TSTP Solution File: SWW497_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW497_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 12:24:54 EDT 2023
% Result : Theorem 8.28s 2.91s
% Output : Refutation 8.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 223
% Syntax : Number of formulae : 401 ( 230 unt; 47 typ; 0 def)
% Number of atoms : 585 ( 310 equ; 0 cnn)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 2261 ( 17 ~; 0 |; 52 &;2017 @)
% ( 23 <=>; 152 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 6 ( 5 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 6 con; 0-4 aty)
% Number of variables : 434 ( 0 ^; 400 !; 0 ?; 434 :)
% ( 34 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
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(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(number_type,type,
number:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(power_type,type,
power:
!>[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(mult_zero_type,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_type,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(number_semiring_type,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_type,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(ab_semigroup_add_type,type,
ab_semigroup_add:
!>[TA: $tType] : $o ).
thf(comm_monoid_mult_type,type,
comm_monoid_mult:
!>[TA: $tType] : $o ).
thf(cancel_semigroup_add_type,type,
cancel_semigroup_add:
!>[TA: $tType] : $o ).
thf(linord581940658strict_type,type,
linord581940658strict:
!>[TA: $tType] : $o ).
thf(real_normed_vector_type,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_type,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(cancel146912293up_add_type,type,
cancel146912293up_add:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(real_n2089651433ebra_1_type,type,
real_n2089651433ebra_1:
!>[TA: $tType] : $o ).
thf(real_n1866405975lgebra_type,type,
real_n1866405975lgebra:
!>[TA: $tType] : $o ).
thf(complex1_type,type,
complex1: real > real > complex ).
thf(complex_case_type,type,
complex_case:
!>[TA: $tType] : ( ( fun @ real @ ( fun @ real @ TA ) ) > complex > TA ) ).
thf(complex_rec_type,type,
complex_rec:
!>[TA: $tType] : ( ( fun @ real @ ( fun @ real @ TA ) ) > complex > TA ) ).
thf(fundam1563812824_csqrt_type,type,
fundam1563812824_csqrt: complex > complex ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : 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(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : 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(sqrt_type,type,
sqrt: real > real ).
thf(power_power_type,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(norm_norm_type,type,
norm_norm:
!>[TA: $tType] : ( TA > real ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(x_type,type,
x: real ).
thf(y_type,type,
y: real ).
thf(z_type,type,
z: complex ).
thf(84,axiom,
number @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(365,plain,
number @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(75,axiom,
ring_char_0 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(347,plain,
ring_char_0 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(43,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(234,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(78,axiom,
semiring_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(352,plain,
semiring_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(173,axiom,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_number__of__is__id) ).
thf(628,plain,
! [A: int] :
( ( number_number_of @ int @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(49,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_33_number__of__reorient) ).
thf(249,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)],[49]) ).
thf(138,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_semiring__one__add__one__is__two) ).
thf(523,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(21,axiom,
comm_monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__mult) ).
thf(202,plain,
comm_monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(36,axiom,
! [A: real,B: real,C: real,D: real] :
( ( ( complex1 @ D @ C )
= ( complex1 @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_complex_Oinject) ).
thf(217,plain,
! [A: real,B: real,C: real,D: real] :
( ( ( ( complex1 @ D @ C )
= ( complex1 @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( complex1 @ D @ C )
= ( complex1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(56,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_47_add__left__cancel) ).
thf(276,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)],[56]) ).
thf(93,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_one__reorient) ).
thf(385,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(92,axiom,
semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(384,plain,
semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(142,axiom,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_add__Pls) ).
thf(533,plain,
! [A: int] :
( ( plus_plus @ int @ pls @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(129,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_mult__1) ).
thf(500,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(8,axiom,
~ ! [A: real,B: real] :
( z
!= ( complex1 @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
thf(185,plain,
~ ! [A: real,B: real] :
( z
!= ( complex1 @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(69,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_power__one) ).
thf(320,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat] :
( ( power_power @ TA @ ( one_one @ TA ) @ A )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(154,axiom,
comm_monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) ).
thf(565,plain,
comm_monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(7,axiom,
number_ring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(184,plain,
number_ring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(171,axiom,
number_semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(619,plain,
number_semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(81,axiom,
number @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(357,plain,
number @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
power @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(196,plain,
power @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(152,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( one_one @ TA )
= ( number_number_of @ TA @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_semiring__norm_I110_J) ).
thf(559,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( one_one @ TA )
= ( number_number_of @ TA @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(104,axiom,
ab_semigroup_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(421,plain,
ab_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(102,axiom,
( z
= ( complex1 @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_z) ).
