%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV621_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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:00:04 AM UTC 2026
% Result : Theorem 53.13s 29.13s
% Output : Refutation 54.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 160
% Syntax : Number of formulae : 322 ( 156 unt; 0 typ; 0 def)
% Number of atoms : 1077 ( 234 equ; 0 cnn)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 5451 ( 68 ~; 18 |; 74 &;4929 @)
% ( 24 <=>; 338 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 49 ( 47 usr; 6 con; 0-5 aty)
% Number of variables : 562 ( 0 ^; 552 !; 10 ?; 562 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(real_type,type,
real: $tType ).
thf(one_decl,type,
one:
!>[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(mult_zero_decl,type,
mult_zero:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_0_decl,type,
semiring_0:
!>[TA: $tType] : $o ).
thf(monoid_mult_decl,type,
monoid_mult:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[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(division_ring_decl,type,
division_ring:
!>[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(comm_monoid_add_decl,type,
comm_monoid_add:
!>[TA: $tType] : $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors:
!>[TA: $tType] : $o ).
thf(linordered_field_decl,type,
linordered_field:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(field_inverse_zero_decl,type,
field_inverse_zero:
!>[TA: $tType] : $o ).
thf(ordered_ab_group_add_decl,type,
ordered_ab_group_add:
!>[TA: $tType] : $o ).
thf(ring_n68954251visors_decl,type,
ring_n68954251visors:
!>[TA: $tType] : $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors:
!>[TA: $tType] : $o ).
thf(divisi14063676e_zero_decl,type,
divisi14063676e_zero:
!>[TA: $tType] : $o ).
thf(linord1117847801e_zero_decl,type,
linord1117847801e_zero:
!>[TA: $tType] : $o ).
thf(big_co1399186613setsum_decl,type,
big_co1399186613setsum:
!>[TA: $tType,TB: $tType] : ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ fun ) ) ).
thf(combb_decl,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TB @ ( TC @ fun ) ) > ( TC @ ( TA @ fun ) ) > ( TB @ ( TA @ fun ) ) ) ).
thf(combc_decl,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) @ ( TB @ fun ) ) ) ).
thf(combk_decl,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( TB @ ( TA @ fun ) ) ) ).
thf(combs_decl,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( TA @ ( TB @ fun ) @ ( TC @ fun ) ) > ( TB @ ( TC @ fun ) ) > ( TA @ ( TC @ fun ) ) ) ).
thf(fFT_Mirabelle_root_decl,type,
fFT_Mirabelle_root: nat > complex ).
thf(inverse_divide_decl,type,
inverse_divide:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(power_power_decl,type,
power_power:
!>[TA: $tType] : ( TA > ( TA @ ( nat @ fun ) ) ) ).
thf(ord_atLeastLessThan_decl,type,
ord_atLeastLessThan:
!>[TA: $tType] : ( TA > TA > ( bool @ ( TA @ fun ) ) ) ).
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(k_decl,type,
k: nat ).
thf(n_decl,type,
n: nat ).
thf(116,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_power__one__right) ).
thf(479,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(43,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_diff__self) ).
thf(234,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(139,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(555,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_zero__less__power) ).
thf(333,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(49,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_divide__pos__neg) ).
thf(249,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(128,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_diff__0__eq__0) ).
thf(523,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(47,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(247,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_divide__pos__pos) ).
thf(408,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(9,axiom,
real @ linordered_field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field) ).
thf(170,plain,
real @ linordered_field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(107,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_gr0I) ).
thf(440,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(123,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_nat__power__less__imp__less) ).
thf(511,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(91,axiom,
complex @ field_inverse_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield__inverse__zero) ).
thf(385,plain,
complex @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(79,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(340,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(13,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(174,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,axiom,
real @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(185,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(63,axiom,
complex @ ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oab__group__add) ).
thf(301,plain,
complex @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(142,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_nat__less__cases) ).
thf(565,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(20,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(184,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(145,axiom,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_diff__self__eq__0) ).
thf(587,plain,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(81,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__not__refl2) ).
thf(344,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(25,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(189,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(101,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_diff__less__mono2) ).
thf(416,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__imp__diff__less) ).
