%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV617_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 : n014.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 09:00:02 AM UTC 2026
% Result : Theorem 12.85s 5.00s
% Output : Refutation 14.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 125
% Syntax : Number of formulae : 252 ( 92 unt; 0 typ; 0 def)
% Number of atoms : 689 ( 239 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 2858 ( 62 ~; 27 |; 72 &;2367 @)
% ( 30 <=>; 300 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 37 ( 35 usr; 4 con; 0-4 aty)
% Number of variables : 456 ( 0 ^; 456 !; 0 ?; 456 :)
% Comments :
%------------------------------------------------------------------------------
thf(complex_type,type,
complex: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $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(zero_neq_one_decl,type,
zero_neq_one:
!>[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(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(fFT_Mirabelle_root_decl,type,
fFT_Mirabelle_root: nat > complex ).
thf(inverse_divide_decl,type,
inverse_divide:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
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 > nat > TA ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(k_decl,type,
k: nat ).
thf(n_decl,type,
n: nat ).
thf(69,axiom,
complex @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Omult__zero) ).
thf(385,plain,
complex @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(108,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_mult__zero__left) ).
thf(537,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_mult__cancel2) ).
thf(545,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( B @ ( A @ ( nat @ times_times ) ) ) )
=> ( ( B
= ( nat @ zero_zero ) )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(10,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(138,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(94,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( 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_16_nat__zero__less__power__iff) ).
thf(468,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( 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)],[94]) ).
thf(64,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 @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_divide__neg__neg) ).
thf(352,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 @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) )
<=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_mult__le__cancel2) ).
thf(247,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) )
=> ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( B @ ( A @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( C @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(85,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_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)],[85]) ).
thf(55,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_power__strict__increasing__iff) ).
thf(320,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 ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(117,axiom,
( ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( n @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) )
= ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( k @ ( n @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096_I_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_J_A_094_An_A_N_A1_J_A_P_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_A_N_A1_J_A_061_I_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_An_J_A_094_Ak_A_N_A1_J_A_P_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_A_N_A1_J_096) ).
thf(565,plain,
( ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( n @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) )
= ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( k @ ( n @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(23,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_divide__self) ).
thf(196,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
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_58_linorder__neqE__linordered__idom) ).
thf(157,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(126,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_power__one__over) ).
thf(606,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA] :
( ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ one_one @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ one_one @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) )
<=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat__mult__eq__1__iff) ).
thf(325,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ one_one ) )
=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(89,axiom,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_root__nonzero) ).
thf(448,plain,
! [A: nat] :
( ( A @ fFT_Mirabelle_root )
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(86,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 ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_power__strict__mono) ).
thf(443,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 ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(27,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_mult__0__right) ).
thf(211,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(103,axiom,
complex @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Oone) ).
thf(514,plain,
complex @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(119,axiom,
complex @ field,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield) ).
thf(574,plain,
complex @ field,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_mult__is__0) ).
thf(480,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) )
=> ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
| ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( 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_35_divide__less__0__iff) ).
thf(397,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 @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( 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)],[75]) ).
thf(6,axiom,
nat @ one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(132,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(74,axiom,
complex @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Power_Opower) ).
thf(396,plain,
complex @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(7,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(133,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(80,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 @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_divide__pos__pos) ).
thf(428,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 @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_zero__less__one) ).
thf(452,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(41,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_zero__less__power) ).
thf(270,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: TA] :
( ( B @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,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 @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_divide__pos__neg) ).
thf(220,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 @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(62,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 @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_diff__less) ).
thf(349,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 @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(16,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(160,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(115,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_not__one__less__zero) ).
thf(561,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(48,axiom,
complex @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ono__zero__divisors) ).
thf(297,plain,
complex @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(83,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_le0) ).
thf(435,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(56,axiom,
n @ ( k @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_assms_I2_J) ).
thf(324,plain,
n @ ( k @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(45,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) ) @ ( B @ ( C @ ( nat @ power_power ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_nat__power__less__imp__less) ).
