TSTP Solution File: NUM924_40 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM924_40 : TPTP v8.2.0. Released v8.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Mon May 22 15:41:05 EDT 2023
% Result : Unsatisfiable 12.68s 8.81s
% Output : Proof 13.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 110
% Syntax : Number of formulae : 215 ( 63 unt; 36 typ; 0 def)
% Number of atoms : 666 ( 26 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 681 ( 255 ~; 231 |; 0 &)
% ( 170 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 11 >; 10 *; 0 +; 0 <<)
% Number of predicates : 23 ( 21 usr; 15 prp; 0-4 aty)
% Number of functors : 35 ( 35 usr; 25 con; 0-2 aty)
% Number of variables : 216 (; 183 !; 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(pls_type,type,
pls: int ).
tff(fact_fact_int_type,type,
fact_fact_int: fun_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(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(ord_less_int_type,type,
ord_less_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(pred_type,type,
pred: fun_int_int ).
tff(minus_minus_int_type,type,
minus_minus_int: fun_int_fun_int_int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(uminus_uminus_int_type,type,
uminus_uminus_int: fun_int_int ).
tff(min_type,type,
min: int ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(hAPP_real_bool_type,type,
hAPP_real_bool: ( fun_real_bool * real ) > bool ).
tff(hAPP_int_real_type,type,
hAPP_int_real: ( fun_int_real * int ) > real ).
tff(ring_1_of_int_real_type,type,
ring_1_of_int_real: fun_int_real ).
tff(hAPP_r1134773055l_bool_type,type,
hAPP_r1134773055l_bool: ( fun_re413263731l_bool * real ) > fun_real_bool ).
tff(number267125858f_real_type,type,
number267125858f_real: fun_int_real ).
tff(ord_less_real_type,type,
ord_less_real: fun_re413263731l_bool ).
tff(real_int_type,type,
real_int: fun_int_real ).
tff(zero_zero_real_type,type,
zero_zero_real: real ).
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))))),hAPP_int_int(fact_fact_int,pls)) = 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)),hAPP_int_int(fact_fact_int,pls))),t) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(pred,pls))) = 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)),hAPP_int_int(fact_fact_int,pls))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = 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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))),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))))),hAPP_int_int(fact_fact_int,pls)) = 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)),hAPP_int_int(fact_fact_int,pls))),t) ) ),
inference(rewrite,[status(thm)],]) ).
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) )
<=> ( 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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = 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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))),t) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,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(5,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/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
tff(6,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)],[5,4]) ).
tff(7,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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = 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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))),t),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,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))))),hAPP_int_int(fact_fact_int,pls)) = 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)),hAPP_int_int(fact_fact_int,pls))),t),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(pred,pls))) = 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)),hAPP_int_int(fact_fact_int,pls))),t),
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
( ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))) = 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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(pred,pls))) = 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))))),hAPP_int_int(fact_fact_int,pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,min)) = 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(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))) = 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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,min)) = 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(minus_minus_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))))),hAPP_int_int(number_number_of_int,min)) = 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(rewrite,[status(thm)],]) ).
tff(13,axiom,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,min)) = 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1502__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096) ).
tff(14,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,min)) = 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)],[13,12]) ).
tff(15,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(uminus_uminus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))) = 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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(pred,pls))) = 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))))),hAPP_int_int(fact_fact_int,pls)),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,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))))),hAPP_int_int(fact_fact_int,pls)) = hAPP_int_int(hAPP_int_fun_int_int(minus_minus_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))))),hAPP_int_int(number_number_of_int,hAPP_int_int(pred,pls))),
inference(symmetry,[status(thm)],[16]) ).
tff(18,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))))),hAPP_int_int(fact_fact_int,pls)) = 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)),hAPP_int_int(fact_fact_int,pls))),t),
inference(transitivity,[status(thm)],[17,9]) ).
tff(19,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) ),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t)))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
^ [Z_2: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) )
<=> ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [Z_2: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),Z_2)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),Z_2)) )
<=> ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [Z_2: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),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_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),Z_2)) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) )
<=> ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),Z_2)) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) )
<=> ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_int__one__le__iff__zero__less) ).
tff(31,plain,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),Z_2)) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),Z_2)) ),
inference(modus_ponens,[status(thm)],[31,28]) ).
tff(33,plain,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ),
inference(modus_ponens,[status(thm)],[32,26]) ).
tff(34,plain,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) ),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( ~ ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5__096_126_A1_A_060_061_At_096) ).
tff(42,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),t)),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),t)),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t)),
inference(modus_ponens,[status(thm)],[43,38]) ).
tff(45,plain,
( ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
( ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),t))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t)),
inference(unit_resolution,[status(thm)],[46,37]) ).
tff(48,plain,
^ [N_1: int] :
refl(( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) )
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) )
<=> ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [N_1: int] :
rewrite(( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),N_1)) )
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),N_1)) )
<=> ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [N_1: int] :
rewrite(( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) )
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),N_1)) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) )
<=> ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),N_1)) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) )
<=> ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4439_real__of__int__gt__zero__cancel__iff) ).
