TSTP Solution File: NUM925+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 : Sun Sep 18 13:12:44 EDT 2022
% Result : Theorem 11.51s 8.01s
% Output : Proof 11.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 81
% Syntax : Number of formulae : 163 ( 61 unt; 22 typ; 0 def)
% Number of atoms : 864 ( 394 equ)
% Maximal formula atoms : 28 ( 6 avg)
% Number of connectives : 1099 ( 459 ~; 354 |; 86 &)
% ( 165 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 83 ( 83 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 9 >; 7 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 20 ( 20 usr; 13 con; 0-2 aty)
% Number of variables : 188 ( 161 !; 0 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
tff(pls_type,type,
pls: $i ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( $i * $i ) > $i ).
tff(hAPP_int_nat_type,type,
hAPP_int_nat: ( $i * $i ) > $i ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( $i * $i ) > $i ).
tff(bit1_type,type,
bit1: $i ).
tff(bit0_type,type,
bit0: $i ).
tff(number_number_of_nat_type,type,
number_number_of_nat: $i ).
tff(hAPP_int_fun_nat_int_type,type,
hAPP_int_fun_nat_int: ( $i * $i ) > $i ).
tff(n_type,type,
n: $i ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: $i ).
tff(hAPP_int_fun_int_int_type,type,
hAPP_int_fun_int_int: ( $i * $i ) > $i ).
tff(fact_fact_int_type,type,
fact_fact_int: $i ).
tff(plus_plus_int_type,type,
plus_plus_int: $i ).
tff(power_power_int_type,type,
power_power_int: $i ).
tff(number_number_of_int_type,type,
number_number_of_int: $i ).
tff(zero_zero_int_type,type,
zero_zero_int: $i ).
tff(one_one_int_type,type,
one_one_int: $i ).
tff(is_int_type,type,
is_int: $i > $o ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( $i * $i ) > $i ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( $i * $i ) > $i ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: $i ).
tff(1,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(number_number_of_int,pls) )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(number_number_of_int,pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int ) )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(6,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_int_int(number_number_of_int,pls),
inference(modus_ponens,[status(thm)],[7,2]) ).
tff(9,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = pls,
inference(modus_ponens,[status(thm)],[8,1]) ).
tff(10,plain,
( ( hAPP_int_int(fact_fact_int,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) )
<=> ( hAPP_int_int(fact_fact_int,pls) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
( ( hAPP_int_int(fact_fact_int,zero_zero_int) = one_one_int )
<=> ( hAPP_int_int(fact_fact_int,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ( hAPP_int_int(fact_fact_int,zero_zero_int) = one_one_int )
<=> ( hAPP_int_int(fact_fact_int,zero_zero_int) = one_one_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
hAPP_int_int(fact_fact_int,zero_zero_int) = one_one_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4273_fact__0__int) ).
tff(14,plain,
hAPP_int_int(fact_fact_int,zero_zero_int) = one_one_int,
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
hAPP_int_int(fact_fact_int,hAPP_int_int(number_number_of_int,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(fact_fact_int,pls) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = hAPP_int_int(fact_fact_int,pls),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n)),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = pls,
inference(transitivity,[status(thm)],[22,9]) ).
tff(24,plain,
^ [B_1_1: $i,B_2_1: $i] :
refl(
( is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> is_int(hAPP_nat_int(B_1_1,B_2_1)) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
<=> ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
tff(28,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1)),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] : is_int(hAPP_nat_int(B_1_1,B_2_1))
| is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
is_int(hAPP_nat_int(semiri1621563631at_int,n)),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
^ [B_1_1: $i,B_2_1: $i] :
refl(
( ( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
^ [B_1_1: $i,B_2_1: $i] :
rewrite(
( ( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) )
<=> ( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) )),
inference(bind,[status(th)],]) ).
tff(37,plain,
( ! [B_1_1: $i,B_2_1: $i] :
( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) )
<=> ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [B_1_1: $i,B_2_1: $i] :
( is_int(B_2_1)
=> is_int(hAPP_int_int(B_1_1,B_2_1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Int__Oint_000tc__Int__Oint) ).
tff(39,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
( ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) )
<=> ( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( ~ ! [B_1_1: $i,B_2_1: $i] :
( is_int(hAPP_int_int(B_1_1,B_2_1))
| ~ is_int(B_2_1) )
| is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(unit_resolution,[status(thm)],[45,42]) ).
tff(47,plain,
is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[46,32]) ).
tff(48,plain,
^ [Z_1: $i] :
refl(
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [Z_1: $i] :
rewrite(
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [Z_1: $i] :
rewrite(
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_nat_int(semiri1621563631at_int,Z_1))) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_736_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
tff(56,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[57,51]) ).
tff(59,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(modus_ponens,[status(thm)],[59,49]) ).
tff(61,plain,
( ~ ! [Z_1: $i] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,Z_1)))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(64,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,hAPP_int_int(bit1,pls))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))) ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_zero__le__one) ).