thf(416,plain,
( z
= ( complex1 @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(37,axiom,
ring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(228,plain,
ring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(60,axiom,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_nat__1__add__1) ).
thf(289,plain,
( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
= ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(112,axiom,
! [A: real,B: real] :
( ( norm_norm @ complex @ ( complex1 @ B @ A ) )
= ( sqrt @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_complex__norm) ).
thf(448,plain,
! [A: real,B: real] :
( ( norm_norm @ complex @ ( complex1 @ B @ A ) )
= ( sqrt @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(52,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_19_add__Bit0__Bit0) ).
thf(261,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)],[52]) ).
thf(35,axiom,
mult_zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(216,plain,
mult_zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(30,axiom,
ring_11004092258visors @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(211,plain,
ring_11004092258visors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(76,axiom,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_semiring__numeral__1__eq__1) ).
thf(348,plain,
! [TA: $tType] :
( ( number_semiring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(79,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_add__special_I3_J) ).
thf(353,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( number_number_of @ TA @ A ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ A @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(167,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_norm__eq__zero) ).
thf(602,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ! [A: TA] :
( ( ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( norm_norm @ TA @ A )
= ( zero_zero @ real ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(95,axiom,
! [TA: $tType] :
( ( real_n1866405975lgebra @ TA )
=> ! [A: nat,B: TA] :
( ( norm_norm @ TA @ ( power_power @ TA @ B @ A ) )
= ( power_power @ real @ ( norm_norm @ TA @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_norm__power) ).
thf(396,plain,
! [TA: $tType] :
( ( real_n1866405975lgebra @ TA )
=> ! [A: nat,B: TA] :
( ( norm_norm @ TA @ ( power_power @ TA @ B @ A ) )
= ( power_power @ real @ ( norm_norm @ TA @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
! [A: int] :
( ( pls
= ( bit0 @ A ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_rel__simps_I38_J) ).
thf(428,plain,
! [A: int] :
( ( ( pls
= ( bit0 @ A ) )
=> ( pls = A ) )
& ( ( pls = A )
=> ( pls
= ( bit0 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(132,axiom,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_one__is__num__one) ).
thf(507,plain,
( ( one_one @ int )
= ( number_number_of @ int @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(25,axiom,
linord581940658strict @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(206,plain,
linord581940658strict @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(140,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ B )
= ( times_times @ TA @ B @ ( power_power @ TA @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_power__commutes) ).
thf(527,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: nat,B: TA] :
( ( times_times @ TA @ ( power_power @ TA @ B @ A ) @ B )
= ( times_times @ TA @ B @ ( power_power @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(67,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(312,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(42,axiom,
number_semiring @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(233,plain,
number_semiring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
number_ring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(248,plain,
number_ring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(20,axiom,
number @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(201,plain,
number @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(85,axiom,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Bit0__def) ).
thf(366,plain,
! [A: int] :
( ( bit0 @ A )
= ( plus_plus @ int @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(134,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_27_plus__numeral__code_I9_J) ).
thf(512,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)],[134]) ).
thf(111,axiom,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_power__eq__0__iff) ).
thf(439,plain,
! [TA: $tType] :
( ( ( power @ TA )
& ( mult_zero @ TA )
& ( no_zero_divisors @ TA )
& ( zero_neq_one @ TA ) )
=> ! [A: nat,B: TA] :
( ( ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( A
!= ( zero_zero @ nat ) ) )
=> ( ( power_power @ TA @ B @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(94,axiom,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_rel__simps_I39_J) ).
thf(392,plain,
! [A: int] :
( pls
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(106,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_85_power2__eq__square__number__of) ).
thf(424,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)],[106]) ).
thf(11,axiom,
number_ring @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(192,plain,
number_ring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,axiom,
real_n1866405975lgebra @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) ).
thf(275,plain,
real_n1866405975lgebra @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(120,axiom,
! [A: real,B: real] :
( ( sqrt @ ( times_times @ real @ B @ A ) )
= ( times_times @ real @ ( sqrt @ B ) @ ( sqrt @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_real__sqrt__mult) ).
thf(467,plain,
! [A: real,B: real] :
( ( sqrt @ ( times_times @ real @ B @ A ) )
= ( times_times @ real @ ( sqrt @ B ) @ ( sqrt @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(16,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(197,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(109,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_87_number__of__mult) ).
thf(435,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)],[109]) ).
thf(159,axiom,
semiring @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring) ).
thf(583,plain,
semiring @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(115,axiom,
zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(461,plain,
zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(149,axiom,
! [TA: $tType] :
( ( real_n2089651433ebra_1 @ TA )
=> ( ( norm_norm @ TA @ ( one_one @ TA ) )
= ( one_one @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_norm__one) ).
