%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM952_5 : TPTP v9.3.1. Released v6.0.0.
% 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 : n020.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 08:10:31 AM UTC 2026
% Result : Theorem 7.59s 3.65s
% Output : Refutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 111
% Syntax : Number of formulae : 224 ( 132 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 223 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2571 ( 28 ~; 5 |; 29 &;2388 @)
% ( 11 <=>; 110 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 24 usr; 5 con; 0-3 aty)
% Number of variables : 350 ( 0 ^; 350 !; 0 ?; 350 :)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zprime_decl,type,
zprime: int > $o ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(min_decl,type,
min: int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(legendre_decl,type,
legendre: int > int > int ).
thf(quadRes_decl,type,
quadRes: int > int > $o ).
thf(dvd_dvd_decl,type,
dvd_dvd:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(m_decl,type,
m: int ).
thf(s_decl,type,
s: int ).
thf(7,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(125,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nat__numeral__1__eq__1) ).
thf(193,plain,
( ( pls @ bit1 @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_add__number__of__diff1) ).
thf(442,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_numeral__1__eq__1) ).
thf(365,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(80,axiom,
! [A: int] :
( ( ( A @ bit1 )
= min )
<=> ( A = min ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I47_J) ).
thf(352,plain,
! [A: int] :
( ( ( A = min )
=> ( ( A @ bit1 )
= min ) )
& ( ( ( A @ bit1 )
= min )
=> ( A = min ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(92,axiom,
int @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(408,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(64,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_semiring__norm_I110_J) ).
thf(308,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one )
= ( pls @ bit1 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_zprime__power__zdvd__cancel__right) ).
thf(217,plain,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( C @ ( A @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(53,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_mult__Pls) ).
thf(276,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(89,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
<=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_zmult__eq__1__iff) ).
thf(385,plain,
! [A: int,B: int] :
( ( ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) )
=> ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) ) )
& ( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( ( A
= ( min @ ( int @ number_number_of ) ) )
& ( B
= ( min @ ( int @ number_number_of ) ) ) )
| ( ( A
= ( int @ one_one ) )
& ( B
= ( int @ one_one ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(76,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__number__of__left) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(57,axiom,
min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096) ).
thf(288,plain,
min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__numeral__1) ).
thf(436,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(49,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I48_J) ).
thf(257,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,axiom,
! [A: int,B: int,C: int,D: int,E: int] :
( ( D @ ( E @ ( int @ dvd_dvd ) ) )
=> ( ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
<=> ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_zdvd__period) ).
thf(189,plain,
! [A: int,B: int,C: int,D: int,E: int] :
( ( D @ ( E @ ( int @ dvd_dvd ) ) )
=> ( ( ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) )
& ( ( B @ ( C @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) )
=> ( B @ ( D @ ( A @ ( int @ times_times ) ) @ ( C @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( E @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(97,axiom,
( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096) ).
thf(421,plain,
( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(16,axiom,
! [A: int] :
( ( A @ bit0 )
!= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I45_J) ).
thf(152,plain,
! [A: int] :
( ( A @ bit0 )
!= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_eq__number__of) ).
thf(289,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(107,axiom,
( ( min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) )
= ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
thf(448,plain,
( ( min @ ( int @ number_number_of ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) )
= ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(23,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(179,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(70,axiom,
! [A: int] :
( ( A @ bit0 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_diff__bin__simps_I5_J) ).
thf(321,plain,
! [A: int] :
( ( A @ bit0 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(87,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(376,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(34,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_right__diff__distrib__number__of) ).
thf(211,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(48,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I50_J) ).
thf(253,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(4,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_add__Bit0__Bit1) ).
thf(116,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(66,axiom,
min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096) ).
thf(312,plain,
min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(63,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(307,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(104,axiom,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_zpower__zpower) ).
thf(439,plain,
! [A: nat,B: nat,C: int] :
( ( A @ ( B @ ( C @ ( int @ power_power ) ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ times_times ) ) @ ( C @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(51,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_diff__bin__simps_I9_J) ).
thf(270,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(30,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__Pls__right) ).
thf(201,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_diff__bin__simps_I10_J) ).
thf(220,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(74,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_number__of__diff) ).
thf(334,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(61,axiom,
! [A: int] :
( min
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_rel__simps_I42_J) ).
thf(302,plain,
! [A: int] :
( min
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(79,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_diff__bin__simps_I4_J) ).
thf(349,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_power__m1__even) ).
thf(429,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( min @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(10,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_add__Pls) ).
thf(137,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ plus_plus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(29,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I39_J) ).
thf(197,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(71,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_zadd__power2) ).
thf(324,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(56,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_right__distrib__number__of) ).
thf(285,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(40,axiom,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_nat__mult__2__right) ).
