TSTP Solution File: NUM924+8 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ddEr55vmQN true

% Computer : n024.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 : Thu Aug 31 12:44:50 EDT 2023

% Result   : Theorem 59.14s 9.12s
% Output   : Refutation 59.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   43
% Syntax   : Number of formulae    :  130 ( 106 unt;  24 typ;   0 def)
%            Number of atoms       :  106 (  95 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives : 2081 (   5   ~;   0   |;   0   &;2076   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   3 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (  16   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   26 (  24 usr;  14 con; 0-4 aty)
%            Number of variables   :   54 (   0   ^;  54   !;   0   ?;  54   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
    hBOOL: $i > $o ).

thf(t_type,type,
    t: $i ).

thf(nat_type,type,
    nat: $i ).

thf(nat_1_type,type,
    nat_1: $i ).

thf(ti_type,type,
    ti: $i > $i > $i ).

thf(m_type,type,
    m: $i ).

thf(number_number_of_type,type,
    number_number_of: $i > $i ).

thf(succ_type,type,
    succ: $i ).

thf(one_one_type,type,
    one_one: $i > $i ).

thf(bit0_type,type,
    bit0: $i ).

thf(times_times_type,type,
    times_times: $i > $i ).

thf(s_type,type,
    s: $i ).

thf(power_power_type,type,
    power_power: $i > $i ).

thf(zero_zero_type,type,
    zero_zero: $i > $i ).

thf(bit1_type,type,
    bit1: $i ).

thf(pred_type,type,
    pred: $i ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i > $i > $i ).

thf(pls_type,type,
    pls: $i ).

thf(ord_less_type,type,
    ord_less: $i > $i ).

thf(suc_type,type,
    suc: $i ).

thf(fun_type,type,
    fun: $i > $i > $i ).

thf(int_type,type,
    int: $i ).

thf(bool_type,type,
    bool: $i ).

thf(plus_plus_type,type,
    plus_plus: $i > $i ).

thf(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
    hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ t ) ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ ( zero_zero @ int ) ) ) ).

thf(zip_derived_cl275,plain,
    hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ t ) ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ ( zero_zero @ int ) ) ),
    inference(cnf,[status(esa)],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).

thf(fact_22_number__of__is__id,axiom,
    ! [K_4: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ K_4 )
      = ( ti @ int @ K_4 ) ) ).

thf(zip_derived_cl301,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( ti @ int @ X0 ) ),
    inference(cnf,[status(esa)],[fact_22_number__of__is__id]) ).

thf(fact_2899_succ__pred,axiom,
    ! [X: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X ) )
      = ( ti @ int @ X ) ) ).

thf(zip_derived_cl4693,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) )
      = ( ti @ int @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2899_succ__pred]) ).

thf(zip_derived_cl8528,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl301,zip_derived_cl4693]) ).

thf(fact_2901_pred__Bit0,axiom,
    ! [K_4: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ K_4 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ K_4 ) ) ) ).

thf(zip_derived_cl4695,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4695_001,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(fact_2900_pred__Bit1,axiom,
    ! [K_4: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ K_4 ) )
      = ( hAPP @ int @ int @ bit0 @ K_4 ) ) ).

thf(zip_derived_cl4694,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2900_pred__Bit1]) ).

thf(fact_122_Bit0__Pls,axiom,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ) ).

thf(zip_derived_cl455,plain,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ),
    inference(cnf,[status(esa)],[fact_122_Bit0__Pls]) ).

thf(fact_1526_succ__Bit1,axiom,
    ! [K_4: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ K_4 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ K_4 ) ) ) ).

thf(zip_derived_cl2556,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2556_002,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(fact_1525_succ__Pls,axiom,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ) ).

thf(zip_derived_cl2555,plain,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(cnf,[status(esa)],[fact_1525_succ__Pls]) ).

thf(fact_112_one__is__num__one,axiom,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ).

thf(zip_derived_cl440,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ),
    inference(cnf,[status(esa)],[fact_112_one__is__num__one]) ).

thf(zip_derived_cl8528_003,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl301,zip_derived_cl4693]) ).

thf(zip_derived_cl4694_004,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2900_pred__Bit1]) ).

thf(zip_derived_cl455_005,plain,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ),
    inference(cnf,[status(esa)],[fact_122_Bit0__Pls]) ).

