%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/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 08:10:25 AM UTC 2026
% Result : Theorem 45.43s 12.65s
% Output : Refutation 49.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 660
% Syntax : Number of formulae : 1322 ( 458 unt; 0 typ; 0 def)
% Number of atoms : 3466 ( 768 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 37030 ( 237 ~; 68 |; 303 &;34649 @)
% ( 146 <=>;1627 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 69 usr; 16 con; 0-4 aty)
% Number of variables : 2659 ( 0 ^;2623 !; 36 ?;2659 :)
% Comments :
%------------------------------------------------------------------------------
thf(hAPP_decl,type,
hAPP: $i > $i > $i > $i > $i ).
thf(nat_decl,type,
nat: $i ).
thf(int_decl,type,
int: $i ).
thf(power_power_decl,type,
power_power: $i > $i > $i ).
thf(plus_plus_decl,type,
plus_plus: $i > $i > $i ).
thf(one_one_decl,type,
one_one: $i > $i ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat: $i > $i ).
thf(n_decl,type,
n: $i ).
thf(number_number_of_decl,type,
number_number_of: $i > $i > $i ).
thf(bit0_decl,type,
bit0: $i ).
thf(bit1_decl,type,
bit1: $i ).
thf(pls_decl,type,
pls: $i ).
thf(zero_zero_decl,type,
zero_zero: $i > $i ).
thf(preorder_decl,type,
preorder: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(bool_decl,type,
bool: $i ).
thf(fun_decl,type,
fun: $i > $i > $i ).
thf(ord_less_decl,type,
ord_less: $i > $i ).
thf(order_decl,type,
order: $i > $o ).
thf(ord_less_eq_decl,type,
ord_less_eq: $i > $i ).
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(linorder_decl,type,
linorder: $i > $o ).
thf(linordered_semiring_decl,type,
linordered_semiring: $i > $o ).
thf(times_times_decl,type,
times_times: $i > $i ).
thf(ord_decl,type,
ord: $i > $o ).
thf(power_decl,type,
power: $i > $o ).
thf(real_decl,type,
real: $i ).
thf(linordered_semidom_decl,type,
linordered_semidom: $i > $o ).
thf(cancel146912293up_add_decl,type,
cancel146912293up_add: $i > $o ).
thf(dense_linorder_decl,type,
dense_linorder: $i > $o ).
thf(fFalse_decl,type,
fFalse: $i ).
thf(semiri456707255roduct_decl,type,
semiri456707255roduct: $i > $o ).
thf(no_zero_divisors_decl,type,
no_zero_divisors: $i > $o ).
thf(zero_neq_one_decl,type,
zero_neq_one: $i > $o ).
thf(linordered_idom_decl,type,
linordered_idom: $i > $o ).
thf(number_decl,type,
number: $i > $o ).
thf(comm_monoid_add_decl,type,
comm_monoid_add: $i > $o ).
thf(zero_decl,type,
zero: $i > $o ).
thf(linord20386208strict_decl,type,
linord20386208strict: $i > $o ).
thf(fTrue_decl,type,
fTrue: $i ).
thf(semiring_char_0_decl,type,
semiring_char_0: $i > $o ).
thf(if_decl,type,
if: $i > $i ).
thf(number_ring_decl,type,
number_ring: $i > $o ).
thf(ring_char_0_decl,type,
ring_char_0: $i > $o ).
thf(cancel_semigroup_add_decl,type,
cancel_semigroup_add: $i > $o ).
thf(monoid_add_decl,type,
monoid_add: $i > $o ).
thf(ab_semigroup_add_decl,type,
ab_semigroup_add: $i > $o ).
thf(ordere236663937imp_le_decl,type,
ordere236663937imp_le: $i > $o ).
thf(sqrt_decl,type,
sqrt: $i ).
thf(number_semiring_decl,type,
number_semiring: $i > $o ).
thf(mult_zero_decl,type,
mult_zero: $i > $o ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(ordere223160158up_add_decl,type,
ordere223160158up_add: $i > $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add: $i > $o ).
thf(one_decl,type,
one: $i > $o ).
thf(linord893533164strict_decl,type,
linord893533164strict: $i > $o ).
thf(linordered_ring_decl,type,
linordered_ring: $i > $o ).
thf(semiring_1_decl,type,
semiring_1: $i > $o ).
thf(monoid_mult_decl,type,
monoid_mult: $i > $o ).
thf(ordere779506340up_add_decl,type,
ordere779506340up_add: $i > $o ).
thf(linord581940658strict_decl,type,
linord581940658strict: $i > $o ).
thf(ordere216010020id_add_decl,type,
ordere216010020id_add: $i > $o ).
thf(ring_11004092258visors_decl,type,
ring_11004092258visors: $i > $o ).
thf(semiring_0_decl,type,
semiring_0: $i > $o ).
thf(comm_semiring_1_decl,type,
comm_semiring_1: $i > $o ).
thf(m1_decl,type,
m1: $i ).
thf(tn_decl,type,
tn: $i ).
thf(succ_decl,type,
succ: $i ).
thf(t_decl,type,
t: $i ).
thf(576,axiom,
! [A: $i] :
( ( A @ one )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oone__class_Oone_res) ).
thf(2630,plain,
! [A: $i] :
( ( A @ one )
=> ( ( A @ one_one @ ( A @ ti ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(524,axiom,
! [A: $i] :
( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_eq__number__of__0) ).
thf(2452,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) )
& ( ( ( A @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(239,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(1411,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_order__le__less__trans) ).
thf(1024,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(484,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
thf(2306,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(250,axiom,
nat @ linord20386208strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring__strict) ).
thf(1454,plain,
nat @ linord20386208strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(330,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( nat @ one_one @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
thf(1767,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( nat @ one_one @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(468,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_less__number__of__int__code) ).
thf(2263,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(526,axiom,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pos2) ).
thf(2463,plain,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( H @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_xt4) ).
thf(893,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( H @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(551,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_int__0__less__1) ).
thf(2544,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(276,axiom,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_add__less__le__mono) ).
thf(1554,plain,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(442,axiom,
! [A: $i,B: $i] :
( ( B @ monoid_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_arg1) ).
thf(2163,plain,
! [A: $i,B: $i] :
( ( B @ monoid_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(81,axiom,
real @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
thf(892,plain,
real @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(278,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_zpower__int) ).
thf(1559,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(157,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
thf(1105,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(567,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_add__increasing) ).
thf(2595,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(539,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_zero__less__two) ).
thf(2499,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(344,axiom,
int @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Omult__zero) ).
thf(1818,plain,
int @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_nat__add__left__cancel) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(498,axiom,
nat @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).
thf(2363,plain,
nat @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(573,axiom,
! [A: $i] :
( ( A @ monoid_mult )
=> ! [B: $i] :
( ( B @ ( A @ one_one @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_power__one) ).
thf(2622,plain,
! [A: $i] :
( ( A @ monoid_mult )
=> ! [B: $i] :
( ( B @ ( A @ one_one @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(632,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A )
=> ( B
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__eq__self__zero) ).
thf(2808,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A )
=> ( B
= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(537,axiom,
( ( succ @ ( int @ ( int @ fun ) @ ti ) )
= succ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Osucc_res) ).
thf(2495,plain,
( ( succ @ ( int @ ( int @ fun ) @ ti ) )
= succ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(547,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_of__nat__add) ).
thf(2527,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(565,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_of__nat__less__imp__less) ).
thf(2590,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_linorder__not__le) ).
thf(741,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(321,axiom,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_zero__is__num__zero) ).
thf(1728,plain,
( ( int @ zero_zero )
= ( pls @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(212,axiom,
( ( tn @ ( nat @ ti ) )
= tn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_tn_____res) ).
thf(1305,plain,
( ( tn @ ( nat @ ti ) )
= tn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(247,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_power__strict__increasing__iff) ).
thf(1437,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(68,axiom,
real @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) ).
thf(861,plain,
real @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(261,axiom,
( ( nat @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_Numeral1__eq1__nat) ).
thf(1486,plain,
( ( nat @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(485,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_semiring__numeral__0__eq__0) ).
thf(2309,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(544,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_even__less__0__iff) ).
thf(2512,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(370,axiom,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
thf(1924,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(454,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_add__leE) ).
thf(2210,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(249,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) )
<=> ( ( A
= ( nat @ zero_zero ) )
& ( B
!= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_nat__power__eq__0__iff) ).
thf(1443,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( nat @ zero_zero ) )
& ( B
!= ( nat @ zero_zero ) ) )
=> ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( A
= ( nat @ zero_zero ) )
& ( B
!= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(622,axiom,
! [A: $i] :
( ( A @ monoid_mult )
=> ! [B: $i] :
( ( nat @ one_one @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_power__one__right) ).
thf(2776,plain,
! [A: $i] :
( ( A @ monoid_mult )
=> ! [B: $i] :
( ( nat @ one_one @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(474,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_sum__power2__ge__zero) ).
thf(2282,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(289,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_zero__le__imp__of__nat) ).
thf(1591,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(598,axiom,
int @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
thf(2686,plain,
int @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(214,axiom,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_transfer__int__nat__numerals_I4_J) ).
thf(1310,plain,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(324,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_zless__imp__add1__zle) ).
thf(1735,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(446,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_not__sum__power2__lt__zero) ).
thf(2184,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(359,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_add__Bit1__Bit0) ).
thf(1872,plain,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(193,axiom,
int @ linord20386208strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring__strict) ).
thf(1233,plain,
int @ linord20386208strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(53,axiom,
real @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Nat_Osemiring__char__0) ).
thf(814,plain,
real @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( F @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( G @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_order__le__less__subst1) ).
thf(698,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( F @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( G @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(432,axiom,
nat @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).
thf(2146,plain,
nat @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(252,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ semiring_1_of_nat @ ( A @ ( nat @ fun ) @ ti ) )
= ( A @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_Osemiring__1__class_Oof__nat_res) ).
thf(1458,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( A @ semiring_1_of_nat @ ( A @ ( nat @ fun ) @ ti ) )
= ( A @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(562,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).
thf(2575,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(148,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_add__less__cancel__right) ).
thf(1078,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(244,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_less__eq__int__code_I13_J) ).
thf(1426,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(329,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_Nat__Transfer_Otransfer__int__nat__relations_I3_J) ).
thf(1761,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_order__neq__le__trans) ).
thf(747,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(300,axiom,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( ( B @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_power__0__left__number__of) ).
thf(1640,plain,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( ( B @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(564,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_zero__less__power__nat__eq) ).
thf(2580,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B
= ( nat @ zero_zero ) ) )
=> ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(145,axiom,
int @ cancel_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__semigroup__add) ).
thf(1063,plain,
int @ cancel_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(639,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_add__strict__increasing2) ).
thf(2844,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_zero__less__mult__pos2) ).
thf(1222,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(497,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
thf(2360,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(153,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_add__nonpos__nonpos) ).
thf(1095,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(349,axiom,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
thf(1835,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(118,axiom,
real @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) ).
thf(1001,plain,
real @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(367,axiom,
! [A: $i] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_plus__nat_Oadd__0) ).
thf(1914,plain,
! [A: $i] :
( ( A @ ( nat @ zero_zero @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(460,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( A
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_exp__eq__1) ).
thf(2227,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( A
= ( nat @ one_one ) ) )
=> ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) ) )
& ( ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) )
=> ( ( B
= ( nat @ zero_zero ) )
| ( A
= ( nat @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(248,axiom,
~ ( pls @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
thf(1441,plain,
~ ( pls @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(399,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_number__of__add) ).
thf(2020,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(295,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_zero__le__power) ).
thf(1613,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(292,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ zero_zero @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_mult__less__cancel__left__neg) ).
thf(1601,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ zero_zero @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(412,axiom,
nat @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__add) ).
thf(2082,plain,
nat @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ zero_zero @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_mult__le__cancel__left__neg) ).
thf(1724,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( A @ zero_zero @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(231,axiom,
! [A: $i,B: $i] :
( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_zle__add1__eq__le) ).
thf(1366,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(271,axiom,
! [A: $i] :
( ( A @ semiring_char_0 )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_of__nat__eq__iff) ).
thf(1529,plain,
! [A: $i] :
( ( A @ semiring_char_0 )
=> ! [B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(269,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ one_one @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_one__power2) ).
thf(1518,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ one_one @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(511,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_nonneg__int__cases) ).
thf(2405,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_power__strict__increasing) ).
thf(1243,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(162,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
thf(1127,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ) )
& ( ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(619,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_add__special_I3_J) ).
thf(2763,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(112,axiom,
real @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) ).
thf(973,plain,
real @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_linorder__antisym__conv1) ).
thf(1046,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(303,axiom,
! [A: $i,B: $i] :
( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_zless__add1__eq) ).
thf(1650,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(369,axiom,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Bit0__def) ).
thf(1921,plain,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_add__pos__nonneg) ).
thf(1228,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(297,axiom,
nat @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(1623,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(586,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] : ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_of__nat__less__two__power) ).
thf(2654,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] : ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_linorder__le__less__linear) ).
thf(1055,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(208,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_of__nat__less__iff) ).
thf(1287,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(317,axiom,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_add__strict__mono) ).
thf(1709,plain,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(403,axiom,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_zero__eq__power2) ).
thf(2039,plain,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(304,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_add__le__imp__le__left) ).
thf(1660,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(469,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_add__nonneg__pos) ).
