TSTP Solution File: ITP140^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP140^1 : 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 : n017.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 04:02:27 EDT 2023

% Result   : Theorem 0.15s 0.50s
% Output   : Proof 0.15s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_paraco1605129243lle_tv,type,
    paraco1605129243lle_tv: $tType ).

thf(ty_paraco1604210848lle_fm,type,
    paraco1604210848lle_fm: $tType ).

thf(ty_list_char,type,
    list_char: $tType ).

thf(ty_i,type,
    i: list_char > paraco1605129243lle_tv ).

thf(ty_paraco1325918602e_eval,type,
    paraco1325918602e_eval: ( list_char > paraco1605129243lle_tv ) > paraco1604210848lle_fm > paraco1605129243lle_tv ).

thf(ty_paraco69239110le_Con,type,
    paraco69239110le_Con: paraco1604210848lle_fm > paraco1604210848lle_fm > paraco1604210848lle_fm ).

thf(ty_p1,type,
    p1: paraco1604210848lle_fm ).

thf(ty_paraco1344940915le_Det,type,
    paraco1344940915le_Det: $o > paraco1605129243lle_tv ).

thf(ty_p2,type,
    p2: paraco1604210848lle_fm ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ( paraco1325918602e_eval @ i @ p1 )
       != ( paraco1344940915le_Det @ ~ $false ) )
     => ~ ( ( ( ( paraco1325918602e_eval @ i @ p2 )
              = ( paraco1344940915le_Det @ ~ $false ) )
           => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
              = ( paraco1325918602e_eval @ i @ p1 ) ) )
         => ~ ( ( ( paraco1325918602e_eval @ i @ p2 )
               != ( paraco1344940915le_Det @ ~ $false ) )
             => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
                = ( paraco1344940915le_Det @ $false ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( paraco1325918602e_eval @ i @ p2 )
      = ( paraco1344940915le_Det @ ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( ( ( paraco1325918602e_eval @ i @ p1 )
          = ( paraco1344940915le_Det @ ~ $false ) )
       => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
          = ( paraco1325918602e_eval @ i @ p2 ) ) )
     => ~ sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ( ( paraco1325918602e_eval @ i @ p1 )
          = ( paraco1325918602e_eval @ i @ p2 ) )
       => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
          = ( paraco1325918602e_eval @ i @ p1 ) ) )
     => ~ ( ( ( paraco1325918602e_eval @ i @ p1 )
           != ( paraco1325918602e_eval @ i @ p2 ) )
         => ~ sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: paraco1604210848lle_fm] :
        ~ ( ( ( ( paraco1325918602e_eval @ i @ p1 )
              = ( paraco1325918602e_eval @ i @ X1 ) )
           => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ X1 ) )
              = ( paraco1325918602e_eval @ i @ p1 ) ) )
         => ~ ( ( ( paraco1325918602e_eval @ i @ p1 )
               != ( paraco1325918602e_eval @ i @ X1 ) )
             => ~ ( ( ( ( paraco1325918602e_eval @ i @ p1 )
                      = ( paraco1344940915le_Det @ ~ $false ) )
                   => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ X1 ) )
                      = ( paraco1325918602e_eval @ i @ X1 ) ) )
                 => ~ ( ( ( paraco1325918602e_eval @ i @ p1 )
                       != ( paraco1344940915le_Det @ ~ $false ) )
                     => ~ ( ( ( ( paraco1325918602e_eval @ i @ X1 )
                              = ( paraco1344940915le_Det @ ~ $false ) )
                           => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ X1 ) )
                              = ( paraco1325918602e_eval @ i @ p1 ) ) )
                         => ~ ( ( ( paraco1325918602e_eval @ i @ X1 )
                               != ( paraco1344940915le_Det @ ~ $false ) )
                             => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ X1 ) )
                                = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( ( paraco1325918602e_eval @ i @ p1 )
       != ( paraco1325918602e_eval @ i @ p2 ) )
     => ~ sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: paraco1604210848lle_fm,X2: paraco1604210848lle_fm] :
        ~ ( ( ( ( paraco1325918602e_eval @ i @ X1 )
              = ( paraco1325918602e_eval @ i @ X2 ) )
           => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ X1 @ X2 ) )
              = ( paraco1325918602e_eval @ i @ X1 ) ) )
         => ~ ( ( ( paraco1325918602e_eval @ i @ X1 )
               != ( paraco1325918602e_eval @ i @ X2 ) )
             => ~ ( ( ( ( paraco1325918602e_eval @ i @ X1 )