thf(228,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_zero__less__diff) ).
thf(261,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_one__neq__zero) ).
thf(216,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
real @ divisi14063676e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) ).
thf(164,plain,
real @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(108,axiom,
! [A: real,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ! [D: real] :
( ( ( ( B @ ( D @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( D @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_realpow__pos__nth__unique) ).
thf(443,plain,
! [A: real,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ! [D: real] :
( ( ( ( B @ ( D @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( D @ ( real @ zero_zero @ ( real @ ord_less ) ) ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(69,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power__less__imp__less__exp) ).
thf(321,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_atLeastLessThan__eq__iff) ).
thf(376,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) ) )
& ( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(159,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_le__0__eq) ).
thf(646,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)],[159]) ).
thf(125,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(514,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( A @ ( B @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ aa ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(82,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(348,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TC @ ( TB @ ( TA @ combs ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TC @ ( TB @ fun ) @ ( TA @ aa ) ) ) @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(148,axiom,
complex @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(602,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(95,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(397,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ one_one @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_power__one__over) ).
thf(280,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ one_one @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_divide__strict__right__mono) ).
thf(221,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( C @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power__strict__increasing) ).
thf(293,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( C @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(66,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_less__nat__zero__code) ).
thf(307,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(48,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(248,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(31,axiom,
! [A: bool @ ( nat @ fun ),B: nat] :
( ! [C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
<=> ! [C: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_all__nat__less__eq) ).
thf(201,plain,
! [A: bool @ ( nat @ fun ),B: nat] :
( ( ! [C: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ! [C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) )
& ( ! [C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ! [C: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) )
=> ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(130,axiom,
complex @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__0) ).
thf(534,plain,
complex @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(37,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(220,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(87,axiom,
complex @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ogroup__add) ).
thf(366,plain,
complex @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(64,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_less__not__refl) ).
thf(302,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(275,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(4,axiom,
real @ field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield) ).
thf(165,plain,
real @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(192,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(154,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_diffs0__imp__equal) ).
thf(630,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(51,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ ab_group_add )
=> ! [A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ minus_minus @ ( TA @ ( TB @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ ( TB @ ( TA @ combs ) ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_setsum__subtractf) ).
thf(252,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ ab_group_add )
=> ! [A: bool @ ( TA @ fun ),B: TB @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ minus_minus @ ( TA @ ( TB @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ ( TB @ ( TA @ combs ) ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( A @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ minus_minus @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ big_co1399186613setsum ) @ ( complex @ ( bool @ ( nat @ fun ) @ fun ) @ ( complex @ ( nat @ fun ) @ aa ) ) ) @ ( complex @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( complex @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_root__summation) ).
thf(329,plain,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ big_co1399186613setsum ) @ ( complex @ ( bool @ ( nat @ fun ) @ fun ) @ ( complex @ ( nat @ fun ) @ aa ) ) ) @ ( complex @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( complex @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(119,axiom,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_power__0) ).
thf(493,plain,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(111,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_right__minus__eq) ).
thf(456,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(24,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(188,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(8,axiom,
real @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(169,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_field__power__not__zero) ).
thf(225,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(78,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(339,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(138,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(554,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__neq__one) ).
thf(476,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(129,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_one__reorient) ).
thf(526,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)],[129]) ).
thf(157,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_less__iff__diff__less__0) ).
thf(637,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(146,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_nat__neq__iff) ).
thf(590,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(29,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(193,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(133,axiom,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_root__unity) ).
thf(537,plain,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) )
= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(160,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_diff__commute) ).
thf(654,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(12,axiom,
real @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(173,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(44,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_neq0__conv) ).
thf(237,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(155,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_less__irrefl__nat) ).
thf(633,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_divide__zero__left) ).
thf(508,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(68,axiom,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_mult__eq__0__iff) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ ring_n68954251visors )
=> ! [A: TA,B: TA] :
( ( ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
= ( TA @ zero_zero ) )
| ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(161,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_power__one) ).
thf(657,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(96,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 @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_power__eq__0__iff) ).
thf(398,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 @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(99,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: bool @ ( TB @ fun )] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_setsum__0) ).