tff(68,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,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,hAPP_int_int(bit1,pls)))),
inference(modus_ponens,[status(thm)],[68,65]) ).
tff(70,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))),
inference(modus_ponens,[status(thm)],[69,64]) ).
tff(71,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls))),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
^ [Ya: $i,Xa: $i] :
refl(
( ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
<=> ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [Ya: $i,Xa: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( is_int(Ya)
& is_int(Xa) )
<=> ~ ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
( ~ ( is_int(Ya)
& is_int(Xa) )
<=> ~ ~ ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
rewrite(
( ~ ~ ( ~ is_int(Xa)
| ~ is_int(Ya) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
( ~ ( is_int(Ya)
& is_int(Xa) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya) ) )),
rewrite(
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) )
<=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )),
( ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) )),
rewrite(
( ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) )),
( ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) )
<=> ( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) )
<=> ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [Ya: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa)) )),
rewrite(
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
<=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) )),
rewrite(
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya)) )),
( ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) )
<=> ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya)) ) )),
rewrite(
( ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya)) )
<=> ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) ) )),
( ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) )
<=> ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) )
<=> ! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
^ [Ya: $i,Xa: $i] :
trans(
monotonicity(
rewrite(
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
<=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) ) )),
rewrite(
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa)) )),
rewrite(
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) )),
( ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) )),
rewrite(
( ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) ) )),
( ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) )
<=> ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
^ [Ya: $i,Xa: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )),
rewrite(
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )),
( ( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ( ( is_int(Ya)
& is_int(Xa) )
=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) ) )),
rewrite(
( ( ( is_int(Ya)
& is_int(Xa) )
=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya)) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) )),
( ( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [Ya: $i,Xa: $i] :
( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) )
<=> ! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,axiom,
! [Ya: $i,Xa: $i] :
( ( is_int(Ya)
& is_int(Xa) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
=> ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_add__nonneg__eq__0__iff) ).
tff(84,plain,
! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [Ya: $i,Xa: $i] :
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( Ya = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Ya))
| ~ ( is_int(Ya)
& is_int(Xa) ) ),
inference(modus_ponens,[status(thm)],[84,80]) ).
tff(86,plain,
! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Xa))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = hAPP_int_int(number_number_of_int,pls) )
<=> ( ( Xa = hAPP_int_int(number_number_of_int,pls) )
& ( Ya = hAPP_int_int(number_number_of_int,pls) ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,hAPP_int_int(number_number_of_int,pls)),Ya)) ),
inference(modus_ponens,[status(thm)],[85,79]) ).
tff(87,plain,
! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) ),
inference(modus_ponens,[status(thm)],[86,77]) ).
tff(88,plain,
! [Ya: $i,Xa: $i] :
( ~ ( is_int(Ya)
& is_int(Xa) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ( ( Xa = pls )
& ( Ya = pls ) ) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ),
inference(modus_ponens,[status(thm)],[88,75]) ).
tff(90,plain,
! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) ),
inference(modus_ponens,[status(thm)],[89,73]) ).
tff(91,plain,
( is_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))
<=> is_int(hAPP_int_int(fact_fact_int,pls)) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( is_int(one_one_int)
<=> is_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( is_int(one_one_int)
<=> is_int(one_one_int) ),
inference(rewrite,[status(thm)],]) ).
tff(94,axiom,
is_int(one_one_int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Groups_Oone__class_Oone_000tc__Int__Oint) ).
tff(95,plain,
is_int(one_one_int),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
is_int(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),
inference(modus_ponens,[status(thm)],[95,92]) ).
tff(97,plain,
is_int(hAPP_int_int(fact_fact_int,pls)),
inference(modus_ponens,[status(thm)],[96,91]) ).
tff(98,plain,
( ( ~ ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
| ~ is_int(hAPP_int_int(fact_fact_int,pls))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n)))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ) )
<=> ( ~ ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
| ~ is_int(hAPP_int_int(fact_fact_int,pls))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n)))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ~ ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
| ~ is_int(hAPP_int_int(fact_fact_int,pls))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n)))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(100,plain,
( ~ ! [Ya: $i,Xa: $i] :
( ~ is_int(Xa)
| ~ is_int(Ya)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Xa))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),Ya))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = pls )
<=> ~ ( ( Xa != pls )
| ( Ya != pls ) ) ) )
| ~ is_int(hAPP_int_int(fact_fact_int,pls))
| ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_int_int(fact_fact_int,pls)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n)))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ is_int(hAPP_nat_int(semiri1621563631at_int,n))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,pls),hAPP_nat_int(semiri1621563631at_int,n)))
| ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ) ),
inference(unit_resolution,[status(thm)],[100,97,90,71]) ).
tff(102,plain,
( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ),
inference(unit_resolution,[status(thm)],[101,32,62]) ).
