TSTP Solution File: NUM925_3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n019.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 13:12:43 EDT 2022

% Result   : Theorem 0.94s 0.90s
% Output   : Proof 0.97s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   48
% Syntax   : Number of formulae    :   85 (  30 unt;  20 typ;   0 def)
%            Number of atoms       :  131 (  96 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   86 (  24   ~;   4   |;   0   &)
%                                         (  58 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   17 (  12   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   8 con; 0-2 aty)
%            Number of variables   :   22 (  18   !;   0   ?;  22   :)

% Comments : 
%------------------------------------------------------------------------------
tff(hBOOL_type,type,
    hBOOL: bool > $o ).

tff(hAPP_int_bool_type,type,
    hAPP_int_bool: ( fun_int_bool * int ) > bool ).

tff(plus_plus_int_type,type,
    plus_plus_int: ( int * int ) > int ).

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(number_number_of_int_type,type,
    number_number_of_int: int > int ).

tff(bit1_type,type,
    bit1: int > int ).

tff(succ_type,type,
    succ: int > int ).

tff(min_type,type,
    min: int ).

tff(hAPP_i1948725293t_bool_type,type,
    hAPP_i1948725293t_bool: ( fun_int_fun_int_bool * int ) > fun_int_bool ).

tff(ord_less_int_type,type,
    ord_less_int: fun_int_fun_int_bool ).

tff(plus_plus_nat_type,type,
    plus_plus_nat: ( nat * nat ) > nat ).

tff(number_number_of_nat_type,type,
    number_number_of_nat: int > nat ).

tff(power_power_int_type,type,
    power_power_int: int > fun_nat_int ).

tff(bit0_type,type,
    bit0: int > int ).

tff(pls_type,type,
    pls: int ).

tff(zero_zero_int_type,type,
    zero_zero_int: int ).

tff(one_one_int_type,type,
    one_one_int: int ).

tff(zero_zero_nat_type,type,
    zero_zero_nat: nat ).

tff(1,plain,
    ^ [A_1: int] :
      refl(
        ( ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
        <=> ( A_1 = succ(min) ) )
      <=> ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
        <=> ( A_1 = succ(min) ) ) )),
    inference(bind,[status(th)],]) ).

tff(2,plain,
    ( ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
      <=> ( A_1 = succ(min) ) )
  <=> ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
      <=> ( A_1 = succ(min) ) ) ),
    inference(quant_intro,[status(thm)],[1]) ).

tff(3,plain,
    ^ [A_1: int] :
      rewrite(
        ( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
        <=> ( A_1 = number_number_of_int(succ(min)) ) )
      <=> ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
        <=> ( A_1 = succ(min) ) ) )),
    inference(bind,[status(th)],]) ).

tff(4,plain,
    ( ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
      <=> ( A_1 = number_number_of_int(succ(min)) ) )
  <=> ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
      <=> ( A_1 = succ(min) ) ) ),
    inference(quant_intro,[status(thm)],[3]) ).

tff(5,plain,
    ^ [A_1: int] :
      rewrite(
        ( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
        <=> ( A_1 = number_number_of_int(pls) ) )
      <=> ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
        <=> ( A_1 = number_number_of_int(succ(min)) ) ) )),
    inference(bind,[status(th)],]) ).

tff(6,plain,
    ( ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
      <=> ( A_1 = number_number_of_int(pls) ) )
  <=> ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
      <=> ( A_1 = number_number_of_int(succ(min)) ) ) ),
    inference(quant_intro,[status(thm)],[5]) ).

tff(7,plain,
    ^ [A_1: int] :
      rewrite(
        ( ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
        <=> ( A_1 = zero_zero_int ) )
      <=> ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
        <=> ( A_1 = number_number_of_int(pls) ) ) )),
    inference(bind,[status(th)],]) ).

tff(8,plain,
    ( ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) )
  <=> ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
      <=> ( A_1 = number_number_of_int(pls) ) ) ),
    inference(quant_intro,[status(thm)],[7]) ).

tff(9,plain,
    ( ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) )
  <=> ! [A_1: int] :
        ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
      <=> ( A_1 = zero_zero_int ) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(10,axiom,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
    <=> ( A_1 = zero_zero_int ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_zero__eq__power2) ).

tff(11,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int )
    <=> ( A_1 = zero_zero_int ) ),
    inference(modus_ponens,[status(thm)],[10,9]) ).

tff(12,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
    <=> ( A_1 = number_number_of_int(pls) ) ),
    inference(modus_ponens,[status(thm)],[11,8]) ).

tff(13,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
    <=> ( A_1 = number_number_of_int(succ(min)) ) ),
    inference(modus_ponens,[status(thm)],[12,6]) ).

tff(14,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
    <=> ( A_1 = succ(min) ) ),
    inference(modus_ponens,[status(thm)],[13,4]) ).

tff(15,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
    <=> ( A_1 = succ(min) ) ),
    inference(skolemize,[status(sab)],[14]) ).

tff(16,plain,
    ! [A_1: int] :
      ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
    <=> ( A_1 = succ(min) ) ),
    inference(modus_ponens,[status(thm)],[15,2]) ).

tff(17,plain,
    ( ~ ! [A_1: int] :
          ( ( hAPP_nat_int(power_power_int(A_1),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
        <=> ( A_1 = succ(min) ) )
    | ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
    <=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ) ),
    inference(quant_inst,[status(thm)],]) ).