thf(224,plain,
! [A: nat] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(17,axiom,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_pos__zmult__eq__1__iff__lemma) ).
thf(156,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ times_times ) ) )
= ( int @ one_one ) )
=> ( ( B
= ( min @ ( int @ number_number_of ) ) )
| ( B
= ( int @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_add__number__of__eq) ).
thf(169,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(12,axiom,
! [A: int] :
( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime )
=> ( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Legendre__1mod4) ).
thf(141,plain,
! [A: int] :
( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime )
=> ( ( int @ one_one @ ( A @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(111,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_rel__simps_I38_J) ).
thf(457,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(21,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_power__even__eq) ).
thf(173,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat,B: TA] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) @ ( B @ ( TA @ power_power ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_rel__simps_I44_J) ).
thf(129,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_plus__numeral__code_I9_J) ).
thf(371,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(77,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_diff__bin__simps_I3_J) ).
thf(343,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(81,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_zdvd__zdiffD) ).
thf(360,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(65,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(311,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zspecial__product) ).
thf(412,plain,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(54,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_number__of__Bit1) ).
thf(279,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ bit1 @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(15,axiom,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( B @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_zadd__power3) ).
thf(149,plain,
! [A: int,B: int] :
( ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( int @ plus_plus ) ) @ ( int @ power_power ) ) )
= ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) ) @ ( B @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( pls @ bit1 @ bit1 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ times_times ) ) @ ( pls @ bit1 @ bit1 @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(24,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
<=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_zdvd__reduce) ).
thf(180,plain,
! [A: int,B: int,C: int] :
( ( ( B @ ( C @ ( int @ dvd_dvd ) ) )
=> ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) ) )
& ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(59,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_times__numeral__code_I5_J) ).
thf(296,plain,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(22,axiom,
pls != min,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I37_J) ).
thf(176,plain,
pls != min,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_power2__sum) ).
thf(423,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: TA,B: TA] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( B @ ( TA @ plus_plus ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ times_times ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ power_power ) ) @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) @ ( TA @ plus_plus ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,axiom,
! [A: int] :
( ( pls @ ( A @ ( int @ minus_minus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_diff__bin__simps_I1_J) ).
thf(402,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ minus_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(31,axiom,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_Bit0__def) ).
thf(204,plain,
! [A: int] :
( ( A @ bit0 )
= ( A @ ( A @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mult__Bit1) ).
thf(445,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(67,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Bit0__Pls) ).
thf(313,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(13,axiom,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_Numeral1__eq1__nat) ).
thf(144,plain,
( ( nat @ one_one )
= ( pls @ bit1 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I51_J) ).
thf(159,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_zprime__2) ).
thf(172,plain,
pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( int @ one_one @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( s @ ( int @ power_power ) ) @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( int @ dvd_dvd ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(37,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(219,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_number__of__reorient) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(42,axiom,
! [A: nat,B: int,C: int] :
( ( C @ zprime )
=> ( ( A @ ( B @ ( int @ power_power ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_zprime__zdvd__power) ).
thf(230,plain,
! [A: nat,B: int,C: int] :
( ( C @ zprime )
=> ( ( A @ ( B @ ( int @ power_power ) ) @ ( C @ ( int @ dvd_dvd ) ) )
=> ( B @ ( C @ ( int @ dvd_dvd ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
thf(318,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(82,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_left__distrib__number__of) ).
thf(362,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(109,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_int__distrib_I1_J) ).
thf(451,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(11,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(140,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_rel__simps_I49_J) ).
thf(330,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(39,axiom,
nat @ semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(223,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(62,axiom,
int @ ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(306,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_mult__number__of__left) ).
thf(299,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
thf(267,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ ( TA @ number_number_of ) @ ( A @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: int] :
( ( A @ bit1 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_diff__bin__simps_I6_J) ).
thf(426,plain,
! [A: int] :
( ( A @ bit1 @ ( min @ ( int @ minus_minus ) ) )
= ( A @ ( min @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(86,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_nat__1__add__1) ).
thf(374,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(55,axiom,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_power2__eq__square__number__of) ).
thf(282,plain,
! [TA: $tType] :
( ( ( TA @ number )
& ( TA @ monoid_mult ) )
=> ! [A: int] :
( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ power_power ) ) )
= ( A @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(72,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_int__distrib_I4_J) ).
thf(327,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(93,axiom,
min != pls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_rel__simps_I40_J) ).
thf(409,plain,
min != pls,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(108,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(450,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I2_J) ).
thf(250,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(112,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(465,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(25,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add__Bit0__Bit0) ).
thf(186,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,axiom,
( ( min @ bit1 )
= min ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_Bit1__Min) ).
thf(114,plain,
( ( min @ bit1 )
= min ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_one__power2) ).
