TSTP Solution File: NUM926+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:43:25 EDT 2023
% Result : Theorem 5.65s 2.37s
% Output : Refutation 6.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 146
% Syntax : Number of formulae : 272 ( 154 unt; 22 typ; 0 def)
% Number of atoms : 441 ( 186 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 2444 ( 21 ~; 6 |; 43 &;2232 @)
% ( 36 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 7 con; 0-2 aty)
% Number of variables : 490 ( 0 ^; 476 !; 14 ?; 490 :)
% Comments :
%------------------------------------------------------------------------------
thf(plus_plus_int_type,type,
plus_plus_int: $i > $i > $i ).
thf(power_power_int_type,type,
power_power_int: $i > $i > $i ).
thf(number_number_of_nat_type,type,
number_number_of_nat: $i > $i ).
thf(bit0_type,type,
bit0: $i > $i ).
thf(bit1_type,type,
bit1: $i > $i ).
thf(pls_type,type,
pls: $i ).
thf(times_times_int_type,type,
times_times_int: $i > $i > $i ).
thf(number_number_of_int_type,type,
number_number_of_int: $i > $i ).
thf(m_type,type,
m: $i ).
thf(one_one_int_type,type,
one_one_int: $i ).
thf(ord_less_int_type,type,
ord_less_int: $i > $i > $o ).
thf(ord_less_eq_int_type,type,
ord_less_eq_int: $i > $i > $o ).
thf(times_times_nat_type,type,
times_times_nat: $i > $i > $i ).
thf(plus_plus_nat_type,type,
plus_plus_nat: $i > $i > $i ).
thf(power_power_nat_type,type,
power_power_nat: $i > $i > $i ).
thf(one_one_nat_type,type,
one_one_nat: $i ).
thf(t_type,type,
t: $i ).
thf(zprime_type,type,
zprime: $i > $o ).
thf(s_type,type,
s: $i ).
thf(twoSqu526106917sum2sq_type,type,
twoSqu526106917sum2sq: $i > $o ).
thf(ord_less_eq_nat_type,type,
ord_less_eq_nat: $i > $i > $o ).
thf(ord_less_nat_type,type,
ord_less_nat: $i > $i > $o ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
<=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_zless__le) ).
thf(129,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ A @ B )
=> ( ( ord_less_eq_int @ A @ B )
& ( A != B ) ) )
& ( ( ( ord_less_eq_int @ A @ B )
& ( A != B ) )
=> ( ord_less_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(122,axiom,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(558,plain,
( ( t = one_one_int )
=> ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(138,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ C @ ( times_times_nat @ ( times_times_nat @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(347,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) )
= ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_zadd__power3) ).
thf(352,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__eq__int__code_I15_J) ).
thf(408,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zadd__zless__mono) ).
thf(449,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ord_less_int @ C @ D )
=> ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(27,axiom,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_zprime__2) ).
thf(202,plain,
zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_zpower__zadd__distrib) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ A @ ( plus_plus_nat @ B @ C ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_zadd__commute) ).
thf(472,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(9,axiom,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(153,plain,
! [A: $i] :
( ( power_power_nat @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(404,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(55,axiom,
! [A: $i] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(320,plain,
! [A: $i] :
( ( times_times_nat @ A @ A )
= ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( plus_plus_int @ A @ B )
= ( plus_plus_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I31_J) ).
thf(504,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_zmult__assoc) ).
thf(344,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_zadd__power2) ).
thf(542,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(84,axiom,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_p) ).
thf(421,plain,
zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(57,axiom,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06) ).
thf(325,plain,
( ( ord_less_int @ one_one_int @ t )
=> ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(30,axiom,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_power2__eq__square__number__of) ).
thf(216,plain,
! [A: $i] :
( ( power_power_int @ ( number_number_of_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(100,axiom,
! [A: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_rel__simps_I29_J) ).
thf(475,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(102,axiom,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_zmult__commute) ).
thf(485,plain,
! [A: $i,B: $i] :
( ( times_times_int @ A @ B )
= ( times_times_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_less__number__of__int__code) ).
thf(238,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_less__int__code_I13_J) ).
thf(480,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(147,plain,
! [A: $i,B: $i] :
( ( times_times_nat @ A @ B )
= ( times_times_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_zadd__left__commute) ).
thf(397,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[75]) ).