tff(18,plain,
    ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
  <=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
    inference(unit_resolution,[status(thm)],[17,16]) ).

tff(19,plain,
    ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) )
  <=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(20,plain,
    ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) )
  <=> ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(21,plain,
    ( ( hAPP_nat_int(power_power_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(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(22,plain,
    ( ( hAPP_nat_int(power_power_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(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(23,plain,
    ( ~ ( ( hAPP_nat_int(power_power_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(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(24,axiom,
    ~ ( ( hAPP_nat_int(power_power_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/sandbox/benchmark/theBenchmark.p',conj_0) ).

tff(25,plain,
    hAPP_nat_int(power_power_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)],[24,23]) ).

tff(26,plain,
    hAPP_nat_int(power_power_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)],[25,22]) ).

tff(27,plain,
    hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = number_number_of_int(pls),
    inference(modus_ponens,[status(thm)],[26,21]) ).

tff(28,plain,
    hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(succ(min))))) = number_number_of_int(succ(min)),
    inference(modus_ponens,[status(thm)],[27,20]) ).

tff(29,plain,
    hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min),
    inference(modus_ponens,[status(thm)],[28,19]) ).

tff(30,plain,
    ( ~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
      <=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) )
    | ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) != succ(min) )
    | ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
    inference(tautology,[status(thm)],]) ).

tff(31,plain,
    ( ~ ( ( hAPP_nat_int(power_power_int(plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))),plus_plus_nat(number_number_of_nat(bit1(succ(min))),number_number_of_nat(bit1(succ(min))))) = succ(min) )
      <=> ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) )
    | ( plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min) ) ),
    inference(unit_resolution,[status(thm)],[30,29]) ).

tff(32,plain,
    plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)) = succ(min),
    inference(unit_resolution,[status(thm)],[31,18]) ).

tff(33,plain,
    ( ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) )
  <=> ( succ(min) = number_number_of_int(succ(min)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(34,plain,
    ( ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) )
  <=> ( number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(35,plain,
    ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
  <=> ( number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(36,plain,
    ( ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) )
  <=> ( zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ) ),
    inference(rewrite,[status(thm)],]) ).

tff(37,axiom,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_transfer__int__nat__numerals_I1_J) ).

tff(38,plain,
    zero_zero_int = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
    inference(modus_ponens,[status(thm)],[37,36]) ).

tff(39,plain,
    number_number_of_int(pls) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(pls)),
    inference(modus_ponens,[status(thm)],[38,35]) ).

tff(40,plain,
    number_number_of_int(succ(min)) = hAPP_nat_int(semiri1621563631at_int,number_number_of_nat(succ(min))),
    inference(modus_ponens,[status(thm)],[39,34]) ).

tff(41,plain,
    succ(min) = number_number_of_int(succ(min)),
    inference(modus_ponens,[status(thm)],[40,33]) ).

tff(42,plain,
    number_number_of_int(succ(min)) = succ(min),
    inference(symmetry,[status(thm)],[41]) ).

tff(43,plain,
    hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))) = hAPP_i1948725293t_bool(ord_less_int,succ(min)),
    inference(monotonicity,[status(thm)],[42]) ).

tff(44,plain,
    hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)),
    inference(monotonicity,[status(thm)],[43,32]) ).

tff(45,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n))))
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))) ),
    inference(monotonicity,[status(thm)],[44]) ).

tff(46,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)))
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
    inference(symmetry,[status(thm)],[45]) ).

tff(47,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min)))
  <=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
    inference(monotonicity,[status(thm)],[46]) ).

tff(48,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min))))
  <=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))) ),
    inference(rewrite,[status(thm)],]) ).

tff(49,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls)))
  <=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(50,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int))
  <=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls))) ),
    inference(rewrite,[status(thm)],]) ).

tff(51,plain,
    ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int))
  <=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)) ),
    inference(rewrite,[status(thm)],]) ).

tff(52,axiom,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_bin__less__0__simps_I1_J) ).

tff(53,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),zero_zero_int)),
    inference(modus_ponens,[status(thm)],[52,51]) ).

tff(54,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),number_number_of_int(pls))),
    inference(modus_ponens,[status(thm)],[53,50]) ).

tff(55,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),number_number_of_int(succ(min)))),
    inference(modus_ponens,[status(thm)],[54,49]) ).

tff(56,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,succ(min)),succ(min))),
    inference(modus_ponens,[status(thm)],[55,48]) ).

tff(57,plain,
    ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(modus_ponens,[status(thm)],[56,47]) ).

tff(58,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n))))
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(59,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n))))
  <=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(60,plain,
    ( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_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),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))) ),
    inference(rewrite,[status(thm)],]) ).

tff(61,axiom,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).

tff(62,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),plus_plus_int(one_one_int,hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(modus_ponens,[status(thm)],[61,60]) ).

tff(63,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(pls)),plus_plus_int(number_number_of_int(bit1(pls)),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(modus_ponens,[status(thm)],[62,59]) ).

tff(64,plain,
    hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,number_number_of_int(succ(min))),plus_plus_int(number_number_of_int(bit1(succ(min))),hAPP_nat_int(semiri1621563631at_int,n)))),
    inference(modus_ponens,[status(thm)],[63,58]) ).

tff(65,plain,
    $false,
    inference(unit_resolution,[status(thm)],[64,57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM925_3 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n019.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 15:51:05 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.94/0.90  % SZS status Theorem
% 0.94/0.90  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------