%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV629_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:05 AM UTC 2026
% Result : Theorem 16.02s 5.90s
% Output : Refutation 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 155
% Syntax : Number of formulae : 312 ( 170 unt; 0 typ; 0 def)
% Number of atoms : 704 ( 257 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 2481 ( 48 ~; 11 |; 80 &;2078 @)
% ( 25 <=>; 239 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 43 usr; 5 con; 0-4 aty)
% Number of variables : 406 ( 0 ^; 398 !; 8 ?; 406 :)
% 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(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(power_decl,type,
power:
!>[TA: $tType] : $o ).
thf(field_decl,type,
field:
!>[TA: $tType] : $o ).
thf(sgn_if_decl,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(semiring_0_decl,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(ab_group_add_decl,type,
ab_group_add:
!>[TA: $tType] : $o ).
thf(number_semiring_decl,type,
number_semiring:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(real_normed_vector_decl,type,
real_normed_vector:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(real_n2089651433ebra_1_decl,type,
real_n2089651433ebra_1:
!>[TA: $tType] : $o ).
thf(cnj_decl,type,
cnj: complex > complex ).
thf(ii_decl,type,
ii: complex ).
thf(fFT_Mirabelle_root_decl,type,
fFT_Mirabelle_root: nat > complex ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(sgn_sgn_decl,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(if_decl,type,
if:
!>[TA: $tType] : ( bool > TA > TA > TA ) ).
thf(iszero_decl,type,
iszero:
!>[TA: $tType] : ( TA > $o ) ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(semiring_1_Nats_decl,type,
semiring_1_Nats:
!>[TA: $tType] : ( bool @ ( TA @ fun ) ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > nat > TA ) ).
thf(vector_space_decl,type,
vector_space:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TA @ fun ) @ ( TB @ fun ) ) > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(40,axiom,
int @ sgn_if,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(270,plain,
int @ sgn_if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(139,axiom,
complex @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(561,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(66,axiom,
! [A: bool @ ( int @ fun )] :
( ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
<=> ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_transfer__int__nat__quantifiers_I2_J) ).
thf(365,plain,
! [A: bool @ ( int @ fun )] :
( ( ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
=> ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ) )
& ( ? [B: int] :
( ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
=> ? [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ power_power ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_power__decreasing) ).
thf(479,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less_eq ) ) )
=> ( C @ ( A @ ( TA @ power_power ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(124,axiom,
! [A: int] :
( ( A @ ( complex @ number_number_of ) @ cnj )
= ( A @ ( complex @ number_number_of ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_complex__cnj__number__of) ).
thf(518,plain,
! [A: int] :
( ( A @ ( complex @ number_number_of ) @ cnj )
= ( A @ ( complex @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ one_one @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Nats__1) ).
thf(481,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ one_one @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(62,axiom,
int @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(352,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(6,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(170,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fFalse @ ( TA @ if ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(127,axiom,
complex @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(523,plain,
complex @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ power_power ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_power__increasing) ).
thf(449,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( B @ ( A @ ( TA @ power_power ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(31,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ? [B: nat] :
( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_zero__le__imp__eq__int) ).
thf(247,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ? [B: nat] :
( A
= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_sgn__0__0) ).
thf(202,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(151,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_of__nat__le__iff) ).
thf(597,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_iszero__0) ).
thf(385,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ zero_zero @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(132,axiom,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_power__0__left) ).
thf(533,plain,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(8,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_of__nat__eq__iff) ).
thf(174,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_sgn__zero) ).
thf(185,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TB,C: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( C @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( ( A @ ( B @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TB @ zero_zero ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_vector__space_Oscale__eq__0__iff) ).
thf(288,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TB,C: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( C @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TB @ zero_zero ) ) )
=> ( ( A @ ( B @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( C @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TB @ zero_zero ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(72,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_less__eq__nat_Osimps_I1_J) ).
thf(389,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(141,axiom,
! [A: nat,B: complex] :
( ( A @ ( B @ ( complex @ power_power ) ) @ cnj )
= ( A @ ( B @ cnj @ ( complex @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_complex__cnj__power) ).