thf(zip_derived_cl2555_006,plain,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(cnf,[status(esa)],[fact_1525_succ__Pls]) ).

thf(zip_derived_cl8540,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(fact_1528_succ__def,axiom,
    ! [K_4: $i] :
      ( ( hAPP @ int @ int @ succ @ K_4 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ K_4 ) @ ( one_one @ int ) ) ) ).

thf(zip_derived_cl2558,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( one_one @ int ) ) ),
    inference(cnf,[status(esa)],[fact_1528_succ__def]) ).

thf(zip_derived_cl8540_007,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(zip_derived_cl8574,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2558,zip_derived_cl8540]) ).

thf(zip_derived_cl8528_008,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl301,zip_derived_cl4693]) ).

thf(zip_derived_cl4695_009,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4695_010,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4694_011,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2900_pred__Bit1]) ).

thf(zip_derived_cl455_012,plain,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ),
    inference(cnf,[status(esa)],[fact_122_Bit0__Pls]) ).

thf(zip_derived_cl2556_013,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2556_014,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2555_015,plain,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(cnf,[status(esa)],[fact_1525_succ__Pls]) ).

thf(zip_derived_cl8540_016,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(zip_derived_cl8574_017,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2558,zip_derived_cl8540]) ).

thf(fact_123_Pls__def,axiom,
    ( pls
    = ( zero_zero @ int ) ) ).

thf(zip_derived_cl456,plain,
    ( pls
    = ( zero_zero @ int ) ),
    inference(cnf,[status(esa)],[fact_123_Pls__def]) ).

thf(zip_derived_cl8888,plain,
    hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) @ m ) ) ) @ t ) ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) @ m ) ) ) @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl275,zip_derived_cl8528,zip_derived_cl4695,zip_derived_cl4695,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2556,zip_derived_cl2556,zip_derived_cl2555,zip_derived_cl8540,zip_derived_cl8574,zip_derived_cl8528,zip_derived_cl4695,zip_derived_cl4695,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2556,zip_derived_cl2556,zip_derived_cl2555,zip_derived_cl8540,zip_derived_cl8574,zip_derived_cl456]) ).

thf(fact_23_zmult__commute,axiom,
    ! [Z_1: $i,W: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ Z_1 ) @ W )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ W ) @ Z_1 ) ) ).

thf(zip_derived_cl302,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(zip_derived_cl302_018,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(zip_derived_cl302_019,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(zip_derived_cl302_020,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(fact_62_mult__Pls,axiom,
    ! [W: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ pls ) @ W )
      = pls ) ).

thf(zip_derived_cl364,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ pls ) @ X0 )
      = pls ),
    inference(cnf,[status(esa)],[fact_62_mult__Pls]) ).

thf(zip_derived_cl8892,plain,
    hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ t ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ m ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) ) ) @ pls ),
    inference(demod,[status(thm)],[zip_derived_cl8888,zip_derived_cl302,zip_derived_cl302,zip_derived_cl302,zip_derived_cl302,zip_derived_cl364]) ).

thf(fact_3_t,axiom,
    ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ ( one_one @ int ) )
    = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ t ) ) ).

thf(zip_derived_cl276,plain,
    ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ ( one_one @ int ) )
    = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ m ) ) @ ( one_one @ int ) ) ) @ t ) ),
    inference(cnf,[status(esa)],[fact_3_t]) ).

thf(fact_1426_numeral__2__eq__2,axiom,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ) ) ).

thf(zip_derived_cl2385,plain,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ) ),
    inference(cnf,[status(esa)],[fact_1426_numeral__2__eq__2]) ).

thf(fact_1102_transfer__nat__int__numerals_I1_J,axiom,
    ( ( zero_zero @ nat )
    = ( hAPP @ int @ nat @ nat_1 @ ( zero_zero @ int ) ) ) ).

thf(zip_derived_cl1888,plain,
    ( ( zero_zero @ nat )
    = ( hAPP @ int @ nat @ nat_1 @ ( zero_zero @ int ) ) ),
    inference(cnf,[status(esa)],[fact_1102_transfer__nat__int__numerals_I1_J]) ).

thf(zip_derived_cl456_021,plain,
    ( pls
    = ( zero_zero @ int ) ),
    inference(cnf,[status(esa)],[fact_123_Pls__def]) ).