tff(103,plain,
( ( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != pls )
<=> ( hAPP_int_int(fact_fact_int,pls) != pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(number_number_of_int,pls) )
<=> ( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != pls ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( one_one_int != zero_zero_int )
<=> ( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(number_number_of_int,pls) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( one_one_int != zero_zero_int )
<=> ( one_one_int != zero_zero_int ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_one__neq__zero) ).
tff(108,plain,
one_one_int != zero_zero_int,
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(number_number_of_int,pls),
inference(modus_ponens,[status(thm)],[108,105]) ).
tff(110,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != pls,
inference(modus_ponens,[status(thm)],[109,104]) ).
tff(111,plain,
hAPP_int_int(fact_fact_int,pls) != pls,
inference(modus_ponens,[status(thm)],[110,103]) ).
tff(112,plain,
( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls )
| ( hAPP_int_int(fact_fact_int,pls) = pls ) ),
inference(tautology,[status(thm)],]) ).
tff(113,plain,
( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) != pls )
| ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) ),
inference(tautology,[status(thm)],]) ).
tff(115,plain,
( ~ ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
<=> ~ ( ( hAPP_int_int(fact_fact_int,pls) != pls )
| ( hAPP_nat_int(semiri1621563631at_int,n) != pls ) ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) != pls ) ),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) != pls,
inference(unit_resolution,[status(thm)],[115,102]) ).
tff(117,plain,
^ [N_52: $i,A_197: $i] :
refl(
( ( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
<=> ( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) )),
inference(bind,[status(th)],]) ).
tff(118,plain,
( ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
<=> ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) ),
inference(quant_intro,[status(thm)],[117]) ).
tff(119,plain,
^ [N_52: $i,A_197: $i] :
trans(
monotonicity(
rewrite(
( ( A_197 = hAPP_int_int(number_number_of_int,pls) )
<=> ( A_197 = pls ) )),
rewrite(
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )),
( ( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) )
<=> ( ~ is_int(A_197)
| ( A_197 = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) )),
rewrite(
( ( ~ is_int(A_197)
| ( A_197 = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
<=> ( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) )),
( ( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) )
<=> ( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [N_52: $i,A_197: $i] :
( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) )
<=> ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
^ [N_52: $i,A_197: $i] :
trans(
monotonicity(
rewrite(
( ( A_197 = zero_zero_int )
<=> ( A_197 = hAPP_int_int(number_number_of_int,pls) ) )),
rewrite(
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
<=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) )),
( ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) )
<=> ( ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) )
| ~ is_int(A_197) ) )),
rewrite(
( ( ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) )
| ~ is_int(A_197) )
<=> ( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) ) )),
( ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) )
<=> ( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) )
<=> ! [N_52: $i,A_197: $i] :
( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) )
<=> ! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
^ [N_52: $i,A_197: $i] :
trans(
monotonicity(
rewrite(
( ( ( A_197 != zero_zero_int )
=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) )
<=> ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) )),
( ( is_int(A_197)
=> ( ( A_197 != zero_zero_int )
=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) )
<=> ( is_int(A_197)
=> ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) ) )),
rewrite(
( ( is_int(A_197)
=> ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) )
<=> ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ) )),
( ( is_int(A_197)
=> ( ( A_197 != zero_zero_int )
=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) )
<=> ( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [N_52: $i,A_197: $i] :
( is_int(A_197)
=> ( ( A_197 != zero_zero_int )
=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) )
<=> ! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,axiom,
! [N_52: $i,A_197: $i] :
( is_int(A_197)
=> ( ( A_197 != zero_zero_int )
=> ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_field__power__not__zero) ).
tff(127,plain,
! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [N_52: $i,A_197: $i] :
( ( A_197 = zero_zero_int )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != zero_zero_int )
| ~ is_int(A_197) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [N_52: $i,A_197: $i] :
( ~ is_int(A_197)
| ( A_197 = hAPP_int_int(number_number_of_int,pls) )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != hAPP_int_int(number_number_of_int,pls) ) ),
inference(modus_ponens,[status(thm)],[128,122]) ).
tff(130,plain,
! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ),
inference(modus_ponens,[status(thm)],[129,120]) ).
tff(131,plain,
! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ),
inference(skolemize,[status(sab)],[130]) ).
tff(132,plain,
! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) ),
inference(modus_ponens,[status(thm)],[131,118]) ).
tff(133,plain,
( ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) )
<=> ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) )
<=> ( ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) )
<=> ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) )
<=> ( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
( ~ ! [N_52: $i,A_197: $i] :
( ( A_197 = pls )
| ~ is_int(A_197)
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,A_197),N_52) != pls ) )
| ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
( ~ is_int(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n)) = pls )
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls ) ),
inference(unit_resolution,[status(thm)],[138,132]) ).
tff(140,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(fact_fact_int,pls)),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != pls,
inference(unit_resolution,[status(thm)],[139,116,47]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 15:52:14 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 11.51/8.01 % SZS status Theorem
% 11.51/8.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------