thf(570,plain,
! [A: nat,B: complex] :
( ( A @ ( B @ ( complex @ power_power ) ) @ cnj )
= ( A @ ( B @ cnj @ ( complex @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(10,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(184,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(115,axiom,
complex @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__1) ).
thf(504,plain,
complex @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(1,conjecture,
( ( nat @ one_one @ fFT_Mirabelle_root )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( nat @ one_one @ fFT_Mirabelle_root )
!= ( complex @ one_one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(157,plain,
( ( nat @ one_one @ fFT_Mirabelle_root )
!= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zero__reorient) ).
thf(189,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(228,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( fTrue @ ( TA @ if ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(90,axiom,
complex @ ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__group__add) ).
thf(448,plain,
complex @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(54,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(316,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
int @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(261,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(103,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(475,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(87,axiom,
complex @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__ring) ).
thf(443,plain,
complex @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(57,axiom,
! [A: complex,B: complex] :
( ( ( B @ cnj )
= ( A @ cnj ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_complex__cnj__cancel__iff) ).
thf(321,plain,
! [A: complex,B: complex] :
( ( ( B = A )
=> ( ( B @ cnj )
= ( A @ cnj ) ) )
& ( ( ( B @ cnj )
= ( A @ cnj ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(19,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_field__power__not__zero) ).
thf(211,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(109,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(485,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(63,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_eq__number__of) ).
thf(353,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(44,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
thf(280,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( TB @ one_one @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_vector__space_Oscale__one) ).
thf(428,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( TB @ one_one @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(38,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_vector__space_Oscale__zero__left) ).
thf(265,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( TB @ zero_zero @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(118,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_int__0) ).
thf(507,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_power__0) ).
thf(467,plain,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(108,axiom,
complex @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber__semiring) ).
thf(484,plain,
complex @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(14,axiom,
int @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(197,plain,
int @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(65,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_nonneg__eq__int) ).
thf(361,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( int @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ~ ( TA @ one_one @ ( TA @ iszero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_not__iszero__1) ).
thf(493,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ~ ( TA @ one_one @ ( TA @ iszero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(23,axiom,
! [A: complex] :
( ( A @ cnj @ cnj )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_complex__cnj__cnj) ).
thf(224,plain,
! [A: complex] :
( ( A @ cnj @ cnj )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(147,axiom,
( ( nat @ zero_zero @ fFT_Mirabelle_root )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_root0) ).
thf(583,plain,
( ( nat @ zero_zero @ fFT_Mirabelle_root )
= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(126,axiom,
complex @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__0) ).
thf(522,plain,
complex @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(144,axiom,
complex @ real_n2089651433ebra_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) ).
thf(578,plain,
complex @ real_n2089651433ebra_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_of__nat__0__le__iff) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(12,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(188,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(169,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(156,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_of__nat__power) ).
thf(610,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_zero__le__one) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(104,axiom,
( ii
!= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_complex__i__not__zero) ).
thf(476,plain,
( ii
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(130,axiom,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: int] :
( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_power__0__left__number__of) ).
thf(526,plain,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: int] :
( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__one__le__zero) ).
thf(515,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(7,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(173,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(114,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(503,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(64,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(360,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_sgn0) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(138,axiom,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_root__unity) ).
thf(558,plain,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(149,axiom,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_int__if__cong) ).
thf(586,plain,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ pp )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( C @ pp )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( C @ ( nat @ if ) ) ) @ ( int @ semiring_1_of_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(46,axiom,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(298,plain,
! [A: nat,B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ power_power ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int] :
( ( ~ ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_of__nat__number__of__lemma) ).
thf(412,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: int] :
( ( ~ ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(121,axiom,
( ( complex @ zero_zero @ cnj )
= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_complex__cnj__zero) ).
thf(513,plain,
( ( complex @ zero_zero @ cnj )
= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(37,axiom,
int @ number_semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(264,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(142,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_one__neq__zero) ).
thf(573,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_one__le__power) ).
thf(444,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(152,axiom,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_transfer__int__nat__numerals_I2_J) ).
thf(601,plain,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(140,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_le__0__eq) ).
thf(562,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_int__power) ).
thf(402,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(145,axiom,
complex @ field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield) ).