thf(zip_derived_cl8316,plain,
    ( ( zero_zero @ nat )
    = ( hAPP @ int @ nat @ nat_1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl1888,zip_derived_cl456]) ).

thf(zip_derived_cl8443,plain,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2385,zip_derived_cl8316]) ).

thf(fact_1391_nat__1,axiom,
    ( ( hAPP @ int @ nat @ nat_1 @ ( one_one @ int ) )
    = ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ) ).

thf(zip_derived_cl2322,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( one_one @ int ) )
    = ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ),
    inference(cnf,[status(esa)],[fact_1391_nat__1]) ).

thf(zip_derived_cl8316_022,plain,
    ( ( zero_zero @ nat )
    = ( hAPP @ int @ nat @ nat_1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl1888,zip_derived_cl456]) ).

thf(zip_derived_cl8351,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( one_one @ int ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2322,zip_derived_cl8316]) ).

thf(zip_derived_cl8540_023,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(zip_derived_cl8584,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8351,zip_derived_cl8540]) ).

thf(zip_derived_cl8613,plain,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8443,zip_derived_cl8584]) ).

thf(fact_1452_nat__2,axiom,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ) ) ).

thf(zip_derived_cl2431,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ ( number_number_of @ int ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( zero_zero @ nat ) ) ) ),
    inference(cnf,[status(esa)],[fact_1452_nat__2]) ).

thf(zip_derived_cl8528_024,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl301,zip_derived_cl4693]) ).

thf(zip_derived_cl4695_025,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4694_026,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2900_pred__Bit1]) ).

thf(zip_derived_cl455_027,plain,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ),
    inference(cnf,[status(esa)],[fact_122_Bit0__Pls]) ).

thf(zip_derived_cl2556_028,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2555_029,plain,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(cnf,[status(esa)],[fact_1525_succ__Pls]) ).

thf(zip_derived_cl8316_030,plain,
    ( ( zero_zero @ nat )
    = ( hAPP @ int @ nat @ nat_1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl1888,zip_derived_cl456]) ).

thf(zip_derived_cl8584_031,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8351,zip_derived_cl8540]) ).

thf(zip_derived_cl8754,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2431,zip_derived_cl8528,zip_derived_cl4695,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2556,zip_derived_cl2555,zip_derived_cl8316,zip_derived_cl8584]) ).

thf(zip_derived_cl8755,plain,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8613,zip_derived_cl8754]) ).

thf(zip_derived_cl8540_032,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(zip_derived_cl8574_033,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2558,zip_derived_cl8540]) ).

thf(zip_derived_cl8528_034,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ ( number_number_of @ int ) @ X0 )
      = ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl301,zip_derived_cl4693]) ).

thf(zip_derived_cl4695_035,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4695_036,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit0 @ X0 ) )
      = ( hAPP @ int @ int @ bit1 @ ( hAPP @ int @ int @ pred @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_2901_pred__Bit0]) ).

thf(zip_derived_cl4694_037,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ pred @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ X0 ) ),
    inference(cnf,[status(esa)],[fact_2900_pred__Bit1]) ).

thf(zip_derived_cl455_038,plain,
    ( ( hAPP @ int @ int @ bit0 @ pls )
    = pls ),
    inference(cnf,[status(esa)],[fact_122_Bit0__Pls]) ).

thf(zip_derived_cl2556_039,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2556_040,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ bit1 @ X0 ) )
      = ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ succ @ X0 ) ) ),
    inference(cnf,[status(esa)],[fact_1526_succ__Bit1]) ).

thf(zip_derived_cl2555_041,plain,
    ( ( hAPP @ int @ int @ succ @ pls )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(cnf,[status(esa)],[fact_1525_succ__Pls]) ).

thf(zip_derived_cl302_042,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(zip_derived_cl8540_043,plain,
    ( ( one_one @ int )
    = ( hAPP @ int @ int @ bit1 @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl440,zip_derived_cl8528,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2555]) ).

thf(zip_derived_cl8574_044,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( hAPP @ int @ int @ bit1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2558,zip_derived_cl8540]) ).

thf(zip_derived_cl302_045,plain,
    ! [X0: $i,X1: $i] :
      ( ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X1 ) @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ X0 ) @ X1 ) ),
    inference(cnf,[status(esa)],[fact_23_zmult__commute]) ).