thf(412,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: bool @ ( TB @ fun )] :
( ( A @ ( TA @ zero_zero @ ( TB @ ( TA @ combk ) ) @ ( TA @ ( TB @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(150,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_divide__1) ).
thf(618,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(5,axiom,
real @ ring_n68954251visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__no__zero__divisors) ).
thf(166,plain,
real @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
fTrue @ pp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(180,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(147,axiom,
complex @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(601,plain,
complex @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(124,axiom,
complex @ division_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring) ).
thf(513,plain,
complex @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(105,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_less__zeroE) ).
thf(430,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(14,axiom,
real @ ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__group__add) ).
thf(176,plain,
real @ ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(27,axiom,
real @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
thf(191,plain,
real @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(144,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_nat__zero__less__power__iff) ).
thf(577,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(136,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_power__divide) ).
thf(545,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(158,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_gr__implies__not0) ).
thf(641,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(114,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_zero__less__power__nat__eq) ).
thf(466,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) )
=> ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(76,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(335,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(17,axiom,
real @ division_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring) ).
thf(181,plain,
real @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_linorder__neqE__nat) ).
thf(540,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(23,axiom,
real @ linord1117847801e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) ).
thf(187,plain,
real @ linord1117847801e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
real @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(172,plain,
real @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
complex @ ring_n68954251visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) ).
thf(219,plain,
complex @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(103,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zero__less__divide__iff) ).
thf(419,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__not__refl3) ).
thf(230,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(109,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_not__less0) ).
thf(451,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(45,axiom,
complex @ divisi14063676e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) ).
thf(245,plain,
complex @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(88,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(367,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(131,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(535,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(70,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( D = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_atLeastLessThan__inj_I1_J) ).
thf(323,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( D = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_power__strict__mono) ).
thf(213,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( C @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(151,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(621,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( TA @ aa ) ) ) @ ( TB @ ( TC @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ fun ) @ ( TC @ aa ) ) ) @ ( TB @ ( TA @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(127,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_diff__0__right) ).
thf(520,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(50,axiom,
k @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(251,plain,
k @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(156,axiom,
complex @ field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield) ).
thf(636,plain,
complex @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(57,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_divide__strict__right__mono__neg) ).
thf(278,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( C @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_one__less__power) ).
thf(223,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_diff__less) ).
thf(563,plain,
! [A: nat,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__eq__diff__eq) ).
thf(267,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(121,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_divide__self) ).
thf(505,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(6,axiom,
real @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(167,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( C = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_atLeastLessThan__inj_I2_J) ).
thf(490,plain,
! [TA: $tType] :
( ( TA @ linorder )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ ord_atLeastLessThan ) ) )
= ( A @ ( B @ ( TA @ ord_atLeastLessThan ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(1,conjecture,
( ( n @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ big_co1399186613setsum ) @ ( complex @ ( bool @ ( nat @ fun ) @ fun ) @ ( complex @ ( nat @ fun ) @ aa ) ) ) @ ( complex @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ one_one @ ( n @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( n @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ big_co1399186613setsum ) @ ( complex @ ( bool @ ( nat @ fun ) @ fun ) @ ( complex @ ( nat @ fun ) @ aa ) ) ) @ ( complex @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
!= ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ one_one @ ( n @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(162,plain,
( ( n @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ big_co1399186613setsum ) @ ( complex @ ( bool @ ( nat @ fun ) @ fun ) @ ( complex @ ( nat @ fun ) @ aa ) ) ) @ ( complex @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
!= ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ one_one @ ( n @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ one_one @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) @ ( complex @ minus_minus @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) @ ( complex @ inverse_divide @ ( complex @ ( complex @ fun ) @ ( complex @ aa ) ) ) @ ( complex @ ( complex @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(137,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_diff__eq__diff__less) ).
thf(548,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) )
=> ( ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( D @ ( TA @ ord_less ) ) ) )
& ( ( C @ ( D @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) )
= ( A @ ( B @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_root__cancel) ).
thf(255,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) )
= ( A @ ( B @ fFT_Mirabelle_root @ ( complex @ power_power ) @ ( complex @ ( nat @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(30,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_power__inject__exp) ).