thf(285,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ power_power ) ) @ ( B @ ( C @ ( nat @ power_power ) ) @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
<=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_diff__is__0__eq) ).
thf(224,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less_eq ) ) )
=> ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(121,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
<=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_mult__cancel1) ).
thf(578,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) )
=> ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ times_times ) ) )
= ( A @ ( C @ ( nat @ times_times ) ) ) )
=> ( ( C
= ( nat @ zero_zero ) )
| ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(54,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_not__less0) ).
thf(317,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_neq0__conv) ).
thf(188,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)],[22]) ).
thf(71,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_times__divide__eq__right) ).
thf(388,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( C @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( TA @ times_times ) ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(101,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_right__minus__eq) ).
thf(499,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(73,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_divide__zero__left) ).
thf(393,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(104,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 @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_divide__neg__pos) ).
thf(515,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 @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_one__reorient) ).
thf(457,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)],[92]) ).
thf(3,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(129,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(134,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(35,axiom,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_diff__self__eq__0) ).
thf(244,plain,
! [A: nat] :
( ( A @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(52,axiom,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_mult__zero__right) ).
thf(311,plain,
! [TA: $tType] :
( ( TA @ mult_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ times_times ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(49,axiom,
complex @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) ).
thf(298,plain,
complex @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(77,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_85_mult__eq__0__iff) ).
thf(412,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)],[77]) ).
thf(79,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_one__neq__zero) ).
thf(425,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_nonzero__power__divide) ).
thf(430,plain,
! [TA: $tType] :
( ( TA @ field )
=> ! [A: nat,B: TA,C: TA] :
( ( C
!= ( TA @ zero_zero ) )
=> ( ( A @ ( C @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) @ ( A @ ( B @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(19,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_62_nat__less__cases) ).
thf(166,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)],[19]) ).
thf(39,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_diffs0__imp__equal) ).
thf(264,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( ( ( B @ ( A @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(17,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(161,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(43,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_less__zeroE) ).
thf(279,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(72,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 ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_power__strict__increasing) ).
thf(391,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 ) ) @ ( C @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(87,axiom,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__eq__nat_Osimps_I1_J) ).
thf(445,plain,
! [A: nat] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(100,axiom,
complex @ semiring_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Osemiring__0) ).
thf(498,plain,
complex @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(58,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_mult__0) ).
thf(335,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ times_times ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_nat__0__less__mult__iff) ).
thf(181,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
=> ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ times_times ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(109,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 @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_less__iff__diff__less__0) ).
thf(540,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA] :
( ( ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( B @ ( TA @ minus_minus ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(68,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_le__0__eq) ).
thf(377,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)],[68]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_gr__implies__not0) ).
thf(362,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(118,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( ( B @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_power__inject__exp) ).
thf(567,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 ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) ) )
& ( ( ( B @ ( C @ ( TA @ power_power ) ) )
= ( A @ ( C @ ( TA @ power_power ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_power__divide) ).
thf(494,plain,
! [TA: $tType] :
( ( TA @ field_inverse_zero )
=> ! [A: nat,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ power_power ) ) )
= ( A @ ( B @ ( TA @ power_power ) ) @ ( A @ ( C @ ( TA @ power_power ) ) @ ( TA @ inverse_divide ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(107,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus ) ) @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_diff__less__mono2) ).
thf(535,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( ( A @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( A @ ( nat @ minus_minus ) ) @ ( B @ ( A @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(12,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_69_nat__neq__iff) ).
thf(140,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)],[12]) ).
thf(33,axiom,
complex @ divisi14063676e_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero) ).
thf(240,plain,
complex @ divisi14063676e_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(60,axiom,
complex @ group_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ogroup__add) ).
thf(345,plain,
complex @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
<=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_nat__1__eq__mult__iff) ).