thf(551,plain,
! [TA: $tType] :
( ( real_n2089651433ebra_1 @ TA )
=> ( ( norm_norm @ TA @ ( one_one @ TA ) )
= ( one_one @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(58,axiom,
mult_zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(285,plain,
mult_zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(38,axiom,
comm_monoid_mult @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) ).
thf(229,plain,
comm_monoid_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(155,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_20_add__number__of__left) ).
thf(566,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)],[155]) ).
thf(136,axiom,
one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(519,plain,
one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(169,axiom,
cancel146912293up_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(615,plain,
cancel146912293up_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(98,axiom,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus @ complex @ ( complex1 @ D @ C ) @ ( complex1 @ B @ A ) )
= ( complex1 @ ( plus_plus @ real @ D @ B ) @ ( plus_plus @ real @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_complex__add) ).
thf(403,plain,
! [A: real,B: real,C: real,D: real] :
( ( plus_plus @ complex @ ( complex1 @ D @ C ) @ ( complex1 @ B @ A ) )
= ( complex1 @ ( plus_plus @ real @ D @ B ) @ ( plus_plus @ real @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(80,axiom,
ring_11004092258visors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(356,plain,
ring_11004092258visors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(164,axiom,
( ( sqrt @ ( one_one @ real ) )
= ( one_one @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_real__sqrt__one) ).
thf(593,plain,
( ( sqrt @ ( one_one @ real ) )
= ( one_one @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(50,axiom,
( ( sqrt @ ( zero_zero @ real ) )
= ( zero_zero @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_real__sqrt__zero) ).
thf(256,plain,
( ( sqrt @ ( zero_zero @ real ) )
= ( zero_zero @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(150,axiom,
( ( norm_norm @ complex @ z )
= ( one_one @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms) ).
thf(554,plain,
( ( norm_norm @ complex @ z )
= ( one_one @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(139,axiom,
power @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(526,plain,
power @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(147,axiom,
linord219039673up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(547,plain,
linord219039673up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(31,axiom,
zero @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(212,plain,
zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
ab_semigroup_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(193,plain,
ab_semigroup_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(144,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_49_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(537,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)],[144]) ).
thf(135,axiom,
! [A: real,B: real] :
( ( ( sqrt @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= B )
=> ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_real__sqrt__sum__squares__eq__cancel) ).
thf(515,plain,
! [A: real,B: real] :
( ( ( sqrt @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
= B )
=> ( A
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(156,axiom,
! [A: int,B: int] :
( ( ( bit0 @ B )
= ( bit0 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_rel__simps_I48_J) ).
thf(569,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)],[156]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_nat__add__assoc) ).
thf(371,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ ( plus_plus @ nat @ C @ B ) @ A )
= ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(130,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ 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_94_power__mult__distrib) ).
thf(503,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ 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)],[130]) ).
thf(46,axiom,
semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(244,plain,
semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(24,axiom,
real_normed_vector @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(205,plain,
real_normed_vector @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(146,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_46_add__right__cancel) ).
thf(541,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)],[146]) ).
thf(141,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_number__of__Pls) ).
thf(530,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ pls )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(161,axiom,
! [A: nat,B: real] :
( ( sqrt @ ( power_power @ real @ B @ A ) )
= ( power_power @ real @ ( sqrt @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_real__sqrt__power) ).
thf(586,plain,
! [A: nat,B: real] :
( ( sqrt @ ( power_power @ real @ B @ A ) )
= ( power_power @ real @ ( sqrt @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(64,axiom,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ( plus_plus @ TA @ ( times_times @ TA @ B @ B ) @ ( times_times @ TA @ A @ A ) )
= ( zero_zero @ TA ) )
<=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_sum__squares__eq__zero__iff) ).
thf(298,plain,
! [TA: $tType] :
( ( linord581940658strict @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( plus_plus @ TA @ ( times_times @ TA @ B @ B ) @ ( times_times @ TA @ A @ A ) )
= ( zero_zero @ TA ) )
=> ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) ) )
& ( ( ( B
= ( zero_zero @ TA ) )
& ( A
= ( zero_zero @ TA ) ) )
=> ( ( plus_plus @ TA @ ( times_times @ TA @ B @ B ) @ ( times_times @ TA @ A @ A ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_nat__add__left__cancel) ).
thf(264,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(3,axiom,
semiring @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring) ).
thf(180,plain,
semiring @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(90,axiom,
! [A: complex] :
( ( power_power @ complex @ ( fundam1563812824_csqrt @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_csqrt) ).
thf(375,plain,
! [A: complex] :
( ( power_power @ complex @ ( fundam1563812824_csqrt @ A ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(160,axiom,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_nat__numeral__1__eq__1) ).