thf(194,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun )] :
( ! [C: TB] :
( ( B @ ( C @ ( TB @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
=> ( ( B @ ( A @ ( TA @ ( TB @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_setsum__0_H) ).
thf(295,plain,
! [TA: $tType,TB: $tType] :
( ( TA @ comm_monoid_add )
=> ! [A: TA @ ( TB @ fun ),B: bool @ ( TB @ fun )] :
( ! [C: TB] :
( ( B @ ( C @ ( TB @ member ) ) )
=> ( ( C @ ( A @ ( TA @ ( TB @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
=> ( ( B @ ( A @ ( TA @ ( TB @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( TB @ fun ) @ fun ) @ ( TA @ ( TB @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( TB @ fun ) @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(72,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_divide__neg__neg) ).
thf(327,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(67,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(310,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(112,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_not__one__less__zero) ).
thf(463,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(143,axiom,
complex @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(576,plain,
complex @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_right__inverse__eq) ).
thf(359,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) )
& ( ( ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_linorder__neqE__linordered__idom) ).
thf(177,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(18,axiom,
real @ ordered_ab_group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__group__add) ).
thf(182,plain,
real @ ordered_ab_group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType] :
( ( TB @ field )
=> ! [A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ inverse_divide @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ inverse_divide @ ( TA @ ( TB @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ ( TB @ ( TA @ combc ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_setsum__divide__distrib) ).
thf(336,plain,
! [TA: $tType,TB: $tType] :
( ( TB @ field )
=> ! [A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ inverse_divide @ ( TB @ ( TB @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TB @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ inverse_divide @ ( TA @ ( TB @ ( TB @ fun ) @ ( TB @ combb ) ) ) ) @ ( TB @ ( TB @ ( TA @ combc ) ) ) @ ( TB @ ( TA @ fun ) @ ( TB @ aa ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_power__strict__increasing__iff) ).
thf(386,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(113,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(465,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(153,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_divide__zero) ).
thf(627,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(140,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_eq__iff__diff__eq__0) ).
thf(556,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(117,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) )
<=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_divide__less__0__iff) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
& ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) ) )
| ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
& ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_zero__reorient) ).
thf(368,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)],[89]) ).
thf(126,axiom,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ one_one ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( nat @ fun ) @ fun ) @ ( TA @ ( nat @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( TA @ one_one @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ one_one @ ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_geometric__sum) ).
thf(517,plain,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ one_one ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ big_co1399186613setsum ) @ ( TA @ ( bool @ ( nat @ fun ) @ fun ) @ ( TA @ ( nat @ fun ) @ aa ) ) ) @ ( TA @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( TA @ one_one @ ( B @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ one_one @ ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_nonzero__power__divide) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( A @ ( C @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( A @ ( B @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(83,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(351,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: TB @ ( TA @ fun ),C: TC @ ( TB @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ ( TC @ ( TB @ combb ) ) ) ) @ ( TC @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TC @ ( TB @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(93,axiom,
! [A: real,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_realpow__pos__nth) ).
thf(390,plain,
! [A: real,B: nat] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less ) ) )
=> ? [C: real] :
( ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(22,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(186,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
real @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
thf(171,plain,
real @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(102,axiom,
complex @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(418,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(60,axiom,
! [A: nat,B: real] :
( ( B
!= ( real @ one_one ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ big_co1399186613setsum ) @ ( real @ ( bool @ ( nat @ fun ) @ fun ) @ ( real @ ( nat @ fun ) @ aa ) ) ) @ ( real @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( real @ one_one @ ( B @ ( real @ minus_minus @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) @ ( real @ one_one @ ( A @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) @ ( real @ minus_minus @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) @ ( real @ inverse_divide @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_sumr__geometric) ).
thf(290,plain,
! [A: nat,B: real] :
( ( B
!= ( real @ one_one ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ big_co1399186613setsum ) @ ( real @ ( bool @ ( nat @ fun ) @ fun ) @ ( real @ ( nat @ fun ) @ aa ) ) ) @ ( real @ ( bool @ ( nat @ fun ) @ aa ) ) ) )
= ( real @ one_one @ ( B @ ( real @ minus_minus @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) @ ( real @ one_one @ ( A @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ aa ) ) ) @ ( real @ minus_minus @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) @ ( real @ inverse_divide @ ( real @ ( real @ fun ) @ ( real @ aa ) ) ) @ ( real @ ( real @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(46,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(246,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_divide__self__if) ).