thf(579,plain,
complex @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(73,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_int__eq__0__conv) ).
thf(391,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(98,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(466,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(60,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( A @ ( TA @ iszero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_iszero__def) ).
thf(335,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( A @ ( TA @ iszero ) ) )
& ( ( A @ ( TA @ iszero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TB,B: TA,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
<=> ( ( B
= ( TA @ zero_zero ) )
| ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_vector__space_Oscale__cancel__right) ).
thf(236,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TB,B: TA,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( ( ( B
= ( TA @ zero_zero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( B @ ( A @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( B
= ( TA @ zero_zero ) )
| ( C = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(9,axiom,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_number__of__int) ).
thf(181,plain,
! [TA: $tType] :
( ( TA @ number_semiring )
=> ! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(133,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_one__reorient) ).
thf(540,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(3,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(159,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(154,axiom,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_sgn__one) ).
thf(604,plain,
! [TA: $tType] :
( ( TA @ real_n2089651433ebra_1 )
=> ( ( TA @ one_one @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_of__nat__1) ).
thf(406,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(42,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_mem__def) ).
thf(274,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_number__of__reorient) ).
thf(377,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(92,axiom,
! [A: nat] :
( ( A @ ( complex @ semiring_1_of_nat ) @ cnj )
= ( A @ ( complex @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_complex__cnj__of__nat) ).
thf(451,plain,
! [A: nat] :
( ( A @ ( complex @ semiring_1_of_nat ) @ cnj )
= ( A @ ( complex @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_sgn__sgn) ).
thf(271,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(119,axiom,
complex @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Nat_Osemiring__char__0) ).
thf(509,plain,
complex @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_power__eq__0__iff__number__of) ).
thf(434,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: int,B: TA] :
( ( ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( ( A @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(71,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_le0) ).
thf(387,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(150,axiom,
( ii
!= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_complex__i__not__one) ).
thf(594,plain,
( ii
!= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(107,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(483,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(33,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( C
!= ( TB @ zero_zero ) )
=> ( ( ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_vector__space_Oscale__left__imp__eq) ).
thf(251,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TA,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( C
!= ( TB @ zero_zero ) )
=> ( ( ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_Nats__0) ).
thf(198,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( TA @ semiring_1_Nats @ ( TA @ zero_zero @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(94,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(462,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(125,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(521,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(74,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(399,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: bool @ ( TA @ fun ),B: TA] :
( ( TA @ semiring_1_Nats @ ( B @ ( TA @ member ) ) )
=> ( ! [C: nat] : ( C @ ( TA @ semiring_1_of_nat ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Nats__induct) ).
thf(278,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: bool @ ( TA @ fun ),B: TA] :
( ( TA @ semiring_1_Nats @ ( B @ ( TA @ member ) ) )
=> ( ! [C: nat] : ( C @ ( TA @ semiring_1_of_nat ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(22,axiom,
int @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(223,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( TA @ semiring_1_Nats @ ( A @ ( TA @ member ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( TA @ semiring_1_of_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_Nats__cases) ).
thf(306,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: TA] :
( ( TA @ semiring_1_Nats @ ( A @ ( TA @ member ) ) )
=> ~ ! [B: nat] :
( A
!= ( B @ ( TA @ semiring_1_of_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(116,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(505,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(83,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(431,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(101,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(473,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(490,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(4,axiom,
! [A: bool @ ( int @ fun )] :
( ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) )
<=> ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_transfer__int__nat__quantifiers_I1_J) ).
thf(162,plain,
! [A: bool @ ( int @ fun )] :
( ( ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp )
=> ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) )
& ( ! [B: int] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( B @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) )
=> ! [B: nat] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( bool @ ( int @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(134,axiom,
complex @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(548,plain,
complex @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(68,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TB,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_vector__space_Oscale__zero__right) ).
thf(374,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TB,B: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( B @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_power__mono) ).
thf(209,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less_eq ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(61,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ab_group_add )
& ( TA @ field ) )
=> ! [A: TB,B: TB,C: TA,D: TB @ ( TB @ fun ) @ ( TA @ fun )] :
( ( D @ ( TB @ ( TA @ vector_space ) ) )
=> ( ( ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) )
<=> ( ( C
= ( TA @ zero_zero ) )
| ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_vector__space_Oscale__cancel__left) ).