thf(2269,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(540,axiom,
! [A: $i] : ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_zero__zle__int) ).
thf(2501,plain,
! [A: $i] : ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(456,axiom,
! [A: $i,B: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
!= ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_rel__simps_I49_J) ).
thf(2217,plain,
! [A: $i,B: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
!= ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(559,axiom,
! [A: $i] :
( ( ( A @ ring_char_0 )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) )
<=> ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_eq__number__of) ).
thf(2562,plain,
! [A: $i] :
( ( ( A @ ring_char_0 )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) ) )
& ( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ number_number_of ) ) )
=> ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(570,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) )
=> ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ hBOOL ) )
<=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_imp__le__cong) ).
thf(2603,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) )
=> ( ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ hBOOL ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ hBOOL ) ) )
& ( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ hBOOL ) )
=> ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(658,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zadd__0) ).
thf(2916,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(591,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
( ( A
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_zero__less__imp__eq__int) ).
thf(2667,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
( ( A
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
& ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_xt1_I1_J) ).
thf(719,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(493,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_zero__less__double__add__iff__zero__less__single__add) ).
thf(2339,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(42,axiom,
real @ linord20386208strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) ).
thf(785,plain,
real @ linord20386208strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(218,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_less__eq__number__of__int__code) ).
thf(1323,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_less__eq__real__def) ).
thf(838,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] :
~ ( B @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_order__less__irrefl) ).
thf(917,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] :
~ ( B @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
real @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add) ).
thf(702,plain,
real @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D = B )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_ord__le__eq__trans) ).
thf(751,plain,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D = B )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_less__eq__int__code_I15_J) ).
thf(1577,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(251,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_number__of__succ) ).
thf(1455,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_zadd__int__left) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_xt1_I10_J) ).
thf(934,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_add__leD1) ).
thf(1191,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(514,axiom,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_succ__Bit0) ).
thf(2420,plain,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ dense_linorder )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_dense__le) ).
thf(902,plain,
! [A: $i] :
( ( A @ dense_linorder )
=> ! [B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ comm_monoid_add )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_add__0) ).
thf(1147,plain,
! [A: $i] :
( ( A @ comm_monoid_add )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(579,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_mult__strict__right__mono) ).
thf(2635,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(438,axiom,
t @ ( int @ one_one @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_t1) ).
thf(2158,plain,
t @ ( int @ one_one @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(360,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__le__cancel__left) ).
thf(1875,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(636,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( fFalse @ ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_2_1_T) ).
thf(2829,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( fFalse @ ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_nat__less__cases) ).
thf(2169,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
thf(1087,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(110,axiom,
real @ dense_linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Odense__linorder) ).
thf(969,plain,
real @ dense_linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_le__eq__less__or__eq) ).
thf(2373,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(282,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( B @ number_number_of ) @ ( B @ ti ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_res) ).
thf(1572,plain,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( B @ number_number_of ) @ ( B @ ti ) )
= ( A @ ( B @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(343,axiom,
! [A: $i] :
( ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_succ__def) ).
thf(1815,plain,
! [A: $i] :
( ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(264,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_bin__less__0__simps_I3_J) ).
thf(1494,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ zero_zero @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(458,axiom,
! [A: $i] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_int__less__0__conv) ).
thf(2222,plain,
! [A: $i] :
~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(625,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_add__special_I2_J) ).
thf(2782,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(135,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_xt1_I9_J) ).
thf(1040,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(466,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_nat__le__linear) ).
thf(2259,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(222,axiom,
int @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oord) ).
thf(1334,plain,
int @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(428,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_nat__less__le) ).
thf(2122,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(386,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_semiring__norm_I110_J) ).
thf(1978,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(555,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_zadd__left__mono) ).
thf(2555,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( B @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( A @ ( C @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
& ( B @ ( C @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_real__lbound__gt__zero) ).
thf(1489,plain,
! [A: $i,B: $i] :
( ( B @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( A @ ( C @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
& ( B @ ( C @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(242,axiom,
int @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(1415,plain,
int @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(572,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] :
( ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_of__nat__0__less__iff) ).
thf(2616,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] :
( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(254,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add__less__imp__less__left) ).
thf(1465,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(311,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_less__special_I3_J) ).
thf(1682,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ fun ) @ ti ) )
= ( A @ if ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_If_res) ).
thf(834,plain,
! [A: $i] :
( ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ fun ) @ ti ) )
= ( A @ if ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(168,axiom,
n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( m1 @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_mn) ).
thf(1151,plain,
n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( m1 @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_not__leE) ).
thf(937,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_order__less__trans) ).
thf(1020,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_trans__less__add1) ).
thf(2254,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(491,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_zero__less__one) ).
thf(2335,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_order__le__neq__trans) ).
thf(966,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(207,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_less__not__refl3) ).
thf(1283,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(410,axiom,
int @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ono__zero__divisors) ).
thf(2073,plain,
int @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(373,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_power__strict__mono) ).
thf(1928,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(473,axiom,
int @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__add) ).
thf(2281,plain,
int @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(448,axiom,
! [A: $i,B: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_zadd__power2) ).
thf(2190,plain,
! [A: $i,B: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(106,axiom,
( ( fTrue @ ( bool @ ti ) )
= fTrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fTrue_res) ).
thf(956,plain,
( ( fTrue @ ( bool @ ti ) )
= fTrue ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(73,axiom,
( ( sqrt @ ( real @ ( real @ fun ) @ ti ) )
= sqrt ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_NthRoot_Osqrt_res) ).
thf(866,plain,
( ( sqrt @ ( real @ ( real @ fun ) @ ti ) )
= sqrt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(548,axiom,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_transfer__int__nat__numerals_I1_J) ).
thf(2530,plain,
( ( int @ zero_zero )
= ( nat @ zero_zero @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(503,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_add__strict__increasing) ).
thf(2371,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(226,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_power__mono) ).
thf(1351,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(117,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_real__le__antisym) ).
thf(998,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(420,axiom,
! [A: $i] :
( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) )
!= ( real @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_real__sqrt__not__eq__zero) ).
thf(2103,plain,
! [A: $i] :
( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) )
!= ( real @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(180,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_rel__simps_I14_J) ).
thf(1201,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(270,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).
thf(1521,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) )
=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(609,axiom,
! [A: $i,B: $i] :
~ ( A @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_not__add__less1) ).
thf(2718,plain,
! [A: $i,B: $i] :
~ ( A @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(280,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_power__less__power__Suc) ).
thf(1564,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(645,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_nat__add__commute) ).
thf(2861,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
thf(1215,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(156,axiom,
nat @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber__semiring) ).
thf(1104,plain,
nat @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(197,axiom,
nat @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oord) ).
thf(1242,plain,
nat @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(395,axiom,
! [A: $i] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_odd__nonzero) ).
thf(2011,plain,
! [A: $i] :
( ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
!= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(92,axiom,
bool @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oord) ).
thf(920,plain,
bool @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(453,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_zless__int) ).
thf(2204,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(95,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( ~ ( C @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_less__fun__def) ).
thf(925,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ( ( ~ ( C @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( C @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(404,axiom,
nat @ mult_zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Omult__zero) ).
thf(2047,plain,
nat @ mult_zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(335,axiom,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_succ__Bit1) ).
thf(1783,plain,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_zadd__assoc) ).
thf(2296,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(582,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_less__imp__of__nat__less) ).
thf(2641,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(413,axiom,
! [A: $i,B: $i] :
( ( B @ power )
=> ( ( A @ ( B @ ti ) @ ( B @ power_power ) )
= ( A @ ( B @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_arg1) ).
thf(2083,plain,
! [A: $i,B: $i] :
( ( B @ power )
=> ( ( A @ ( B @ ti ) @ ( B @ power_power ) )
= ( A @ ( B @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_2_res) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_linorder__antisym__conv2) ).
thf(678,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(531,axiom,
nat @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Power_Opower) ).
thf(2473,plain,
nat @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_one__less__power) ).
thf(1199,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(499,axiom,
nat @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).
thf(2364,plain,
nat @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_real__le__linear) ).
thf(714,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(357,axiom,
nat @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(1868,plain,
nat @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(322,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_add__pos__pos) ).
thf(1730,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ( B @ ( A @ fun ) @ ord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oord) ).
thf(798,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ( B @ ( A @ fun ) @ ord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(142,axiom,
int @ linord893533164strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) ).
thf(1057,plain,
int @ linord893533164strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(521,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_nat__add__left__cancel__less) ).
thf(2441,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(512,axiom,
! [A: $i] :
( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_nat__1__add__number__of) ).
thf(2409,plain,
! [A: $i] :
( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(517,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_le__add2) ).
thf(2428,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_linorder__neqE) ).
thf(1042,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_zadd__strict__right__mono) ).
thf(1355,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(69,axiom,
real @ monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__add) ).
thf(862,plain,
real @ monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(433,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_mult__neg__pos) ).
thf(2147,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(327,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_double__eq__0__iff) ).
thf(1751,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(307,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
<=> ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_power__inject__exp) ).
thf(1666,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B = C )
=> ( ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_linorder__less__linear) ).
thf(693,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(44,axiom,
! [A: $i] :
( ( ( A @ ( bool @ ti ) )
= fFalse )
| ( ( A @ ( bool @ ti ) )
= fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_3_1_T) ).
thf(788,plain,
! [A: $i] :
( ( ( A @ ( bool @ ti ) )
= fFalse )
| ( ( A @ ( bool @ ti ) )
= fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
<=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_order__eq__iff) ).
thf(815,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) )
& ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(429,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_mult__strict__left__mono__neg) ).
thf(2132,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(396,axiom,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
thf(2015,plain,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(362,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( C @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_sum__squares__gt__zero__iff) ).
thf(1883,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) )
=> ( C @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(235,axiom,
! [A: $i] : ( A @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_zle__refl) ).
thf(1387,plain,
! [A: $i] : ( A @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(364,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_less__eq__int__code_I14_J) ).
thf(1900,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_xt1_I4_J) ).
thf(825,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(557,axiom,
int @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Omonoid__mult) ).
thf(2560,plain,
int @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(631,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_power2__eq__imp__eq) ).
thf(2805,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(90,axiom,
real @ ord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oord) ).
thf(916,plain,
real @ ord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(527,axiom,
! [A: $i,B: $i] :
~ ( B @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_not__add__less2) ).
thf(2464,plain,
! [A: $i,B: $i] :
~ ( B @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(130,axiom,
real @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__0) ).
thf(1032,plain,
real @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(575,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_add__neg__nonpos) ).
thf(2628,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(589,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_add__less__imp__less__right) ).
thf(2663,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_order__less__asym) ).
thf(665,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(57,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(830,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(350,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_le__special_I3_J) ).
thf(1836,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(494,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_rel__simps_I31_J) ).
thf(2345,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(614,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_mult__strict__left__mono) ).
thf(2741,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(299,axiom,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_rel__simps_I21_J) ).
thf(1634,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(424,axiom,
pls @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_rel__simps_I19_J) ).
thf(2112,plain,
pls @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(113,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_real__less__def) ).
thf(974,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(408,axiom,
! [A: $i] : ( A @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( real @ number_number_of ) @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ one_one @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_two__realpow__ge__one) ).
thf(2068,plain,
! [A: $i] : ( A @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( real @ number_number_of ) @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ one_one @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(345,axiom,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
<=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add__right__cancel) ).
thf(1819,plain,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(298,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_sum__power2__le__zero__iff) ).
thf(1624,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(554,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( D @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_realpow__pos__nth__unique) ).
thf(2547,plain,
! [A: $i,B: $i] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ! [D: $i] :
( ( ( ( B @ ( D @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( D @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
=> ( D = C ) )
& ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(487,axiom,
( pls
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
thf(2313,plain,
( pls
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(482,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( nat @ zero_zero @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
thf(2300,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i] :
( ( nat @ zero_zero @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(388,axiom,
! [A: $i,B: $i] :
( ( A != B )
<=> ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_nat__neq__iff) ).
thf(1983,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_not__less__iff__gr__or__eq) ).
thf(874,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(654,axiom,
nat @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).
thf(2895,plain,
nat @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(353,axiom,
! [A: $i] :
( ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_rel__simps_I12_J) ).
thf(1856,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_add__Bit1__Bit1) ).
thf(1587,plain,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(120,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_leI) ).
thf(1006,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(581,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( fTrue @ ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_If_1_1_T) ).
thf(2638,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( fTrue @ ( A @ if @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(12,axiom,
real @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semidom) ).
thf(697,plain,
real @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(194,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_mult__right__le__imp__le) ).
thf(1234,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ti ) @ ( B @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_4_arg2) ).
thf(1794,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ti ) @ ( B @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(380,axiom,
! [A: $i] :
( ? [B: $i] :
( ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
<=> ? [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_transfer__int__nat__quantifiers_I2_J) ).
thf(1953,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
( ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
& ( ? [B: $i] :
( ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ? [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(563,axiom,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_not__less0) ).
thf(2577,plain,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(146,axiom,
! [A: $i] :
( ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_rel__simps_I29_J) ).
thf(1064,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(158,axiom,
! [A: $i] :
( ( pls @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
thf(1111,plain,
! [A: $i] :
( ( pls @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(190,axiom,
int @ linord581940658strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring__strict) ).
thf(1227,plain,
int @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(164,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_rel__simps_I15_J) ).
thf(1138,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(644,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( pls @ ( A @ number_number_of ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_add__numeral__0__right) ).