thf(37,axiom,
! [A: $i] :
( ( ord_less_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I5_J) ).
thf(243,plain,
! [A: $i] :
( ( ( ord_less_int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(54,axiom,
! [A: $i,B: $i] :
( ( ( bit1 @ A )
= ( bit1 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_rel__simps_I51_J) ).
thf(312,plain,
! [A: $i,B: $i] :
( ( ( ( bit1 @ A )
= ( bit1 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit1 @ A )
= ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_less__int__code_I16_J) ).
thf(307,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(38,axiom,
~ ( ord_less_int @ pls @ pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I2_J) ).
thf(248,plain,
~ ( ord_less_int @ pls @ pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(70,axiom,
! [A: $i] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power2__eq__square__number__of) ).
thf(380,plain,
! [A: $i] :
( ( power_power_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(26,axiom,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t__l__p) ).
thf(201,plain,
ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(51,axiom,
! [A: $i] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(302,plain,
! [A: $i] :
( ( times_times_int @ A @ A )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(41,axiom,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_nat__mult__2) ).
thf(260,plain,
! [A: $i] :
( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(561,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_rel__simps_I32_J) ).
thf(392,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(86,axiom,
! [A: $i] :
( ( number_number_of_int @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_number__of__is__id) ).
thf(424,plain,
! [A: $i] :
( ( number_number_of_int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(192,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(79,axiom,
twoSqu526106917sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_qf1pt) ).
thf(407,plain,
twoSqu526106917sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(98,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_rel__simps_I15_J) ).
thf(467,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(104,axiom,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_power2__eq__square) ).
thf(493,plain,
! [A: $i] :
( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zle__linear) ).
thf(156,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
| ( ord_less_eq_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(169,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_nat @ ( power_power_nat @ A @ B ) @ C )
= ( power_power_nat @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(141,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_eq__number__of) ).
thf(328,plain,
! [A: $i,B: $i] :
( ( ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( number_number_of_int @ A )
= ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(103,axiom,
! [A: $i] :
( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
<=> ( ord_less_eq_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_rel__simps_I22_J) ).
thf(488,plain,
! [A: $i] :
( ( ( ord_less_eq_int @ pls @ ( bit1 @ A ) )
=> ( ord_less_eq_int @ pls @ A ) )
& ( ( ord_less_eq_int @ pls @ A )
=> ( ord_less_eq_int @ pls @ ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_less__int__code_I14_J) ).
thf(225,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_rel__simps_I17_J) ).
thf(339,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_less__eq__int__code_I14_J) ).
thf(526,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(166,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ ( times_times_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] : ( ord_less_eq_int @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_zle__refl) ).
thf(161,plain,
! [A: $i] : ( ord_less_eq_int @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_rel__simps_I10_J) ).
thf(375,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_int @ ( bit0 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(513,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ B @ ( times_times_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(88,axiom,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nat__mult__2__right) ).
thf(430,plain,
! [A: $i] :
( ( times_times_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(77,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_nat__1__add__1) ).
thf(402,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)],[77]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add1__zle__eq) ).
thf(545,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(81,axiom,
ord_less_eq_int @ one_one_int @ t,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_tpos) ).
thf(413,plain,
ord_less_eq_int @ one_one_int @ t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(144,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_zle__trans) ).
thf(181,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ( ord_less_eq_int @ C @ A )
=> ( ord_less_eq_int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(63,axiom,
( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_one__power2) ).
thf(350,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)],[63]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(172,plain,
! [A: $i,B: $i] :
( ( plus_plus_nat @ A @ B )
= ( plus_plus_nat @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(219,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(44,axiom,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_power2__eq__square) ).
thf(274,plain,
! [A: $i] :
( ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times_nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(83,axiom,
! [A: $i,B: $i] :
( ( twoSqu526106917sum2sq @ B )
=> ( ( twoSqu526106917sum2sq @ A )
=> ( twoSqu526106917sum2sq @ ( times_times_int @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_is__mult__sum2sq) ).
thf(419,plain,
! [A: $i,B: $i] :
( ( twoSqu526106917sum2sq @ B )
=> ( ( twoSqu526106917sum2sq @ A )
=> ( twoSqu526106917sum2sq @ ( times_times_int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__eq__int__code_I16_J) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(108,axiom,
ord_less_eq_int @ pls @ pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I19_J) ).
