TSTP Solution File: ITP198^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP198^1 : 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 : n003.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 04:02:51 EDT 2023

% Result   : Theorem 0.19s 0.49s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_produc1020032539e_real,type,
    produc1020032539e_real: $tType ).

thf(ty_set_variable_real,type,
    set_variable_real: $tType ).

thf(ty_produc1993135732e_real,type,
    produc1993135732e_real: $tType ).

thf(ty_produc104944723e_real,type,
    produc104944723e_real: $tType ).

thf(ty_char,type,
    char: $tType ).

thf(ty_denotational_interp,type,
    denotational_interp: $tType ).

thf(ty_real,type,
    real: $tType ).

thf(ty_denotational_Games,type,
    denotational_Games: denotational_interp > char > set_variable_real > set_variable_real ).

thf(ty_produc141013715e_real,type,
    produc141013715e_real: ( char > real > real ) > produc104944723e_real > produc1020032539e_real ).

thf(ty_eigen__0,type,
    eigen__0: char ).

thf(ty_denotational_Funcs,type,
    denotational_Funcs: denotational_interp > char > real > real ).

thf(ty_denotational_Consts,type,
    denotational_Consts: denotational_interp > char > real ).

thf(ty_produc2007437005e_real,type,
    produc2007437005e_real: ( char > real > $o ) > ( char > set_variable_real > set_variable_real ) > produc104944723e_real ).

thf(ty_denotational_Preds,type,
    denotational_Preds: denotational_interp > char > real > $o ).

thf(ty_d,type,
    d: real ).

thf(ty_f,type,
    f: char ).

thf(ty_if_real,type,
    if_real: $o > real > real > real ).

thf(ty_eigen__1,type,
    eigen__1: real ).

thf(ty_produc2125489830e_real,type,
    produc2125489830e_real: ( char > real ) > produc1020032539e_real > produc1993135732e_real ).

thf(ty_denota1150374853interp,type,
    denota1150374853interp: produc1993135732e_real > denotational_interp ).

thf(ty_i,type,
    i: denotational_interp ).

thf(sP1,plain,
    ( sP1
  <=> ( denotational_Preds @ i @ eigen__0 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: char > real > $o,X2: char > set_variable_real > set_variable_real] :
        ( ( denotational_Preds
          @ ( denota1150374853interp
            @ ( produc2125489830e_real
              @ ^ [X3: char] : ( if_real @ ( X3 = f ) @ d @ ( denotational_Consts @ i @ X3 ) )
              @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ X1 @ X2 ) ) ) ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: char > set_variable_real > set_variable_real] :
        ( ( denotational_Preds
          @ ( denota1150374853interp
            @ ( produc2125489830e_real
              @ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
              @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ X1 ) ) ) ) )
        = ( denotational_Preds @ i ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: char > real > real,X2: char > real > $o,X3: char > set_variable_real > set_variable_real] :
        ( ( denotational_Preds
          @ ( denota1150374853interp
            @ ( produc2125489830e_real
              @ ^ [X4: char] : ( if_real @ ( X4 = f ) @ d @ ( denotational_Consts @ i @ X4 ) )
              @ ( produc141013715e_real @ X1 @ ( produc2007437005e_real @ X2 @ X3 ) ) ) ) )
        = X2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( denotational_Preds
        @ ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) ) )
      = ( denotational_Preds @ i ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( denotational_Preds
        @ ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
        @ eigen__0
        @ eigen__1 )
      = sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: char] :
        ( ( denotational_Preds
          @ ( denota1150374853interp
            @ ( produc2125489830e_real
              @ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
              @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
          @ X1 )
        = ( denotational_Preds @ i @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: char > real,X2: char > real > real,X3: char > real > $o,X4: char > set_variable_real > set_variable_real] :
        ( ( denotational_Preds @ ( denota1150374853interp @ ( produc2125489830e_real @ X1 @ ( produc141013715e_real @ X2 @ ( produc2007437005e_real @ X3 @ X4 ) ) ) ) )
        = X3 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( denotational_Preds
      @ ( denota1150374853interp
        @ ( produc2125489830e_real
          @ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
          @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
      @ eigen__0
      @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: real] :
        ( ( denotational_Preds
          @ ( denota1150374853interp
            @ ( produc2125489830e_real
              @ ^ [X2: char] : ( if_real @ ( X2 = f ) @ d @ ( denotational_Consts @ i @ X2 ) )
              @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
          @ eigen__0
          @ X1 )
        = ( denotational_Preds @ i @ eigen__0 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ( denotational_Preds
        @ ( denota1150374853interp
          @ ( produc2125489830e_real
            @ ^ [X1: char] : ( if_real @ ( X1 = f ) @ d @ ( denotational_Consts @ i @ X1 ) )
            @ ( produc141013715e_real @ ( denotational_Funcs @ i ) @ ( produc2007437005e_real @ ( denotational_Preds @ i ) @ ( denotational_Games @ i ) ) ) ) )
        @ eigen__0 )
      = ( denotational_Preds @ i @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(conj_0,conjecture,
    sP5 ).

thf(h0,negated_conjecture,
    ~ sP5,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ sP7,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP11,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP10,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h5,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP6
    | ~ sP9
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP10
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP11
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( ~ sP5
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP8
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_0_Preds__mkinterp,axiom,
    sP8 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h5,h6,fact_0_Preds__mkinterp]) ).

thf(11,plain,
    ( ~ sP6
    | sP9
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP10
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP11
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP7
    | sP11 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP5
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(17,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP4
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(19,plain,
    ( ~ sP8
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(20,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h4,h3,h2,h1,h0])],[11,12,13,14,15,16,17,18,19,h7,h8,fact_0_Preds__mkinterp]) ).

thf(21,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h4,h3,h2,h1,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h4,10,20,h5,h6,h7,h8]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h2,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,21,h4]) ).

thf(23,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h2,h1,h0]),tab_fe(discharge,[h3])],[h2,22,h3]) ).

thf(24,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,23,h2]) ).

thf(25,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h0]),tab_fe(discharge,[h1])],[h0,24,h1]) ).

thf(0,theorem,
    sP5,
    inference(contra,[status(thm),contra(discharge,[h0])],[25,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP198^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33  % Computer : n003.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Sun Aug 27 12:07:09 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.19/0.49  % SZS status Theorem
% 0.19/0.49  % Mode: cade22sinegrackle2x6978
% 0.19/0.49  % Steps: 848
% 0.19/0.49  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------