TSTP Solution File: NUM996_5 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM996_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:43:59 EDT 2023
% Result : Theorem 7.07s 2.59s
% Output : Refutation 7.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 170
% Syntax : Number of formulae : 312 ( 144 unt; 30 typ; 0 def)
% Number of atoms : 474 ( 255 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 3083 ( 19 ~; 3 |; 22 &;2872 @)
% ( 11 <=>; 156 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 26 usr; 4 con; 0-3 aty)
% Number of variables : 555 ( 0 ^; 534 !; 0 ?; 555 :)
% ( 21 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(semiring_type,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_type,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_type,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_type,type,
comm_semiring:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_type,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(ab_semigroup_mult_type,type,
ab_semigroup_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(ordere142940540dd_abs_type,type,
ordere142940540dd_abs:
!>[TA: $tType] : $o ).
thf(ab_sem1668676832m_mult_type,type,
ab_sem1668676832m_mult:
!>[TA: $tType] : $o ).
thf(semiri456707255roduct_type,type,
semiri456707255roduct:
!>[TA: $tType] : $o ).
thf(abs_abs_type,type,
abs_abs:
!>[TA: $tType] : ( TA > TA ) ).
thf(plus_plus_type,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_type,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(bit0_type,type,
bit0: int > int ).
thf(bit1_type,type,
bit1: int > int ).
thf(pls_type,type,
pls: int ).
thf(number_number_of_type,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(v_type,type,
v: int ).
thf(w_type,type,
w: int ).
thf(91,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).
thf(365,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ A )
= ( times_times @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(249,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(124,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_add__Bit0__Bit0) ).
thf(468,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit0 @ A ) )
= ( bit0 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(48,axiom,
ordere142940540dd_abs @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__group__add__abs) ).
thf(234,plain,
ordere142940540dd_abs @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(129,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_plus__numeral__code_I9_J) ).
thf(481,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(88,axiom,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( number_number_of @ TA @ B )
= A )
<=> ( A
= ( number_number_of @ TA @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_number__of__reorient) ).
thf(352,plain,
! [TA: $tType] :
( ( number @ TA )
=> ! [A: TA,B: int] :
( ( ( ( number_number_of @ TA @ B )
= A )
=> ( A
= ( number_number_of @ TA @ B ) ) )
& ( ( A
= ( number_number_of @ TA @ B ) )
=> ( ( number_number_of @ TA @ B )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(105,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(408,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(41,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).
thf(217,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA,C: TA] :
( ( power_power @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( power_power @ TA @ C @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(117,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_semiring__mult__2__right) ).
thf(449,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(95,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(379,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(114,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).
thf(440,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(62,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( times_times @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) )
= ( power_power @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
thf(269,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( times_times @ TA @ ( power_power @ TA @ C @ B ) @ ( power_power @ TA @ C @ A ) )
= ( power_power @ TA @ C @ ( plus_plus @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(97,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_number__of__mult) ).
thf(385,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( times_times @ int @ B @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1,conjecture,
( ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= ( plus_plus @ int @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ v ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ w ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
!= ( plus_plus @ int @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ v ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ w ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(142,plain,
( ( plus_plus @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ v @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ w @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
!= ( plus_plus @ int @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ v ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs @ int @ w ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(84,axiom,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_add__imp__eq) ).
thf(340,plain,
! [TA: $tType] :
( ( cancel146912293up_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(12,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(153,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(107,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I39_J) ).
thf(417,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(113,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I49_J) ).
thf(436,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(29,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_add__Pls) ).
thf(184,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(33,axiom,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_mult__Pls) ).
thf(196,plain,
! [A: int] :
( ( times_times @ int @ pls @ A )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(120,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add__Pls__right) ).
thf(460,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(16,axiom,
comm_semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(157,plain,
comm_semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(108,axiom,
! [TA: $tType] :
( ( ( monoid_mult @ TA )
& ( number @ TA ) )
=> ! [A: int] :
( ( power_power @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_power2__eq__square__number__of) ).
thf(421,plain,
! [TA: $tType] :
( ( ( monoid_mult @ TA )
& ( number @ TA ) )
=> ! [A: int] :
( ( power_power @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( number_number_of @ TA @ A ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(67,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_mult__idem) ).
thf(284,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(11,axiom,
comm_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring) ).
thf(152,plain,
comm_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(75,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ D @ ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).