thf(509,plain,
ord_less_eq_int @ pls @ pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( ( number_number_of_nat @ A )
= B )
<=> ( B
= ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_number__of__reorient) ).
thf(451,plain,
! [A: $i,B: $i] :
( ( ( ( number_number_of_nat @ A )
= B )
=> ( B
= ( number_number_of_nat @ A ) ) )
& ( ( B
= ( number_number_of_nat @ A ) )
=> ( ( number_number_of_nat @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_power2__sum) ).
thf(567,plain,
! [A: $i,B: $i] :
( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ A @ ( times_times_int @ B @ ( times_times_int @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( ( bit0 @ A )
= ( bit0 @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_rel__simps_I48_J) ).
thf(208,plain,
! [A: $i,B: $i] :
( ( ( ( bit0 @ A )
= ( bit0 @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( bit0 @ A )
= ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_int @ B @ C )
=> ( ord_less_int @ ( plus_plus_int @ B @ A ) @ ( plus_plus_int @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_zadd__strict__right__mono) ).
thf(323,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[56]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
= ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(462,plain,
! [A: $i,B: $i] :
( ( power_power_int @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_int @ ( power_power_int @ A @ B ) @ ( power_power_int @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(112,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
<=> ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__number__of__eq__not__less) ).
thf(521,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) )
=> ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) ) )
& ( ~ ( ord_less_nat @ ( number_number_of_nat @ B ) @ ( number_number_of_nat @ A ) )
=> ( ord_less_eq_nat @ ( number_number_of_nat @ A ) @ ( number_number_of_nat @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(438,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ A @ ( times_times_int @ B @ C ) )
= ( times_times_int @ ( times_times_int @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_le__number__of__eq__not__less) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) ) )
& ( ~ ( ord_less_int @ ( number_number_of_int @ B ) @ ( number_number_of_int @ A ) )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(40,axiom,
~ ! [A: $i] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25__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(255,plain,
~ ! [A: $i] :
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
!= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(111,axiom,
! [A: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ pls )
<=> ( ord_less_int @ A @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_rel__simps_I12_J) ).
thf(516,plain,
! [A: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ pls )
=> ( ord_less_int @ A @ pls ) )
& ( ( ord_less_int @ A @ pls )
=> ( ord_less_int @ ( bit1 @ A ) @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(355,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ ( plus_plus_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(553,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_rel__simps_I33_J) ).
thf(295,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_less__number__of) ).
thf(282,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ C ) )
= ( power_power_nat @ A @ ( plus_plus_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_rel__simps_I34_J) ).
thf(414,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit1 @ A ) @ ( bit1 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( ( number_number_of_int @ A )
= B )
<=> ( B
= ( number_number_of_int @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_number__of__reorient) ).
thf(263,plain,
! [A: $i,B: $i] :
( ( ( ( number_number_of_int @ A )
= B )
=> ( B
= ( number_number_of_int @ A ) ) )
& ( ( B
= ( number_number_of_int @ A ) )
=> ( ( number_number_of_int @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_zle__add1__eq__le) ).
thf(441,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_int @ A @ ( plus_plus_int @ B @ one_one_int ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I14_J) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_zadd__assoc) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[59]) ).
thf(92,axiom,
! [A: $i] :
( ( plus_plus_int @ ( number_number_of_int @ A ) @ one_one_int )
= ( number_number_of_int @ ( plus_plus_int @ A @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_add__special_I3_J) ).
thf(446,plain,
! [A: $i] :
( ( 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)],[92]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) )
= ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(386,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[72]) ).
thf(121,axiom,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Numeral1__eq1__nat) ).
thf(556,plain,
( one_one_nat
= ( number_number_of_nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ C @ ( times_times_int @ ( times_times_int @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_rel__simps_I16_J) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_zadd__left__mono) ).
thf(368,plain,
! [A: $i,B: $i,C: $i] :
( ( ord_less_eq_int @ B @ C )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_less__int__code_I15_J) ).
thf(250,plain,
! [A: $i,B: $i] :
( ( ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_int @ A @ B ) )
& ( ( ord_less_int @ A @ B )
=> ( ord_less_int @ ( bit1 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(97,axiom,
( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= one_one_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_one__power2) ).
thf(465,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)],[97]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ C @ D ) )
= ( times_times_nat @ A @ ( times_times_nat @ B @ ( times_times_nat @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zless__linear) ).