thf(584,plain,
( ( number_number_of @ nat @ ( bit1 @ pls ) )
= ( one_one @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(153,axiom,
! [A: real,B: real,C: real,D: real] :
( ( power_power @ real @ ( sqrt @ ( times_times @ real @ ( plus_plus @ real @ ( power_power @ real @ D @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ real @ ( plus_plus @ real @ ( power_power @ real @ D @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_real__sqrt__sum__squares__mult__squared__eq) ).
thf(562,plain,
! [A: real,B: real,C: real,D: real] :
( ( power_power @ real @ ( sqrt @ ( times_times @ real @ ( plus_plus @ real @ ( power_power @ real @ D @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( times_times @ real @ ( plus_plus @ real @ ( power_power @ real @ D @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ C @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( plus_plus @ real @ ( power_power @ real @ B @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(59,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_24_add__Bit0__Bit1) ).
thf(286,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)],[59]) ).
thf(157,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_35_add__numeral__0) ).
thf(577,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)],[157]) ).
thf(61,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_36_add__numeral__0__right) ).
thf(291,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)],[61]) ).
thf(23,axiom,
number_semiring @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(204,plain,
number_semiring @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
no_zero_divisors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(191,plain,
no_zero_divisors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(97,axiom,
zero_neq_one @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(402,plain,
zero_neq_one @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(177,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_one__power2) ).
thf(641,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( one_one @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(68,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_nat__add__right__cancel) ).
thf(313,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( plus_plus @ nat @ C @ B )
= ( plus_plus @ nat @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(119,axiom,
cancel_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(466,plain,
cancel_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(73,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_34_number__of__add) ).
thf(335,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)],[73]) ).
thf(45,axiom,
! [A: real,B: real] :
( ( ( sqrt @ B )
= ( sqrt @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_real__sqrt__eq__iff) ).
thf(236,plain,
! [A: real,B: real] :
( ( ( ( sqrt @ B )
= ( sqrt @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( sqrt @ B )
= ( sqrt @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(181,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(145,axiom,
no_zero_divisors @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(540,plain,
no_zero_divisors @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(99,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_78_right__distrib__number__of) ).
thf(406,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)],[99]) ).
thf(39,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)],[39]) ).
thf(47,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_71_arith__simps_I32_J) ).
thf(245,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)],[47]) ).
thf(133,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zero__power2) ).
thf(509,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( power_power @ TA @ ( zero_zero @ TA ) @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(170,axiom,
! [TA: $tType,A: real,B: real,C: fun @ real @ ( fun @ real @ TA )] :
( ( complex_case @ TA @ C @ ( complex1 @ B @ A ) )
= ( aa @ real @ TA @ ( aa @ real @ ( fun @ real @ TA ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_complex_Osimps_I2_J) ).
thf(616,plain,
! [TA: $tType,A: real,B: real,C: fun @ real @ ( fun @ real @ TA )] :
( ( complex_case @ TA @ C @ ( complex1 @ B @ A ) )
= ( aa @ real @ TA @ ( aa @ real @ ( fun @ real @ TA ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(166,axiom,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nat__add__commute) ).
thf(599,plain,
! [A: nat,B: nat] :
( ( plus_plus @ nat @ B @ A )
= ( plus_plus @ nat @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(83,axiom,
! [TA: $tType,A: real,B: real,C: fun @ real @ ( fun @ real @ TA )] :
( ( complex_rec @ TA @ C @ ( complex1 @ B @ A ) )
= ( aa @ real @ TA @ ( aa @ real @ ( fun @ real @ TA ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_complex_Orecs) ).
thf(362,plain,
! [TA: $tType,A: real,B: real,C: fun @ real @ ( fun @ real @ TA )] :
( ( complex_rec @ TA @ C @ ( complex1 @ B @ A ) )
= ( aa @ real @ TA @ ( aa @ real @ ( fun @ real @ TA ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_Bit1__def) ).
thf(451,plain,
! [A: int] :
( ( bit1 @ A )
= ( plus_plus @ int @ ( plus_plus @ int @ ( one_one @ int ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(54,axiom,
! [A: int] :
( ( bit1 @ A )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_rel__simps_I46_J) ).
thf(271,plain,
! [A: int] :
( ( bit1 @ A )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(27,axiom,
monoid_mult @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(208,plain,
monoid_mult @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(124,axiom,
no_zero_divisors @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(477,plain,
no_zero_divisors @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(127,axiom,
! [TA: $tType] :
( ( real_n1866405975lgebra @ TA )
=> ! [A: TA,B: TA] :
( ( norm_norm @ TA @ ( times_times @ TA @ B @ A ) )
= ( times_times @ real @ ( norm_norm @ TA @ B ) @ ( norm_norm @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_norm__mult) ).