thf(367,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) )
=> ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) ) )
& ( ( ( nat @ one_one )
= ( A @ ( B @ ( nat @ times_times ) ) ) )
=> ( ( A
= ( nat @ one_one ) )
& ( B
= ( nat @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(4,axiom,
nat @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(130,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ power_power ) ) @ ( 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_77_zero__less__power__nat__eq) ).
thf(299,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ( A
= ( nat @ zero_zero ) ) )
=> ( A @ ( B @ ( nat @ power_power ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ power_power ) ) @ ( 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)],[50]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_power__one) ).
thf(267,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: nat] :
( ( A @ ( TA @ one_one @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(34,axiom,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
= ( complex @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_root__unity) ).
thf(241,plain,
! [A: nat] :
( ( A @ ( A @ fFT_Mirabelle_root @ ( complex @ power_power ) ) )
= ( complex @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(9,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_68_linorder__neqE__nat) ).
thf(135,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)],[9]) ).
thf(116,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_less__imp__diff__less) ).
thf(563,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(122,axiom,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_field__power__not__zero) ).
thf(589,plain,
! [TA: $tType] :
( ( TA @ ring_11004092258visors )
=> ! [A: nat,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
!= ( TA @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(18,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_less__not__refl3) ).
thf(162,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(37,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 ) ) )
= ( A @ ( B @ fFT_Mirabelle_root @ ( complex @ power_power ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_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 ) ) )
= ( A @ ( B @ fFT_Mirabelle_root @ ( complex @ power_power ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(113,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__nat__zero__code) ).
thf(557,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(44,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_divide__1) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA] :
( ( TA @ one_one @ ( A @ ( TA @ inverse_divide ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(24,axiom,
complex @ ring_n68954251visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors) ).
thf(199,plain,
complex @ ring_n68954251visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(20,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_less__not__refl2) ).
thf(177,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
( ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( k @ ( n @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) )
= ( complex @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
( ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( k @ ( n @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) )
!= ( complex @ zero_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(127,plain,
( ( complex @ one_one @ ( k @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ one_one @ ( k @ ( n @ ( n @ fFT_Mirabelle_root @ ( complex @ power_power ) ) @ ( complex @ power_power ) ) @ ( complex @ minus_minus ) ) @ ( complex @ inverse_divide ) ) )
!= ( complex @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( B = A )
<=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_eq__iff__diff__eq__0) ).
thf(338,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( A @ ( B @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(110,axiom,
complex @ zero_neq_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Ozero__neq__one) ).
thf(544,plain,
complex @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(14,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_less__irrefl__nat) ).
thf(154,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(124,axiom,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_minus__nat_Odiff__0) ).
thf(600,plain,
! [A: nat] :
( ( nat @ zero_zero @ ( A @ ( nat @ minus_minus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(70,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 ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_power__strict__decreasing) ).
thf(386,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 ) ) @ ( B @ ( A @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(53,axiom,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_diff__0__eq__0) ).
thf(314,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ minus_minus ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(99,axiom,
complex @ division_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Odivision__ring) ).
thf(497,plain,
complex @ division_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(465,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(112,axiom,
complex @ ring_11004092258visors,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors) ).
thf(556,plain,
complex @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(105,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA,C: TA] :
( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( 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_34_divide__less__cancel) ).
thf(517,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 ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) )
& ( ( B @ ( A @ ( TA @ inverse_divide ) ) @ ( B @ ( C @ ( TA @ inverse_divide ) ) @ ( 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)],[105]) ).
thf(38,axiom,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( C @ ( D @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_diff__eq__diff__less) ).
thf(258,plain,
! [TA: $tType] :
( ( TA @ ordered_ab_group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( 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)],[38]) ).
thf(63,axiom,
complex @ field_inverse_zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Fields_Ofield__inverse__zero) ).
thf(351,plain,
complex @ field_inverse_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(11,axiom,
nat @ power,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(139,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(82,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 ) ) @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_divide__strict__right__mono__neg) ).
thf(433,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 ) ) @ ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_power__less__imp__less__exp) ).
