%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM925_2 : TPTP v9.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:22:24 AM UTC 2025
% Result : Theorem 0.44s 0.60s
% Output : Proof 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 25
% Syntax : Number of formulae : 56 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 202 ( 98 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 247 ( 111 ~; 79 |; 0 &)
% ( 51 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 98 ( 88 !; 0 ?; 98 :)
% 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(number_number_of_nat_type,type,
number_number_of_nat: int > nat ).
tff(bit0_type,type,
bit0: int > int ).
tff(bit1_type,type,
bit1: int > int ).
tff(pls_type,type,
pls: int ).
tff(power_power_int_type,type,
power_power_int: int > fun_nat_int ).
tff(hAPP_int_int_type,type,
hAPP_int_int: ( fun_int_int * int ) > int ).
tff(n_type,type,
n: nat ).
tff(semiri1621563631at_int_type,type,
semiri1621563631at_int: fun_nat_int ).
tff(plus_plus_int_type,type,
plus_plus_int: int > fun_int_int ).
tff(one_one_int_type,type,
one_one_int: int ).
tff(hAPP_i1948725293t_bool_type,type,
hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).
tff(zero_zero_int_type,type,
zero_zero_int: int ).
tff(ord_less_int_type,type,
ord_less_int: fun_int_fun_int_bool ).
tff(1,plain,
^ [A_24: int] :
refl(( ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) )
<=> ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) )
<=> ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) )
<=> ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [A_24: int] :
trans(rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_24 != zero_zero_int ) )
<=> ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) )),
rewrite(( ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) )
<=> ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) )),
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_24 != zero_zero_int ) )
<=> ~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [A_24: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_24 != zero_zero_int ) )
<=> ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A_24: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls))))))
<=> ( A_24 != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_zero__less__power2) ).
tff(7,plain,
! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ~ ! [A_24: int] :
~ ( ( A_24 = zero_zero_int )
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_24),number_number_of_nat(bit0(bit1(pls)))))) )
| ~ ( ( hAPP_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_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
~ ( ( hAPP_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_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(unit_resolution,[status(thm)],[11,10]) ).
tff(13,plain,
^ [N_17: nat,A_60: int] :
refl(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
<=> ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,plain,
( ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
<=> ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(16,plain,
^ [N_17: nat,A_60: int] :
rewrite(( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17))) )
<=> ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17))) )
<=> ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,axiom,
! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60))
=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_zero__less__power) ).
tff(19,plain,
! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ),
inference(modus_ponens,[status(thm)],[19,15]) ).
tff(21,plain,
! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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(25,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) )
<=> ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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(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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
( ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )
<=> ( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(31,plain,
( ~ ! [N_17: nat,A_60: int] :
( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(A_60),N_17)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),A_60)) )
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_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_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))),
inference(unit_resolution,[status(thm)],[31,25,22]) ).
tff(33,plain,
( ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
<=> ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ( ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
~ ( ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(36,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(modus_ponens,[status(thm)],[36,33]) ).
tff(38,plain,
^ [N_23: nat,A_62: int] :
refl(( ( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
<=> ( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
<=> ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
<=> ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [N_23: nat,A_62: int] :
rewrite(( ( ( A_62 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
<=> ( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [N_23: nat,A_62: int] :
( ( A_62 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
<=> ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [N_23: nat,A_62: int] :
( ( A_62 != zero_zero_int )
=> ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_field__power__not__zero) ).
tff(44,plain,
! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) )
<=> ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ( ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) )
<=> ( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ) ),
inference(transitivity,[status(thm)],[50,48]) ).
tff(52,plain,
( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [N_23: nat,A_62: int] :
( ( A_62 = zero_zero_int )
| ( hAPP_nat_int(power_power_int(A_62),N_23) != zero_zero_int ) )
| ( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int )
| ( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = zero_zero_int,
inference(unit_resolution,[status(thm)],[53,47,37]) ).
tff(55,plain,
( ( ( hAPP_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_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) )
| ( hAPP_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_int,zero_zero_int),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
$false,
inference(unit_resolution,[status(thm)],[55,54,32,12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM925_2 : TPTP v9.0.0. Released v5.3.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 02:05:09 EDT 2025
% 0.20/0.33 % CPUTime :
% 0.44/0.60 % SZS status Theorem
% 0.44/0.60 % SZS output start Proof
% See solution above
% 0.49/0.65 % E exiting
%------------------------------------------------------------------------------