%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925_4 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:25 AM UTC 2025
% Result : Theorem 4.41s 4.61s
% Output : Proof 4.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 39
% Syntax : Number of formulae : 83 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 522 ( 262 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 703 ( 306 ~; 239 |; 23 &)
% ( 100 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 12 con; 0-2 aty)
% Number of variables : 128 ( 113 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
hBOOL: bool > $o ).
tff(hAPP_int_bool_type,type,
hAPP_int_bool: ( fun_int_bool * int ) > bool ).
tff(hAPP_nat_int_type,type,
hAPP_nat_int: ( fun_nat_int * nat ) > int ).
tff(n_type,type,
n: nat ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: fun_nat_int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(ord_less_eq_int_type,type,
ord_less_eq_int: fun_int_fun_int_bool ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * 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(one_one_int_type,type,
one_one_int: int ).
tff(plus_plus_int_type,type,
plus_plus_int: fun_int_fun_int_int ).
tff(hAPP_int_nat_type,type,
hAPP_int_nat: ( fun_int_nat * int ) > nat ).
tff(pls_type,type,
pls: int ).
tff(bit1_type,type,
bit1: fun_int_int ).
tff(bit0_type,type,
bit0: fun_int_int ).
tff(number_number_of_nat_type,type,
number_number_of_nat: fun_int_nat ).
tff(hAPP_int_fun_nat_int_type,type,
hAPP_int_fun_nat_int: ( fun_int_fun_nat_int * int ) > fun_nat_int ).
tff(power_power_int_type,type,
power_power_int: fun_int_fun_nat_int ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(1,plain,
( ( one_one_int != zero_zero_int )
<=> ( one_one_int != zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
one_one_int != zero_zero_int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_one__neq__zero) ).
tff(3,plain,
one_one_int != zero_zero_int,
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int )
| ( one_one_int = zero_zero_int ) ),
inference(tautology,[status(thm)],[]) ).
tff(5,plain,
( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[4,3]) ).
tff(6,plain,
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),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,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),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',fact_18_zero__power2) ).
tff(8,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(symmetry,[status(thm)],[8]) ).
tff(10,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(11,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(12,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(13,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)],[12,11]) ).
tff(14,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)],[13,10]) ).
tff(15,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)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(transitivity,[status(thm)],[14,9]) ).
tff(16,plain,
^ [X_20: int,Y_16: int] :
refl(( ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
^ [X_20: int,Y_16: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X_20: int,Y_16: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
<=> ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,axiom,
! [X_20: int,Y_16: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1979_order__less__imp__le) ).
tff(22,plain,
! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) ),
inference(modus_ponens,[status(thm)],[24,17]) ).
tff(26,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,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,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,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
tff(28,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,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
( ( ~ ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [X_20: int,Y_16: int] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_20),Y_16))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X_20),Y_16)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(unit_resolution,[status(thm)],[31,28,25]) ).
tff(33,plain,
^ [X_61: int,Y_51: int] :
refl(( ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [X_61: int,Y_51: int] :
trans(monotonicity(trans(monotonicity(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ( X_61 = Y_51 ) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ( X_61 = Y_51 ) ) ) )),
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ( X_61 = Y_51 ) ) )
<=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61)) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) )
<=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61)) ) )),
( ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) ) )
<=> ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61)) ) ) )),
rewrite(( ( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61)) ) )
<=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),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,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) ) )
<=> ( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X_61: int,Y_51: int] :
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) ) )
<=> ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X_61: int,Y_51: int] :
( ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
=> ( X_61 = Y_51 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_889_power2__eq__imp__eq) ).
tff(39,plain,
! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,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(44,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).
tff(45,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int)),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ 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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ 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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ 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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
<=> ( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ 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),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X_61: int,Y_51: int] :
( ( X_61 = Y_51 )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),Y_51))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),X_61))
| ( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X_61),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,Y_51),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),zero_zero_int))
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),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,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)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,zero_zero_int),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(unit_resolution,[status(thm)],[51,45,42,32,15]) ).
tff(53,plain,
( ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) )
| ~ ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
| ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != zero_zero_int ) ),
inference(tautology,[status(thm)],[]) ).
tff(54,plain,
( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(unit_resolution,[status(thm)],[53,52,5]) ).
tff(55,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(56,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(57,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int)),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
^ [Ya: int,Xa: int] :
refl(( ( ~ 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
<=> ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
^ [Ya: int,Xa: int] :
trans(monotonicity(trans(trans(monotonicity(rewrite(( ( ( Xa = zero_zero_int )
& ( 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 ) ) )
<=> ( ( 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(( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ~ ( ( Xa != zero_zero_int )
| ( 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 ) ) )),
( ( ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int )
<=> ( ( Xa = zero_zero_int )
& ( 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 ) ) )),
rewrite(( ~ ( ( ( 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 ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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 ) ) )
<=> ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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)) )
<=> ( ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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(( ( ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [Ya: int,Xa: 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)) )
<=> ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [Ya: int,Xa: 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)) )
<=> ! [Ya: int,Xa: 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)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
^ [Ya: int,Xa: int] :
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)) ) )),
inference(bind,[status(th)],[]) ).
tff(64,plain,
( ! [Ya: int,Xa: 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 ) ) ) ) )
<=> ! [Ya: int,Xa: 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)) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [Ya: int,Xa: 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 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_add__nonneg__eq__0__iff) ).
tff(66,plain,
! [Ya: int,Xa: 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)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [Ya: int,Xa: 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)) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [Ya: int,Xa: 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)) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[69,59]) ).
tff(71,plain,
( ( ~ ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) )
<=> ( ~ ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [Ya: int,Xa: 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))
| ~ ( ( ( Xa != zero_zero_int )
| ( Ya != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Xa),Ya) = zero_zero_int ) ) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),one_one_int))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n)))
| ~ ( ( ( one_one_int != zero_zero_int )
| ( hAPP_nat_int(semiri1621563631at_int,n) != zero_zero_int ) )
<=> ( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n))),
inference(unit_resolution,[status(thm)],[73,70,57,54]) ).
tff(75,plain,
^ [Z_1: nat] :
refl(( 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,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [Z_1: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [Z_1: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1)))
<=> ! [Z_1: nat] : 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(78,axiom,
! [Z_1: nat] : 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(79,plain,
! [Z_1: nat] : 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)],[78,77]) ).
tff(80,plain,
! [Z_1: nat] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,Z_1))),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [Z_1: nat] : 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)],[80,76]) ).
tff(82,plain,
( ~ ! [Z_1: nat] : 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,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,81,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM925_4 : TPTP v9.0.0. Released v5.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:06:42 EDT 2025
% 0.12/0.33 % CPUTime :
% 4.41/4.61 % SZS status Theorem
% 4.41/4.61 % SZS output start Proof
% See solution above
% 4.84/5.01 % E exiting
%------------------------------------------------------------------------------