thf(478,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat,C: TA] :
( ( C @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( ( A @ ( C @ ( TA @ power_power ) ) @ ( B @ ( C @ ( TA @ power_power ) ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(42,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_divide__self__if) ).
thf(272,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( ( A
!= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(346,plain,
! [TA: $tType] :
( ( TA @ comm_semiring_1 )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
<=> ( B @ ( A @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_zero__less__diff) ).
thf(214,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ minus_minus ) ) @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(46,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) )
<=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_right__inverse__eq) ).
thf(287,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA] :
( ( B
!= ( TA @ zero_zero ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) ) )
& ( ( ( B @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ one_one ) )
=> ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(13,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_less__not__refl) ).
thf(151,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,axiom,
k @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_assms_I1_J) ).
thf(447,plain,
k @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(76,axiom,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_power__0__left) ).
thf(405,plain,
! [TA: $tType] :
( ( ( TA @ semiring_0 )
& ( TA @ power ) )
=> ! [A: nat] :
( ( ( A
!= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( TA @ zero_zero @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(78,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_zero__neq__one) ).
thf(422,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(125,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__0__right) ).
thf(603,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ minus_minus ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(26,axiom,
complex @ monoid_mult,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Omonoid__mult) ).
thf(210,plain,
complex @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(47,axiom,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_power__one__right) ).
thf(294,plain,
! [TA: $tType] :
( ( TA @ monoid_mult )
=> ! [A: TA] :
( ( nat @ one_one @ ( A @ ( TA @ power_power ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(102,axiom,
! [TA: $tType] :
( ( TA @ linord1117847801e_zero )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( 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_36_zero__less__divide__iff) ).
thf(506,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 @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( 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)],[102]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_diff__divide__distrib) ).
thf(437,plain,
! [TA: $tType] :
( ( TA @ division_ring )
=> ! [A: TA,B: TA,C: TA] :
( ( A @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ inverse_divide ) ) )
= ( A @ ( B @ ( TA @ inverse_divide ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(106,axiom,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_power__0) ).
thf(532,plain,
! [TA: $tType] :
( ( TA @ power )
=> ! [A: TA] :
( ( nat @ zero_zero @ ( A @ ( TA @ power_power ) ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_diff__commute) ).
thf(575,plain,
! [A: nat,B: nat,C: nat] :
( ( A @ ( B @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) )
= ( B @ ( A @ ( C @ ( nat @ minus_minus ) ) @ ( nat @ minus_minus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(5,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(131,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,axiom,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
<=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_power__eq__0__iff) ).
thf(200,plain,
! [TA: $tType] :
( ( ( TA @ zero_neq_one )
& ( TA @ no_zero_divisors )
& ( TA @ mult_zero )
& ( TA @ power ) )
=> ! [A: nat,B: TA] :
( ( ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) )
=> ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( B @ ( TA @ power_power ) ) )
= ( TA @ zero_zero ) )
=> ( ( A
!= ( nat @ zero_zero ) )
& ( B
= ( TA @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat] :
( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) )
<=> ( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_mult__le__cancel1) ).
thf(354,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) )
=> ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) ) )
& ( ( A @ ( C @ ( nat @ times_times ) ) @ ( B @ ( C @ ( nat @ times_times ) ) @ ( nat @ ord_less_eq ) ) )
=> ( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(51,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 ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_divide__strict__right__mono) ).
thf(309,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 ) ) @ ( A @ ( C @ ( TA @ inverse_divide ) ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(114,axiom,
complex @ zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___Groups_Ozero) ).
thf(560,plain,
complex @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_diff__self) ).
thf(491,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( A @ ( A @ ( TA @ minus_minus ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(30,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 @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_one__less__power) ).
thf(222,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 @ one_one @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(123,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_zero__reorient) ).
thf(592,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)],[123]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_divide__zero) ).
thf(454,plain,
! [TA: $tType] :
( ( TA @ divisi14063676e_zero )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ inverse_divide ) ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(32,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( D = C )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_diff__eq__diff__eq) ).