thf(316,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ D @ ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(58,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(261,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(179,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(115,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A )
= ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
thf(443,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: nat,C: TA] :
( ( power_power @ TA @ ( power_power @ TA @ C @ B ) @ A )
= ( power_power @ TA @ C @ ( times_times @ nat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(50,axiom,
comm_semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(238,plain,
comm_semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(139,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_times__numeral__code_I5_J) ).
thf(514,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( number_number_of @ int @ B ) @ ( number_number_of @ int @ A ) )
= ( number_number_of @ int @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(128,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(480,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(39,axiom,
! [A: nat] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_nat__mult__2__right) ).
thf(211,plain,
! [A: nat] :
( ( times_times @ nat @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_rel__simps_I48_J) ).
thf(253,plain,
! [A: int,B: int] :
( ( ( ( bit0 @ B )
= ( bit0 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit0 @ B )
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
number @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(147,plain,
number @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_power3__eq__cube) ).
thf(221,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ ( times_times @ TA @ A @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(119,axiom,
! [A: int,B: int] :
( ( ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
<=> ( ( abs_abs @ int @ B )
= ( abs_abs @ int @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_power2__eq__iff__abs__eq) ).
thf(453,plain,
! [A: int,B: int] :
( ( ( ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
=> ( ( abs_abs @ int @ B )
= ( abs_abs @ int @ A ) ) )
& ( ( ( abs_abs @ int @ B )
= ( abs_abs @ int @ A ) )
=> ( ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(53,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(243,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ B @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(60,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA,B: TA] :
( ( power_power @ TA @ ( plus_plus @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_power2__sum) ).
thf(265,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA,B: TA] :
( ( power_power @ TA @ ( plus_plus @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( power_power @ TA @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(73,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_add__right__cancel) ).
thf(307,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(118,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(452,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(35,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_abs__idempotent) ).
thf(201,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( abs_abs @ TA @ A ) )
= ( abs_abs @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(42,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(220,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(80,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(334,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(87,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_mult__numeral__1__right) ).
thf(349,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit1 @ pls ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(71,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( D != C )
& ( B != A ) )
<=> ( ( plus_plus @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) )
!= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_crossproduct__noteq) ).
thf(297,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( D != C )
& ( B != A ) )
=> ( ( plus_plus @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) )
!= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ C @ B ) ) ) )
& ( ( ( plus_plus @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) )
!= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ C @ B ) ) )
=> ( ( D != C )
& ( B != A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(109,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_left__distrib__number__of) ).
thf(424,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: int,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ ( number_number_of @ TA @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ ( number_number_of @ TA @ A ) ) @ ( times_times @ TA @ B @ ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(64,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(275,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
thf(165,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(130,axiom,
! [A: int] :
( ( 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/sandbox2/benchmark/theBenchmark.p',fact_55_cube__square) ).
thf(484,plain,
! [A: int] :
( ( 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)],[130]) ).
thf(133,axiom,
! [A: int,B: int,C: int] :
( ( times_times @ int @ C @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ int @ ( times_times @ int @ C @ B ) @ ( times_times @ int @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_int__distrib_I2_J) ).
thf(493,plain,
! [A: int,B: int,C: int] :
( ( times_times @ int @ C @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ int @ ( times_times @ int @ C @ B ) @ ( times_times @ int @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(44,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(224,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ D @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ D @ B ) @ ( plus_plus @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(15,axiom,
number_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(156,plain,
number_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ ( abs_abs @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_power2__abs) ).
thf(388,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ ( abs_abs @ TA @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(22,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_mult__2__right) ).
thf(169,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(135,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I46_J) ).
thf(499,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(83,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(339,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(32,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__left__imp__eq) ).
thf(193,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(141,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).
thf(526,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(78,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
thf(328,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(125,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ A @ B ) )
= ( times_times @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
thf(471,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ C @ B ) @ ( times_times @ TA @ A @ B ) )
= ( times_times @ TA @ ( plus_plus @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(93,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rel__simps_I44_J) ).
thf(371,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(136,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_mult__Bit0) ).
thf(503,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit0 @ B ) @ A )
= ( bit0 @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(85,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_add__Bit1__Bit0) ).
thf(343,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit1 @ B ) @ ( bit0 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(102,axiom,
! [A: int] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_quartic__square__square) ).
thf(398,plain,
! [A: int] :
( ( power_power @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(7,axiom,
ab_semigroup_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__mult) ).
