TSTP Solution File: SEU920^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SEU920^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n025.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 17:37:53 EDT 2023

% Result   : Theorem 0.22s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   30 (  11 unt;   7 typ;   1 def)
%            Number of atoms       :   37 (  16 equ;   0 cnn)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   73 (  33   ~;   3   |;   0   &;  27   @)
%                                         (   4 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Number of types       :    4 (   3 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   9 usr;   8 con; 0-2 aty)
%            Number of variables   :   34 (   1   ^;  33   !;   0   ?;  34   :)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

thf(ty_c,type,
    c: $tType ).

thf(ty_a,type,
    a: $tType ).

thf(ty_eigen__3,type,
    eigen__3: a ).

thf(ty_eigen__1,type,
    eigen__1: b > c ).

thf(ty_eigen__2,type,
    eigen__2: c ).

thf(ty_eigen__0,type,
    eigen__0: a > b ).

thf(h0,assumption,
    ! [X1: a > $o,X2: a] :
      ( ( X1 @ X2 )
     => ( X1 @ ( eps__0 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(eigendef_eigen__3,definition,
    ( eigen__3
    = ( eps__0
      @ ^ [X1: a] :
          ( ( eigen__1 @ ( eigen__0 @ X1 ) )
         != eigen__2 ) ) ),
    introduced(definition,[new_symbols(definition,[eigen__3])]) ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: c] :
        ~ ! [X2: a] :
            ( ( eigen__1 @ ( eigen__0 @ X2 ) )
           != X1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ( ( eigen__1 @ ( eigen__0 @ X1 ) )
       != eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: b] :
        ( ( eigen__1 @ X1 )
       != eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( eigen__1 @ ( eigen__0 @ eigen__3 ) )
      = eigen__2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(cFN_THM_4_pme,conjecture,
    ! [X1: a > b,X2: b > c] :
      ( ! [X3: c] :
          ~ ! [X4: a] :
              ( ( X2 @ ( X1 @ X4 ) )
             != X3 )
     => ! [X3: c] :
          ~ ! [X4: b] :
              ( ( X2 @ X4 )
             != X3 ) ) ).

thf(h1,negated_conjecture,
    ~ ! [X1: a > b,X2: b > c] :
        ( ! [X3: c] :
            ~ ! [X4: a] :
                ( ( X2 @ ( X1 @ X4 ) )
               != X3 )
       => ! [X3: c] :
            ~ ! [X4: b] :
                ( ( X2 @ X4 )
               != X3 ) ),
    inference(assume_negation,[status(cth)],[cFN_THM_4_pme]) ).

thf(h2,assumption,
    ~ ! [X1: b > c] :
        ( ! [X2: c] :
            ~ ! [X3: a] :
                ( ( X1 @ ( eigen__0 @ X3 ) )
               != X2 )
       => ! [X2: c] :
            ~ ! [X3: b] :
                ( ( X1 @ X3 )
               != X2 ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sP1
     => ! [X1: c] :
          ~ ! [X2: b] :
              ( ( eigen__1 @ X2 )
             != X1 ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ! [X1: c] :
        ~ ! [X2: b] :
            ( ( eigen__1 @ X2 )
           != X1 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP3,
    introduced(assumption,[]) ).

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

thf(2,plain,
    ( sP2
    | sP4 ),
    inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3]) ).

thf(3,plain,
    ( ~ sP1
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0])],[1,2,3,h4,h6]) ).

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__2)],[h5,4,h6]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,5,h4,h5]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,6,h3]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,7,h2]) ).

thf(9,plain,
    $false,
    inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[8,h0]) ).

thf(0,theorem,
    ! [X1: a > b,X2: b > c] :
      ( ! [X3: c] :
          ~ ! [X4: a] :
              ( ( X2 @ ( X1 @ X4 ) )
             != X3 )
     => ! [X3: c] :
          ~ ! [X4: b] :
              ( ( X2 @ X4 )
             != X3 ) ),
    inference(contra,[status(thm),contra(discharge,[h1])],[8,h1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : SEU920^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36  % Computer : n025.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Wed Aug 23 18:53:05 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.22/0.42  % SZS status Theorem
% 0.22/0.42  % Mode: cade22grackle2xfee4
% 0.22/0.42  % Steps: 22
% 0.22/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------