thf(186,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
| ( A = B )
| ( ord_less_int @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_less__eq__int__code_I13_J) ).
thf(290,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( bit0 @ A ) @ ( bit0 @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_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 ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power2__sum) ).
thf(235,plain,
! [A: $i,B: $i] :
( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus_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 ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(383,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ ( times_times_int @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(115,axiom,
! [A: $i] :
( ( power_power_int @ A @ one_one_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(536,plain,
! [A: $i] :
( ( power_power_int @ A @ one_one_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(287,plain,
! [A: $i,B: $i] :
( ( power_power_nat @ A @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) )
= ( times_times_nat @ ( power_power_nat @ A @ B ) @ ( power_power_nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(89,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__eq__number__of__int__code) ).
thf(433,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
= ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(510,plain,
! [A: $i,B: $i,C: $i] :
( ( 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)],[109]) ).
thf(50,axiom,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_nat__numeral__1__eq__1) ).
thf(300,plain,
( ( number_number_of_nat @ ( bit1 @ pls ) )
= one_one_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
= ( times_times_nat @ ( times_times_nat @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(85,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_t) ).
thf(422,plain,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(124,axiom,
! [A: $i] :
( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ A ) )
= ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_add__special_I2_J) ).
thf(564,plain,
! [A: $i] :
( ( 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)],[124]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_zless__imp__add1__zle) ).
thf(305,plain,
! [A: $i,B: $i] :
( ( ord_less_int @ A @ B )
=> ( ord_less_eq_int @ ( plus_plus_int @ A @ one_one_int ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(1,conjecture,
? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(126,plain,
~ ? [A: $i,B: $i] :
( ( 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 ) ) ) ) )
= ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( ( 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/sandbox/benchmark/theBenchmark.p',fact_62_add__nat__number__of) ).
thf(358,plain,
! [A: $i,B: $i] :
( ( ( 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)],[66]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_zle__antisym) ).
thf(195,plain,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ A @ B )
=> ( ( ord_less_eq_int @ B @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(76,axiom,
( ( plus_plus_int @ one_one_int @ one_one_int )
= ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_one__add__one__is__two) ).
thf(400,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)],[76]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(427,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
= ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(459,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( times_times_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ C @ D ) )
= ( times_times_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( times_times_nat @ A @ ( times_times_nat @ B @ C ) )
= ( times_times_nat @ B @ ( times_times_nat @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ ( plus_plus_nat @ C @ D ) )
= ( plus_plus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
<=> ( ord_less_eq_int @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_le__number__of) ).
thf(277,plain,
! [A: $i,B: $i] :
( ( ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) )
=> ( ord_less_eq_int @ A @ B ) )
& ( ( ord_less_eq_int @ A @ B )
=> ( ord_less_eq_int @ ( number_number_of_int @ A ) @ ( number_number_of_int @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_zpower__zpower) ).
thf(501,plain,
! [A: $i,B: $i,C: $i] :
( ( power_power_int @ ( power_power_int @ A @ B ) @ C )
= ( power_power_int @ A @ ( times_times_nat @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(32,axiom,
! [A: $i] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_cube__square) ).
thf(222,plain,
! [A: $i] :
( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(105,axiom,
! [A: $i] :
( ( ord_less_int @ pls @ ( bit0 @ A ) )
<=> ( ord_less_int @ pls @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_rel__simps_I4_J) ).
thf(496,plain,
! [A: $i] :
( ( ( ord_less_int @ pls @ ( bit0 @ A ) )
=> ( ord_less_int @ pls @ A ) )
& ( ( ord_less_int @ pls @ A )
=> ( ord_less_int @ pls @ ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(581,plain,
$false,
inference(cvc4,[status(thm)],[129,558,138,347,352,408,449,202,550,472,153,404,320,389,504,344,542,189,421,325,216,475,485,238,480,147,397,243,312,307,248,380,201,302,260,561,392,424,192,407,467,493,156,169,141,328,488,225,339,526,166,161,375,513,430,402,545,413,144,181,350,172,219,274,419,230,509,451,567,271,208,323,198,462,521,438,531,255,516,355,553,295,282,150,414,263,441,370,336,446,175,386,556,539,203,368,250,465,158,186,290,235,383,536,287,433,510,300,183,422,564,305,126,358,195,400,427,459,163,178,277,501,222,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM926+1 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 17:06:06 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.46/1.01 % [INFO] Parsing done (163ms).