thf(2858,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( pls @ ( A @ number_number_of ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(525,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_zle__antisym) ).
thf(2460,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(400,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_le__neq__implies__less) ).
thf(2023,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(97,axiom,
real @ linord893533164strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) ).
thf(933,plain,
real @ linord893533164strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(558,axiom,
int @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).
thf(2561,plain,
int @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(174,axiom,
( ( pls @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_Bit0__Pls) ).
thf(1182,plain,
( ( pls @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(253,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_mult__le__cancel__left__pos) ).
thf(1461,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_order__less__le) ).
thf(669,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ linordered_semiring )
=> ( ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ times_times ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Otimes__class_Otimes_res) ).
thf(686,plain,
! [A: $i] :
( ( A @ linordered_semiring )
=> ( ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ times_times ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(486,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(2312,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(351,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_bin__less__0__simps_I4_J) ).
thf(1842,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ zero_zero @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_zadd__int) ).
thf(1584,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(315,axiom,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_rel__simps_I22_J) ).
thf(1700,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(338,axiom,
! [A: $i] :
( ( A @ monoid_add )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_add__0__left) ).
thf(1791,plain,
! [A: $i] :
( ( A @ monoid_add )
=> ! [B: $i] :
( ( B @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ~ ( A @ zero_zero @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_not__one__le__zero) ).
thf(1207,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ~ ( A @ zero_zero @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_order__less__imp__le) ).
thf(884,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(219,axiom,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_add__mono) ).
thf(1329,plain,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(382,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_zle__linear) ).
thf(1964,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_add__le__mono) ).
thf(1942,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(584,axiom,
! [A: $i,B: $i] :
( ( B @ cancel_semigroup_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_res) ).
thf(2649,plain,
! [A: $i,B: $i] :
( ( B @ cancel_semigroup_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_xt1_I12_J) ).
thf(970,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(61,axiom,
real @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
thf(837,plain,
real @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_1_res) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) @ ( C @ ti ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(332,axiom,
! [A: $i] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_Nat_Oadd__0__right) ).
thf(1776,plain,
! [A: $i] :
( ( nat @ zero_zero @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(596,axiom,
! [A: $i] :
( ( A @ ab_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(2681,plain,
! [A: $i] :
( ( A @ ab_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(638,axiom,
! [A: $i] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_neq0__conv) ).
thf(2836,plain,
! [A: $i] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(534,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_int__power) ).
thf(2487,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) )
=> ( ( ( B @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
<=> ( ( A @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_conj__le__cong) ).
thf(1266,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) )
=> ( ( ( ( A @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
& ( ( ( B @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ( ( A @ hBOOL )
& ( C @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(538,axiom,
! [A: $i] :
( ( A @ linord893533164strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_comm__mult__strict__left__mono) ).
thf(2497,plain,
! [A: $i] :
( ( A @ linord893533164strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(341,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_zero__less__power__nat__eq__number__of) ).
thf(1799,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) )
=> ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D = B )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_ord__less__eq__trans) ).
thf(1002,plain,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D = B )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(471,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_nonneg__eq__int) ).
thf(2272,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ~ ! [B: $i] :
( A
!= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( B @ ( A @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_real__add__left__mono) ).
thf(1759,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( B @ ( A @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(523,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_le__imp__0__less) ).
thf(2450,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
<=> ( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_linorder__neq__iff) ).
thf(985,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) )
& ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(167,axiom,
int @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(1150,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(201,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(1249,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(275,axiom,
! [A: $i] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_le0) ).
thf(1552,plain,
! [A: $i] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(642,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ one_one @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
=> ( C @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_int__ge__induct) ).
thf(2851,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ one_one @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
=> ( C @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(114,axiom,
real @ linord581940658strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring__strict) ).
thf(984,plain,
real @ linord581940658strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( G @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_order__less__le__subst2) ).
thf(911,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( G @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(542,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_power__less__imp__less__base) ).
thf(2505,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(620,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_trans__less__add2) ).
thf(2766,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(291,axiom,
( ( t @ ( int @ ti ) )
= t ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_t_____res) ).
thf(1599,plain,
( ( t @ ( int @ ti ) )
= t ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_number__of__Bit0) ).
thf(1246,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_rel__simps_I32_J) ).
thf(2140,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(617,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(2756,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(216,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
thf(1318,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(661,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( A @ ( C @ ( nat @ fun ) @ ti ) @ ( C @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_1_arg1) ).
thf(2926,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( A @ ( C @ ( nat @ fun ) @ ti ) @ ( C @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(452,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(2203,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(333,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_power2__le__imp__le) ).
thf(1779,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_linorder__not__less) ).
thf(805,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(93,axiom,
real @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) ).
thf(921,plain,
real @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_add__lessD1) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(509,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_mult__left__le__imp__le) ).
thf(2402,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(306,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_add__number__of__left) ).
thf(1663,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(457,axiom,
int @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(2221,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ! [E: $i] : ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_le__fun__def) ).
thf(1026,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ( ! [E: $i] : ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ! [E: $i] : ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(323,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).
thf(1732,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(578,axiom,
nat @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(2634,plain,
nat @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(246,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_le__antisym) ).
thf(1434,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(604,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_zero__less__power) ).
thf(2702,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(553,axiom,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_number__of2) ).
thf(2546,plain,
pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_order__le__imp__less__or__eq) ).
thf(765,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(140,axiom,
real @ linorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Olinorder) ).
thf(1054,plain,
real @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_less__imp__neq) ).
thf(1035,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(502,axiom,
! [A: $i] :
( ( A @ monoid_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_add__0__right) ).
thf(2368,plain,
! [A: $i] :
( ( A @ monoid_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_le__funE) ).
thf(953,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(176,axiom,
! [A: $i] :
( ( real @ one_one @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( real @ one_one @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_real__sqrt__lt__1__iff) ).
thf(1185,plain,
! [A: $i] :
( ( ( real @ one_one @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( real @ one_one @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( real @ one_one @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( real @ one_one @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ~ ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_less__le__not__le) ).
thf(773,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( ( ~ ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [A: $i] : ( A @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_real__le__refl) ).
thf(794,plain,
! [A: $i] : ( A @ ( A @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(515,axiom,
! [A: $i] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_gr0I) ).
thf(2423,plain,
! [A: $i] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(1,conjecture,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
!= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
!= ( int @ zero_zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(662,plain,
~ ( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
!= ( int @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_pinf_I8_J) ).
thf(906,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(365,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_le__special_I4_J) ).
thf(1906,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(30,axiom,
real @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ozero__neq__one) ).
thf(750,plain,
real @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(594,axiom,
! [A: $i] :
( ( A @ linordered_semiring )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_mult__right__less__imp__less) ).
thf(2677,plain,
! [A: $i] :
( ( A @ linordered_semiring )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_add__less__mono1) ).
thf(1698,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(434,axiom,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_nat__1__add__1) ).
thf(2149,plain,
( ( nat @ one_one @ ( nat @ one_one @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(259,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_zero__le__power2) ).
thf(1483,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(560,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_trans__le__add2) ).
thf(2570,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(372,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(1927,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_ord__eq__le__trans) ).
thf(689,plain,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(546,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( B @ ( D @ ( A @ fun ) @ ti ) @ ( D @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_0_arg1) ).
thf(2524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( B @ ( D @ ( A @ fun ) @ ti ) @ ( D @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_ord__eq__less__trans) ).
thf(733,plain,
! [A: $i] :
( ( A @ ord )
=> ! [B: $i,C: $i,D: $i] :
( ( C = D )
=> ( ( B @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(163,axiom,
! [A: $i] :
( ( A @ comm_monoid_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_add_Ocomm__neutral) ).
thf(1135,plain,
! [A: $i] :
( ( A @ comm_monoid_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(611,axiom,
! [A: $i] :
( ( A @ ( pls @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).
thf(2729,plain,
! [A: $i] :
( ( A @ ( pls @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(301,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(1648,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(656,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_sum__power2__eq__zero__iff) ).
thf(2904,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(310,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_add__le__imp__le__right) ).
thf(1680,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ hBOOL )
=> ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ if @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ hAPP ) ) ) @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) )
& ( ( C @ hBOOL )
=> ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ if @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ hAPP ) ) ) @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_int__if__cong) ).
thf(1154,plain,
! [A: $i,B: $i,C: $i] :
( ( ~ ( C @ hBOOL )
=> ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ if @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ hAPP ) ) ) @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) )
& ( ( C @ hBOOL )
=> ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ if @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ hAPP ) ) ) @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(405,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_zless__linear) ).
thf(2048,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
| ( A = B )
| ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(459,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_power__le__imp__le__exp) ).
thf(2225,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(608,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_nat__power__less__imp__less) ).
thf(2716,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(634,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_mono__nat__linear__lb) ).
thf(2817,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(430,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add__le__cancel__right) ).
thf(2134,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(296,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ~ ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_le__nat__number__of) ).
thf(1615,plain,
! [A: $i,B: $i] :
( ( ( ~ ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(236,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_sum__power2__gt__zero__iff) ).
thf(1389,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) )
=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
| ( ( B @ ( A @ ti ) )
!= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(627,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_nat__add__left__cancel__le) ).
thf(2789,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_le__trans) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(588,axiom,
! [A: $i] :
( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_real__sqrt__gt__1__iff) ).
thf(2657,plain,
! [A: $i] :
( ( ( A @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( real @ one_one @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(641,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_one__le__power) ).
thf(2849,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(593,axiom,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i,C: $i] :
( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
=> ( ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
!= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_field__power__not__zero) ).
thf(2674,plain,
! [A: $i] :
( ( A @ ring_11004092258visors )
=> ! [B: $i,C: $i] :
( ( ( C @ ( A @ ti ) )
!= ( A @ zero_zero ) )
=> ( ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
!= ( A @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(397,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_less__imp__le__nat) ).
thf(2016,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_real__le__trans) ).
thf(958,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(238,axiom,
! [A: $i] :
( ( pls
= ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_rel__simps_I38_J) ).
thf(1403,plain,
! [A: $i] :
( ( ( pls = A )
=> ( pls
= ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ) )
& ( ( pls
= ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(601,axiom,
int @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Opreorder) ).
thf(2695,plain,
int @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(262,axiom,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
thf(1488,plain,
pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(440,axiom,
int @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ocomm__semiring__1) ).
thf(2161,plain,
int @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(99,axiom,
real @ linordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__ring) ).
thf(936,plain,
real @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(478,axiom,
nat @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ono__zero__divisors) ).
thf(2293,plain,
nat @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(215,axiom,
! [A: $i] :
( ( real @ zero_zero @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( real @ zero_zero @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_real__sqrt__lt__0__iff) ).
thf(1312,plain,
! [A: $i] :
( ( ( real @ zero_zero @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( real @ zero_zero @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( real @ zero_zero @ ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( real @ zero_zero @ ( A @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(613,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( nat @ one_one @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_of__nat__1) ).
thf(2738,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( nat @ one_one @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(355,axiom,
n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
thf(1865,plain,
n @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(143,axiom,
( ( real @ zero_zero )
!= ( real @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_real__zero__not__eq__one) ).
thf(1058,plain,
( ( real @ zero_zero )
!= ( real @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(221,axiom,
! [A: $i] : ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
thf(1332,plain,
! [A: $i] : ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_semiring__one__add__one__is__two) ).
thf(1092,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(606,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_eq__imp__le) ).
thf(2706,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(556,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_3_arg1) ).
thf(2557,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ti ) @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_nat__add__right__cancel) ).
thf(1258,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A = C )
=> ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(532,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( B
= ( nat @ zero_zero ) )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_nat__zero__less__power__iff) ).
thf(2474,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( nat @ zero_zero ) )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B
= ( nat @ zero_zero ) )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_add__number__of__eq) ).
thf(1224,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ one_one @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
=> ( C @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_int__gr__induct) ).
thf(2193,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( int @ one_one @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ one_one @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
=> ( C @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(336,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_power__increasing__iff) ).
thf(1786,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(196,axiom,
! [A: $i,B: $i] :
( ( B @ ab_semigroup_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_arg1) ).
thf(1239,plain,
! [A: $i,B: $i] :
( ( B @ ab_semigroup_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(390,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_numeral__1__eq__1) ).
thf(1997,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_3_res) ).
thf(2166,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(151,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ~ ( A @ zero_zero @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_not__one__less__zero) ).
thf(1090,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ~ ( A @ zero_zero @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(58,axiom,
real @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__idom) ).
thf(831,plain,
real @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(435,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(2151,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( B = C )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_order__eq__refl) ).
thf(1011,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( B = C )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(225,axiom,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_semiring__norm_I113_J) ).
thf(1349,plain,
( ( nat @ zero_zero )
= ( pls @ ( nat @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(481,axiom,
int @ number_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(2299,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_of__nat__less__0__iff) ).
thf(1144,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(426,axiom,
! [A: $i,B: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
!= ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_rel__simps_I50_J) ).
thf(2116,plain,
! [A: $i,B: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
!= ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] : ( B @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_order__refl) ).
thf(737,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] : ( B @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(643,axiom,
( ( m1 @ ( int @ ti ) )
= m1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_m1_____res) ).
thf(2856,plain,
( ( m1 @ ( int @ ti ) )
= m1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(655,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( A @ zero_zero )
= ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_double__zero__sym) ).
thf(2896,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( A @ zero_zero )
= ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( A @ zero_zero )
= ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(70,axiom,
real @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oab__semigroup__add) ).
