%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n009.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 11:41:53 EDT 2023

% Result   : Theorem 28.14s 28.33s
% Output   : Proof 28.14s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_nat,type,
    nat: $tType ).

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

thf(ty_zero_zero_int,type,
    zero_zero_int: int ).

thf(ty_min,type,
    min: int ).

thf(ty_ord_less_int,type,
    ord_less_int: int > int > $o ).

thf(ty_power_power_nat,type,
    power_power_nat: nat > nat > nat ).

thf(ty_eigen__2,type,
    eigen__2: int ).

thf(ty_number_number_of_nat,type,
    number_number_of_nat: int > nat ).

thf(ty_bit1,type,
    bit1: int > int ).

thf(ty_m,type,
    m: int ).

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

thf(ty_n,type,
    n: nat ).

thf(ty_times_times_int,type,
    times_times_int: int > int > int ).

thf(ty_number_number_of_int,type,
    number_number_of_int: int > int ).

thf(ty_eigen__1,type,
    eigen__1: int ).

thf(ty_one_one_int,type,
    one_one_int: int ).

thf(ty_semiri1621563631at_int,type,
    semiri1621563631at_int: nat > int ).

thf(ty_zero_zero_nat,type,
    zero_zero_nat: nat ).

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

thf(ty_plus_plus_int,type,
    plus_plus_int: int > int > int ).

thf(ty_pls,type,
    pls: int ).

thf(ty_eigen__0,type,
    eigen__0: int ).

thf(ty_twoSqu919416604sum2sq,type,
    twoSqu919416604sum2sq: int > $o ).

thf(ty_zcong,type,
    zcong: int > int > int > $o ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: nat] :
        ( ( ( semiri1621563631at_int @ X1 )
          = zero_zero_int )
        = ( X1 = zero_zero_nat ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
      = zero_zero_nat ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_less_int @ ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( zero_zero_int
      = ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( semiri1621563631at_int @ ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
      = zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: nat] :
        ~ ( ord_less_int @ ( semiri1621563631at_int @ X1 ) @ zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
        = zero_zero_int )
      = ( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
        = zero_zero_int ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: int] :
        ( ( ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
          = zero_zero_int )
        = ( X1 = zero_zero_int ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP5 = sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) )
      = zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
      = zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj_0,conjecture,
    ~ sP12 ).

thf(h0,negated_conjecture,
    sP12,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    zcong @ ( power_power_int @ eigen__0 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: int] :
        ( ( plus_plus_int @ ( power_power_int @ eigen__1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
       != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ( plus_plus_int @ ( power_power_int @ eigen__1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ eigen__2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
    = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP8
    | sP3
    | ~ sP11
    | ~ sP4 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | sP4 ),
    inference(symeq,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP10
    | sP5
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP7
    | ~ sP12
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | ~ sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP9
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_287_of__nat__less__0__iff,axiom,
    sP6 ).

thf(fact_43_int__eq__0__conv,axiom,
    sP1 ).

thf(fact_10_zero__eq__power2,axiom,
    sP9 ).

thf(fact_8_zero__power2,axiom,
    sP2 ).

thf(fact_0_n1pos,axiom,
    sP8 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h4,h5,h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,h0,fact_287_of__nat__less__0__iff,fact_43_int__eq__0__conv,fact_10_zero__eq__power2,fact_8_zero__power2,fact_0_n1pos]) ).

thf(fact_838_IH,axiom,
    ~ ( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
     => ~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[fact_838_IH,8,h4,h5]) ).

thf(10,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[fact_838_IH,9,h4,h5]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,10,h3]) ).

thf(fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A,axiom,
    ~ ! [X1: int,X2: int] :
        ( ( plus_plus_int @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ X2 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
       != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ).

thf(12,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A,11,h2]) ).

thf(fact_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4,axiom,
    ~ ! [X1: int] :
        ~ ( zcong @ ( power_power_int @ X1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ).

thf(13,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4,12,h1]) ).

thf(0,theorem,
    ~ sP12,
    inference(contra,[status(thm),contra(discharge,[h0])],[13,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% 0.06/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n009.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Aug 25 13:34:21 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 28.14/28.33  % SZS status Theorem
% 28.14/28.33  % Mode: cade22sinegrackle2xfaf3
% 28.14/28.33  % Steps: 18864
% 28.14/28.33  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------