% 1.56/1.02 % [INFO] Running in sequential loop mode.
% 1.83/1.21 % [INFO] eprover registered as external prover.
% 1.83/1.21 % [INFO] cvc4 registered as external prover.
% 1.83/1.22 % [INFO] Scanning for conjecture ...
% 2.15/1.32 % [INFO] Found a conjecture and 123 axioms. Running axiom selection ...
% 2.19/1.39 % [INFO] Axiom selection finished. Selected 123 axioms (removed 0 axioms).
% 2.54/1.48 % [INFO] Problem is first-order (TPTP FOF).
% 2.54/1.49 % [INFO] Type checking passed.
% 2.79/1.49 % [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 ...
% 5.65/2.36 % External prover 'cvc4' found a proof!
% 5.65/2.36 % [INFO] Killing All external provers ...
% 5.65/2.37 % Time passed: 1845ms (effective reasoning time: 1338ms)
% 5.65/2.37 % 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)>
% 5.65/2.37 % Axioms used in derivation (123): fact_30_zle__trans, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_41_zadd__zless__mono, fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_15_one__power2, fact_71_zless__imp__add1__zle, fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_7_zadd__power2, fact_61_zadd__left__mono, fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_51_rel__simps_I34_J, fact_23_add__special_I3_J, fact_31_zle__antisym, fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_106_number__of__reorient, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_69_less__int__code_I14_J, fact_26_zle__refl, fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_60_zadd__strict__right__mono, fact_46_nat__mult__2__right, fact_117_rel__simps_I16_J, fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_9_power2__sum, fact_107_rel__simps_I51_J, fact_14_one__power2, fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_47_nat__1__add__1, fact_110_zmult__commute, fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_55_rel__simps_I19_J, fact_66_rel__simps_I5_J, fact_63_nat__numeral__1__eq__1, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_68_rel__simps_I33_J, fact_59_less__eq__number__of__int__code, fact_0_tpos, fact_22_add__special_I2_J, fact_36_zpower__zpower, fact_112_zadd__assoc, fact_109_zmult__assoc, fact_39_less__number__of, fact_67_less__eq__int__code_I15_J, fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_28_zless__le, fact_50_less__eq__int__code_I16_J, fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_114_zadd__commute, fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_122_rel__simps_I32_J, fact_120_rel__simps_I22_J, fact_118_rel__simps_I10_J, fact_24_one__add__one__is__two, fact_116_less__int__code_I15_J, fact_3_t__l__p, fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_52_rel__simps_I2_J, fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_18_power2__eq__square, fact_115_rel__simps_I12_J, fact_119_rel__simps_I4_J, fact_10_power2__sum, fact_111_number__of__is__id, fact_12_power2__eq__square__number__of, fact_53_less__int__code_I13_J, fact_62_add__nat__number__of, fact_75_is__mult__sum2sq, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_48_less__int__code_I16_J, fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06, fact_58_less__number__of__int__code, fact_29_zless__linear, fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_4_p, fact_13_cube__square, fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_64_Numeral1__eq1__nat, fact_65_rel__simps_I29_J, fact_37_le__number__of__eq__not__less, fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_108_rel__simps_I48_J, fact_54_rel__simps_I14_J, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_49_rel__simps_I17_J, fact_40_le__number__of, fact_44_zpower__zadd__distrib, fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_56_less__eq__int__code_I13_J, fact_57_rel__simps_I31_J, fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_5_t, fact_105_number__of__reorient, fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, fact_25__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_73_zle__add1__eq__le, fact_113_zadd__left__commute, fact_74_zprime__2, fact_11_power2__eq__square__number__of, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_6_qf1pt, fact_104_eq__number__of, fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_121_less__eq__int__code_I14_J, fact_38_le__number__of__eq__not__less, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, fact_45_nat__mult__2, fact_72_add1__zle__eq, fact_19_power2__eq__square, fact_70_rel__simps_I15_J, fact_8_zadd__power3, fact_27_zle__linear, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 5.65/2.37 % No. of inferences in proof: 250
% 5.65/2.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1845 ms resp. 1338 ms w/o parsing
% 6.09/2.44 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.09/2.44 % [INFO] Killing All external provers ...
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