thf(148,plain,
ab_semigroup_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_add__numeral__0__right) ).
thf(180,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ A @ ( number_number_of @ TA @ pls ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(149,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(138,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(513,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(111,axiom,
! [A: int] :
( ( abs_abs @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ ( abs_abs @ int @ A ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_abs__power3__distrib) ).
thf(430,plain,
! [A: int] :
( ( abs_abs @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ ( abs_abs @ int @ A ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_eq__number__of) ).
thf(291,plain,
! [TA: $tType] :
( ( ( number_ring @ TA )
& ( ring_char_0 @ TA ) )
=> ! [A: int,B: int] :
( ( ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( number_number_of @ TA @ B )
= ( number_number_of @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(66,axiom,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_mult__Bit1) ).
thf(281,plain,
! [A: int,B: int] :
( ( times_times @ int @ ( bit1 @ B ) @ A )
= ( plus_plus @ int @ ( bit0 @ ( times_times @ int @ B @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(36,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).
thf(204,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ ( times_times @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(99,axiom,
! [A: int,B: int] :
( ( power_power @ int @ ( plus_plus @ int @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ A ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zadd__power2) ).
thf(391,plain,
! [A: int,B: int] :
( ( power_power @ int @ ( plus_plus @ int @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) @ A ) ) @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(96,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).
thf(382,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(74,axiom,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_ab__semigroup__mult__class_Omult__ac_I1_J) ).
thf(313,plain,
! [TA: $tType] :
( ( ab_semigroup_mult @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(3,axiom,
number_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(144,plain,
number_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(81,axiom,
! [A: real] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_four__x__squared) ).
thf(335,plain,
! [A: real] :
( ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ real @ ( times_times @ real @ ( number_number_of @ real @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(18,axiom,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ D @ C ) @ ( plus_plus @ TA @ ( times_times @ TA @ B @ C ) @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_combine__common__factor) ).
thf(159,plain,
! [TA: $tType] :
( ( semiring @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( plus_plus @ TA @ ( times_times @ TA @ D @ C ) @ ( plus_plus @ TA @ ( times_times @ TA @ B @ C ) @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( plus_plus @ TA @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(187,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(23,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_power2__eq__square) ).
thf(172,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(46,axiom,
cancel_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(230,plain,
cancel_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(90,axiom,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(362,plain,
! [TA: $tType] :
( ( ab_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( plus_plus @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ C @ ( plus_plus @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(127,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_mult__2) ).
thf(477,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(52,axiom,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__Bit0__Bit1) ).
thf(240,plain,
! [A: int,B: int] :
( ( plus_plus @ int @ ( bit0 @ B ) @ ( bit1 @ A ) )
= ( bit1 @ ( plus_plus @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(14,axiom,
semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(155,plain,
semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).
thf(278,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ C @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(100,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(394,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(72,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(306,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(132,axiom,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_comm__semiring__class_Odistrib) ).
thf(490,plain,
! [TA: $tType] :
( ( comm_semiring @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(19,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_add__number__of__left) ).
thf(162,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ ( plus_plus @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(131,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_mult__left__idem) ).
thf(487,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA,B: TA] :
( ( times_times @ TA @ B @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(4,axiom,
semiri456707255roduct @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(145,plain,
semiri456707255roduct @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
cancel146912293up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(150,plain,
cancel146912293up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I51_J) ).
thf(409,plain,
! [A: int,B: int] :
( ( ( ( bit1 @ B )
= ( bit1 @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( bit1 @ B )
= ( bit1 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(34,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_Bit0__Pls) ).
thf(199,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(79,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Bit0__def) ).
thf(331,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(121,axiom,
comm_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring) ).
thf(463,plain,
comm_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(82,axiom,
ab_semigroup_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__mult) ).
thf(338,plain,
ab_semigroup_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(89,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_power__even__eq) ).
thf(359,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( power_power @ TA @ B @ ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
= ( power_power @ TA @ ( power_power @ TA @ B @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(13,axiom,
ordere142940540dd_abs @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) ).
thf(154,plain,
ordere142940540dd_abs @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_mult__number__of__left) ).
thf(175,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA,B: int,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( times_times @ TA @ ( number_number_of @ TA @ B ) @ A ) )
= ( times_times @ TA @ ( number_number_of @ TA @ ( times_times @ int @ C @ B ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(116,axiom,
! [A: int,B: int,C: int] :
( ( times_times @ int @ ( plus_plus @ int @ C @ B ) @ A )
= ( plus_plus @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_int__distrib_I1_J) ).