thf(342,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ab_group_add )
& ( TA @ field ) )
=> ! [A: TB,B: TB,C: TA,D: TB @ ( TB @ fun ) @ ( TA @ fun )] :
( ( D @ ( TB @ ( TA @ vector_space ) ) )
=> ( ( ( ( C
= ( TA @ zero_zero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) )
=> ( ( C
= ( TA @ zero_zero ) )
| ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_power__one__right) ).
thf(553,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(129,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(525,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_zpower__int) ).
thf(580,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ power_power ) ) )
= ( A @ ( B @ ( nat @ power_power ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(409,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(51,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(310,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(58,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(331,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(148,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(585,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(95,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(463,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_power__one) ).
thf(470,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(143,axiom,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le__refl) ).
thf(576,plain,
! [A: nat] : ( A @ ( A @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat] : ( TA @ semiring_1_Nats @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_of__nat__in__Nats) ).
thf(314,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ! [A: nat] : ( TA @ semiring_1_Nats @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(89,axiom,
( ( complex @ one_one @ cnj )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_complex__cnj__one) ).
thf(446,plain,
( ( complex @ one_one @ cnj )
= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(137,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_transfer__int__nat__numerals_I1_J) ).
thf(556,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(128,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(524,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(113,axiom,
! [A: complex] :
( ( ( A @ cnj )
= ( complex @ zero_zero ) )
<=> ( A
= ( complex @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_complex__cnj__zero__iff) ).
thf(495,plain,
! [A: complex] :
( ( ( A
= ( complex @ zero_zero ) )
=> ( ( A @ cnj )
= ( complex @ zero_zero ) ) )
& ( ( ( A @ cnj )
= ( complex @ zero_zero ) )
=> ( A
= ( complex @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(32,axiom,
int @ ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__group__add) ).
thf(250,plain,
int @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(97,axiom,
complex @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Oring__char__0) ).
thf(465,plain,
complex @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(26,axiom,
int @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(231,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(123,axiom,
complex @ real_normed_vector,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__normed__vector) ).
thf(517,plain,
complex @ real_normed_vector,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(56,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(319,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(48,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__le__power) ).
thf(304,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(81,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_power__eq__0__iff) ).
thf(418,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(135,axiom,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_root__nonzero) ).
thf(549,plain,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(214,plain,
! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(28,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(235,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(246,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(85,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(433,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(120,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_of__nat__0) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(47,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__number__of) ).
thf(300,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(84,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(432,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(36,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__le__imp__of__nat) ).
thf(262,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] : ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(405,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(67,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(373,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(153,axiom,
complex @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(603,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(102,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(474,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(75,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_int__1) ).
thf(400,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(131,axiom,
complex @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(532,plain,
complex @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(117,axiom,
complex @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Int_Onumber) ).
thf(506,plain,
complex @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(39,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(268,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(96,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(464,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(59,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TB,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_vector__space_Oscale__left__commute) ).
thf(332,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ field )
& ( TA @ ab_group_add ) )
=> ! [A: TA,B: TB,C: TB,D: TA @ ( TA @ fun ) @ ( TB @ fun )] :
( ( D @ ( TA @ ( TB @ vector_space ) ) )
=> ( ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(16,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__zle__int) ).
thf(200,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(155,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_zero__neq__one) ).
thf(607,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(50,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(309,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(21,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(222,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(93,axiom,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_int__le__0__conv) ).
thf(454,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(27,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ab_group_add )
& ( TA @ field ) )
=> ! [A: TA,B: TA,C: TB,D: TB @ ( TB @ fun ) @ ( TA @ fun )] :
( ( D @ ( TB @ ( TA @ vector_space ) ) )
=> ( ( C
!= ( TB @ zero_zero ) )
=> ( ( ( C @ ( B @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( C @ ( A @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_vector__space_Oscale__right__imp__eq) ).