thf(863,plain,
real @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(182,axiom,
( ( int @ zero_zero )
!= ( int @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_int__0__neq__1) ).
thf(1209,plain,
( ( int @ zero_zero )
!= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(610,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ? [C: $i] :
( B
= ( C @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_zle__iff__zadd) ).
thf(2721,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_xt1_I8_J) ).
thf(900,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(595,axiom,
( ( bit1 @ ( int @ ( int @ fun ) @ ti ) )
= bit1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit1_res) ).
thf(2679,plain,
( ( bit1 @ ( int @ ( int @ fun ) @ ti ) )
= bit1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(455,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_power2__less__0) ).
thf(2214,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i] :
~ ( A @ zero_zero @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(505,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( ( D @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_less__add__eq__less) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( ( D @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_less__int__code_I15_J) ).
thf(1894,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(536,axiom,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_add__strict__right__mono) ).
thf(2493,plain,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(41,axiom,
real @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ozero) ).
thf(784,plain,
real @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(580,axiom,
int @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocomm__monoid__add) ).
thf(2637,plain,
int @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(160,axiom,
! [A: $i] :
( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_int__eq__0__conv) ).
thf(1117,plain,
! [A: $i] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(116,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_le__funD) ).
thf(996,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(475,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( A @ ti ) @ ( B @ ( D @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_0_arg2) ).
thf(2284,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( A @ ti ) @ ( B @ ( D @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(375,axiom,
! [A: $i] :
( ( A @ zero )
=> ! [B: $i] :
( ( ( A @ zero_zero )
= ( B @ ( A @ ti ) ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_zero__reorient) ).
thf(1933,plain,
! [A: $i] :
( ( A @ zero )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( A @ zero_zero )
= ( B @ ( A @ ti ) ) ) )
& ( ( ( A @ zero_zero )
= ( B @ ( A @ ti ) ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(384,axiom,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_add__right__imp__eq) ).
thf(1969,plain,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( B @ power )
=> ( ( A @ ( B @ power_power ) @ ( B @ ( nat @ fun ) @ ti ) )
= ( A @ ( B @ power_power ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Power_Opower__class_Opower_res) ).
thf(1307,plain,
! [A: $i,B: $i] :
( ( B @ power )
=> ( ( A @ ( B @ power_power ) @ ( B @ ( nat @ fun ) @ ti ) )
= ( A @ ( B @ power_power ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(445,axiom,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
!= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_rel__simps_I46_J) ).
thf(2180,plain,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
!= ( B @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_xt1_I11_J) ).
thf(811,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
!= ( B @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(33,axiom,
real @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
thf(758,plain,
real @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
real @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Oring__char__0) ).
thf(858,plain,
real @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(574,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
thf(2625,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(624,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_add__nonpos__neg) ).
thf(2780,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(467,axiom,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_nat__number__of__Pls) ).
thf(2261,plain,
( ( pls @ ( nat @ number_number_of ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(171,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
thf(1162,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(618,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_rel__simps_I16_J) ).
thf(2757,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(354,axiom,
! [A: $i,B: $i] :
( ( B @ ab_semigroup_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_1_res) ).
thf(1862,plain,
! [A: $i,B: $i] :
( ( B @ ab_semigroup_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ ord )
=> ( ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless_res) ).
thf(848,plain,
! [A: $i] :
( ( A @ ord )
=> ( ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(626,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_less__not__refl2) ).
thf(2785,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(89,axiom,
real @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(915,plain,
real @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_pos__add__strict) ).
thf(1293,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(607,axiom,
! [A: $i] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_int__one__le__iff__zero__less) ).
thf(2710,plain,
! [A: $i] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(312,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_less__int__code_I13_J) ).
thf(1688,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(277,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A
= ( int @ one_one ) )
| ( A
= ( int @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_int__pos__lt__two__imp__zero__or__one) ).
thf(1556,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A
= ( int @ one_one ) )
| ( A
= ( int @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( B @ preorder )
=> ( B @ ( A @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(769,plain,
! [A: $i,B: $i] :
( ( B @ preorder )
=> ( B @ ( A @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(550,axiom,
! [A: $i] : ( A @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_le__refl) ).
thf(2542,plain,
! [A: $i] : ( A @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_order__le__less) ).
thf(943,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_order__less__imp__triv) ).
thf(1022,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(463,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_power__less__imp__less__exp) ).
thf(2252,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(490,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_less__special_I2_J) ).
thf(2329,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(96,axiom,
real @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oone) ).
thf(932,plain,
real @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(144,axiom,
! [A: $i] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_less__eq__nat_Osimps_I1_J) ).
thf(1061,plain,
! [A: $i] : ( A @ ( nat @ zero_zero @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(520,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_int__0) ).
thf(2439,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(500,axiom,
nat @ number,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(2365,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(257,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_less__special_I1_J) ).
thf(1474,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( ( A @ ord )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( H @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_xt6) ).
thf(868,plain,
! [A: $i,B: $i] :
( ( ( A @ ord )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( H @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( C @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(414,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_rel__simps_I33_J) ).
thf(2086,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( F @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( G @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_order__less__le__subst1) ).
thf(780,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( F @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( G @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_order__less__imp__not__eq) ).
thf(1015,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(629,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_double__add__le__zero__iff__single__add__le__zero) ).
thf(2797,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(566,axiom,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
thf(2592,plain,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
= ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(577,axiom,
nat @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2633,plain,
nat @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_add__leD2) ).
thf(2101,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ semiri456707255roduct )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
= ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
<=> ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_add__0__iff) ).
thf(1250,plain,
! [A: $i] :
( ( A @ semiri456707255roduct )
=> ! [B: $i,C: $i] :
( ( ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ ti ) )
= ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ fun ) @ ti ) @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_2_arg1) ).
thf(2303,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ fun ) @ ti ) @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(279,axiom,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat__numeral__1__eq__1) ).
thf(1562,plain,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) )
= ( nat @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(184,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_power2__less__imp__less) ).
thf(1213,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(36,axiom,
real @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Ocomm__monoid__add) ).
thf(768,plain,
real @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(406,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_less__nat__number__of) ).
thf(2051,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
=> ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( nat @ number_number_of ) @ ( A @ ( nat @ number_number_of ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(199,axiom,
int @ cancel146912293up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ocancel__ab__semigroup__add) ).
thf(1245,plain,
int @ cancel146912293up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( H @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_xt7) ).
thf(851,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( H @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(155,axiom,
! [A: $i,B: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_real__sqrt__sum__squares__ge__zero) ).
thf(1102,plain,
! [A: $i,B: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less_eq @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(313,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_less__mono__imp__le__mono) ).
thf(1694,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( E @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_order__antisym) ).
thf(922,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ dense_linorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( E @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( E @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_dense__le__bounded) ).
thf(722,plain,
! [A: $i] :
( ( A @ dense_linorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( E @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( E @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(132,axiom,
real @ comm_semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ocomm__semiring__1) ).
thf(1034,plain,
real @ comm_semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(342,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_less__or__eq__imp__le) ).
thf(1809,plain,
! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(422,axiom,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( int @ ti ) @ ( B @ number_number_of ) )
= ( A @ ( B @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_Onumber__class_Onumber__of_arg1) ).
thf(2107,plain,
! [A: $i,B: $i] :
( ( B @ number )
=> ( ( A @ ( int @ ti ) @ ( B @ number_number_of ) )
= ( A @ ( B @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(590,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_trans__le__add1) ).
thf(2665,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(255,axiom,
! [A: $i] :
( ( ( A @ linorder )
& ( A @ number ) )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_le__number__of__eq__not__less) ).
thf(1467,plain,
! [A: $i] :
( ( ( A @ linorder )
& ( A @ number ) )
=> ! [B: $i,C: $i] :
( ( ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(470,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_n0) ).
thf(2271,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(585,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_add__less__mono) ).
thf(2652,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_zadd__left__commute) ).
thf(1277,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( C @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(267,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_of__nat__power) ).
thf(1509,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(597,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_mult__less__imp__less__right) ).
thf(2684,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(101,axiom,
real @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Osemiring__1) ).
thf(939,plain,
real @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(568,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_power__eq__imp__eq__base) ).
thf(2597,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( C @ ( D @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(393,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).
thf(2005,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ power_power ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_zadd__zless__mono) ).
thf(1413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(657,axiom,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_bin__less__0__simps_I1_J) ).
thf(2914,plain,
~ ( int @ zero_zero @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(285,axiom,
tn @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_tn0) ).
thf(1583,plain,
tn @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(305,axiom,
int @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oab__semigroup__add) ).
thf(1662,plain,
int @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(571,axiom,
! [A: $i] :
( ( A @ linordered_semiring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_mult__left__less__imp__less) ).
thf(2614,plain,
! [A: $i] :
( ( A @ linordered_semiring )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(417,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_mult__strict__right__mono__neg) ).
thf(2096,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(648,axiom,
int @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__0) ).
thf(2878,plain,
int @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(541,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_add__nonneg__nonneg) ).
thf(2503,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(465,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ti ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_4_arg1) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ fun ) @ ti ) @ ( A @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(640,axiom,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_less__zeroE) ).
thf(2846,plain,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_minf_I6_J) ).
thf(1018,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(331,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_rel__simps_I34_J) ).
thf(1770,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
!= ( B @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_order__less__imp__not__eq2) ).
thf(855,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
!= ( B @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(381,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_plus__numeral__code_I9_J) ).
thf(1961,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ number_number_of ) @ ( A @ ( int @ number_number_of ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ~ ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( C @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_ex__least__nat__le) ).
thf(2397,plain,
! [A: $i,B: $i] :
( ~ ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( C @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ ord )
=> ( ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
thf(705,plain,
! [A: $i] :
( ( A @ ord )
=> ( ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(79,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( H @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_xt5) ).
thf(887,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( G @ ( H @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( H @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
=> ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(281,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_less__number__of) ).
thf(1566,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(293,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_of__nat__0__le__iff) ).
thf(1605,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(635,axiom,
! [A: $i] :
( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_le__0__eq) ).
thf(2821,plain,
! [A: $i] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( nat @ zero_zero @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(506,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_add__gr__0) ).
thf(2386,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) @ ( D @ ti ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_0_res) ).
thf(1230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ord )
=> ( ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) @ ( D @ ti ) )
= ( C @ ( B @ ( D @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(653,axiom,
! [A: $i] :
( ! [B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
<=> ! [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_transfer__int__nat__quantifiers_I1_J) ).
thf(2888,plain,
! [A: $i] :
( ( ! [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ! [B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) )
& ( ! [B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ! [B: $i] : ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(650,axiom,
! [A: $i] :
( ( A @ cancel146912293up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_add__imp__eq) ).
thf(2882,plain,
! [A: $i] :
( ( A @ cancel146912293up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(600,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_le__number__of) ).
thf(2689,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ? [C: $i] :
( B
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_le__iff__add) ).
thf(1070,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_order__trans) ).
thf(872,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(407,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_int__int__eq) ).
thf(2060,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ zero_zero )
= ( pls @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_semiring__norm_I112_J) ).
thf(1400,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ zero_zero )
= ( pls @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(612,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_less__int__code_I16_J) ).
thf(2732,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(376,axiom,
int @ linordered_ring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__ring) ).
thf(1941,plain,
int @ linordered_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(26,axiom,
real @ semiri456707255roduct,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) ).
thf(739,plain,
real @ semiri456707255roduct,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(545,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_double__add__less__zero__iff__single__add__less__zero) ).
thf(2518,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ zero_zero @ ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(415,axiom,
! [A: $i] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_less__irrefl__nat) ).
thf(2092,plain,
! [A: $i] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(337,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(1790,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(245,axiom,
( ( pls @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_succ__Pls) ).
thf(1432,plain,
( ( pls @ ( succ @ ( int @ ( int @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_order__less__asym_H) ).
thf(1038,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ power )
=> ! [B: $i] :
( ( nat @ zero_zero @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_power__0) ).
thf(1869,plain,
! [A: $i] :
( ( A @ power )
=> ! [B: $i] :
( ( nat @ zero_zero @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(492,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_mult__less__imp__less__left) ).
thf(2337,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(472,axiom,
! [A: $i,B: $i] :
( ~ ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( A @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_ex__least__nat__less) ).
thf(2276,plain,
! [A: $i,B: $i] :
( ~ ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( nat @ one_one @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
& ! [D: $i] :
( ( C @ ( D @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( A @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(347,axiom,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_add__strict__left__mono) ).
thf(1830,plain,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(552,axiom,
nat @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(2545,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( pls @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add__numeral__0) ).
thf(1218,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( pls @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(529,axiom,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_add__le__less__mono) ).
thf(2468,plain,
! [A: $i] :
( ( A @ ordere223160158up_add )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(587,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(2656,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(318,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_int__1) ).
thf(1711,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(660,axiom,
! [A: $i] :
( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_less__0__number__of) ).
thf(2920,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( nat @ number_number_of ) @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_xt1_I3_J) ).
thf(791,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(273,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_one__add__one__is__two) ).
thf(1543,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( A @ one_one @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(187,axiom,
int @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Oorder) ).
thf(1221,plain,
int @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(227,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_zle__trans) ).
thf(1353,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(71,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(864,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( G @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_order__le__less__subst2) ).
thf(727,plain,
! [A: $i,B: $i] :
( ( ( A @ order )
& ( B @ order ) )
=> ! [C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( ! [G: $i,H: $i] :
( ( H @ ( G @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( G @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(340,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_power__strict__decreasing) ).