thf(446,plain,
! [A: int,B: int,C: int] :
( ( times_times @ int @ ( plus_plus @ int @ C @ B ) @ A )
= ( plus_plus @ int @ ( times_times @ int @ C @ A ) @ ( times_times @ int @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(92,axiom,
! [A: nat] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__mult__2) ).
thf(368,plain,
! [A: nat] :
( ( times_times @ nat @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ nat @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(56,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_abs__power2) ).
thf(250,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( abs_abs @ TA @ ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(123,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ A ) )
= ( times_times @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_abs__mult__self) ).
thf(465,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( abs_abs @ TA @ A ) @ ( abs_abs @ TA @ A ) )
= ( times_times @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(47,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
thf(231,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( plus_plus @ TA @ C @ B ) @ A )
= ( plus_plus @ TA @ ( times_times @ TA @ C @ A ) @ ( times_times @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(140,axiom,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ B @ C ) ) )
<=> ( ( D = B )
| ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_crossproduct__eq) ).
thf(517,plain,
! [TA: $tType] :
( ( semiri456707255roduct @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( ( plus_plus @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ B @ C ) ) )
=> ( ( D = B )
| ( C = A ) ) )
& ( ( ( D = B )
| ( C = A ) )
=> ( ( plus_plus @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ D @ A ) @ ( times_times @ TA @ B @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(76,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_add__numeral__0) ).
thf(319,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ pls ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
linordered_idom @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(158,plain,
linordered_idom @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(103,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_rel__simps_I50_J) ).
thf(401,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(112,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_semiring__mult__2) ).
thf(433,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) @ A )
= ( plus_plus @ TA @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(37,axiom,
! [A: nat,B: nat,C: int] :
( ( power_power @ int @ ( power_power @ int @ C @ B ) @ A )
= ( power_power @ int @ C @ ( times_times @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_zpower__zpower) ).
thf(207,plain,
! [A: nat,B: nat,C: int] :
( ( power_power @ int @ ( power_power @ int @ C @ B ) @ A )
= ( power_power @ int @ C @ ( times_times @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(63,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).
thf(272,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( times_times @ TA @ ( times_times @ TA @ D @ C ) @ ( times_times @ TA @ B @ A ) )
= ( times_times @ TA @ ( times_times @ TA @ D @ B ) @ ( times_times @ TA @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(86,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).
thf(346,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( times_times @ TA @ ( times_times @ TA @ C @ B ) @ A )
= ( times_times @ TA @ ( times_times @ TA @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(69,axiom,
comm_semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(290,plain,
comm_semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(94,axiom,
semiri456707255roduct @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(378,plain,
semiri456707255roduct @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(49,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_add__number__of__eq) ).
thf(235,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(54,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_number__of__add) ).
thf(246,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( number_number_of @ TA @ ( plus_plus @ int @ B @ A ) )
= ( plus_plus @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_times_Oidem) ).
thf(214,plain,
! [TA: $tType] :
( ( ab_sem1668676832m_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(68,axiom,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_right__distrib__number__of) ).
thf(287,plain,
! [TA: $tType] :
( ( ( number @ TA )
& ( semiring @ TA ) )
=> ! [A: TA,B: TA,C: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ C ) @ ( plus_plus @ TA @ B @ A ) )
= ( plus_plus @ TA @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ B ) @ ( times_times @ TA @ ( number_number_of @ TA @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(10,axiom,
ab_semigroup_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(151,plain,
ab_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
cancel_semigroup_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(146,plain,
cancel_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(104,axiom,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( plus_plus @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) )
= ( plus_plus @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_abs__add__abs) ).
thf(405,plain,
! [TA: $tType] :
( ( ordere142940540dd_abs @ TA )
=> ! [A: TA,B: TA] :
( ( abs_abs @ TA @ ( plus_plus @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) )
= ( plus_plus @ TA @ ( abs_abs @ TA @ B ) @ ( abs_abs @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(31,axiom,
! [A: int,B: int] :
( ( power_power @ int @ ( plus_plus @ int @ B @ A ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ B ) @ ( 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/sandbox2/benchmark/theBenchmark.p',fact_5_zadd__power3) ).
