%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM924_40 : TPTP v9.0.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:22 AM UTC 2025
% Result : Unsatisfiable 4.33s 4.54s
% Output : Proof 4.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 57
% Syntax : Number of formulae : 133 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 562 ( 5 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 648 ( 258 ~; 188 |; 10 &)
% ( 167 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 39 ( 39 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 23 ( 21 usr; 17 prp; 0-3 aty)
% Number of functors : 32 ( 32 usr; 20 con; 0-2 aty)
% Number of variables : 216 ( 191 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(hAPP_int_fun_int_int_type,type,
hAPP_int_fun_int_int: ( fun_int_fun_int_int * int ) > fun_int_int ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(hAPP_int_nat_type,type,
hAPP_int_nat: ( fun_int_nat * int ) > nat ).
tff(pls_type,type,
pls: int ).
tff(bit1_type,type,
bit1: fun_int_int ).
tff(bit0_type,type,
bit0: fun_int_int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: fun_int_nat ).
tff(hAPP_int_fun_nat_int_type,type,
hAPP_int_fun_nat_int: ( fun_int_fun_nat_int * int ) > fun_nat_int ).
tff(s_type,type,
s: int ).
tff(power_power_int_type,type,
power_power_int: fun_int_fun_nat_int ).
tff(plus_plus_int_type,type,
plus_plus_int: fun_int_fun_int_int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(t_type,type,
t: int ).
tff(m_type,type,
m: int ).
tff(number_number_of_int_type,type,
number_number_of_int: fun_int_int ).
tff(times_times_int_type,type,
times_times_int: fun_int_fun_int_int ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(hAPP_nat_bool_type,type,
hAPP_nat_bool: ( fun_nat_bool * nat ) > bool ).
tff(nat_1_type,type,
nat_1: fun_int_nat ).
tff(hAPP_n1699378549t_bool_type,type,
hAPP_n1699378549t_bool: ( fun_nat_fun_nat_bool * nat ) > fun_nat_bool ).
tff(ord_less_nat_type,type,
ord_less_nat: fun_nat_fun_nat_bool ).
tff(hAPP_rat_bool_type,type,
hAPP_rat_bool: ( fun_rat_bool * rat ) > bool ).
tff(hAPP_int_rat_type,type,
hAPP_int_rat: ( fun_int_rat * int ) > rat ).
tff(number_number_of_rat_type,type,
number_number_of_rat: fun_int_rat ).
tff(hAPP_r2115560837t_bool_type,type,
hAPP_r2115560837t_bool: ( fun_rat_fun_rat_bool * rat ) > fun_rat_bool ).
tff(ord_less_rat_type,type,
ord_less_rat: fun_rat_fun_rat_bool ).
tff(ord_less_eq_rat_type,type,
ord_less_eq_rat: fun_rat_fun_rat_bool ).
tff(1,plain,
( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_t) ).
tff(3,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),
inference(monotonicity,[status(thm)],[3]) ).
tff(5,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int))) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int))) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
^ [W_1: int,Z_2: int] :
refl(( ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) )
<=> ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) )
<=> ! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W_1: int,Z_2: int] :
trans(trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> ~ ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )),
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ~ ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) )),
rewrite(( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ~ ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) )),
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) )),
rewrite(( ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) )
<=> ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) )),
( ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2727_zless__nat__conj) ).
tff(14,plain,
! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W_1: int,Z_2: int] :
( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
& hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
( ~ ! [W_1: int,Z_2: int] :
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2))) )
| ~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
~ ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))) ),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [X_1: int,Y_2: int] :
refl(( ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) )
<=> ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) )
<=> ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) )
<=> ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_less__number__of) ).
tff(24,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_1),Y_2)) )
| ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [V: int,W_1: int] :
refl(( ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) )
<=> ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) )
<=> ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) )
<=> ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [V: int,W_1: int] :
trans(rewrite(( ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1)))
<=> ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V))) )
<=> ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) )),
rewrite(( ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) )
<=> ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) )),
( ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1)))
<=> ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V))) )
<=> ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [V: int,W_1: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1)))
<=> ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V))) )
<=> ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [V: int,W_1: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1)))
<=> ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_le__number__of__eq__not__less) ).