thf(433,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(132,axiom,
complex @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(536,plain,
complex @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(98,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_less__eq__nat_Osimps_I1_J) ).
thf(410,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(7,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(168,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,axiom,
real @ field_inverse_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield__inverse__zero) ).
thf(190,plain,
real @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(19,axiom,
real @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ogroup__add) ).
thf(183,plain,
real @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(149,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) )
<=> ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_divide__less__cancel) ).
thf(603,plain,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA,C: TA] :
( ( ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) )
=> ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( B @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) )
=> ( ( B
!= ( TA @ zero_zero ) )
& ( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( C @ ( TA @ ord_less ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_power__strict__decreasing) ).
thf(305,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: TA,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( TA @ one_one @ ( A @ ( TA @ ord_less ) ) )
=> ( C @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( B @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(32,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_minus__nat_Odiff__0) ).
thf(210,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( nat @ ( nat @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(71,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(326,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(341,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(85,axiom,
n @ ( k @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(358,plain,
n @ ( k @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(59,axiom,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_power__0__left) ).
thf(283,plain,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) @ ( TA @ ( nat @ aa ) ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(100,axiom,
complex @ comm_monoid_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ocomm__monoid__add) ).
thf(415,plain,
complex @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(74,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(332,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_diff__divide__distrib) ).
thf(427,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( A @ ( C @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ minus_minus @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(94,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_le0) ).
thf(395,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(152,axiom,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TB @ comm_monoid_add )
=> ! [A: bool @ ( TC @ fun ),B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TC @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ combb ) ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TC @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TC @ fun ) @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ big_co1399186613setsum ) @ ( TA @ ( TB @ ( bool @ ( TC @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ combb ) ) ) ) @ ( TB @ ( bool @ ( TC @ fun ) @ ( TA @ combc ) ) ) @ ( TB @ ( TA @ fun ) @ ( bool @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_setsum__commute) ).
thf(624,plain,
! [TA: $tType,TB: $tType,TC: $tType] :
( ( TB @ comm_monoid_add )
=> ! [A: bool @ ( TC @ fun ),B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ) @ ( TC @ fun )] :
( ( A @ ( B @ ( C @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TC @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ combb ) ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ fun ) @ ( bool @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( TC @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TC @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TC @ fun ) @ aa ) ) ) )
= ( B @ ( A @ ( C @ ( TB @ ( TA @ ( TC @ combc ) ) ) @ ( TB @ ( TC @ big_co1399186613setsum ) @ ( TA @ ( TB @ ( bool @ ( TC @ fun ) @ fun ) @ ( TB @ ( TC @ fun ) @ combb ) ) ) ) @ ( TB @ ( bool @ ( TC @ fun ) @ ( TA @ combc ) ) ) @ ( TB @ ( TA @ fun ) @ ( bool @ ( TC @ fun ) @ aa ) ) ) @ ( TB @ ( TA @ big_co1399186613setsum ) @ ( TB @ ( bool @ ( TA @ fun ) @ fun ) @ ( TB @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( TA @ fun ) @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(84,axiom,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_root__nonzero) ).
thf(354,plain,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(135,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_zero__less__one) ).
thf(543,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(34,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(215,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(120,axiom,
! [A: bool @ ( nat @ fun ),B: nat] :
( ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( C @ ( nat @ ord_less ) ) ) )
<=> ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_ex__nat__less__eq) ).
thf(496,plain,
! [A: bool @ ( nat @ fun ),B: nat] :
( ( ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) ) )
=> ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( C @ ( nat @ ord_less ) ) ) ) )
& ( ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( C @ ( nat @ ord_less ) ) ) )
=> ? [C: nat] :
( ( C @ ( A @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_atLeastLessThan ) ) @ ( C @ ( nat @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(110,axiom,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_divide__neg__pos) ).