thf(190,plain,
! [A: int,B: int] :
( ( power_power @ int @ ( plus_plus @ int @ B @ A ) @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
= ( plus_plus @ int @ ( plus_plus @ int @ ( plus_plus @ int @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power @ int @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ A ) ) @ ( times_times @ int @ ( times_times @ int @ ( number_number_of @ int @ ( bit1 @ ( bit1 @ pls ) ) ) @ B ) @ ( 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)],[31]) ).
thf(28,axiom,
comm_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring) ).
thf(183,plain,
comm_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(21,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(168,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(59,axiom,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(262,plain,
! [TA: $tType] :
( ( comm_semiring_1 @ TA )
=> ! [A: TA,B: TA] :
( ( plus_plus @ TA @ B @ A )
= ( plus_plus @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(38,axiom,
semiri456707255roduct @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
thf(210,plain,
semiri456707255roduct @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(51,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(239,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(126,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_arith__simps_I32_J) ).
thf(474,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int,B: int] :
( ( times_times @ TA @ ( number_number_of @ TA @ B ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( times_times @ int @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(137,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rel__simps_I38_J) ).
thf(506,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(61,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(268,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(101,axiom,
! [A: int] :
( ( abs_abs @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ ( abs_abs @ int @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_abs__power2__distrib) ).
thf(395,plain,
! [A: int] :
( ( abs_abs @ int @ ( power_power @ int @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( power_power @ int @ ( abs_abs @ int @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(122,axiom,
semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(464,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(110,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mult__numeral__1) ).
thf(427,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( number_number_of @ TA @ ( bit1 @ pls ) ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(25,axiom,
ab_semigroup_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__mult) ).
thf(178,plain,
ab_semigroup_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_number__of__is__id) ).
thf(227,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(77,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_add__left__cancel) ).
thf(322,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(134,axiom,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__right__imp__eq) ).
thf(496,plain,
! [TA: $tType] :
( ( cancel_semigroup_add @ TA )
=> ! [A: TA,B: TA,C: TA] :
( ( ( plus_plus @ TA @ C @ B )
= ( plus_plus @ TA @ A @ B ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(545,plain,
$false,
inference(cvc4,[status(thm)],[365,249,468,234,481,352,408,217,449,379,440,269,385,142,340,153,417,436,184,196,460,157,421,284,152,316,261,179,443,238,514,480,211,253,147,221,453,243,265,307,452,201,220,334,349,297,424,275,165,484,493,224,156,388,169,499,339,193,526,328,471,371,503,343,398,148,180,149,513,430,291,281,204,391,382,313,144,335,159,187,172,230,362,477,240,155,278,394,306,490,162,487,145,150,409,199,331,463,338,359,154,175,446,368,250,465,231,517,319,158,401,433,207,272,346,290,378,235,246,214,287,151,146,405,190,183,168,262,210,239,474,506,268,395,464,427,178,227,322,496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM996_5 : TPTP v8.1.2. Released v6.0.0.
% 0.05/0.11 % Command : run_Leo-III %s %d
% 0.11/0.29 % Computer : n032.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Thu May 18 16:57:35 EDT 2023
% 0.11/0.29 % CPUTime :
% 0.68/0.72 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.90 % [INFO] Parsing done (172ms).
% 1.11/0.90 % [INFO] Running in sequential loop mode.
% 1.81/1.10 % [INFO] eprover registered as external prover.
% 1.81/1.10 % [INFO] cvc4 registered as external prover.
% 1.81/1.11 % [INFO] Scanning for conjecture ...
% 2.01/1.20 % [INFO] Found a conjecture and 141 axioms. Running axiom selection ...
% 2.31/1.28 % [INFO] Axiom selection finished. Selected 139 axioms (removed 2 axioms).
% 2.74/1.39 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.74/1.41 % [INFO] Type checking passed.
% 2.74/1.41 % [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 ...
% 7.07/2.58 % External prover 'cvc4' found a proof!
% 7.07/2.58 % [INFO] Killing All external provers ...