thf(1797,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_le__funI) ).
thf(1008,plain,
! [A: $i,B: $i] :
( ( B @ ord )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) @ ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ ord_less_eq @ ( bool @ ( B @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( B @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( B @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(402,axiom,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( B
!= ( nat @ zero_zero ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( B
= ( nat @ zero_zero ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_power__0__left) ).
thf(2030,plain,
! [A: $i] :
( ( ( A @ semiring_0 )
& ( A @ power ) )
=> ! [B: $i] :
( ( ( B
!= ( nat @ zero_zero ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( B
= ( nat @ zero_zero ) )
=> ( ( B @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_zero__le__double__add__iff__zero__le__single__add) ).
thf(1372,plain,
! [A: $i] :
( ( A @ linord219039673up_add )
=> ! [B: $i] :
( ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(361,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
thf(1881,plain,
! [A: $i,B: $i] :
( ( B @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ order )
=> ( B @ ( A @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(859,plain,
! [A: $i,B: $i] :
( ( B @ order )
=> ( B @ ( A @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(425,axiom,
! [A: $i] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
thf(2113,plain,
! [A: $i] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_order__less__not__sym) ).
thf(703,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(516,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_add__neg__neg) ).
thf(2426,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( A @ zero_zero @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(387,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_mult__strict__mono_H) ).
thf(1981,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(260,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(1485,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(385,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_of__nat__le__iff) ).
thf(1972,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_order__less__le__trans) ).
thf(1052,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(266,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
thf(1506,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(383,axiom,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_add__left__imp__eq) ).
thf(1966,plain,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(651,axiom,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_add__left__mono) ).
thf(2885,plain,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(602,axiom,
! [A: $i] :
( ( A @ zero_neq_one )
=> ( ( A @ zero_zero )
!= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_zero__neq__one) ).
thf(2696,plain,
! [A: $i] :
( ( A @ zero_neq_one )
=> ( ( A @ zero_zero )
!= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(647,axiom,
! [A: $i] :
( ( A @ one )
=> ! [B: $i] :
( ( ( A @ one_one )
= ( B @ ( A @ ti ) ) )
<=> ( ( B @ ( A @ ti ) )
= ( A @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_one__reorient) ).
thf(2870,plain,
! [A: $i] :
( ( A @ one )
=> ! [B: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( A @ one_one ) )
=> ( ( A @ one_one )
= ( B @ ( A @ ti ) ) ) )
& ( ( ( A @ one_one )
= ( B @ ( A @ ti ) ) )
=> ( ( B @ ( A @ ti ) )
= ( A @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(217,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_add__increasing2) ).
thf(1321,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(240,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(1412,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_linorder__antisym__conv3) ).
thf(759,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(583,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_le__special_I2_J) ).
thf(2643,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(356,axiom,
! [A: $i] :
( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_real__sqrt__gt__zero) ).
thf(1866,plain,
! [A: $i] :
( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_xt1_I6_J) ).
thf(771,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(302,axiom,
int @ linordered_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semiring) ).
thf(1649,plain,
int @ linordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(496,axiom,
! [A: $i] :
( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( nat @ one_one @ ( A @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( nat @ one_one @ ( A @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_nat__number__of__add__1) ).
thf(2352,plain,
! [A: $i] :
( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( nat @ one_one @ ( A @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( nat @ one_one @ ( A @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_zero__power2) ).
thf(1084,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ zero_zero @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(334,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_mult__le__less__imp__less) ).
thf(1781,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(80,axiom,
real @ linordered_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Olinordered__semiring) ).
thf(891,plain,
real @ linordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(615,axiom,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_zero__le__imp__eq__int) ).
thf(2743,plain,
! [A: $i] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
( A
= ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(535,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ti ) @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_3_arg2) ).
thf(2490,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ ti ) @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(447,axiom,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__nat__zero__code) ).
thf(2187,plain,
! [A: $i] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(423,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_power__gt1__lemma) ).
thf(2110,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ one_one @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(122,axiom,
real @ ring_11004092258visors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors) ).
thf(1010,plain,
real @ ring_11004092258visors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(659,axiom,
nat @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).
thf(2919,plain,
nat @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(283,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_mult__strict__mono) ).
thf(1575,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(288,axiom,
nat @ linordered_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semiring) ).
thf(1590,plain,
nat @ linordered_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(309,axiom,
! [A: $i] :
( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_rel__simps_I5_J) ).
thf(1674,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(477,axiom,
! [A: $i] :
( ( A @ zero )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ozero__class_Ozero_res) ).
thf(2290,plain,
! [A: $i] :
( ( A @ zero )
=> ( ( A @ zero_zero @ ( A @ ti ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(549,axiom,
! [A: $i,B: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) )
= ( real @ zero_zero ) )
<=> ( ( B
= ( real @ zero_zero ) )
& ( A
= ( real @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_realpow__two__sum__zero__iff) ).
thf(2532,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( real @ zero_zero ) )
& ( A
= ( real @ zero_zero ) ) )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) )
= ( real @ zero_zero ) ) )
& ( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( B @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) @ ( real @ plus_plus ) @ ( real @ ( real @ hAPP ) ) ) )
= ( real @ zero_zero ) )
=> ( ( B
= ( real @ zero_zero ) )
& ( A
= ( real @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(633,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_less__eq__int__code_I16_J) ).
thf(2811,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(326,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_le__special_I1_J) ).
thf(1745,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ number_number_of ) @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(401,axiom,
! [A: $i] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_number__of1) ).
thf(2026,plain,
! [A: $i] :
( ( A @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
& ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(519,axiom,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
<=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_add__left__cancel) ).
thf(2431,plain,
! [A: $i] :
( ( A @ cancel_semigroup_add )
=> ! [B: $i,C: $i,D: $i] :
( ( ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) )
=> ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(436,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_semiring__number__of__add__1) ).
thf(2152,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(507,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_semiring__numeral__1__eq__1) ).
thf(2394,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( A @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(224,axiom,
! [A: $i] :
( ( A @ number )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) )
<=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_number__of__reorient) ).
thf(1341,plain,
! [A: $i] :
( ( A @ number )
=> ! [B: $i,C: $i] :
( ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) )
=> ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) ) )
& ( ( ( B @ ( A @ number_number_of ) )
= ( C @ ( A @ ti ) ) )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(418,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_number__of__Bit1) ).
thf(2098,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ number_number_of ) @ ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(23,axiom,
( ( fFalse @ ( bool @ ti ) )
= fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fFalse_res) ).
thf(731,plain,
( ( fFalse @ ( bool @ ti ) )
= fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_minf_I8_J) ).
thf(786,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( C @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( D @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(522,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
thf(2447,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_xt1_I7_J) ).
thf(667,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(450,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ti ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_4_res) ).
thf(2198,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ti ) )
= ( C @ ( B @ ( A @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(441,axiom,
t @ ( int @ one_one @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_tpos) ).
thf(2162,plain,
t @ ( int @ one_one @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(183,axiom,
int @ ordere779506340up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__ab__semigroup__add) ).
thf(1212,plain,
int @ ordere779506340up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(294,axiom,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__special_I4_J) ).
thf(1607,plain,
! [A: $i] :
( ( ( A @ linordered_idom )
& ( A @ number_ring ) )
=> ! [B: $i] :
( ( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ one_one @ ( B @ ( A @ number_number_of ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(427,axiom,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_mult__neg__neg) ).
thf(2120,plain,
! [A: $i] :
( ( A @ linord581940658strict )
=> ! [B: $i,C: $i] :
( ( A @ zero_zero @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ zero_zero @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(479,axiom,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_mult__less__le__imp__less) ).
thf(2294,plain,
! [A: $i] :
( ( A @ linord20386208strict )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( D @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(488,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_odd__less__0) ).
thf(2315,plain,
! [A: $i] :
( ( ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ zero_zero @ ( A @ ( A @ ( int @ one_one @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( int @ zero_zero @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(389,axiom,
! [A: $i] :
( ( A @ zero_neq_one )
=> ( ( A @ one_one )
!= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_one__neq__zero) ).
thf(1994,plain,
! [A: $i] :
( ( A @ zero_neq_one )
=> ( ( A @ one_one )
!= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(623,axiom,
nat @ comm_monoid_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).
thf(2779,plain,
nat @ comm_monoid_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(137,axiom,
real @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Oorder) ).
thf(1045,plain,
real @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(316,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_number__of__Pls) ).
thf(1706,plain,
! [A: $i] :
( ( A @ number_ring )
=> ( ( pls @ ( A @ number_number_of ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(178,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_zle__int) ).
thf(1193,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(416,axiom,
int @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Power_Opower) ).
thf(2095,plain,
int @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_linorder__le__cases) ).
thf(832,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_linorder__linear) ).
thf(684,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_linorder__cases) ).
thf(716,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(800,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(392,axiom,
( ( bit0 @ ( int @ ( int @ fun ) @ ti ) )
= bit0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_res) ).
thf(2003,plain,
( ( bit0 @ ( int @ ( int @ fun ) @ ti ) )
= bit0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_1_arg2) ).
thf(2287,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ power )
=> ( ( B @ ( nat @ ti ) @ ( A @ ( C @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( C @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(268,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_less__int__code_I14_J) ).
thf(1512,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( bool @ ti ) @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_2_arg2) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( bool @ ti ) @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(437,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_add__Bit0__Bit1) ).
thf(2155,plain,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(154,axiom,
! [A: $i,B: $i] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_realpow__pos__nth) ).
thf(1097,plain,
! [A: $i,B: $i] :
( ( B @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( ( B @ ( C @ ( real @ power_power ) @ ( real @ ( nat @ hAPP ) ) ) )
= A )
& ( C @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_rel__simps_I17_J) ).
thf(1546,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(290,axiom,
! [A: $i] :
( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_zero__less__int__conv) ).
thf(1593,plain,
! [A: $i] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ zero_zero @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(308,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(1673,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(394,axiom,
! [A: $i,B: $i] :
( ( B @ monoid_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_0_res) ).
thf(2008,plain,
! [A: $i,B: $i] :
( ( B @ monoid_add )
=> ( ( A @ ( B @ plus_plus ) @ ( B @ ( B @ fun ) @ ti ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(211,axiom,
! [A: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_power2__ge__self) ).
thf(1303,plain,
! [A: $i] : ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(621,axiom,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_add__nonneg__eq__0__iff) ).
thf(2768,plain,
! [A: $i] :
( ( A @ ordere216010020id_add )
=> ! [B: $i,C: $i] :
( ( C @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) )
& ( ( C @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(72,axiom,
real @ ordere236663937imp_le,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) ).
thf(865,plain,
real @ ordere236663937imp_le,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(258,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_semiring__add__number__of) ).
thf(1480,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i,C: $i] :
( ( C @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ number_number_of ) @ ( C @ ( A @ number_number_of ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( C @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(451,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_power__decreasing) ).
thf(2201,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ one_one @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(230,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_linorder__neqE__nat) ).
thf(1363,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(616,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) )
<=> ( ( B
= ( nat @ zero_zero ) )
& ( A
= ( nat @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_add__is__0) ).
thf(2746,plain,
! [A: $i,B: $i] :
( ( ( ( B
= ( nat @ zero_zero ) )
& ( A
= ( nat @ zero_zero ) ) )
=> ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) ) )
& ( ( ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( nat @ zero_zero ) )
=> ( ( B
= ( nat @ zero_zero ) )
& ( A
= ( nat @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(605,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( A @ one_one @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_less__add__one) ).
thf(2704,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i] : ( A @ one_one @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(501,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_zero__le__one) ).
thf(2366,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ( A @ one_one @ ( A @ zero_zero @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(131,axiom,
real @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Orderings_Opreorder) ).
thf(1033,plain,
real @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(510,axiom,
nat @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Omonoid__mult) ).
thf(2404,plain,
nat @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_order__less__imp__not__less) ).
thf(828,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
real @ power,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Power_Opower) ).
thf(696,plain,
real @ power,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(105,axiom,
real @ monoid_mult,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Groups_Omonoid__mult) ).
thf(955,plain,
real @ monoid_mult,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_pinf_I6_J) ).
thf(796,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i] :
? [C: $i] :
! [D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( D @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
real @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__semiring) ).
thf(886,plain,
real @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(223,axiom,
! [A: $i] :
( ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_rel__simps_I10_J) ).
thf(1335,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(409,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_nat__add__assoc) ).
thf(2070,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(561,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_number__of__int) ).
thf(2572,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( A @ number_number_of ) )
= ( B @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(173,axiom,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_power__eq__0__iff__number__of) ).
thf(1172,plain,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( C @ ( nat @ number_number_of ) @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( ( C @ ( nat @ number_number_of ) )
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(897,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(513,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_nat__add__left__commute) ).
thf(2417,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_order__antisym__conv) ).
thf(960,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(628,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_le__add1) ).
thf(2795,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(256,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(1473,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(374,axiom,
! [A: $i] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_less__not__refl) ).
thf(1930,plain,
! [A: $i] :
~ ( A @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(27,axiom,
real @ no_zero_divisors,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Ono__zero__divisors) ).
thf(740,plain,
real @ no_zero_divisors,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(439,axiom,
( ( pls @ ( int @ ti ) )
= pls ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OPls_res) ).
thf(2159,plain,
( ( pls @ ( int @ ti ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(346,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( B @ ( A @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_mult__Bit1) ).