thf(454,plain,
! [TA: $tType] :
( ( TA @ linordered_field )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( B @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(660,plain,
$false,
inference(e,[status(thm)],[479,234,555,333,249,523,247,408,170,440,511,385,340,174,185,301,565,184,587,344,189,416,228,261,216,164,443,321,376,646,514,348,602,397,280,221,293,307,248,201,534,220,366,302,275,165,192,630,252,329,493,456,188,169,225,339,554,476,526,637,590,193,537,654,173,237,633,508,311,657,398,412,618,166,180,601,513,430,176,191,577,545,641,466,335,181,540,187,172,219,419,230,451,245,367,535,323,213,621,520,251,636,278,223,563,267,505,167,490,162,548,255,194,295,327,310,463,576,359,177,182,336,386,465,627,556,482,368,517,258,351,390,186,171,418,290,246,433,536,410,168,190,183,603,305,210,326,341,358,283,415,332,427,395,624,354,543,215,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV621_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.08 % 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
% 0.14/0.57 % Computer : n020.cluster.edu
% 0.14/0.57 % Model : x86_64 x86_64
% 0.14/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.57 % Memory : 8046.5625MB
% 0.14/0.57 % OS : Linux 6.8.0-71-generic
% 0.14/0.57 % CPULimit : 300
% 0.14/0.57 % WCLimit : 300
% 0.14/0.57 % DateTime : Sat Sep 26 14:39:05 UTC 2026
% 0.14/0.57 % CPUTime :
% 0.14/0.57 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
% 0.98/1.17 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.61/1.49 % [INFO] Parsing done (322ms).
% 2.10/1.50 % [INFO] Running in sequential loop mode.
% 3.31/1.90 % [INFO] eprover registered as external prover.
% 3.31/1.91 % [INFO] Scanning for conjecture ...
% 3.68/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 159 axioms. Running axiom selection ...
% 4.16/2.25 % [INFO] Axiom selection finished. Selected 159 axioms (removed 0 axioms).
% 5.01/2.48 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.34/2.53 % [INFO] Type checking passed.
% 5.34/2.54 % [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 ...
% 53.13/29.12 % External prover 'e' found a proof!
% 53.13/29.12 % [INFO] Killing All external provers ...
% 53.13/29.12 % Time passed: 28403ms (effective reasoning time: 27609ms)
% 53.13/29.12 % 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)>
% 53.13/29.13 % Axioms used in derivation (159): arity_Complex_Ocomplex___Groups_Oone, fact_36_divide__less__cancel, arity_RealDef_Oreal___Groups_Oordered__ab__group__add, fact_92_root__cancel, arity_Nat_Onat___Groups_Omonoid__mult, help_COMBS_1_1_U, fact_8_power__one, fact_41_zero__reorient, fact_58_zero__less__diff, fact_81_one__neq__zero, arity_RealDef_Oreal___Fields_Olinordered__field, fact_84_gr__implies__not0, fact_7_setsum__0, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero, arity_RealDef_Oreal___Rings_Osemiring__0, fact_29_zero__less__power, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_23_power__strict__increasing, arity_Complex_Ocomplex___Power_Opower, fact_61_neq0__conv, fact_63_ex__nat__less__eq, arity_RealDef_Oreal___Groups_Ozero, fact_45_setsum__commute, arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero, fact_11_diff__self, fact_3_geometric__sum, fact_50_divide__1, fact_59_less__zeroE, arity_Nat_Onat___Power_Opower, fact_52_power__divide, fact_28_less__iff__diff__less__0, arity_RealDef_Oreal___Fields_Ofield__inverse__zero, fact_96_le0, arity_RealDef_Oreal___Rings_Oring__no__zero__divisors, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, fact_44_root__summation, fact_34_divide__pos__neg, fact_64_zero__less__one, fact_14_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_6_power__eq__0__iff, fact_86_diff__less, fact_24_power__less__imp__less__exp, fact_4_power__0, fact_35_divide__pos__pos, fact_75_less__not__refl3, arity_HOL_Obool___Orderings_Olinorder, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_22_atLeastLessThan__eq__iff, fact_95_less