TSTP Solution File: ITP130^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP130^1 : 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 : n015.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 04:02:21 EDT 2023

% Result   : Theorem 0.20s 0.74s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

thf(ty_ya,type,
    ya: int ).

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

thf(ty_power_power_real,type,
    power_power_real: real > nat > real ).

thf(ty_ord_less_real,type,
    ord_less_real: real > real > $o ).

thf(ty_suc,type,
    suc: nat > nat ).

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

thf(ty_pm,type,
    pm: nat ).

thf(ty_na,type,
    na: int ).

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

thf(ty_zero_zero_int,type,
    zero_zero_int: int ).

thf(ty_p,type,
    p: nat ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_less_int @ na @ ( power_power_int @ ya @ p ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( power_power_real @ ( ring_1_of_int_real @ ya ) @ p )
      = ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ ( suc @ pm ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ p ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( p
      = ( suc @ pm ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: nat] :
        ( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ ya ) @ X1 ) )
        = ( ord_less_int @ na @ ( power_power_int @ ya @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ya = zero_zero_int ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: int,X2: int,X3: nat] :
        ( ( ord_less_real @ ( ring_1_of_int_real @ X1 ) @ ( power_power_real @ ( ring_1_of_int_real @ X2 ) @ X3 ) )
        = ( ord_less_int @ X1 @ ( power_power_int @ X2 @ X3 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: int,X2: nat] :
        ( ( ord_less_real @ ( ring_1_of_int_real @ na ) @ ( power_power_real @ ( ring_1_of_int_real @ X1 ) @ X2 ) )
        = ( ord_less_int @ na @ ( power_power_int @ X1 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP4 = sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(conj_0,conjecture,
    sP3 ).

thf(h0,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ ( ord_less_int @ ya @ zero_zero_int ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ord_less_int @ na @ zero_zero_int ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ord_less_int @ zero_zero_int @ ya,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP7,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | sP3
    | ~ sP2
    | sP8 ),
    inference(mating_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP2
    | ~ sP5
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP11
    | sP4
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP6
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ~ sP8,
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP9
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_86_p,axiom,
    sP5 ).

thf(fact_81_yyn,axiom,
    sP1 ).

thf(fact_3_of__int__power__less__of__int__cancel__iff,axiom,
    sP9 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h1,h2,h1,h2,h0])],[1,2,3,4,5,6,7,h0,fact_86_p,fact_81_yyn,fact_3_of__int__power__less__of__int__cancel__iff]) ).

thf(fact_19_y00,axiom,
    ~ sP7 ).

thf(9,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h4,h1,h2,h1,h2,h0])],[h4,fact_19_y00]) ).

thf(fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062,axiom,
    ( ~ ( ord_less_int @ zero_zero_int @ ya )
   => sP7 ) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[fact_20__092_060open_0620_A_060_Ay_A_092_060or_062_Ay_A_061_A0_092_060close_062,8,9,h3,h4]) ).

thf(fact_25_not_I2_J,axiom,
    ~ ( ~ ( ord_less_int @ ya @ zero_zero_int )
     => ( ord_less_int @ na @ zero_zero_int ) ) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h1,h2])],[fact_25_not_I2_J,10,h1,h2]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_25_not_I2_J,11,h1,h2]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP130^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.16/0.34  % Computer : n015.cluster.edu
% 0.16/0.34  % Model    : x86_64 x86_64
% 0.16/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34  % Memory   : 8042.1875MB
% 0.16/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34  % CPULimit : 300
% 0.16/0.34  % WCLimit  : 300
% 0.16/0.34  % DateTime : Sun Aug 27 11:29:38 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.20/0.74  % SZS status Theorem
% 0.20/0.74  % Mode: cade22sinegrackle2x6978
% 0.20/0.74  % Steps: 7538
% 0.20/0.74  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------