tff(35,plain,
! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ~ ! [V: int,W_1: int] :
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,W_1)),hAPP_int_rat(number_number_of_rat,V)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,V)),hAPP_int_rat(number_number_of_rat,W_1))) )
| ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,plain,
^ [X_1: int,Y_2: int] :
refl(( ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) )
<=> ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) )
<=> ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) )
<=> ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_le__number__of) ).
tff(45,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
( ~ ! [X_1: int,Y_2: int] :
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,X_1)),hAPP_int_rat(number_number_of_rat,Y_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_1),Y_2)) )
| ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ),
inference(unit_resolution,[status(thm)],[48,47]) ).
tff(50,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
tff(52,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) )
| hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) ),
inference(tautology,[status(thm)],[]) ).
tff(54,plain,
( ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)) )
| hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))),
inference(unit_resolution,[status(thm)],[54,49]) ).
tff(56,plain,
( ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))) )
| ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
| ~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_eq_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
~ hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int))),
inference(unit_resolution,[status(thm)],[56,55,40]) ).
tff(58,plain,
( ~ ( hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)) )
| hBOOL(hAPP_rat_bool(hAPP_r2115560837t_bool(ord_less_rat,hAPP_int_rat(number_number_of_rat,zero_zero_int)),hAPP_int_rat(number_number_of_rat,zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(unit_resolution,[status(thm)],[58,57,28]) ).
tff(60,plain,
^ [A_158: int,B_119: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
<=> ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
<=> ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
^ [A_158: int,B_119: int] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158)) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119)) ) )
<=> ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119)))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1167_zero__less__mult__pos) ).
tff(66,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int))) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_p0) ).
tff(72,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int))),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
<=> ( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(unit_resolution,[status(thm)],[75,72,69]) ).
tff(77,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
inference(unit_resolution,[status(thm)],[76,59]) ).
tff(78,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
( ( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
<=> hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))) )
| ~ ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))),
inference(unit_resolution,[status(thm)],[80,79,19]) ).
tff(82,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
tff(84,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
( ~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) )
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int)))) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
~ ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ),
inference(unit_resolution,[status(thm)],[86,81]) ).
tff(88,plain,
^ [Z_2: int,W_1: int] :
refl(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(89,plain,
( ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
^ [Z_2: int,W_1: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [Z_2: int,W_1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
<=> ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [Z_2: int,W_1: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
=> ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2739_nat__less__eq__zless) ).
tff(94,plain,
! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
( ( ~ ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) )
<=> ( ~ ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
( ~ ! [Z_2: int,W_1: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),W_1))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,W_1)),hAPP_int_nat(nat_1,Z_2)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,W_1),Z_2)) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)))
| ( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_nat,hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),hAPP_int_nat(nat_1,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),zero_zero_int))) ) ),
inference(unit_resolution,[status(thm)],[100,97]) ).
tff(102,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),m)),one_one_int)),t))),
inference(unit_resolution,[status(thm)],[101,87]) ).
tff(103,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int))),
inference(modus_ponens,[status(thm)],[102,7]) ).
tff(104,plain,
^ [A_238: int] :
refl(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
<=> ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
<=> ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,axiom,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_zero__le__power2) ).
tff(108,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),
inference(modus_ponens,[status(thm)],[109,105]) ).
tff(111,plain,
( ~ ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_238),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(112,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
^ [B_71: int,A_83: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
<=> ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
( ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
<=> ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
^ [B_71: int,A_83: int] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71))) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71))) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71))) ) )
<=> ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,axiom,
! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2166_add__nonneg__nonneg) ).
tff(119,plain,
! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ),
inference(modus_ponens,[status(thm)],[119,115]) ).
tff(121,plain,
! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ),
inference(skolemize,[status(sab)],[120]) ).
tff(122,plain,
! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) ),
inference(modus_ponens,[status(thm)],[121,114]) ).
tff(123,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_720_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
tff(125,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
( ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) )
<=> ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) )
<=> ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) )
<=> ( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [B_71: int,A_83: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_83),B_71)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_83))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),B_71)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,s),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),one_one_int))),
inference(unit_resolution,[status(thm)],[131,125,122,112]) ).
tff(133,plain,
$false,
inference(unit_resolution,[status(thm)],[132,103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM924_40 : TPTP v9.0.0. Released v8.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:06:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.33/4.54 % SZS status Unsatisfiable
% 4.33/4.54 % SZS output start Proof
% See solution above
% 4.79/4.94 % E exiting
%------------------------------------------------------------------------------