thf(418,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(5,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_semiring__numeral__1__eq__1) ).
thf(119,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(44,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(235,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(102,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_number__of__is__id) ).
thf(433,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(32,axiom,
( ~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) )
=> ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
!= ( int @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_126_061_A1_096) ).
thf(207,plain,
( ~ ( min @ ( int @ number_number_of ) @ ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ quadRes ) )
=> ( ( int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ ( min @ ( int @ number_number_of ) @ legendre ) )
!= ( int @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_number__of__mult) ).
thf(346,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
thf(214,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( A @ ( pls @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_add__Bit1__Bit0) ).
thf(315,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_p) ).
thf(432,plain,
int @ one_one @ ( m @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) @ zprime,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(14,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_arith__simps_I32_J) ).
thf(146,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(91,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_mult__Bit0) ).
thf(405,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_mult__numeral__1__right) ).
thf(273,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA] :
( ( pls @ bit1 @ ( TA @ number_number_of ) @ ( A @ ( TA @ times_times ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(33,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(210,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_Bit1__def) ).
thf(126,plain,
! [A: int] :
( ( A @ bit1 )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(28,axiom,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_zprime__power__zdvd__cancel__left) ).
thf(195,plain,
! [A: int,B: nat,C: int,D: int] :
( ( D @ zprime )
=> ( ~ ( C @ ( D @ ( int @ dvd_dvd ) ) )
=> ( ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) )
=> ( A @ ( B @ ( D @ ( int @ power_power ) ) @ ( int @ dvd_dvd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(95,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_diff__bin__simps_I7_J) ).
thf(415,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(45,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_number__of__add) ).
thf(239,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(46,axiom,
! [A: int] :
( ( min
= ( A @ bit1 ) )
<=> ( min = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_rel__simps_I43_J) ).
thf(242,plain,
! [A: int] :
( ( ( min = A )
=> ( min
= ( A @ bit1 ) ) )
& ( ( min
= ( A @ bit1 ) )
=> ( min = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(41,axiom,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_eq__number__of__Pls__Min) ).
thf(227,plain,
( ( pls @ ( int @ number_number_of ) )
!= ( min @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(110,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_int__distrib_I2_J) ).
thf(454,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ ( C @ ( int @ times_times ) ) )
= ( A @ ( C @ ( int @ times_times ) ) @ ( B @ ( C @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_int__distrib_I3_J) ).
thf(232,plain,
! [A: int,B: int,C: int] :
( ( A @ ( B @ ( C @ ( int @ minus_minus ) ) @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( A @ ( C @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(75,axiom,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_nat__mult__2) ).
thf(337,plain,
! [A: nat] :
( ( A @ ( pls @ bit1 @ bit0 @ ( nat @ number_number_of ) @ ( nat @ times_times ) ) )
= ( A @ ( A @ ( nat @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(6,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_left__diff__distrib__number__of) ).
thf(122,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(466,plain,
$false,
inference(e,[status(thm)],[125,193,442,365,352,408,308,217,276,385,340,288,436,257,189,421,152,289,448,179,321,376,211,253,116,312,307,439,270,201,220,334,302,349,429,137,197,324,285,224,156,169,141,457,173,129,371,343,360,311,412,279,149,180,296,176,423,402,204,445,313,144,159,172,113,219,377,230,318,362,451,140,330,223,306,299,267,426,374,282,327,409,450,368,250,465,186,114,418,119,235,433,207,346,214,315,432,146,405,273,210,126,195,415,239,242,227,454,232,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM952_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % 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
% 0.12/0.53 % Computer : n020.cluster.edu
% 0.12/0.53 % Model : x86_64 x86_64
% 0.12/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.53 % Memory : 8046.5625MB
% 0.12/0.53 % OS : Linux 6.8.0-71-generic
% 0.12/0.53 % CPULimit : 300
% 0.12/0.53 % WCLimit : 300
% 0.12/0.53 % DateTime : Sat Sep 26 04:23:20 UTC 2026
% 0.12/0.53 % CPUTime :
% 0.12/0.53 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.00/1.13 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.41 % [INFO] Parsing done (282ms).
% 1.67/1.43 % [INFO] Running in sequential loop mode.
% 2.42/1.81 % [INFO] eprover registered as external prover.
% 2.42/1.82 % [INFO] Scanning for conjecture ...
% 2.59/1.98 % [INFO] Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ...
% 2.82/2.09 % [INFO] Axiom selection finished. Selected 110 axioms (removed 2 axioms).
% 3.28/2.26 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.28/2.28 % [INFO] Type checking passed.
% 3.28/2.29 % [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 ...
% 7.59/3.65 % External prover 'e' found a proof!
% 7.59/3.65 % [INFO] Killing All external provers ...