thf(zip_derived_cl8893,plain,
    ( ( hAPP @ int @ int @ succ @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) )
    = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ t ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( times_times @ int ) @ m ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl276,zip_derived_cl8755,zip_derived_cl8540,zip_derived_cl8574,zip_derived_cl8528,zip_derived_cl4695,zip_derived_cl4695,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2556,zip_derived_cl2556,zip_derived_cl2555,zip_derived_cl302,zip_derived_cl8540,zip_derived_cl8574,zip_derived_cl302]) ).

thf(conj_0,conjecture,
    hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ ( one_one @ int ) ) ) @ ( zero_zero @ int ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ ( one_one @ int ) ) ) @ ( zero_zero @ int ) ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl8306,plain,
    ~ ( hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) @ ( one_one @ int ) ) ) @ ( zero_zero @ int ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(zip_derived_cl8443_046,plain,
    ( ( hAPP @ int @ nat @ ( number_number_of @ nat ) @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2385,zip_derived_cl8316]) ).

thf(zip_derived_cl2558_047,plain,
    ! [X0: $i] :
      ( ( hAPP @ int @ int @ succ @ X0 )
      = ( hAPP @ int @ int @ ( hAPP @ int @ ( fun @ int @ int ) @ ( plus_plus @ int ) @ X0 ) @ ( one_one @ int ) ) ),
    inference(cnf,[status(esa)],[fact_1528_succ__def]) ).

thf(zip_derived_cl456_048,plain,
    ( pls
    = ( zero_zero @ int ) ),
    inference(cnf,[status(esa)],[fact_123_Pls__def]) ).

thf(zip_derived_cl8527,plain,
    ~ ( hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ) ) ) ) @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl8306,zip_derived_cl8443,zip_derived_cl2558,zip_derived_cl456]) ).

thf(zip_derived_cl8584_049,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ pls ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl8351,zip_derived_cl8540]) ).

thf(zip_derived_cl8627,plain,
    ~ ( hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) ) @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl8527,zip_derived_cl8584]) ).

thf(zip_derived_cl8754_050,plain,
    ( ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) )
    = ( hAPP @ nat @ nat @ suc @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl2431,zip_derived_cl8528,zip_derived_cl4695,zip_derived_cl4694,zip_derived_cl455,zip_derived_cl2556,zip_derived_cl2555,zip_derived_cl8316,zip_derived_cl8584]) ).

thf(zip_derived_cl8819,plain,
    ~ ( hBOOL @ ( hAPP @ int @ bool @ ( hAPP @ int @ ( fun @ int @ bool ) @ ( ord_less @ int ) @ ( hAPP @ int @ int @ succ @ ( hAPP @ nat @ int @ ( hAPP @ int @ ( fun @ nat @ int ) @ ( power_power @ int ) @ s ) @ ( hAPP @ int @ nat @ nat_1 @ ( hAPP @ int @ int @ bit0 @ ( hAPP @ int @ int @ bit1 @ pls ) ) ) ) ) ) @ pls ) ),
    inference(demod,[status(thm)],[zip_derived_cl8627,zip_derived_cl8754]) ).

thf(zip_derived_cl10266,plain,
    $false,
    inference(demod,[status(thm)],[zip_derived_cl8892,zip_derived_cl8893,zip_derived_cl8819]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% 0.07/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.ddEr55vmQN true
% 0.13/0.34  % Computer : n024.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 Aug 25 15:25:09 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  % Running portfolio for 300 s
% 0.13/0.35  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in FO mode
% 0.20/0.67  % Total configuration time : 435
% 0.20/0.67  % Estimated wc time : 1092
% 0.20/0.67  % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.69  % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.71  % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.90/0.72  % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.90/0.73  % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 1.26/0.74  % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 1.26/0.74  % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 1.26/0.75  % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 59.14/9.12  % Solved by fo/fo13.sh.
% 59.14/9.12  % done 0 iterations in 8.359s
% 59.14/9.12  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 59.14/9.12  % SZS output start Refutation
% See solution above
% 59.14/9.13  
% 59.14/9.13  
% 59.14/9.13  % Terminating...
% 59.63/9.19  % Runner terminated.
% 59.63/9.19  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------