thf(1827,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( B @ ( A @ ( int @ times_times @ ( int @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(518,axiom,
nat @ semiring_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__0) ).
thf(2430,plain,
nat @ semiring_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(169,axiom,
( ( n @ ( nat @ ti ) )
= n ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_n_____res) ).
thf(1152,plain,
( ( n @ ( nat @ ti ) )
= n ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(630,axiom,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_transfer__int__nat__numerals_I3_J) ).
thf(2803,plain,
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(233,axiom,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_add__less__cancel__left) ).
thf(1378,plain,
! [A: $i] :
( ( A @ ordere236663937imp_le )
=> ! [B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(528,axiom,
nat @ linord893533164strict,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) ).
thf(2467,plain,
nat @ linord893533164strict,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(229,axiom,
! [A: $i] :
( ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_rel__simps_I27_J) ).
thf(1357,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( pls @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_xt1_I2_J) ).
thf(908,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(265,axiom,
! [A: $i] :
( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_real__sqrt__gt__0__iff) ).
thf(1500,plain,
! [A: $i] :
( ( ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( sqrt @ ( real @ ( real @ hAPP ) ) ) @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( real @ zero_zero @ ( real @ ord_less @ ( bool @ ( real @ fun ) @ ( real @ hAPP ) ) ) @ ( bool @ ( real @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(543,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= B )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_less__imp__add__positive) ).
thf(2507,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( ( ( C @ ( A @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= B )
& ( C @ ( nat @ zero_zero @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(371,axiom,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_add__right__mono) ).
thf(1925,plain,
! [A: $i] :
( ( A @ ordere779506340up_add )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(319,axiom,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
<=> ( ( C
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_power__eq__0__iff) ).
thf(1713,plain,
! [A: $i] :
( ( ( A @ zero_neq_one )
& ( A @ no_zero_divisors )
& ( A @ mult_zero )
& ( A @ power ) )
=> ! [B: $i,C: $i] :
( ( ( ( C
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) )
=> ( ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) )
=> ( ( C
!= ( nat @ zero_zero ) )
& ( ( B @ ( A @ ti ) )
= ( A @ zero_zero ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(195,axiom,
! [A: $i] :
( ( A @ linordered_ring )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( C @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_not__sum__squares__lt__zero) ).
thf(1236,plain,
! [A: $i] :
( ( A @ linordered_ring )
=> ! [B: $i,C: $i] :
~ ( A @ zero_zero @ ( C @ ( C @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( B @ ( B @ ( A @ times_times @ ( A @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(462,axiom,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__nat__number__of) ).
thf(2241,plain,
! [A: $i,B: $i] :
( ( ~ ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( ~ ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( nat @ number_number_of ) ) ) ) ) )
& ( ( pls @ ( B @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( nat @ number_number_of ) @ ( B @ ( nat @ number_number_of ) @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( nat @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(569,axiom,
! [A: $i,B: $i] :
( ( B @ cancel_semigroup_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Oplus__class_Oplus_2_arg1) ).
thf(2600,plain,
! [A: $i,B: $i] :
( ( B @ cancel_semigroup_add )
=> ( ( A @ ( B @ ti ) @ ( B @ plus_plus ) )
= ( A @ ( B @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
thf(1384,plain,
! [A: $i] :
( ( A @ comm_semiring_1 )
=> ! [B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( C @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(272,axiom,
! [A: $i,B: $i] :
( ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_add1__zle__eq) ).
thf(1537,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( int @ one_one @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(599,axiom,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_power__increasing) ).
thf(2687,plain,
! [A: $i] :
( ( A @ linordered_semidom )
=> ! [B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ one_one @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( C @ ( B @ ( A @ power_power ) @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(646,axiom,
! [A: $i] :
( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
thf(2864,plain,
! [A: $i] :
( ( ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( pls @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(533,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zadd__0__right) ).
thf(2484,plain,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(603,axiom,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_semiring__1__add__number__of) ).
thf(2699,plain,
! [A: $i] :
( ( A @ number_semiring )
=> ! [B: $i] :
( ( B @ ( pls @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ number_number_of ) @ ( A @ one_one @ ( A @ plus_plus ) @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( succ @ ( int @ ( int @ hAPP ) ) ) @ ( A @ number_number_of ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(220,axiom,
int @ number_semiring,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__semiring) ).
thf(1331,plain,
int @ number_semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_leD) ).
thf(803,plain,
! [A: $i] :
( ( A @ linorder )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(379,axiom,
! [A: $i] :
( ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_rel__simps_I44_J) ).
thf(1945,plain,
! [A: $i] :
( ( ( A = pls )
=> ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= pls ) )
& ( ( ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(325,axiom,
! [A: $i] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_int__le__0__conv) ).
thf(1737,plain,
! [A: $i] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(352,axiom,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( ~ ( B @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( B @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ number_number_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_of__nat__number__of__lemma) ).
thf(1848,plain,
! [A: $i] :
( ( A @ number_ring )
=> ! [B: $i] :
( ( ~ ( B @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) )
& ( ( B @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( nat @ number_number_of ) @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(461,axiom,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__Bit0__Bit0) ).
thf(2238,plain,
! [A: $i,B: $i] :
( ( B @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( A @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( A @ ( int @ plus_plus ) @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(243,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_zless__le) ).
thf(1416,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( int @ ord_less @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(495,axiom,
int @ ordere223160158up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) ).
thf(2351,plain,
int @ ordere223160158up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(421,axiom,
nat @ ab_semigroup_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oab__semigroup__add) ).
thf(2106,plain,
nat @ ab_semigroup_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(530,axiom,
! [A: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_quartic__square__square) ).
thf(2470,plain,
! [A: $i] :
( ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( bit0 @ ( int @ ( int @ hAPP ) ) ) @ ( nat @ number_number_of ) @ ( A @ ( int @ power_power ) @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(592,axiom,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_transfer__int__nat__numerals_I2_J) ).
thf(2672,plain,
( ( int @ one_one )
= ( nat @ one_one @ ( int @ semiring_1_of_nat @ ( int @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(649,axiom,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( nat @ zero_zero @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_of__nat__0) ).
thf(2879,plain,
! [A: $i] :
( ( A @ semiring_1 )
=> ( ( nat @ zero_zero @ ( A @ semiring_1_of_nat @ ( A @ ( nat @ hAPP ) ) ) )
= ( A @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(489,axiom,
! [A: $i] :
( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_eq__0__number__of) ).
thf(2321,plain,
! [A: $i] :
( ( ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL )
=> ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) ) )
& ( ( ( nat @ zero_zero )
= ( A @ ( nat @ number_number_of ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq @ ( bool @ ( int @ fun ) @ ( int @ hAPP ) ) ) @ ( bool @ ( int @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(378,axiom,
int @ ordere216010020id_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oordered__comm__monoid__add) ).
thf(1944,plain,
int @ ordere216010020id_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_xt1_I5_J) ).
thf(940,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(652,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(2887,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(175,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(1184,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(411,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_rel__simps_I51_J) ).
thf(2074,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ) )
& ( ( ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) )
= ( B @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(398,axiom,
( ( int @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
thf(2018,plain,
( ( int @ one_one )
= ( pls @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) @ ( int @ number_number_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(637,axiom,
! [A: $i] :
( pls
!= ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_rel__simps_I39_J) ).
thf(2832,plain,
! [A: $i] :
( pls
!= ( A @ ( bit1 @ ( int @ ( int @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(368,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_gr__implies__not0) ).
thf(1917,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_linorder__neqE__linordered__idom) ).
thf(755,plain,
! [A: $i] :
( ( A @ linordered_idom )
=> ! [B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( ~ ( C @ ( B @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ ord_less @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( bool @ ti ) @ hBOOL )
<=> ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(708,plain,
! [A: $i] :
( ( ( A @ hBOOL )
=> ( A @ ( bool @ ti ) @ hBOOL ) )
& ( ( A @ ( bool @ ti ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_add__le__mono1) ).
thf(1912,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ plus_plus ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(3138,plain,
$false,
inference(e,[status(thm)],[2630,2452,1411,1024,2306,1454,1767,2263,2463,893,2544,1554,2163,892,1559,1105,2595,2499,1818,1295,2363,2622,2808,2495,2527,2590,741,1728,1305,1437,861,1486,2309,2512,1924,2210,1443,2776,2282,1591,2686,1310,1735,2184,1872,1233,814,698,2146,1458,2575,1078,1426,1761,747,1640,2580,1063,2844,1222,2360,1095,1835,1001,1914,2227,1441,2020,1613,1601,2082,1724,1366,1529,1518,2405,1243,1127,2763,973,1046,1650,1921,1228,1623,2654,1055,1287,1709,2039,1660,2269,2501,2217,2562,2603,2916,2667,719,2339,785,1323,838,917,702,751,1577,1455,1832,934,1191,2420,902,1147,2635,2158,1875,2829,2169,1087,969,2373,1572,1815,1494,2222,2782,1040,2259,1334,2122,1978,2555,1489,1415,2616,1465,1682,834,1151,937,1020,2254,2335,966,1283,2073,1928,2281,2190,956,866,2530,2371,1351,998,2103,1201,1521,2718,1564,2861,1215,1104,1242,2011,920,2204,925,2047,1783,2296,2641,2083,2000,678,2473,1199,2364,714,1868,1730,798,1057,2441,2409,2428,1042,1355,862,2147,1751,1666,693,788,815,2132,2015,1883,1387,1900,825,2560,2805,916,2464,1032,2628,2663,665,830,1836,2345,2741,1634,2112,974,2068,1819,1624,2547,2313,2300,1983,874,2895,1856,1587,1006,2638,697,1234,1794,1953,2577,1064,1111,1227,1138,2858,2460,2023,933,2561,1182,1461,669,686,2312,1842,1584,1700,1791,1207,884,1329,1964,1942,2649,970,837,1114,1776,2681,2836,2487,1266,2497,1799,1002,2272,1759,2450,985,1150,1249,1552,2851,984,911,2505,2766,1599,1246,2140,2756,1318,2926,2203,1779,805,921,1170,2402,1663,2221,1026,1732,2634,1434,2702,2546,765,1054,1035,2368,953,1185,773,794,2423,662,906,1906,750,2677,1698,2149,1483,2570,1927,689,2524,733,1135,2729,1648,2904,1680,1154,2048,2225,2716,2817,2134,1615,1389,2789,1125,2657,2849,2674,2016,958,1403,2695,1488,2161,936,2293,1312,2738,1865,1058,1332,1092,2706,2557,1258,2474,1224,2193,1786,1239,1997,2166,1090,831,2151,1011,1349,2299,1144,2116,737,2856,2896,863,1209,2721,900,2679,2214,2383,1894,2493,784,2637,1117,996,2284,1933,1969,1307,2180,811,758,858,2625,2780,2261,1162,2757,1862,848,2785,915,1293,2710,1688,1556,769,2542,943,1022,2252,2329,932,1061,2439,2365,1474,868,2086,780,1015,2797,2592,2633,2101,1250,2303,1562,1213,768,2051,1245,851,1102,1694,922,722,1034,1809,2107,2665,1467,2271,2652,1277,1509,2684,939,2597,2005,1413,2914,1583,1662,2614,2096,2878,2503,2256,2846,1018,1770,855,1961,2397,705,887,1566,1605,2821,2386,1230,2888,2882,2689,1070,872,2060,1400,2732,1941,739,2518,2092,1790,1432,1038,1869,2337,2276,1830,2545,1218,2468,2656,1711,2920,791,1543,1221,1353,864,727,1797,1008,2030,1372,1881,859,2113,703,2426,1981,1485,1972,1052,1506,1966,2885,2696,2870,1321,1412,759,2643,1866,771,1649,2352,1084,1781,891,2743,2490,2187,2110,1010,2919,1575,1590,1674,2290,2532,2811,1745,2026,2431,2152,2394,1341,2098,731,786,2447,667,2198,2162,1212,1607,2120,2294,2315,1994,2779,1045,1706,1193,2095,832,684,716,800,2003,2287,1512,1280,2155,1097,1546,1593,1673,2008,1303,2768,865,1480,2201,1363,2746,2704,2366,1033,2404,828,696,955,796,886,1335,2070,2572,1172,897,2417,960,2795,1473,1930,740,2159,1827,2430,1152,2803,1378,2467,1357,908,1500,2507,1925,1713,1236,2241,2600,1384,1537,2687,2864,2484,2699,1331,803,1945,1737,1848,2238,1416,2351,2106,2470,2672,2879,2321,1944,940,2887,1184,2074,2018,2832,1917,755,708,1912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.27/0.52 % Computer : n020.cluster.edu
% 0.27/0.52 % Model : x86_64 x86_64
% 0.27/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.52 % Memory : 8046.5625MB
% 0.27/0.52 % OS : Linux 6.8.0-71-generic
% 0.27/0.52 % CPULimit : 300
% 0.27/0.52 % WCLimit : 300
% 0.27/0.52 % DateTime : Sat Sep 26 04:20:19 UTC 2026
% 0.27/0.52 % CPUTime :
% 0.27/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.97/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.65/1.44 % [INFO] Parsing done (437ms).
% 2.65/1.45 % [INFO] Running in sequential loop mode.
% 4.83/1.99 % [INFO] eprover registered as external prover.
% 4.83/2.00 % [INFO] Scanning for conjecture ...