% 7.59/3.65 % Time passed: 2975ms (effective reasoning time: 2214ms)
% 7.59/3.65 % 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)>
% 7.59/3.65 % Axioms used in derivation (110): arity_Nat_Onat___Rings_Osemiring, fact_36_left__distrib__number__of, fact_54_diff__bin__simps_I5_J, fact_89_zdvd__period, fact_31_Bit1__Min, arity_Nat_Onat___Groups_Omonoid__mult, fact_41_arith__simps_I32_J, fact_91_zspecial__product, fact_25_mult__Pls, fact_76_zmult__eq__1__iff, fact_1__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096, fact_45_add__Bit1__Bit0, fact_69_number__of__is__id, arity_Nat_Onat___Rings_Osemiring__1, fact_48_diff__bin__simps_I9_J, fact_32_rel__simps_I37_J, arity_Int_Oint___Int_Oring__char__0, fact_72_Legendre__1mod4, fact_4_power2__eq__square__number__of, fact_80_times__numeral__code_I5_J, fact_0__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096, fact_11__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096, fact_9_mult__Bit1, fact_58_nat__mult__2, fact_87_number__of__add, fact_2_p, arity_Nat_Onat___Int_Onumber__semiring, fact_42_add__number__of__left, fact_12_zadd__power2, fact_7_add__special_I3_J, fact_75_pos__zmult__eq__1__iff__lemma, fact_47_diff__bin__simps_I10_J, fact_71_power__even__eq, fact_61_int__distrib_I3_J, arity_Int_Oint___Rings_Oring, fact_39_right__diff__distrib__number__of, fact_86_number__of__mult, fact_67_zprime__2, arity_Int_Oint___Int_Onumber__semiring, fact_26_mult__Bit0, arity_Int_Oint___Int_Onumber__ring, fact_43_add__number__of__eq, fact_65_zprime__power__zdvd__cancel__right, fact_66_zprime__power__zdvd__cancel__left, arity_Int_Oint___Rings_Osemiring__1, fact_44_nat__numeral__1__eq__1, fact_96_semiring__norm_I110_J, fact_93_mult__numeral__1, fact_40_mult__number__of__left, fact_6_add__special_I2_J, fact_49_diff__bin__simps_I3_J, fact_95_semiring__numeral__1__eq__1, fact_34_rel__simps_I45_J, fact_5_one__power2, fact_22_rel__simps_I44_J, fact_92_number__of__Bit1, fact_88_Bit1__def, fact_38_left__diff__distrib__number__of, arity_Int_Oint___Groups_Omonoid__mult, fact_28_diff__bin__simps_I7_J, fact_59_nat__mult__2__right, fact_68_number__of__reorient, fact_90_zdvd__reduce, fact_81_int__distrib_I1_J, fact_78_add__Pls, fact_62_int__distrib_I4_J, fact_35_rel__simps_I42_J, fact_17_rel__simps_I48_J, fact_77_add__Pls__right, arity_Int_Oint___Rings_Osemiring, fact_13_zadd__power3, fact_24_Bit0__Pls, fact_83_plus__numeral__code_I9_J, fact_57_zprime__zdvd__power, fact_19_rel__simps_I39_J, fact_37_right__distrib__number__of, fact_85_add__numeral__0__right, fact_63_zdvd__zdiffD, fact_8_one__add__one__is__two, fact_51_nat__1__add__1, fact_94_mult__numeral__1__right, fact_23_rel__simps_I38_J, fact_21_rel__simps_I49_J, fact_60_diff__bin__simps_I1_J, arity_Nat_Onat___Int_Onumber, fact_53_diff__bin__simps_I6_J, fact_64_Numeral1__eq1__nat, fact_50__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_126_061_A1_096, fact_3__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096, fact_14_power2__sum, fact_82_int__distrib_I2_J, fact_73_power__m1__even, fact_46_add__Bit0__Bit1, fact_29_rel__simps_I47_J, fact_20_rel__simps_I50_J, fact_56_number__of__diff, fact_10_numeral__1__eq__1, fact_79_Bit0__def, fact_55_zpower__zpower, arity_Int_Oint___Int_Onumber, fact_74_add__number__of__diff1, fact_33_rel__simps_I40_J, fact_27_add__Bit0__Bit0, fact_16_rel__simps_I51_J, fact_18_rel__simps_I46_J, fact_30_rel__simps_I43_J, fact_84_add__numeral__0, fact_15_eq__number__of, fact_52_diff__bin__simps_I4_J, fact_70_eq__number__of__Pls__Min
% 7.59/3.65 % No. of inferences in proof: 224
% 7.59/3.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2975 ms resp. 2214 ms w/o parsing
% 8.05/3.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.05/3.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------