thf(232,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA,C: TA,D: TA] :
( ( ( C @ ( D @ ( TA @ minus_minus ) ) )
= ( A @ ( B @ ( TA @ minus_minus ) ) ) )
=> ( ( ( B = A )
=> ( D = C ) )
& ( ( D = C )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(612,plain,
$false,
inference(e,[status(thm)],[385,537,545,138,468,352,247,440,320,565,196,157,606,325,448,443,211,514,574,480,397,132,396,133,428,452,270,220,349,160,561,297,435,324,285,224,578,317,188,388,499,393,515,457,129,134,244,311,298,412,425,430,166,264,161,279,391,445,498,335,181,540,377,362,567,494,535,140,240,345,367,130,299,267,241,135,563,589,162,255,557,282,199,177,127,338,544,154,600,386,314,497,465,556,517,258,351,139,433,478,272,346,214,287,151,447,405,422,603,210,294,506,437,532,575,131,200,354,309,560,491,222,592,454,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV617_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.11 % 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
% 0.23/0.47 % Computer : n014.cluster.edu
% 0.23/0.47 % Model : x86_64 x86_64
% 0.23/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.47 % Memory : 8046.5625MB
% 0.23/0.47 % OS : Linux 6.8.0-71-generic
% 0.23/0.47 % CPULimit : 300
% 0.23/0.47 % WCLimit : 300
% 0.23/0.47 % DateTime : Sat Sep 26 14:37:31 UTC 2026
% 0.23/0.47 % CPUTime :
% 0.23/0.48 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
% 1.01/0.94 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.22/1.33 % [INFO] Parsing done (388ms).
% 2.22/1.35 % [INFO] Running in sequential loop mode.
% 3.80/1.93 % [INFO] eprover registered as external prover.
% 3.80/1.94 % [INFO] Scanning for conjecture ...
% 4.28/2.17 % [INFO] Found a conjecture (or negated_conjecture) and 126 axioms. Running axiom selection ...
% 4.57/2.34 % [INFO] Axiom selection finished. Selected 124 axioms (removed 2 axioms).
% 5.44/2.62 % [INFO] Problem is typed first-order (TPTP TFF).
% 5.44/2.66 % [INFO] Type checking passed.
% 5.44/2.66 % [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 ...
% 12.85/4.99 % External prover 'e' found a proof!
% 12.85/4.99 % [INFO] Killing All external provers ...
% 12.85/5.00 % Time passed: 4395ms (effective reasoning time: 3631ms)
% 12.85/5.00 % 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)>
% 12.85/5.00 % Axioms used in derivation (124): fact_60_minus__nat_Odiff__0, fact_81_less__eq__nat_Osimps_I1_J, fact_63_diff__less__mono2, fact_36_zero__less__divide__iff, fact_93_nat__1__eq__mult__iff, fact_62_nat__less__cases, fact_87_mult__cancel2, fact_55_diff__0__eq__0, fact_86_times__divide__eq__right, arity_Nat_Onat___Groups_Omonoid__mult, fact_72_zero__neq__one, fact_25_power__strict__decreasing, fact_38_zero__reorient, fact_6_divide__zero__left, fact_82_le0, fact_77_zero__less__power__nat__eq, fact_79_root__cancel, fact_94_nat__mult__eq__1__iff, fact_34_divide__less__cancel, arity_Complex_Ocomplex___Rings_Ocomm__semiring__1, arity_Complex_Ocomplex___Fields_Odivision__ring__inverse__zero, arity_Complex_Ocomplex___Power_Opower, arity_Complex_Ocomplex___Rings_Oring__1__no__zero__divisors, fact_53_zero__less__one, fact_96_mult__le__cancel1, fact_19_one__less__power, fact_24_power__strict__increasing__iff, arity_Nat_Onat___Power_Opower, fact_8_power__eq__0__iff, fact_9_diff__self, arity_Complex_Ocomplex___Rings_Ono__zero__divisors, fact_17_power__0, fact_69_nat__neq__iff, fact_11_nonzero__power