thf(232,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ ab_group_add )
& ( TA @ field ) )
=> ! [A: TA,B: TA,C: TB,D: TB @ ( TB @ fun ) @ ( TA @ fun )] :
( ( D @ ( TB @ ( TA @ vector_space ) ) )
=> ( ( C
!= ( TB @ zero_zero ) )
=> ( ( ( C @ ( B @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( C @ ( A @ ( D @ ( TB @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_sgn__zero__iff) ).
thf(254,plain,
! [TA: $tType] :
( ( TA @ real_normed_vector )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,axiom,
int @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(227,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(613,plain,
$false,
inference(e,[status(thm)],[270,561,365,479,518,481,352,170,523,449,247,202,597,385,533,174,185,288,389,570,184,504,157,189,228,448,316,261,475,443,321,211,485,353,280,428,265,507,467,484,197,361,493,224,583,522,578,317,188,169,610,488,476,526,515,173,503,360,311,558,586,298,412,513,264,573,444,601,562,402,579,391,466,335,236,181,540,159,604,406,274,377,451,271,509,434,387,594,483,251,198,462,521,399,278,223,306,505,431,473,490,162,548,374,209,342,553,525,580,409,310,331,585,463,470,576,314,446,556,524,495,250,465,231,517,319,304,418,549,214,235,246,433,510,300,432,262,405,373,603,474,400,532,506,268,464,332,200,607,309,222,454,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV629_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 14:38:25 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.97/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.50/1.27 % [INFO] Parsing done (337ms).
% 1.50/1.28 % [INFO] Running in sequential loop mode.
% 2.78/1.55 % [INFO] eprover registered as external prover.
% 2.78/1.55 % [INFO] Scanning for conjecture ...
% 3.02/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 156 axioms. Running axiom selection ...
% 3.32/1.73 % [INFO] Axiom selection finished. Selected 154 axioms (removed 2 axioms).
% 4.02/1.91 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.02/1.93 % [INFO] Type checking passed.
% 4.02/1.93 % [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 ...
% 4.94/2.24 % [INFO] [Domain constraints] Detected constraint on bool
% 4.94/2.24 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 16.02/5.89 % External prover 'e' found a proof!
% 16.02/5.89 % [INFO] Killing All external provers ...
% 16.02/5.89 % Time passed: 5388ms (effective reasoning time: 4612ms)
% 16.02/5.89 % 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)>
% 16.02/5.90 % Axioms used in derivation (154): fact_52_zero__neq__one, arity_Nat_Onat___Groups_Omonoid__mult, fact_8_not__iszero__1, fact_78_zero__le__power, fact_36_vector__space_Oscale__right__imp__eq, arity_Int_Oint___Groups_Oone, fact_77_power__mono, fact_87_zero__zle__int, arity_Nat_Onat___Rings_Osemiring__1, arity_Complex_Ocomplex___Nat_Osemiring__char__0, arity_Int_Oint___Int_Oring__char__0, fact_86_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, arity_Int_Oint___Rings_Olinordered__idom, fact_21_Nats__0, fact_92_complex__cnj__number__of, fact_0_root0, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, fact_69_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_74_number__of__reorient, arity_Complex_Ocomplex___Power_Opower, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_27_zero__reorient, fact_3_root__nonzero, arity_Nat_Onat___Int_Onumber__semiring, fact_14_sgn0, fact_17_complex__cnj__zero__iff, fact_46_int__power, arity_Nat_Onat___Power_Opower, fact_25_complex__cnj__cnj, fact_13_complex__cnj__cancel__iff, 