TSTP Solution File: SYO171^5 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO171^5 : 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 : n026.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 : Fri Sep  1 04:45:43 EDT 2023

% Result   : Theorem 0.21s 0.38s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_g,type,
    g: $i > $i > $o ).

thf(ty_f,type,
    f: $i > $i ).

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

thf(sP1,plain,
    ( sP1
  <=> ( ~ ( g @ a @ a )
     => ( g @ a @ ( f @ a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( g @ a @ X1 )
       => ~ ( g @ X1 @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: $i] :
        ( ~ ( g @ X1 @ a )
       => ( g @ ( f @ X1 ) @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ~ ( g @ a @ a )
     => ( g @ ( f @ a ) @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( g @ a @ ( f @ a ) )
     => ~ ( g @ ( f @ a ) @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( g @ a @ ( f @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( g @ a @ a ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP7
     => ~ sP7 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: $i,X2: $i] :
        ( ( g @ X1 @ X2 )
       => ~ ( g @ X2 @ a ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( g @ ( f @ a ) @ a ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: $i] :
        ( ~ ( g @ X1 @ a )
       => ( g @ X1 @ ( f @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(cSYN031_1,conjecture,
    ( ~ ( ~ ( ~ ( sP3
               => ~ sP11 )
           => ~ ! [X1: $i,X2: $i] :
                  ( ( g @ X1 @ X2 )
                 => ( g @ ( f @ X2 ) @ X2 ) ) )
       => ~ ! [X1: $i,X2: $i] :
              ( ( g @ X1 @ X2 )
             => ( g @ X2 @ ( f @ X2 ) ) ) )
   => ~ sP9 ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ~ ( ~ ( sP3
                 => ~ sP11 )
             => ~ ! [X1: $i,X2: $i] :
                    ( ( g @ X1 @ X2 )
                   => ( g @ ( f @ X2 ) @ X2 ) ) )
         => ~ ! [X1: $i,X2: $i] :
                ( ( g @ X1 @ X2 )
               => ( g @ X2 @ ( f @ X2 ) ) ) )
     => ~ sP9 ),
    inference(assume_negation,[status(cth)],[cSYN031_1]) ).

thf(h1,assumption,
    ~ ( ~ ( ~ ( sP3
             => ~ sP11 )
         => ~ ! [X1: $i,X2: $i] :
                ( ( g @ X1 @ X2 )
               => ( g @ ( f @ X2 ) @ X2 ) ) )
     => ~ ! [X1: $i,X2: $i] :
            ( ( g @ X1 @ X2 )
           => ( g @ X2 @ ( f @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ~ ( sP3
         => ~ sP11 )
     => ~ ! [X1: $i,X2: $i] :
            ( ( g @ X1 @ X2 )
           => ( g @ ( f @ X2 ) @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: $i,X2: $i] :
      ( ( g @ X1 @ X2 )
     => ( g @ X2 @ ( f @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP3
     => ~ sP11 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ! [X1: $i,X2: $i] :
      ( ( g @ X1 @ X2 )
     => ( g @ ( f @ X2 ) @ X2 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h8,assumption,
    sP11,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP6
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP8
    | ~ sP7
    | ~ sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP2
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP1
    | sP7
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP7
    | sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP9
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP11
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,h7,h8,h2]) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[h5,10,h7,h8]) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h3,11,h5,h6]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,12,h3,h4]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,13,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ~ ( ~ ( sP3
               => ~ sP11 )
           => ~ ! [X1: $i,X2: $i] :
                  ( ( g @ X1 @ X2 )
                 => ( g @ ( f @ X2 ) @ X2 ) ) )
       => ~ ! [X1: $i,X2: $i] :
              ( ( g @ X1 @ X2 )
             => ( g @ X2 @ ( f @ X2 ) ) ) )
   => ~ sP9 ),
    inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13  % Problem  : SYO171^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.36  % Computer : n026.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Sat Aug 26 06:30:18 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 0.21/0.38  % SZS status Theorem
% 0.21/0.38  % Mode: cade22grackle2xfee4
% 0.21/0.38  % Steps: 33
% 0.21/0.38  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------