%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP097^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n008.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 04:02:03 EDT 2023

% Result   : Theorem 32.07s 32.23s
% Output   : Proof 32.07s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_real,type,
    real: $tType ).

thf(ty_int,type,
    int: $tType ).

thf(ty_d,type,
    d: int ).

thf(ty_ord_less_eq_real,type,
    ord_less_eq_real: real > real > $o ).

thf(ty_power_power_int,type,
    power_power_int: int > nat > int ).

thf(ty_log,type,
    log: real > real > real ).

thf(ty_numeral_numeral_real,type,
    numeral_numeral_real: num > real ).

thf(ty_archim1371465213g_real,type,
    archim1371465213g_real: real > int ).

thf(ty_ring_1_of_int_real,type,
    ring_1_of_int_real: int > real ).

thf(ty_one,type,
    one: num ).

thf(ty_bit0,type,
    bit0: num > num ).

thf(ty_nat2,type,
    nat2: int > nat ).

thf(ty_ord_less_eq_int,type,
    ord_less_eq_int: int > int > $o ).

thf(ty_numeral_numeral_int,type,
    numeral_numeral_int: num > int ).

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( archim1371465213g_real @ ( ring_1_of_int_real @ d ) )
      = d ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_less_eq_real @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) @ ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ord_less_eq_real @ ( ring_1_of_int_real @ d ) @ ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) )
     => ( ord_less_eq_int @ ( archim1371465213g_real @ ( ring_1_of_int_real @ d ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( ring_1_of_int_real @ d )
      = ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ord_less_eq_int @ d @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ord_less_eq_real @ ( ring_1_of_int_real @ d ) @ ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri2110766477t_real @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) )
      = ( ring_1_of_int_real @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ( powr_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) )
      = ( ring_1_of_int_real @ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ord_less_eq_int @ ( archim1371465213g_real @ ( ring_1_of_int_real @ d ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( nat2 @ ( archim1371465213g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ d ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: int] :
        ( ( ord_less_eq_real @ ( ring_1_of_int_real @ d ) @ ( ring_1_of_int_real @ X1 ) )
       => ( ord_less_eq_int @ ( archim1371465213g_real @ ( ring_1_of_int_real @ d ) ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: int] :
        ( ( archim1371465213g_real @ ( ring_1_of_int_real @ X1 ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: real,X2: int] :
        ( ( ord_less_eq_real @ X1 @ ( ring_1_of_int_real @ X2 ) )
       => ( ord_less_eq_int @ ( archim1371465213g_real @ X1 ) @ X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(conj_0,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP10
    | sP6
    | sP1
    | ~ sP2 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP7
    | ~ sP8
    | ~ sP9 ),
    inference(mating_rule,[status(thm)],]) ).

thf(3,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | ~ sP7
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP11
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP5
    | sP9 ),
    inference(symeq,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP12
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP13
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
    sP3 ).

thf(fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,axiom,
    sP8 ).

thf(fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062,axiom,
    sP5 ).

thf(fact_45_ceiling__le,axiom,
    sP13 ).

thf(fact_25_ceiling__of__int,axiom,
    sP12 ).

thf(9,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,h0,fact_103__092_060open_0622_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_A_092_060le_062_A2_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,fact_102__092_060open_0622_Apowr_Areal_A_Inat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_A_061_Areal__of__int_A_I2_A_094_Anat_A_092_060lceil_062log_A2_A_Ireal__of__int_Ad_J_092_060rceil_062_J_092_060close_062,fact_53__092_060open_062real__of__int_Ad_A_061_A2_Apowr_Alog_A2_A_Ireal__of__int_Ad_J_092_060close_062,fact_45_ceiling__le,fact_25_ceiling__of__int]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[9,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ITP097^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.10  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.31  % Computer : n008.cluster.edu
% 0.13/0.31  % Model    : x86_64 x86_64
% 0.13/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31  % Memory   : 8042.1875MB
% 0.13/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31  % CPULimit : 300
% 0.13/0.31  % WCLimit  : 300
% 0.13/0.31  % DateTime : Sun Aug 27 11:21:47 EDT 2023
% 0.17/0.31  % CPUTime  : 
% 32.07/32.23  % SZS status Theorem
% 32.07/32.23  % Mode: cade22sinegrackle2xfaf3
% 32.07/32.23  % Steps: 65873
% 32.07/32.23  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------