% 6.84/2.44 % [INFO] Found a conjecture (or negated_conjecture) and 659 axioms. Running axiom selection ...
% 9.09/2.96 % [INFO] Axiom selection finished. Selected 659 axioms (removed 0 axioms).
% 12.74/3.81 % [INFO] Problem is first-order (TPTP FOF).
% 12.74/3.88 % [INFO] Type checking passed.
% 12.74/3.89 % [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 ...
% 45.43/12.64 % External prover 'e' found a proof!
% 45.43/12.64 % [INFO] Killing All external provers ...
% 45.43/12.64 % Time passed: 11992ms (effective reasoning time: 11186ms)
% 45.43/12.64 % 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)>
% 45.43/12.65 % Axioms used in derivation (659): fact_145_not__less0, fact_46_zadd__left__commute, fact_195_double__add__less__zero__iff__single__add__less__zero, fact_70_rel__simps_I44_J, fact_482_real__sqrt__not__eq__zero, tsy_c_Groups_Oplus__class_Oplus_2_arg1, fact_77_add__Bit0__Bit0, fact_433_order__neq__le__trans, fact_184_power__eq__0__iff, fact_290_transfer__int__nat__quantifiers_I2_J, fact_357_le__add2, fact_210_add__0__iff, fact_2_sum__power2__eq__zero__iff, fact_120_nat__neq__iff, fact_170_of__nat__1, tsy_c_hAPP_4_arg1, arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add, fact_164_field__power__not__zero, arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add, fact_262_le__special_I2_J, fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J, arity_HOL_Obool___Orderings_Oorder, arity_Nat_Onat___Groups_Omonoid__mult, fact_474_mult__strict__mono, fact_140_nat__power__less__imp__less, fact_465_mult__left__le__imp__le, fact_360_nat__add__left__cancel__le, fact_133_add__less__mono1, fact_307_rel__simps_I29_J, fact_13_numeral__1__eq__1, fact_283_less__eq__int__code_I14_J, fact_316_succ__Bit1, fact_36_add__nat__number__of, fact_309_less__int__code_I14_J, fact_125_nat__add__right__cancel, fact_435_leD, arity_Int_Oint___Groups_Oordered__comm__monoid__add, fact_321_power__eq__imp__eq__base, arity_Int_Oint___Groups_Oone, fact_253_of__nat__le__iff, fact_61_int__less__0__conv, arity_Int_Oint___Rings_Olinordered__ring__strict, arity_HOL_Obool___Orderings_Oord, fact_469_mult__less__imp__less__right, fact_325_number__of__succ, fact_396_order__antisym__conv, fact_50_less__special_I1_J, fact_420_linorder__less__linear, arity_Int_Oint___Groups_Oordered__ab__semigroup__add, arity_Int_Oint___Rings_Olinordered__idom, arity_HOL_Obool___Orderings_Opreorder, fact_129_less__not__refl2, arity_Nat_Onat___Rings_Osemiring__1, tsy_c_hAPP_0_arg2, arity_RealDef_Oreal___Rings_Olinordered__ring__strict, fact_12_semiring__norm_I110_J, fact_293_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J, fact_29_nat__1__add__1, arity_Int_Oint___Rings_Olinordered__semiring, fact_299_add__strict__increasing, fact_335_sum__power2__ge__zero, fact_423_order__less__irrefl, fact_280_of__nat__0__le__iff, fact_143_add__gr__0, fact_410_xt1_I9_J, fact_126_nat__add__left__cancel__less, fact_168_of__nat__less__imp__less, fact_384_less__mono__imp__le__mono, fact_364_add__le__mono, fact_403_order__less__asym, arity_Int_Oint___Orderings_Oorder, fact_9_semiring__one__add__one__is__two, fact_236_add__right__mono, fact_4_zero__power2, arity_Int_Oint___Int_Oring__char__0, tsy_c_Int_OPls_res, fact_20_zpower__int, fact_287_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J, fact_139_gr__implies__not0, fact_446_dense__le, fact_202_add__left__cancel, fact_158_Nat__Transfer_Otransfer__int__nat__relations_I1_J, fact_68_rel__simps_I50_J, fact_302_add__nonpos__neg, fact_361_trans__le__add1, fact_172_transfer__int__nat__numerals_I2_J, fact_31_rel__simps_I17_J, fact_358_le__add1, fact_254_zless__le, fact_44_even__less__0__iff, fact_387_le__funE, fact_405_order__less__trans, fact_372_two__realpow__ge__one, fact_272_add__le__less__mono, arity_Nat_Onat___Rings_Olinordered__semiring, fact_294_zle__iff__zadd, fact_183_power__strict__increasing, fact_490_mult__strict__left__mono, fact_312_int__one__le__iff__zero__less, fact_494_mult__less__cancel__left__neg, arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add, tsy_c_hAPP_4_res, fact_235_add__le__cancel__left, fact_412_order__less__imp__triv, arity_Int_Oint___Rings_Olinordered__ring, arity_Int_Oint___Groups_Ocomm__monoid__add, fact_209_one__reorient, arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add, tsy_c_Groups_Oplus__class_Oplus_0_res, fact_470_mult__right__less__imp__less, fact_431_not__leE, arity_RealDef_Oreal___Rings_Osemiring__0, fact_359_le__iff__add, fact_461_order__le__less__subst1, fact_489_comm__mult__strict__left__mono, arity_fun___Orderings_Oord, fact_343_less__eq__nat_Osimps_I1_J, fact_91_add__Bit0__Bit1, arity_Int_Oint___Orderings_Oord, fact_379_real__le__linear, arity_RealDef_Oreal___Groups_Ozero, fact_137_nat__less__cases, fact_380_real__le__trans, fact_88_add__number__of__eq, fact_487_mult__strict__left__mono__neg, fact_22_zadd__int__left, fact_198_add__imp__eq, fact_378_real__le__refl, fact_136_add__lessD1, fact_148_zero__less__power__nat__eq__number__of, fact_171_of__nat__power, tsy_c_hAPP_3_arg2, fact_418_linorder__neqE, arity_RealDef_Oreal___Int_Onumber__semiring, arity_Int_Oint___Orderings_Opreorder, fact_97_sum__power2__gt__zero__iff, arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp, fact_257_le__special_I1_J, arity_Nat_Onat___Int_Onumber__semiring, arity_Nat_Onat___Orderings_Opreorder, fact_371_le__nat__number__of, fact_56_bin__less__0__simps_I4_J, fact_413_order__less__imp__not__eq2, fact_7_add__special_I3_J, fact_109_power__0__left, fact_437_linorder__antisym__conv2, fact_444_xt1_I8_J, fact_211_add_Ocomm__neutral, fact_227_add__neg__neg, fact_473_mult__strict__mono_H, arity_Nat_Onat___Power_Opower, fact_142_nat__zero__less__power__iff, fact_414_order__less__imp__not__eq, fact_130_less__not__refl3, fact_304_eq__0__number__of, fact_298_add__nonneg__pos, arity_Int_Oint___Rings_Oring__1__no__zero__divisors, arity_Int_Oint___Rings_Ono__zero__divisors, fact_197_add__right__imp__eq, fact_138_gr0I, fact_481_real__sqrt__gt__zero, fact_105_transfer__int__nat__numerals_I4_J, fact_342_le0, fact_26_semiring__norm_I113_J, fact_122_nat__add__left__commute, fact_356_real__less__def, fact_75_add__Pls__right, fact_363_add__le__mono1, fact_250_zle__trans, fact_228_add__pos__pos, fact_484_real__sqrt__gt__0__iff, fact_111_zero__less__two, arity_RealDef_Oreal___Groups_Ocancel__ab__semigroup__add, fact_5_zero__eq__power2, fact_454_xt7, tsy_v_m1_____res, arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict, fact_424_linorder__not__less, tsy_c_Int_Onumber__class_Onumber__of_res, fact_479_power__less__power__Suc, fact_232_nat__number__of__add__1, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le, fact_33_less__int__code_I13_J, fact_313_int__le__0__conv, fact_189_pos2, fact_60_zless__add1__eq, fact_40_eq__number__of, tsy_c_Groups_Oplus__class_Oplus_1_res, fact_151_linorder__neqE__linordered__idom, fact_48_int__int__eq, fact_404_xt1_I10_J, tsy_c_Groups_Oplus__class_Oplus_1_arg1, fact_47_zadd__commute, arity_Int_Oint___Int_Onumber__semiring, tsy_c_Orderings_Oord__class_Oless__eq_res, fact_330_zero__le__power2, fact_246_rel__simps_I31_J, arity_Int_Oint___Groups_Ocancel__ab__semigroup__add, fact_214_double__zero__sym, arity_Int_Oint___Int_Onumber__ring, fact_451_xt5, fact_247_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J, fact_241_power__increasing, fact_267_add__nonneg__eq__0__iff, fact_114_less__zeroE, fact_213_add__0__right, fact_242_less__eq__int__code_I16_J, fact_328_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J, arity_Int_Oint___Rings_Osemiring__1, fact_383_ex__least__nat__le, fact_281_rel__simps_I22_J, fact_199_add__left__imp__eq, fact_219_add__less__imp__less__right, fact_295_semiring__1__add__number__of, fact_215_add__0, arity_Nat_Onat___Groups_Ocomm__monoid__add, fact_100_number__of__Bit1, fact_344_le__0__eq, fact_191_less__imp__add__positive, fact_266_add__nonneg__nonneg, fact_355_less__eq__real__def, arity_Nat_Onat___Rings_Omult__zero, tsy_c_hAPP_3_res, fact_66_rel__simps_I46_J, fact_429_order__le__less, fact_206_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J, fact_180_power__inject__exp, fact_375_ex__least__nat__less, tsy_c_fFalse_res, fact_21_int__power, tsy_c_hAPP_3_arg1, arity_Nat_Onat___Rings_Olinordered__semiring__strict, fact_99_number__of__Bit0, fact_101_semiring__numeral__1__eq__1, fact_169_of__nat__add, arity_RealDef_Oreal___Rings_Olinordered__ring, fact_305_eq__number__of__0, fact_402_linorder__cases, fact_52_less__int__code_I15_J, fact_347_less__imp__le__nat, arity_Int_Oint___Rings_Olinordered__semiring__strict, tsy_c_hBOOL_arg1, fact_463_zadd__power2, arity_RealDef_Oreal___Groups_Omonoid__add, fact_6_add__special_I2_J, fact_428_less__le__not__le, fact_376_nonneg__eq__int, fact_146_zero__less__power__nat__eq, fact_80_zadd__0, fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J, arity_RealDef_Oreal___Orderings_Oord, fact_297_add__pos__nonneg, fact_491_mult__strict__right__mono, fact_102_mn, fact_366_add__leD1, fact_308_rel__simps_I15_J, fact_273_not__one__le__zero, arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le, fact_274_zero__le__one, fact_57_bin__less__0__simps_I1_J, fact_457_xt6, fact_59_int__0__less__1, fact_471_mult__le__less__imp__less, fact_390_order__trans, fact_107_of__nat__0__less__iff, fact_127_linorder__neqE__nat, arity_RealDef_Oreal___Rings_Olinordered__semiring__strict, fact_64_odd__less__0, fact_348_le__eq__less__or__eq, arity_RealDef_Oreal___Rings_Ocomm__semiring__1, fact_468_mult__left__less__imp__less, fact_1_t1, fact_395_ord__eq__le__trans, fact_408_xt1_I1_J, help_If_1_1_T, fact_96_power2__less__0, fact_265_double__add__le__zero__iff__single__add__le__zero, fact_301_add__neg__nonpos, fact_103_of__nat__less__two__power, fact_285_rel__simps_I27_J, fact_192_exp__eq__1, fact_329_power2__ge__self, fact_95_zero__less__power2, fact_83_semiring__norm_I112_J, arity_RealDef_Oreal___Rings_Osemiring__1, fact_93_odd__nonzero, arity_fun___Orderings_Oorder, arity_RealDef_Oreal___Orderings_Odense__linorder, fact_352_eq__imp__le, arity_Nat_Onat___Orderings_Olinorder, fact_296_semiring__number__of__add__1, tsy_c_Groups_Oplus__class_Oplus_0_arg1, fact_110_power__strict__decreasing, fact_277_power__mono, fact_318_add1__zle__eq, fact_34_rel__simps_I14_J, fact_370_zle__int, fact_310_rel__simps_I33_J, fact_176_not__one__less__zero, fact_165_power__one, fact_160_less__0__number__of, fact_87_add__number__of__left, fact_115_real__zero__not__eq__one, arity_Nat_Onat___Rings_Osemiring__0, fact_445_real__lbound__gt__zero, fact_263_le__special_I4_J, arity_fun___Orderings_Opreorder, fact_67_rel__simps_I39_J, fact_345_less__or__eq__imp__le, fact_430_leI, tsy_c_hAPP_2_arg2, fact_178_zero__less__power, fact_438_order__le__imp__less__or__eq, fact_483_real__sqrt__lt__0__iff, fact_234_add__le__cancel__right, fact_261_power__le__imp__le__exp, arity_RealDef_Oreal___Int_Onumber__ring, fact_134_add__less__mono, fact_118_not__add__less2, fact_25_nat__number__of__Pls, arity_Int_Oint___Groups_Omonoid__mult, tsy_c_Groups_Otimes__class_Otimes_res, fact_258_le__special_I3_J, fact_368_real__add__