thf(494,plain,
! [TA: $tType] :
( ( real_n1866405975lgebra @ TA )
=> ! [A: TA,B: TA] :
( ( norm_norm @ TA @ ( times_times @ TA @ B @ A ) )
= ( times_times @ real @ ( norm_norm @ TA @ B ) @ ( norm_norm @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(174,axiom,
comm_monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__mult) ).
thf(631,plain,
comm_monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(70,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_77_left__distrib__number__of) ).
thf(323,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)],[70]) ).
thf(32,axiom,
real_n1866405975lgebra @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) ).
thf(213,plain,
real_n1866405975lgebra @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(137,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_72_mult__number__of__left) ).
thf(520,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)],[137]) ).
thf(17,axiom,
ring_11004092258visors @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(198,plain,
ring_11004092258visors @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(116,axiom,
monoid_mult @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(462,plain,
monoid_mult @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(96,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_50_add__left__imp__eq) ).
thf(399,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)],[96]) ).
thf(168,axiom,
! [A: int] :
( ( ( bit0 @ A )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_rel__simps_I44_J) ).
thf(608,plain,
! [A: int] :
( ( ( ( bit0 @ A )
= pls )
=> ( A = pls ) )
& ( ( A = pls )
=> ( ( bit0 @ A )
= pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(65,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_power__one__right) ).
thf(306,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( power_power @ TA @ A @ ( one_one @ nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(110,axiom,
ab_semigroup_add @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(438,plain,
ab_semigroup_add @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(122,axiom,
mult_zero @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(473,plain,
mult_zero @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(162,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit1 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_number__of__Bit1) ).
thf(589,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( number_number_of @ TA @ ( bit1 @ A ) )
= ( plus_plus @ TA @ ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) ) @ ( number_number_of @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(148,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_52_add__right__imp__eq) ).
thf(548,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)],[148]) ).
thf(89,axiom,
monoid_mult @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(374,plain,
monoid_mult @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(13,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(194,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(28,axiom,
zero_neq_one @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(209,plain,
zero_neq_one @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(126,axiom,
! [A: real] :
( ( ( sqrt @ A )
= ( zero_zero @ real ) )
<=> ( A
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_real__sqrt__eq__0__iff) ).
thf(487,plain,
! [A: real] :
( ( ( ( sqrt @ A )
= ( zero_zero @ real ) )
=> ( A
= ( zero_zero @ real ) ) )
& ( ( A
= ( zero_zero @ real ) )
=> ( ( sqrt @ A )
= ( zero_zero @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(158,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_mult__1__right) ).
thf(580,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(63,axiom,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_mult__1__left) ).
thf(295,plain,
! [TA: $tType] :
( ( monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ ( one_one @ TA ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(57,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__add__one__is__two) ).
thf(282,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( plus_plus @ TA @ ( one_one @ TA ) @ ( one_one @ TA ) )
= ( number_number_of @ TA @ ( bit0 @ ( bit1 @ pls ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(100,axiom,
cancel146912293up_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(409,plain,
cancel146912293up_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(18,axiom,
semiring_1 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(199,plain,
semiring_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,axiom,
number @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(182,plain,
number @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(87,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(370,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(117,axiom,
number_semiring @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(463,plain,
number_semiring @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(74,axiom,
! [A: int,B: real,C: real] :
( ( ( complex1 @ C @ B )
= ( number_number_of @ complex @ A ) )
<=> ( ( C
= ( number_number_of @ real @ A ) )
& ( B
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Complex__eq__number__of) ).
thf(338,plain,
! [A: int,B: real,C: real] :
( ( ( ( complex1 @ C @ B )
= ( number_number_of @ complex @ A ) )
=> ( ( C
= ( number_number_of @ real @ A ) )
& ( B
= ( zero_zero @ real ) ) ) )
& ( ( ( C
= ( number_number_of @ real @ A ) )
& ( B
= ( zero_zero @ real ) ) )
=> ( ( complex1 @ C @ B )
= ( number_number_of @ complex @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(121,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_51_add__imp__eq) ).
thf(470,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)],[121]) ).
thf(165,axiom,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_rel__simps_I50_J) ).
thf(595,plain,
! [A: int,B: int] :
( ( bit1 @ B )
!= ( bit0 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_nat__add__left__commute) ).
thf(497,plain,
! [A: nat,B: nat,C: nat] :
( ( plus_plus @ nat @ C @ ( plus_plus @ nat @ B @ A ) )
= ( plus_plus @ nat @ B @ ( plus_plus @ nat @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(40,axiom,
ring_char_0 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(231,plain,
ring_char_0 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(151,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_21_add__number__of__eq) ).
