number__of__Pls) ).
thf(300,plain,
( ( pls @ number_number_of_nat )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(80,axiom,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_zmult__1__right) ).
thf(447,plain,
! [A: int] :
( ( one_one_int @ ( A @ times_times_int ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(17,axiom,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
thf(168,plain,
! [A: int,B: int] :
( ( B @ ( A @ times_times_int ) )
= ( A @ ( B @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(13,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_arith__simps_I32_J) ).
thf(146,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(35,axiom,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ number_number_of_nat @ times_times_nat ) )
= ( C @ ( A @ number_number_of_nat @ times_times_nat ) @ ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_right__distrib__number__of) ).
thf(242,plain,
! [A: int,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat ) @ ( A @ number_number_of_nat @ times_times_nat ) )
= ( C @ ( A @ number_number_of_nat @ times_times_nat ) @ ( B @ ( A @ number_number_of_nat @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(47,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_less__eq__int__code_I13_J) ).
thf(294,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(44,axiom,
! [A: nat,B: nat,C: int] :
( ( C @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ number_number_of_nat @ ( B @ times_times_nat ) @ ( C @ number_number_of_nat @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_left__distrib__number__of) ).
thf(283,plain,
! [A: nat,B: nat,C: int] :
( ( C @ number_number_of_nat @ ( B @ ( A @ plus_plus_nat ) @ times_times_nat ) )
= ( C @ number_number_of_nat @ ( B @ times_times_nat ) @ ( C @ number_number_of_nat @ ( A @ times_times_nat ) @ plus_plus_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(96,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ord_less_eq_int ) )
<=> ( A @ ( pls @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_rel__simps_I21_J) ).
thf(528,plain,
! [A: int] :
( ( ( A @ ( pls @ ord_less_eq_int ) )
=> ( A @ bit0 @ ( pls @ ord_less_eq_int ) ) )
& ( ( A @ bit0 @ ( pls @ ord_less_eq_int ) )
=> ( A @ ( pls @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(83,axiom,
one_one_int @ ( t @ ord_less_int ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_calculation_I1_J) ).
thf(459,plain,
one_one_int @ ( t @ ord_less_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(10,axiom,
! [A: int,B: int] :
( ( ( A @ number_number_of_int )
= B )
<=> ( B
= ( A @ number_number_of_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_number__of__reorient) ).
thf(131,plain,
! [A: int,B: int] :
( ( ( B
= ( A @ number_number_of_int ) )
=> ( ( A @ number_number_of_int )
= B ) )
& ( ( ( A @ number_number_of_int )
= B )
=> ( B
= ( A @ number_number_of_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(43,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_less__eq__int__code_I15_J) ).
thf(277,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(6,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_times__numeral__code_I5_J) ).
thf(122,plain,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ times_times_int ) )
= ( B @ ( A @ times_times_int ) @ number_number_of_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(85,axiom,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_p) ).
thf(469,plain,
one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(61,axiom,
! [A: int] :
( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
<=> ( A != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_zero__less__power2) ).
thf(354,plain,
! [A: int] :
( ( ( A != zero_zero_int )
=> ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) ) )
& ( ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( A @ power_power_int ) @ ( zero_zero_int @ ord_less_int ) )
=> ( A != zero_zero_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
<=> ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_le__number__of__eq__not__less) ).
thf(543,plain,
! [A: int,B: int] :
( ( ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) )
=> ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) ) )
& ( ( B @ number_number_of_int @ ( A @ number_number_of_int @ ord_less_eq_int ) )
=> ~ ( A @ number_number_of_int @ ( B @ number_number_of_int @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(105,axiom,
! [A: int,B: int] :
( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_eq_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_less__eq__int__code_I14_J) ).
thf(560,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_eq_int ) )
=> ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) ) )
& ( ( B @ bit1 @ ( A @ bit0 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_eq_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(90,axiom,
! [A: int,B: int] :
( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
<=> ( B @ ( A @ ord_less_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_rel__simps_I33_J) ).
thf(496,plain,
! [A: int,B: int] :
( ( ( B @ ( A @ ord_less_int ) )
=> ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) ) )
& ( ( B @ bit0 @ ( A @ bit1 @ ord_less_eq_int ) )
=> ( B @ ( A @ ord_less_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(38,axiom,
~ ! [A: int] :
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
!= ( A @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) ).
thf(254,plain,
~ ! [A: int] :
( ( one_one_int @ ( pls @ bit1 @ bit0 @ number_number_of_nat @ ( s @ power_power_int ) @ plus_plus_int ) )
!= ( A @ ( one_one_int @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ number_number_of_int @ times_times_int ) @ plus_plus_int ) @ times_times_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(30,axiom,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat__numeral__1__eq__1) ).
thf(227,plain,
( ( pls @ bit1 @ number_number_of_nat )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(590,plain,
$false,
inference(e,[status(thm)],[347,335,438,217,308,511,269,385,384,174,288,436,110,125,460,189,152,211,480,116,312,248,366,534,302,349,429,197,329,522,551,456,229,566,519,317,403,420,109,488,554,537,393,129,237,508,311,412,430,180,149,191,286,577,259,406,274,567,245,323,140,240,198,490,209,557,414,177,441,502,127,470,314,143,231,450,368,363,556,186,171,158,351,433,272,549,119,378,300,447,168,146,242,294,283,528,459,131,277,122,469,354,543,560,496,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924_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
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 04:17:44 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.25 % [INFO] Parsing done (279ms).