left__mono, fact_249_zle__linear, tsy_c_Int_OBit1_res, fact_291_transfer__int__nat__quantifiers_I1_J, fact_334_power2__less__imp__less, fact_217_add__0__left, fact_252_le__number__of, fact_337_int__pos__lt__two__imp__zero__or__one, fact_392_xt1_I4_J, fact_224_add__less__cancel__right, tsy_c_HOL_Oundefined_res, fact_174_Nat__Transfer_Otransfer__int__nat__functions_I4_J, fact_338_number__of1, fact_54_rel__simps_I10_J, fact_157_of__nat__eq__iff, fact_175_pos__add__strict, fact_427_order__less__le, fact_79_zadd__0__right, arity_RealDef_Oreal___Rings_Olinordered__idom, fact_477_sum__squares__gt__zero__iff, fact_123_nat__add__assoc, arity_Int_Oint___Orderings_Olinorder, fact_398_order__eq__refl, fact_259_power__decreasing, fact_453_pinf_I8_J, fact_322_semiring__add__number__of, help_ti_idem, arity_Nat_Onat___Rings_Olinordered__semidom, fact_185_of__nat__less__0__iff, fact_260_power__increasing__iff, fact_426_linorder__le__less__linear, fact_166_of__nat__less__iff, fact_493_mult__neg__pos, fact_78_Bit0__def, fact_456_minf_I8_J, fact_49_less__special_I3_J, fact_104_transfer__int__nat__numerals_I3_J, fact_374_imp__le__cong, fact_167_less__imp__of__nat__less, fact_244_rel__simps_I19_J, fact_153_add__is__0, fact_323_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J, fact_238_add__mono, tsy_c_Int_Osucc_res, fact_327_power__strict__mono, fact_458_order__le__less__subst2, arity_RealDef_Oreal___Rings_Olinordered__semidom, fact_317_zle__add1__eq__le, arity_Nat_Onat___Rings_Ocomm__semiring__1, fact_73_Pls__def, arity_Int_Oint___Groups_Omonoid__add, arity_Nat_Onat___Groups_Ozero, fact_161_zero__less__int__conv, fact_190_zero__less__imp__eq__int, fact_86_power__eq__0__iff__number__of, arity_Nat_Onat___Groups_Oordered__comm__monoid__add, fact_156_power__one__right, tsy_c_Groups_Oplus__class_Oplus_2_res, fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J, fact_276_zero__le__power, fact_350_le__refl, arity_RealDef_Oreal___Rings_Omult__zero, tsy_c_hAPP_2_arg1, fact_39_Numeral1__eq1__nat, fact_51_rel__simps_I12_J, fact_432_linorder__antisym__conv1, arity_RealDef_Oreal___Groups_Oab__semigroup__add, arity_Nat_Onat___Orderings_Oord, arity_RealDef_Oreal___Int_Oring__char__0, fact_286_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J, arity_RealDef_Oreal___Groups_Ocancel__semigroup__add, fact_82_number__of__Pls, fact_106_realpow__two__sum__zero__iff, fact_441_order__less__le__trans, arity_Nat_Onat___Groups_Oordered__ab__semigroup__add, fact_320_succ__def, fact_448_le__funI, tsy_c_Power_Opower__class_Opower_arg1, fact_208_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J, fact_222_add__strict__right__mono, fact_251_zle__antisym, arity_Int_Oint___Rings_Olinordered__comm__semiring__strict, fact_270_add__nonpos__nonpos, fact_45_zadd__assoc, help_If_3_1_T, help_If_2_1_T, fact_406_xt1_I2_J, fact_275_le__number__of__eq__not__less, fact_147_Nat__Transfer_Otransfer__int__nat__relations_I2_J, arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc, tsy_c_Power_Opower__class_Opower_res, fact_10_quartic__square__square, fact_486_real__sqrt__gt__1__iff, fact_41_number__of__reorient, arity_RealDef_Oreal___Groups_Ocomm__monoid__add, arity_RealDef_Oreal___Orderings_Oorder, fact_152_add__eq__self__zero, arity_Int_Oint___Power_Opower, fact_220_add__strict__mono, fact_389_xt1_I5_J, arity_RealDef_Oreal___Rings_Ono__zero__divisors, fact_271_add__less__le__mono, fact_369_Nat__Transfer_Otransfer__int__nat__relations_I3_J, fact_349_nat__less__le, fact_135_less__add__eq__less, arity_RealDef_Oreal___Orderings_Olinorder, fact_485_real__sqrt__lt__1__iff, arity_RealDef_Oreal___Groups_Olinordered__ab__group__add, fact_419_linorder__antisym__conv3, fact_467_mult__less__imp__less__left, fact_268_add__increasing, fact_62_less__special_I4_J, fact_207_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J, fact_85_add__numeral__0__right, fact_386_linorder__le__cases, arity_Int_Oint___Rings_Osemiring__0, arity_Int_Oint___Groups_Ocancel__semigroup__add, fact_439_order__le__neq__trans, fact_186_power__0, tsy_c_NthRoot_Osqrt_res, fact_226_nat__power__eq__0__iff, fact_480_power__gt1__lemma, fact_353_le__trans, tsy_c_hAPP_1_arg2, fact_179_less__add__one, fact_288_zadd__zless__mono, fact_55_rel__simps_I4_J, fact_362_trans__le__add2, fact_449_pinf_I6_J, fact_121_nat__add__commute, fact_187_of__nat__0, fact_18_less__number__of, fact_8_one__add__one__is__two, fact_478_not__sum__squares__lt__zero, fact_69_rel__simps_I49_J, arity_RealDef_Oreal___Rings_Ozero__neq__one, arity_Int_Oint___Rings_Ocomm__semiring__1, fact_231_tpos, fact_116_less__not__refl, fact_282_rel__simps_I32_J, arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc, fact_367_add__leE, fact_401_le__fun__def, fact_239_add__le__imp__le__right, fact_333_of__nat__number__of__lemma, fact_237_add__left__mono, fact_72_Bit0__Pls, arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add, fact_460_xt4, fact_11_power__0__left__number__of, fact_113_tn0, fact_472_mult__less__le__imp__less, fact_425_linorder__not__le, fact_284_rel__simps_I21_J, arity_RealDef_Oreal___Groups_Oone, arity_Nat_Onat___Int_Onumber, fact_23_zadd__int, arity_RealDef_Oreal___Rings_Oring__1__no__zero__divisors, fact_443_order__le__less__trans, fact_196_zero__reorient, fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J, arity_RealDef_Oreal___Orderings_Opreorder, fact_42_rel__simps_I51_J, arity_Nat_Onat___Nat_Osemiring__char__0, fact_212_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J, tsy_c_hAPP_0_arg1, arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le, fact_14_n0, fact_495_zero__less__mult__pos2, fact_269_add__increasing2, fact_462_real__sqrt__sum__squares__ge__zero, tsy_c_Groups_Ozero__class_Ozero_res, fact_382_int__ge__induct, fact_90_add__Bit1__Bit0, fact_28_int__0, fact_194_zero__less__double__add__iff__zero__less__single__add, arity_Int_Oint___Rings_Ozero__neq__one, arity_Nat_Onat___Groups_Oone, tsy_c_Int_Onumber__class_Onumber__of_arg1, fact_112_int__gr__induct, fact_162_one__neq__zero, fact_331_power2__le__imp__le, fact_450_dense__le__bounded, fact_340_zero__le__imp__eq__int, arity_Int_Oint___Groups_Oab__semigroup__add, fact_411_order__less__asym_H, fact_98_not__sum__power2__lt__zero, fact_264_zero__le__double__add__iff__zero__le__single__add, arity_RealDef_Oreal___Groups_Omonoid__mult, fact_315_succ__Bit0, fact_351_nat__le__linear, fact_488_mult__strict__right__mono__neg, tsy_c_Nat_Osemiring__1__class_Oof__nat_res, fact_303_power__less__imp__less__base, fact_255_zadd__left__mono, tsy_c_hAPP_4_arg2, fact_24_int__1, tsy_c_Int_OBit0_res, fact_476_mult__le__cancel__left__pos, fact_409_ord__eq__less__trans, fact_32_rel__simps_I2_J, arity_Nat_Onat___Orderings_Oorder, fact_332_power2__eq__imp__eq, fact_391_order__antisym, tsy_c_Groups_Oone__class_Oone_res, fact_94_number__of__int, fact_201_add__right__cancel, fact_15_zless__linear, fact_30_less__int__code_I16_J, fact_393_ord__le__eq__trans, fact_400_linorder__linear, arity_RealDef_Oreal___Power_Opower, fact_205_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J, fact_311_less__eq__int__code_I15_J, fact_218_add__less__imp__less__left, fact_43_rel__simps_I48_J, fact_163_zero__neq__one, fact_149_zless__int, fact_289_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J, fact_81_semiring__numeral__0__eq__0, fact_292_zero__zle__int, fact_76_add__Pls, fact_377_mono__nat__linear__lb, fact_233_nat__1__add__number__of, fact_365_add__leD2, fact_141_less__nat__zero__code, fact_65_double__eq__0__iff, fact_464_mult__Bit1, fact_16_less__number__of__int__code, tsy_v_t_____res, arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict, fact_399_order__eq__iff, fact_417_less__imp__neq, fact_397_le__funD, fact_278_one__le__power, fact_128_less__irrefl__nat, fact_256_less__eq__number__of__int__code, fact_381_real__le__antisym, fact_37_one__is__num__one, fact_92_Bit1__def, fact_421_not__less__iff__gr__or__eq, fact_132_trans__less__add2, fact_117_not__add__less1, arity_Nat_Onat___Rings_Ono__zero__divisors, fact_229_realpow__pos__nth__unique, fact_150_less__nat__number__of, fact_58_bin__less__0__simps_I3_J, fact_159_int__if__cong, fact_434_xt1_I12_J, fact_173_Nat__Transfer_Otransfer__int__nat__functions_I1_J, fact_245_less__eq__int__code_I13_J, fact_436_order__less__imp__le, fact_339_number__of2, fact_240_add__le__imp__le__left, tsy_c_hAPP_1_arg1, fact_124_nat__add__left__cancel, tsy_c_hAPP_1_res, fact_475_mult__le__cancel__left__neg, fact_63_less__special_I2_J, arity_Nat_Onat___Groups_Omonoid__add, arity_RealDef_Oreal___Int_Onumber, fact_248_zle__refl, fact_89_number__of__add, fact_416_order__less__not__sym, fact_319_zless__imp__add1__zle, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, arity_Nat_Onat___Groups_Oab__semigroup__add, fact_35_zadd__strict__right__mono, fact_447_less__fun__def, fact_459_order__less__le__subst1, tsy_v_n_____res, fact_415_order__less__imp__not__less, fact_422_linorder__neq__iff, arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add, arity_Int_Oint___Rings_Omult__zero, fact_0_n1pos, fact_279_zero__le__imp__of__nat, fact_346_le__neq__implies__less, arity_RealDef_Oreal___Rings_Olinordered__semiring, tsy_v_tn_____res, fact_108_one__less__power, fact_154_Nat_Oadd__0__right, arity_Int_Oint___Nat_Osemiring__char__0, fact_373_conj__le__cong, fact_306_rel__simps_I5_J, arity_Int_Oint___Rings_Olinordered__semidom, tsy_c_hAPP_0_res, arity_Int_Oint___Groups_Ozero, fact_336_sum__power2__le__zero__iff, fact_354_le__antisym, fact_314_succ__Pls, fact_243_rel__simps_I34_J, fact_74_int__0__neq__1, fact_53_rel__simps_I16_J, fact_230_realpow__pos__nth, fact_204_ab__semigroup__add__class_Oadd__ac_I1_J, fact_407_ord__less__eq__trans, fact_492_mult__neg__neg, fact_394_xt1_I3_J, fact_144_neq0__conv, fact_155_plus__nat_Oadd__0, fact_385_order__refl, fact_27_int__eq__0__conv, fact_324_le__imp__0__less, fact_388_xt1_I6_J, fact_326_add__Bit1__Bit1, arity_Nat_Onat___Rings_Ozero__neq__one, fact_442_xt1_I7_J, fact_38_nat__numeral__1__eq__1, fact_119_number__of__is__id, fact_181_power__strict__increasing__iff, tsy_c_hAPP_2_res, fact_131_trans__less__add1, fact_188_transfer__int__nat__numerals_I1_J, fact_455_order__less__le__subst2, tsy_c_Orderings_Oord__class_Oless_res, fact_177_zero__less__one, fact_300_add__strict__increasing2, fact_440_xt1_I11_J, arity_RealDef_Oreal___Nat_Osemiring__char__0, fact_466_mult__right__le__imp__le, fact_203_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J, tsy_c_fTrue_res, fact_221_add__strict__left__mono, fact_19_zero__is__num__zero, fact_84_add__numeral__0, tsy_c_If_res, arity_Nat_Onat___Groups_Ocancel__semigroup__add, fact_71_rel__simps_I38_J, fact_3_one__power2, fact_182_power__less__imp__less__exp, fact_341_nonneg__int__cases, fact_452_minf_I6_J, fact_223_add__less__cancel__left, fact_17_plus__numeral__code_I9_J
% 45.43/12.65 % No. of inferences in proof: 1322
% 45.43/12.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11992 ms resp. 11186 ms w/o parsing
% 49.90/13.73 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 49.90/13.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------