thf(556,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)],[151]) ).
thf(22,axiom,
power @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(203,plain,
power @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(51,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_numeral__1__eq__1) ).
thf(258,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ( ( number_number_of @ TA @ ( bit1 @ pls ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(77,axiom,
cancel_semigroup_add @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(351,plain,
cancel_semigroup_add @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(175,axiom,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ( ( norm_norm @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_norm__zero) ).
thf(632,plain,
! [TA: $tType] :
( ( real_normed_vector @ TA )
=> ( ( norm_norm @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ real ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(103,axiom,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add__Pls__right) ).
thf(418,plain,
! [A: int] :
( ( plus_plus @ int @ A @ pls )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(91,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_double__eq__0__iff) ).
thf(378,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( plus_plus @ TA @ A @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(44,axiom,
cancel146912293up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(235,plain,
cancel146912293up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
one @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(207,plain,
one @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(125,axiom,
! [A: real,B: real] :
( ( ( complex1 @ B @ A )
= ( one_one @ complex ) )
<=> ( ( B
= ( one_one @ real ) )
& ( A
= ( zero_zero @ real ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_Complex__eq__1) ).
thf(478,plain,
! [A: real,B: real] :
( ( ( ( complex1 @ B @ A )
= ( one_one @ complex ) )
=> ( ( B
= ( one_one @ real ) )
& ( A
= ( zero_zero @ real ) ) ) )
& ( ( ( B
= ( one_one @ real ) )
& ( A
= ( zero_zero @ real ) ) )
=> ( ( complex1 @ B @ A )
= ( one_one @ complex ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(143,axiom,
real_n2089651433ebra_1 @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) ).
thf(536,plain,
real_n2089651433ebra_1 @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(33,axiom,
ab_semigroup_add @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__semigroup__add) ).
thf(214,plain,
ab_semigroup_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(172,axiom,
! [A: int,B: int] :
( ( ( bit1 @ B )
= ( bit1 @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_rel__simps_I51_J) ).
thf(620,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)],[172]) ).
thf(101,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_14_eq__number__of) ).
thf(410,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)],[101]) ).
thf(9,axiom,
cancel_semigroup_add @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) ).
thf(190,plain,
cancel_semigroup_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
monoid_mult @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(183,plain,
monoid_mult @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(105,axiom,
( ( bit0 @ pls )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_Bit0__Pls) ).
thf(422,plain,
( ( bit0 @ pls )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(29,axiom,
cancel146912293up_add @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add) ).
thf(210,plain,
cancel146912293up_add @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_zero__eq__power2) ).
thf(326,plain,
! [TA: $tType] :
( ( ring_11004092258visors @ TA )
=> ! [A: TA] :
( ( ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( power_power @ TA @ A @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(294,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(131,axiom,
linord581940658strict @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
thf(506,plain,
linord581940658strict @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_rel__simps_I49_J) ).
thf(358,plain,
! [A: int,B: int] :
( ( bit0 @ B )
!= ( bit1 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(14,axiom,
no_zero_divisors @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(195,plain,
no_zero_divisors @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(123,axiom,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_mult_Ocomm__neutral) ).
thf(474,plain,
! [TA: $tType] :
( ( comm_monoid_mult @ TA )
=> ! [A: TA] :
( ( times_times @ TA @ A @ ( one_one @ TA ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(176,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_double__zero__sym) ).
thf(635,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= ( plus_plus @ TA @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(118,axiom,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_Numeral1__eq1__nat) ).
thf(464,plain,
( ( one_one @ nat )
= ( number_number_of @ nat @ ( bit1 @ pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(72,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_23_add__Bit1__Bit0) ).
thf(332,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)],[72]) ).
thf(107,axiom,
real_normed_vector @ real,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___RealVector_Oreal__normed__vector) ).
thf(427,plain,
real_normed_vector @ real,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(19,axiom,
mult_zero @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(200,plain,
mult_zero @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
( ( plus_plus @ real @ ( power_power @ real @ x @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
= ( one_one @ real ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( plus_plus @ real @ ( power_power @ real @ x @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( one_one @ real ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(178,plain,
( ( plus_plus @ real @ ( power_power @ real @ x @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power @ real @ y @ ( number_number_of @ nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
!= ( one_one @ real ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(369,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(66,axiom,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_add__special_I2_J) ).
thf(309,plain,
! [TA: $tType] :
( ( number_ring @ TA )
=> ! [A: int] :
( ( plus_plus @ TA @ ( one_one @ TA ) @ ( number_number_of @ TA @ A ) )
= ( number_number_of @ TA @ ( plus_plus @ int @ ( bit1 @ pls ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(34,axiom,
real_n2089651433ebra_1 @ complex,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) ).
