%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : NUM635^2 : TPTP v8.1.2. Released v3.7.0.
% 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 : Thu Aug 31 11:40:01 EDT 2023

% Result   : Theorem 0.17s 0.36s
% Output   : Proof 0.17s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_succ,type,
    succ: $i > $i ).

thf(ty_eigen__0,type,
    eigen__0: $i ).

thf(ty_eigen__1,type,
    eigen__1: $i ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: $i,X2: $i] :
        ( ( ( succ @ X1 )
          = ( succ @ X2 ) )
       => ( X1 = X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: $i] :
        ( ( ( succ @ eigen__0 )
          = ( succ @ X1 ) )
       => ( eigen__0 = X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0 = eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( ( succ @ eigen__0 )
        = ( succ @ eigen__1 ) )
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( succ @ eigen__0 )
      = ( succ @ eigen__1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(satz1,conjecture,
    ! [X1: $i,X2: $i] :
      ( ( X1 != X2 )
     => ( ( succ @ X1 )
       != ( succ @ X2 ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: $i] :
        ( ( X1 != X2 )
       => ( ( succ @ X1 )
         != ( succ @ X2 ) ) ),
    inference(assume_negation,[status(cth)],[satz1]) ).

thf(h1,assumption,
    ~ ! [X1: $i] :
        ( ( eigen__0 != X1 )
       => ( ( succ @ eigen__0 )
         != ( succ @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( ~ sP3
     => ~ sP5 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP5,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP5
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(succ_injective,axiom,
    sP1 ).

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

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,4,h3,h4]) ).

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,5,h2]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,6,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i] :
      ( ( X1 != X2 )
     => ( ( succ @ X1 )
       != ( succ @ X2 ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM635^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.35  % Computer : n026.cluster.edu
% 0.17/0.35  % Model    : x86_64 x86_64
% 0.17/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35  % Memory   : 8042.1875MB
% 0.17/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35  % CPULimit : 300
% 0.17/0.35  % WCLimit  : 300
% 0.17/0.35  % DateTime : Fri Aug 25 12:57:47 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.17/0.36  % SZS status Theorem
% 0.17/0.36  % Mode: cade22grackle2xfee4
% 0.17/0.36  % Steps: 22
% 0.17/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------