% 7.07/2.59 % Time passed: 2181ms (effective reasoning time: 1678ms)
% 7.07/2.59 % 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)>
% 7.07/2.59 % Axioms used in derivation (139): arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_49_abs__power3__distrib, fact_17_rel__simps_I50_J, fact_94_combine__common__factor, fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J, arity_Nat_Onat___Groups_Omonoid__mult, fact_85_add__left__imp__eq, arity_Nat_Onat___Groups_Oab__semigroup__mult, fact_40_plus__numeral__code_I9_J, arity_Int_Oint___Rings_Olinordered__idom, fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J, arity_Int_Oint___Int_Oring__char__0, fact_39_int__distrib_I2_J, fact_70_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J, fact_45_mult__numeral__1, fact_91_comm__semiring__class_Odistrib, fact_35_add__Pls, fact_57_abs__power2__distrib, arity_Nat_Onat___Int_Onumber__semiring, fact_21_Bit0__Pls, fact_51_mult__2, fact_16_rel__simps_I39_J, arity_RealDef_Oreal___Int_Onumber__semiring, fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J, fact_6_power2__sum, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_74_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J, arity_Int_Oint___Rings_Ocomm__semiring, arity_Int_Oint___Groups_Oordered__ab__group__add__abs, arity_Int_Oint___Int_Onumber__semiring, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_82_ab__semigroup__add__class_Oadd__ac_I1_J, fact_65_add__left__cancel, fact_5_zadd__power3, arity_Int_Oint___Int_Onumber__ring, fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, fact_7_add__Bit0__Bit1, fact_61_abs__mult__self, fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_68_mult__idem, fact_87_add__right__imp__eq, fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_23_mult__Bit0, fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_15_rel__simps_I46_J, fact_38_int__distrib_I1_J, arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_43_number__of__mult, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_60_abs__add__abs, arity_RealDef_Oreal___Rings_Ocomm__semiring, fact_44_number__of__add, fact_25_left__distrib__number__of, fact_28_zpower__zpower, fact_19_rel__simps_I44_J, arity_RealDef_Oreal___Int_Onumber__ring, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, fact_63_abs__idempotent, arity_Int_Oint___Groups_Omonoid__mult, fact_67_times_Oidem, fact_34_add__Pls__right, fact_50_semiring__mult__2, fact_26_right__distrib__number__of, fact_3_mult__Bit1, fact_95_crossproduct__eq, arity_RealDef_Oreal___Rings_Olinordered__idom, arity_Nat_Onat___Rings_Ocomm__semiring, fact_22_mult__Pls, fact_47_power3__eq__cube, fact_66_mult__left__idem, fact_75_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J, fact_41_add__numeral__0, arity_Int_Oint___Rings_Osemiring, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_33_power__even__eq, fact_55_cube__square, fact_36_Bit0__def, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_RealDef_Oreal___Int_Oring__char__0, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, fact_72_ab__semigroup__mult__class_Omult__ac_I1_J, fact_90_crossproduct__noteq, fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J, arity_RealDef_Oreal___Rings_Osemiring, fact_13_rel__simps_I51_J, fact_53_mult__2__right, fact_9_add__number__of__eq, fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J, fact_62_four__x__squared, fact_12_eq__number__of, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_8_add__Bit1__Bit0, fact_4_zadd__power2, fact_27_mult__number__of__left, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J, arity_Nat_Onat___Int_Onumber, fact_14_rel__simps_I48_J, fact_11_arith__simps_I32_J, fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J, fact_42_add__numeral__0__right, fact_59_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J, fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J, fact_86_add__imp__eq, fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J, fact_64_add__right__cancel, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_37_times__numeral__code_I5_J, fact_32_number__of__is__id, fact_73_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J, arity_Int_Oint___Groups_Oab__semigroup__add, fact_18_rel__simps_I49_J, fact_30_nat__mult__2__right, arity_Nat_Onat___Rings_Osemiring, fact_48_quartic__square__square, fact_10_add__number__of__left, fact_52_semiring__mult__2__right, arity_Int_Oint___Groups_Oab__semigroup__mult, fact_54_power2__eq__square, fact_29_nat__mult__2, arity_RealDef_Oreal___Int_Onumber, arity_RealDef_Oreal___Groups_Oab__semigroup__mult, arity_Int_Oint___Int_Onumber, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_0_power2__eq__square__number__of, fact_2_power2__abs, fact_71_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J, fact_31_number__of__reorient, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_56_power2__eq__iff__abs__eq, fact_69_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J, fact_1_abs__power2, arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs, fact_24_add__Bit0__Bit0, fact_20_rel__simps_I38_J, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_46_mult__numeral__1__right
% 7.07/2.59 % No. of inferences in proof: 282
% 7.07/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2181 ms resp. 1678 ms w/o parsing
% 7.72/2.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.72/2.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------