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_9_sgn__one, arity_Int_Oint___Groups_Oab__group__add, fact_31_vector__space_Oscale__cancel__right, fact_83_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, fact_48_int__int__eq, fact_15_sgn__zero, arity_Int_Oint___Int_Onumber__semiring, fact_85_transfer__int__nat__quantifiers_I2_J, fact_94_less__eq__nat_Osimps_I1_J, arity_Int_Oint___Int_Onumber__ring, arity_Int_Oint___Rings_Osemiring__1, fact_32_vector__space_Oscale__zero__left, fact_76_not__one__le__zero, fact_40_power__0__left, fact_6_complex__cnj__one, arity_Nat_Onat___Rings_Omult__zero, fact_30_vector__space_Oscale__cancel__left, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_62_power__0__left__number__of, fact_63_int__le__0__conv, fact_38_power__eq__0__iff, fact_53_field__power__not__zero, fact_18_of__nat__0, help_If_1_1_T, fact_91_nonneg__eq__int, fact_16_complex__cnj__zero, fact_42_sgn__sgn, arity_Complex_Ocomplex___Rings_Osemiring__0, fact_72_mem__def, fact_79_number__of__int, fact_39_power__one, arity_Nat_Onat___Rings_Osemiring__0, fact_58_transfer__int__nat__numerals_I1_J, fact_29_vector__space_Oscale__eq__0__iff, arity_Int_Oint___Groups_Omonoid__mult, fact_49_int__eq__0__conv, fact_50_int__0, fact_90_zero__le__imp__eq__int, arity_Complex_Ocomplex___Rings_Omult__zero, arity_Nat_Onat___Rings_Olinordered__semidom, fact_34_vector__space_Oscale__left__commute, fact_95_le__0__eq, fact_84_transfer__int__nat__quantifiers_I1_J, arity_Nat_Onat___Rings_Ocomm__semiring__1, arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1, arity_Nat_Onat___Groups_Ozero, fact_19_iszero__0, fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_20_complex__i__not__zero, fact_5_complex__i__not__one, help_If_3_1_T, help_If_2_1_T, fact_70_power__increasing, fact_10_vector__space_Oscale__one, fact_82_zero__le__imp__of__nat, fact_12_complex__cnj__of__nat, arity_Complex_Ocomplex___Fields_Ofield, fact_1_one__reorient, fact_57_transfer__int__nat__numerals_I2_J, fact_73_power__decreasing, arity_Int_Oint___Power_Opower, fact_59_Nat__Transfer_Otransfer__int__nat__functions_I4_J, arity_Complex_Ocomplex___Int_Onumber__ring, arity_Int_Oint___Rings_Osemiring__0, fact_35_vector__space_Oscale__left__imp__eq, arity_Complex_Ocomplex___Rings_Osemiring__1, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_47_zpower__int, fact_68_power__eq__0__iff__number__of, arity_Nat_Onat___Int_Onumber, fact_61_int__if__cong, fact_93_le0, fact_44_Nats__cases, arity_Nat_Onat___Nat_Osemiring__char__0, fact_88_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_51_one__neq__zero, fact_45_sgn__0__0, arity_Complex_Ocomplex___Groups_Oone, fact_22_int__1, arity_Nat_Onat___Groups_Oone, fact_89_of__nat__number__of__lemma, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_33_vector__space_Oscale__zero__right, fact_4_of__nat__1, arity_Int_Oint___Groups_Osgn__if, fact_60_Nat__Transfer_Otransfer__int__nat__relations_I1_J, fact_55_power__one__right, fact_43_Nats__induct, fact_81_of__nat__0__le__iff, fact_75_zero__le__one, fact_37_power__0, fact_26_complex__cnj__power, fact_2_root__unity, arity_Complex_Ocomplex___Int_Onumber__semiring, fact_23_of__nat__in__Nats, arity_Complex_Ocomplex___Groups_Oab__group__add, help_pp_1_1_U, fact_11_of__nat__eq__iff, fact_80_one__le__power, arity_Nat_Onat___Rings_Ono__zero__divisors, arity_Complex_Ocomplex___Int_Onumber, fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, fact_54_of__nat__power, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Ozero, arity_Int_Oint___Rings_Omult__zero, fact_65_eq__number__of, fact_28_sgn__zero__iff, fact_66_of__nat__le__iff, arity_Int_Oint___Nat_Osemiring__char__0, fact_24_iszero__def, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, arity_Complex_Ocomplex___Groups_Ozero, arity_Nat_Onat___Rings_Ozero__neq__one, fact_96_le__refl, fact_7_Nats__1, arity_Complex_Ocomplex___RealVector_Oreal__normed__vector, fact_67_le__number__of
% 16.02/5.90 % No. of inferences in proof: 312
% 16.02/5.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5388 ms resp. 4612 ms w/o parsing
% 17.15/6.04 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.15/6.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------