tff(56,plain,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,zero_zero_real),hAPP_int_real(real_int,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),N_1)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),N_1)) ),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ),
inference(modus_ponens,[status(thm)],[57,51]) ).
tff(59,plain,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) ),
inference(modus_ponens,[status(thm)],[59,49]) ).
tff(61,plain,
( ~ ! [N_1: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,N_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),N_1)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls)))) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
^ [N_1: int,Ma: int] :
refl(( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
<=> ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [N_1: int,Ma: int] :
rewrite(( ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
<=> ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
<=> ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
<=> ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,axiom,
! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4443_number__of__less__real__of__int__iff) ).
tff(69,plain,
! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(real_int,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ),
inference(modus_ponens,[status(thm)],[69,66]) ).
tff(71,plain,
! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ),
inference(skolemize,[status(sab)],[70]) ).
tff(72,plain,
! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) ),
inference(modus_ponens,[status(thm)],[71,64]) ).
tff(73,plain,
( ~ ! [N_1: int,Ma: int] :
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,N_1)),hAPP_int_real(ring_1_of_int_real,Ma)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,N_1)),Ma)) )
| ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) ),
inference(unit_resolution,[status(thm)],[73,72]) ).
tff(75,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) ),
inference(rewrite,[status(thm)],]) ).
tff(76,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,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))) ),
inference(rewrite,[status(thm)],]) ).
tff(77,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(78,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/sandbox/benchmark/theBenchmark.p',fact_6_p0) ).
tff(79,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)],[78,77]) ).
tff(80,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))),
inference(modus_ponens,[status(thm)],[79,76]) ).
tff(81,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))),
inference(modus_ponens,[status(thm)],[80,75]) ).
tff(82,plain,
( ~ ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) )
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) ),
inference(tautology,[status(thm)],]) ).
tff(83,plain,
( ~ ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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)),hAPP_int_int(fact_fact_int,pls)))) )
| hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls))))) ),
inference(unit_resolution,[status(thm)],[82,81]) ).
tff(84,plain,
hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls))))),
inference(unit_resolution,[status(thm)],[83,74]) ).
tff(85,plain,
( ~ ( hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls)))) )
| ~ hBOOL(hAPP_real_bool(hAPP_r1134773055l_bool(ord_less_real,hAPP_int_real(number267125858f_real,pls)),hAPP_int_real(ring_1_of_int_real,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)),hAPP_int_int(fact_fact_int,pls)))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls)))) ),
inference(tautology,[status(thm)],]) ).
tff(86,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls)))),
inference(unit_resolution,[status(thm)],[85,84,62]) ).
tff(87,plain,
^ [A_158: int,B_119: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [A_158: int,B_119: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
^ [A_158: int,B_119: int] :
trans(monotonicity(rewrite(( 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,hAPP_int_int(number_number_of_int,pls)),B_119)) )),
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,hAPP_int_int(number_number_of_int,pls)),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,hAPP_int_int(number_number_of_int,pls)),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))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),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))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) )),
inference(bind,[status(th)],]) ).
tff(92,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,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,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(94,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(95,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)],[94]) ).
tff(96,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/sandbox/benchmark/theBenchmark.p',fact_1167_zero__less__mult__pos) ).
tff(97,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)],[96,95]) ).
tff(98,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)],[97,93]) ).
tff(99,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[98,92]) ).
tff(100,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[99,90]) ).
tff(101,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,A_158),B_119))) ),
inference(modus_ponens,[status(thm)],[101,88]) ).
tff(103,plain,
( ( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) )
<=> ( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
( ~ ! [A_158: int,B_119: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_119))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),A_158))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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,pls),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),t))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))) ),
inference(unit_resolution,[status(thm)],[105,102]) ).
tff(107,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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)),hAPP_int_int(fact_fact_int,pls))),t))),
inference(unit_resolution,[status(thm)],[106,86,47]) ).
tff(108,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))),
inference(modus_ponens,[status(thm)],[107,22]) ).
tff(109,plain,
^ [A_238: int] :
refl(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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,pls),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(110,plain,
( ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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,pls),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)],[109]) ).
tff(111,plain,
^ [A_238: int] :
rewrite(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),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,pls),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(112,plain,
( ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),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,pls),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)],[111]) ).
tff(113,plain,
^ [A_238: int] :
rewrite(( 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,hAPP_int_int(number_number_of_int,pls)),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(114,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,hAPP_int_int(number_number_of_int,pls)),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)],[113]) ).
tff(115,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(116,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/sandbox/benchmark/theBenchmark.p',fact_214_zero__le__power2) ).
tff(117,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)],[116,115]) ).
tff(118,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),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)],[117,114]) ).
tff(119,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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)],[118,112]) ).
tff(120,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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)],[119]) ).
tff(121,plain,
! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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)],[120,110]) ).
tff(122,plain,
( ~ ! [A_238: int] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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,pls),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(123,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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)],[122,121]) ).