__divide, fact_52_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, fact_71_one__neq__zero, fact_76_not__less0, fact_2_root__nonzero, fact_12_divide__self, fact_30_divide__neg__neg, fact_48_neq0__conv, fact_83_mult__zero__left, fact_23_power__less__imp__less__exp, fact_89_mult__is__0, fact_31_divide__neg__pos, fact_91_mult__0, arity_Nat_Onat___Rings_Omult__zero, arity_Complex_Ocomplex___Rings_Ozero__neq__one, fact_33_divide__pos__pos, fact_68_linorder__neqE__nat, fact_88_mult__cancel1, fact_50_less__nat__zero__code, fact_58_linorder__neqE__linordered__idom, arity_Complex_Ocomplex___Fields_Ofield__inverse__zero, fact_26_less__iff__diff__less__0, fact_67_less__irrefl__nat, arity_Complex_Ocomplex___Rings_Osemiring__0, fact_37_power__inject__exp, fact_7_divide__zero, fact_49_zero__less__diff, fact_92_diff__is__0__eq, arity_Nat_Onat___Rings_Osemiring__0, fact_20_diff__eq__diff__less, fact_85_mult__eq__0__iff, fact_39_one__reorient, fact_45_divide__1, fact_70_less__not__refl, fact_29_divide__strict__right__mono, fact_56_diff__self__eq__0, fact_3_root__unity, arity_Complex_Ocomplex___Rings_Omult__zero, arity_Nat_Onat___Rings_Olinordered__semidom, fact_32_divide__pos__neg, fact_46_diff__divide__distrib, fact_1_assms_I2_J, fact_16_nat__zero__less__power__iff, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_27_zero__less__power, fact_18_nat__power__less__imp__less, arity_Nat_Onat___Groups_Ozero, fact_57_diff__commute, fact_95_mult__le__cancel2, fact_13_right__inverse__eq, fact_73_gr0I, fact_51_less__zeroE, arity_Complex_Ocomplex___Fields_Ofield, fact_10_power__one__over, fact_65_less__not__refl3, fact_44_field__power__not__zero, fact_54_not__one__less__zero, fact_64_less__imp__diff__less, arity_Complex_Ocomplex___Rings_Oring__no__zero__divisors, fact_84_mult__zero__right, fact_4_divide__self__if, fact_22_power__strict__increasing, arity_Complex_Ocomplex___Groups_Oone, fact_41_right__minus__eq, arity_Nat_Onat___Groups_Oone, fact_66_less__not__refl2, fact_35_divide__less__0__iff, arity_Complex_Ocomplex___Groups_Omonoid__mult, fact_43_diff__0__right, fact_21_power__one__right, fact_42_eq__iff__diff__eq__0, fact_15_assms_I1_J, fact_14_power__0__left, fact_75_diff__less, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_0__096_I_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_J_A_094_An_A_N_A1_J_A_P_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_A_N_A1_J_A_061_I_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_An_J_A_094_Ak_A_N_A1_J_A_P_IFFT__Mirabelle__uutasbvzez_Oroot_An_A_094_Ak_A_N_A1_J_096, fact_59_diffs0__imp__equal, fact_78_power__strict__mono, fact_97_nat__0__less__mult__iff, fact_90_mult__0__right, fact_28_divide__strict__right__mono__neg, arity_Nat_Onat___Rings_Ozero__neq__one, arity_Complex_Ocomplex___Groups_Ozero, fact_40_diff__eq__diff__eq, arity_Complex_Ocomplex___Fields_Odivision__ring, fact_80_le__0__eq, arity_Complex_Ocomplex___Groups_Ogroup__add, fact_47_power__divide, fact_5_power__one, fact_74_gr__implies__not0, fact_61_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 12.85/5.00 % No. of inferences in proof: 252
% 12.85/5.00 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4395 ms resp. 3631 ms w/o parsing
% 14.13/5.20 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.13/5.21 % [INFO] Killing All external provers ...
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