__eq__nat_Osimps_I1_J, arity_Nat_Onat___Rings_Omult__zero, fact_74_less__imp__diff__less, fact_76_less__not__refl2, arity_Complex_Ocomplex___Groups_Ocomm__monoid__add, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_57_nonzero__power__divide, fact_21_atLeastLessThan__inj_I1_J, fact_80_less__not__refl, fact_77_less__irrefl__nat, fact_17_diff__eq__diff__less, fact_83_not__less0, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, help_COMBB_1_1_U, arity_Complex_Ocomplex___Fields_Ofield__inverse__zero, fact_56_divide__self, fact_60_less__nat__zero__code, fact_94_le__0__eq, fact_15_nat__zero__less__power__iff, arity_Nat_Onat___Orderings_Olinorder, arity_Complex_Ocomplex___Rings_Osemiring__0, fact_85_gr0I, fact_55_right__inverse__eq, arity_RealDef_Oreal___Fields_Odivision__ring, fact_62_all__nat__less__eq, fact_70_minus__nat_Odiff__0, arity_Nat_Onat___Rings_Osemiring__0, fact_72_nat__less__cases, fact_65_not__one__less__zero, fact_30_divide__strict__right__mono__neg, arity_RealDef_Oreal___Fields_Ofield, fact_16_nat__power__less__imp__less, fact_51_diff__divide__distrib, fact_89_setsum__0_H, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_53_setsum__subtractf, fact_20_atLeastLessThan__inj_I2_J, arity_Complex_Ocomplex___Rings_Omult__zero, arity_Nat_Onat___Rings_Olinordered__semidom, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_42_one__reorient, fact_1_assms_I2_J, fact_27_one__less__power, fact_5_divide__self__if, fact_32_divide__neg__neg, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_46_right__minus__eq, fact_73_diff__less__mono2, fact_48_diff__0__right, arity_Nat_Onat___Groups_Ozero, arity_RealDef_Oreal___Rings_Omult__zero, fact_43_diff__eq__diff__eq, arity_RealDef_Oreal___Groups_Oab__group__add, help_COMBK_1_1_U, arity_Complex_Ocomplex___Fields_Ofield, fact_40_root__nonzero, arity_RealDef_Oreal___Rings_Ono__zero__divisors, arity_RealDef_Oreal___Groups_Ocomm__monoid__add, fact_66_diff__0__eq__0, arity_RealDef_Oreal___Orderings_Olinorder, fact_67_diff__self__eq__0, fact_54_setsum__divide__distrib, help_COMBC_1_1_U, arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors, arity_RealDef_Oreal___Rings_Ozero__neq__one, fact_69_linorder__neqE__linordered__idom, fact_91_realpow__pos__nth__unique, arity_RealDef_Oreal___Groups_Oone, fact_18_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_37_divide__less__0__iff, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_82_zero__neq__one, arity_Nat_Onat___Groups_Oone, fact_19_power__one__right, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_9_divide__zero__left, fact_47_eq__iff__diff__eq__0, fact_68_diff__commute, fact_13_power__one__over, arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero, arity_RealDef_Oreal___Power_Opower, fact_49_field__power__not__zero, help_pp_1_1_U, fact_33_divide__neg__pos, fact_87_zero__less__power__nat__eq, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_2_root__unity, arity_Complex_Ocomplex___Groups_Oab__group__add, fact_93_power__strict__mono, fact_12_power__0__left, fact_38_zero__less__divide__iff, fact_39_power__inject__exp, fact_0_assms_I1_J, fact_78_linorder__neqE__nat, fact_88_sumr__geometric, help_pp_2_1_U, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_97_mult__eq__0__iff, fact_25_power__strict__increasing__iff, fact_71_diffs0__imp__equal, arity_Complex_Ocomplex___Fields_Odivision__ring, fact_31_divide__strict__right__mono, arity_RealDef_Oreal___Groups_Ogroup__add, arity_Complex_Ocomplex___Groups_Ogroup__add, fact_10_divide__zero, fact_79_nat__neq__iff, fact_90_realpow__pos__nth, fact_26_power__strict__decreasing
% 53.13/29.13 % No. of inferences in proof: 322
% 53.13/29.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 28403 ms resp. 27609 ms w/o parsing
% 54.34/29.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 54.34/29.34 % [INFO] Killing All external provers ...
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