tff(124,plain,
( ~ ! [Z_2: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),Z_2))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),Z_2)) )
| ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(125,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls))) ),
inference(unit_resolution,[status(thm)],[124,35]) ).
tff(126,plain,
^ [N: int] :
refl(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) )),
inference(bind,[status(th)],]) ).
tff(127,plain,
( ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
<=> ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) ),
inference(quant_intro,[status(thm)],[126]) ).
tff(128,plain,
^ [N: int] :
trans(monotonicity(rewrite(( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N)) )),
rewrite(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )),
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) )),
rewrite(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) )),
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) )
<=> ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
^ [N: int] :
trans(monotonicity(rewrite(( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N)) )),
rewrite(( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) )),
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) ) )),
rewrite(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) ) )),
( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) ) )),
inference(bind,[status(th)],]) ).
tff(131,plain,
( ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) ) ),
inference(quant_intro,[status(thm)],[130]) ).
tff(132,plain,
( ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
^ [N: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ) )),
inference(bind,[status(th)],]) ).
tff(134,plain,
( ! [N: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) )
<=> ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ) ),
inference(quant_intro,[status(thm)],[133]) ).
tff(135,axiom,
! [N: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4282_fact__ge__one__int) ).
tff(136,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,one_one_int),hAPP_int_int(fact_fact_int,N))) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(fact_fact_int,N))) ),
inference(modus_ponens,[status(thm)],[137,131]) ).
tff(139,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ),
inference(modus_ponens,[status(thm)],[138,129]) ).
tff(140,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ),
inference(skolemize,[status(sab)],[139]) ).
tff(141,plain,
! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) ),
inference(modus_ponens,[status(thm)],[140,127]) ).
tff(142,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(number_number_of_int,pls)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(143,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,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(number_number_of_int,pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(144,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(145,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
tff(146,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(number_number_of_int,pls))),
inference(modus_ponens,[status(thm)],[146,143]) ).
tff(148,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls)),
inference(modus_ponens,[status(thm)],[147,142]) ).
tff(149,plain,
( ( ~ ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls))) )
<=> ( ~ ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(150,plain,
( ~ ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls))) ),
inference(quant_inst,[status(thm)],]) ).
tff(151,plain,
( ~ ! [N: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),N))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,N))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),pls))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls))) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls))),
inference(unit_resolution,[status(thm)],[151,148,141]) ).
tff(153,plain,
( ~ ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls))) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(fact_fact_int,pls)),hAPP_int_int(fact_fact_int,pls)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls))) ),
inference(tautology,[status(thm)],]) ).
tff(154,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls))),
inference(unit_resolution,[status(thm)],[153,152,125]) ).
tff(155,plain,
^ [B_96: int,A_118: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ) )),
inference(bind,[status(th)],]) ).
tff(156,plain,
( ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
<=> ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ) ),
inference(quant_intro,[status(thm)],[155]) ).
tff(157,plain,
^ [B_96: int,A_118: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_96)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_96)) )
<=> ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,plain,
^ [B_96: int,A_118: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_96)) ) )),
inference(bind,[status(th)],]) ).
tff(160,plain,
( ! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) )
<=> ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_96)) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) )
<=> ! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
^ [B_96: int,A_118: int] :
trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96))) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96))) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) )),
inference(bind,[status(th)],]) ).
tff(163,plain,
( ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96))) ) )
<=> ! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,axiom,
! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1864_add__nonneg__pos) ).
tff(165,plain,
! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [B_96: int,A_118: 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,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),B_96)) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,hAPP_int_int(number_number_of_int,pls)),B_96)) ),
inference(modus_ponens,[status(thm)],[166,160]) ).
tff(168,plain,
! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ),
inference(modus_ponens,[status(thm)],[167,158]) ).
tff(169,plain,
! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) ),
inference(modus_ponens,[status(thm)],[169,156]) ).
tff(171,plain,
( ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) )
<=> ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(172,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),hAPP_int_int(fact_fact_int,pls))) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(173,plain,
( ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),hAPP_int_int(fact_fact_int,pls))) )
<=> ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(monotonicity,[status(thm)],[172]) ).
tff(174,plain,
( ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),hAPP_int_int(fact_fact_int,pls))) )
<=> ( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ) ),
inference(transitivity,[status(thm)],[173,171]) ).
tff(175,plain,
( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),hAPP_int_int(fact_fact_int,pls))) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
( ~ ! [B_96: int,A_118: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,A_118),B_96)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),A_118))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),B_96)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),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_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))) ),
inference(unit_resolution,[status(thm)],[176,170]) ).
tff(178,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),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))))),hAPP_int_int(fact_fact_int,pls)))),
inference(unit_resolution,[status(thm)],[177,154,123]) ).
tff(179,plain,
$false,
inference(unit_resolution,[status(thm)],[178,108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUM924_40 : TPTP v8.2.0. Released v8.2.0.
% 0.00/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 22 12:03:55 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 12.68/8.81 % SZS status Unsatisfiable
% 12.68/8.81 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------