thf(215,plain,
real_n2089651433ebra_1 @ complex,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(163,axiom,
power @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(592,plain,
power @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(114,axiom,
! [A: real] :
( ( ( sqrt @ A )
= ( one_one @ real ) )
<=> ( A
= ( one_one @ real ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_real__sqrt__eq__1__iff) ).
thf(454,plain,
! [A: real] :
( ( ( ( sqrt @ A )
= ( one_one @ real ) )
=> ( A
= ( one_one @ real ) ) )
& ( ( A
= ( one_one @ real ) )
=> ( ( sqrt @ A )
= ( one_one @ real ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(41,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(232,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(667,plain,
$false,
inference(cvc4,[status(thm)],[365,347,234,352,628,249,523,202,217,276,385,384,533,500,185,320,565,184,619,357,196,559,421,416,228,289,448,261,216,211,348,353,602,396,428,507,206,527,312,233,248,201,366,512,439,392,424,192,275,467,197,435,583,461,551,285,229,566,519,615,403,356,593,256,554,526,547,212,193,537,515,569,371,503,244,205,541,530,586,298,264,180,375,584,562,286,577,291,204,191,402,641,313,466,335,236,181,540,406,230,245,509,616,599,362,451,271,208,477,494,631,323,213,520,198,462,399,608,306,438,473,589,548,374,194,209,487,580,295,282,409,199,182,370,463,338,470,595,497,231,556,203,258,351,632,418,378,235,207,478,536,214,620,410,190,183,422,210,326,294,506,358,195,474,635,464,332,427,200,178,369,309,215,592,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SWW497_5 : TPTP v8.1.2. Released v6.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 22:47:19 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.67/1.08 % [INFO] Parsing done (200ms).
% 1.67/1.10 % [INFO] Running in sequential loop mode.
% 2.37/1.39 % [INFO] eprover registered as external prover.
% 2.37/1.40 % [INFO] cvc4 registered as external prover.
% 2.37/1.40 % [INFO] Scanning for conjecture ...
% 2.67/1.51 % [INFO] Found a conjecture and 177 axioms. Running axiom selection ...
% 2.79/1.60 % [INFO] Axiom selection finished. Selected 175 axioms (removed 2 axioms).
% 3.35/1.71 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.35/1.72 % [INFO] Type checking passed.
% 3.35/1.73 % [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 ...
% 8.28/2.91 % External prover 'cvc4' found a proof!
% 8.28/2.91 % [INFO] Killing All external provers ...
% 8.28/2.91 % Time passed: 2376ms (effective reasoning time: 1805ms)
% 8.28/2.91 % 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)>
% 8.28/2.91 % Axioms used in derivation (175): fact_6_numeral__1__eq__1, arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra, fact_60_nat__add__left__commute, arity_Nat_Onat___Groups_Omonoid__mult, fact_10_rel__simps_I44_J, fact_30_Bit0__def, arity_Int_Oint___Rings_Olinordered__ring__strict, fact_80_norm__zero, arity_Int_Oint___Groups_Oone, fact_70_double__eq__0__iff, arity_Complex_Ocomplex___Groups_Oab__semigroup__add, arity_Nat_Onat___Rings_Osemiring__1, fact_17__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096, arity_RealDef_Oreal___Rings_Olinordered__ring__strict, arity_Int_Oint___Int_Oring__char__0, fact_86_real__sqrt__mult, fact_95_power__commutes, fact_20_add__number__of__left, arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra, fact_5_add__special_I3_J, fact_92_mult__1, arity_Complex_Ocomplex___Power_Opower, fact_66_real__sqrt__sum__squares__mult__squared__eq, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_61_nat__add__commute, arity_RealDef_Oreal___Groups_Ozero, fact_16_rel__simps_I48_J, fact_82_Complex__eq__1, arity_Nat_Onat___Int_Onumber__semiring, arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add, fact_55_complex__norm, fact_19_add__Bit0__Bit0, arity_RealDef_Oreal___Int_Onumber__semiring, fact_8_Bit0__Pls, fact_69_double__zero__sym, arity_Nat_Onat___Power_Opower, fact_25_nat__1__add__1, arity_RealDef_Oreal___Groups_Ocomm__monoid__mult, fact_1_z, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, arity_Complex_Ocomplex___Int_Oring__char__0, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_21_add__number__of__eq, fact_87_number__of__mult, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Int_Onumber__semiring, fact_28_add__Pls__right, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_46_add__right__cancel, arity_Int_Oint___Int_Onumber__ring, arity_Int_Oint___Rings_Osemiring__1, fact_63_real__sqrt__eq__1__iff, arity_Nat_Onat___Rings_Omult__zero, fact_68_real__sqrt__sum__squares__eq__cancel, fact_83_zero__eq__power2, fact_67_complex_Orecs, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_7_semiring__one__add__one__is__two, fact_48_number__of__is__id, fact_77_left__distrib__number__of, fact_51_add__imp__eq, fact_65_real__sqrt__power, fact_88_norm__mult, fact_76_Complex__eq__number__of, fact_54_power__one__right, fact_39_semiring__norm_I110_J, fact_78_right__distrib__number__of, fact_14_eq__number__of, arity_RealDef_Oreal___Rings_Osemiring__1, fact_79_number__of__Pls, fact_12_rel__simps_I50_J, fact_37_number__of__Bit1, fact_81_norm__eq__zero, arity_Complex_Ocomplex___Rings_Osemiring, fact_85_power2__eq__square__number__of, arity_RealDef_Oreal___Int_Onumber__ring, fact_4_add__special_I2_J, fact_27_plus__numeral__code_I9_J, arity_Int_Oint___Groups_Omonoid__mult, fact_52_add__right__imp__eq, fact_36_add__numeral__0__right, fact_89_sum__squares__eq__zero__iff, fact_42_power__one, fact_94_power__mult__distrib, arity_Complex_Ocomplex___Rings_Omult__zero, fact_64_real__sqrt__eq__iff, fact_49_ab__semigroup__add__class_Oadd__ac_I1_J, fact_74_real__sqrt__zero, arity_Int_Oint___Rings_Osemiring, fact_72_mult__number__of__left, fact_11_rel__simps_I49_J, fact_71_arith__simps_I32_J, fact_24_add__Bit0__Bit1, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1, fact_62_real__sqrt__one, arity_Nat_Onat___Groups_Ozero, fact_56_nat__add__left__cancel, fact_91_mult__1__right, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_RealDef_Oreal___Int_Oring__char__0, fact_53_one__reorient, arity_RealDef_Oreal___Rings_Omult__zero, fact_93_mult__1__left, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, arity_Nat_Onat___Groups_Ocomm__monoid__mult, fact_29_add__Pls, arity_RealDef_Oreal___Rings_Osemiring, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, arity_Complex_Ocomplex___Int_Onumber__ring, fact_38_semiring__numeral__1__eq__1, arity_Int_Oint___Power_Opower, fact_47_add__left__cancel, arity_Int_Oint___Groups_Ocancel__semigroup__add, arity_RealDef_Oreal___RealVector_Oreal__normed__vector, arity_Complex_Ocomplex___Rings_Osemiring__1, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_57_nat__add__right__cancel, arity_RealDef_Oreal___Groups_Oone, arity_Nat_Onat___Int_Onumber, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_73_power__eq__0__iff, fact_13_rel__simps_I39_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_32_Numeral1__eq1__nat, fact_40_norm__one, arity_Complex_Ocomplex___Groups_Oone, arity_RealDef_Oreal___Groups_Omonoid__mult, arity_Nat_Onat___Groups_Oone, fact_31_one__is__num__one, fact_84_zero__power2, fact_90_mult_Ocomm__neutral, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_41_complex__add, arity_Int_Oint___Groups_Oab__semigroup__add, fact_35_add__numeral__0, arity_Nat_Onat___Rings_Osemiring, fact_59_nat__add__assoc, arity_Complex_Ocomplex___Groups_Ocancel__ab__semigroup__add, arity_RealDef_Oreal___Power_Opower, fact_33_number__of__reorient, fact_50_add__left__imp__eq, fact_26_Bit1__def, arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1, fact_23_add__Bit1__Bit0, arity_Complex_Ocomplex___Int_Onumber__semiring, fact_75_real__sqrt__eq__0__iff, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_58_complex_Osimps_I2_J, arity_Complex_Ocomplex___Int_Onumber, arity_RealDef_Oreal___Int_Onumber, fact_22_nat__numeral__1__eq__1, fact_45_complex_Oinject, arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_0_assms, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, fact_3_one__add__one__is__two, fact_44_norm__power, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, fact_34_number__of__add, fact_15_rel__simps_I51_J, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_18_rel__simps_I46_J, arity_Int_Oint___Groups_Ocomm__monoid__mult, fact_2_one__power2, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_9_rel__simps_I38_J, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_43_csqrt
% 8.28/2.91 % No. of inferences in proof: 354
% 8.28/2.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2376 ms resp. 1805 ms w/o parsing
% 8.28/2.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.28/2.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------