% 1.47/1.27 % [INFO] Running in sequential loop mode.
% 2.39/1.66 % [INFO] eprover registered as external prover.
% 2.39/1.67 % [INFO] Scanning for conjecture ...
% 2.77/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 106 axioms. Running axiom selection ...
% 2.98/1.92 % [INFO] Axiom selection finished. Selected 106 axioms (removed 0 axioms).
% 3.34/2.07 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.34/2.09 % [INFO] Type checking passed.
% 3.34/2.09 % [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 ...
% 7.47/3.41 % External prover 'e' found a proof!
% 7.47/3.41 % [INFO] Killing All external provers ...
% 7.47/3.42 % Time passed: 2882ms (effective reasoning time: 2140ms)
% 7.47/3.42 % 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)>
% 7.47/3.42 % Axioms used in derivation (106): fact_105_zero__is__num__zero, fact_35_rel__simps_I34_J, fact_69_zmult__1__right, fact_43_semiring__mult__number__of, fact_47_number__of__mult, fact_53_le__number__of__eq__not__less, fact_39_zless__le, fact_99_left__distrib__number__of, fact_80_less__nat__number__of, fact_25_zmult__commute, fact_57_rel__simps_I32_J, fact_94_rel__simps_I51_J, fact_82_nat__numeral__1__eq__1, fact_64_le__special_I2_J, fact_85_add1__zle__eq, fact_66_mult__Pls, fact_95_rel__simps_I48_J, fact_97_sum__squares__eq__zero__iff, fact_68_less__number__of__int__code, fact_65_nat__1__add__1, fact_11_zero__less__power2, fact_86_zle__add1__eq__le, fact_13_one__power2, fact_73_zadd__zmult__distrib2, fact_49_sum__squares__ge__zero, fact_61_nat__number__of__Pls, fact_55_rel__simps_I22_J, fact_50_le__special_I3_J, fact_34_less__eq__int__code_I16_J, fact_98_left__distrib__number__of, fact_4_calculation_I2_J, fact_0__096t_A_060_A0_096, fact_24_number__of__is__id, fact_78_less__int__code_I14_J, fact_102_zadd__assoc, fact_70_zmult__1, fact_92_number__of__reorient, fact_18_add__special_I3_J, fact_27_times__numeral__code_I5_J, fact_76_less__eq__int__code_I15_J, fact_100_right__distrib__number__of, fact_3_t, fact_10_power2__less__0, fact_37_less__eq__int__code_I13_J, fact_75_rel__simps_I5_J, fact_103_zadd__left__commute, fact_71_plus__numeral__code_I9_J, fact_84_zless__imp__add1__zle, fact_5__096_126_A1_A_060_061_At_096, fact_91_eq__number__of, fact_60_zadd__zless__mono, fact_74_rel__simps_I29_J, fact_15_zero__power2, fact_87_semiring__add__number__of, fact_7_not__sum__power2__lt__zero, fact_96_zless__linear, fact_79_rel__simps_I15_J, fact_31_zle__trans, fact_45_mult__number__of__left, fact_72_zadd__zmult__distrib, fact_56_less__eq__int__code_I14_J, fact_6_p0, fact_40_zadd__left__mono, fact_20__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_, fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096, fact_21_p, fact_90_le__imp__0__less, fact_17_add__special_I2_J, fact_38_rel__simps_I31_J, fact_33_zpower__zadd__distrib, fact_36_rel__simps_I19_J, fact_54_le__number__of__eq__not__less, fact_81_int__one__le__iff__zero__less, fact_93_number__of__reorient, fact_32_zle__antisym, fact_52_less__0__number__of, fact_9_sum__power2__eq__zero__iff, fact_8_sum__power2__gt__zero__iff, fact_23_zle__refl, fact_101_right__distrib__number__of, fact_77_rel__simps_I33_J, fact_83_Numeral1__eq1__nat, fact_41_eq__number__of__0, fact_12_one__power2, fact_42_eq__0__number__of, fact_1_calculation_I1_J, fact_16_zero__eq__power2, fact_26_zle__linear, fact_28_less__eq__number__of__int__code, fact_89_add__nat__number__of, fact_14_zero__power2, fact_67_mult__Bit0, fact_58_rel__simps_I27_J, fact_63_le__special_I4_J, fact_44_semiring__mult__number__of, fact_51_le__special_I1_J, fact_88_semiring__add__number__of, fact_59_rel__simps_I21_J, fact_104_zadd__commute, fact_46_arith__simps_I32_J, fact_48_sum__squares__le__zero__iff, fact_19_t__l__p, fact_22_qf1pt, fact_30_zmult__assoc, fact_29_le__number__of, fact_62_semiring__norm_I113_J
% 7.47/3.42 % No. of inferences in proof: 216
% 7.47/3.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2882 ms resp. 2140 ms w/o parsing
% 7.80/3.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.80/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------