                      = ( paraco1344940915le_Det @ ~ $false ) )
                   => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ X1 @ X2 ) )
                      = ( paraco1325918602e_eval @ i @ X2 ) ) )
                 => ~ ( ( ( paraco1325918602e_eval @ i @ X1 )
                       != ( paraco1344940915le_Det @ ~ $false ) )
                     => ~ ( ( ( ( paraco1325918602e_eval @ i @ X2 )
                              = ( paraco1344940915le_Det @ ~ $false ) )
                           => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ X1 @ X2 ) )
                              = ( paraco1325918602e_eval @ i @ X1 ) ) )
                         => ~ ( ( ( paraco1325918602e_eval @ i @ X2 )
                               != ( paraco1344940915le_Det @ ~ $false ) )
                             => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ X1 @ X2 ) )
                                = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
      = ( paraco1325918602e_eval @ i @ p1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: list_char > paraco1605129243lle_tv,X2: paraco1604210848lle_fm,X3: paraco1604210848lle_fm] :
        ~ ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
              = ( paraco1325918602e_eval @ X1 @ X3 ) )
           => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X2 @ X3 ) )
              = ( paraco1325918602e_eval @ X1 @ X2 ) ) )
         => ~ ( ( ( paraco1325918602e_eval @ X1 @ X2 )
               != ( paraco1325918602e_eval @ X1 @ X3 ) )
             => ~ ( ( ( ( paraco1325918602e_eval @ X1 @ X2 )
                      = ( paraco1344940915le_Det @ ~ $false ) )
                   => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X2 @ X3 ) )
                      = ( paraco1325918602e_eval @ X1 @ X3 ) ) )
                 => ~ ( ( ( paraco1325918602e_eval @ X1 @ X2 )
                       != ( paraco1344940915le_Det @ ~ $false ) )
                     => ~ ( ( ( ( paraco1325918602e_eval @ X1 @ X3 )
                              = ( paraco1344940915le_Det @ ~ $false ) )
                           => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X2 @ X3 ) )
                              = ( paraco1325918602e_eval @ X1 @ X2 ) ) )
                         => ~ ( ( ( paraco1325918602e_eval @ X1 @ X3 )
                               != ( paraco1344940915le_Det @ ~ $false ) )
                             => ( ( paraco1325918602e_eval @ X1 @ ( paraco69239110le_Con @ X2 @ X3 ) )
                                = ( paraco1344940915le_Det @ $false ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( sP2
       => sP8 )
     => ~ ( ~ sP2
         => ( ( paraco1325918602e_eval @ i @ ( paraco69239110le_Con @ p1 @ p2 ) )
            = ( paraco1344940915le_Det @ $false ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP2
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1325918602e_eval @ i @ p2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( paraco1325918602e_eval @ i @ p1 )
      = ( paraco1344940915le_Det @ ~ $false ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(conj_0,conjecture,
    sP8 ).

thf(h0,negated_conjecture,
    ~ sP8,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP11
    | ~ sP2
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP10
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP13
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP3
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | sP12
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( sP4
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP5
    | ~ sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP9
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_5_eval_Osimps_I4_J,axiom,
    sP9 ).

thf(fact_2_a_H,axiom,
    ~ sP12 ).

thf(fact_1_a,axiom,
    sP2 ).

thf(fact_0_a_H_H,axiom,
    ~ sP13 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,h0,fact_5_eval_Osimps_I4_J,fact_2_a_H,fact_1_a,fact_0_a_H_H]) ).

thf(0,theorem,
    sP8,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : ITP140^1 : TPTP v8.1.2. Released v7.5.0.
% 0.05/0.10  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.09/0.31  % Computer : n017.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Sun Aug 27 11:56:26 EDT 2023
% 0.09/0.31  % CPUTime  : 
% 0.15/0.50  % SZS status Theorem
% 0.15/0.50  % Mode: cade22sinegrackle2x6978
% 0.15/0.50  % Steps: 1690
% 0.15/0.50  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------