%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO547^1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n028.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  : 600s
% DateTime : Thu Jul 21 19:33:21 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eps,type,
    eps: ( $i > $o ) > $i ).

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

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

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

thf(sP2,plain,
    ( sP2
  <=> ( !! @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( eigen__0
      @ ( eps
        @ ^ [X1: $i] :
            ~ ( eigen__0 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(def_epscomp,definition,
    ( epscomp
    = ( ^ [X1: $i > $o] :
          ( eps
          @ ^ [X2: $i] :
              ~ ( X1 @ X2 ) ) ) ) ).

thf(choicecomp,conjecture,
    ! [X1: $i > $o] :
      ( ~ ( !! @ X1 )
     => ~ ( X1
          @ ( eps
            @ ^ [X2: $i] :
                ~ ( X1 @ X2 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i > $o] :
        ( ~ ( !! @ X1 )
       => ~ ( X1
            @ ( eps
              @ ^ [X2: $i] :
                  ~ ( X1 @ X2 ) ) ) ),
    inference(assume_negation,[status(cth)],[choicecomp]) ).

thf(h1,assumption,
    ~ ( ~ sP2
     => ~ sP3 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

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

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

thf(1,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(choiceax,axiom,
    ! [X1: $i > $o] :
      ( ~ ! [X2: $i] :
            ~ ( X1 @ X2 )
     => ( X1 @ ( eps @ X1 ) ) ) ).

thf(2,plain,
    ( ~ sP3
    | sP2 ),
    inference(choice_rule,[status(thm)],[choiceax]) ).

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

thf(4,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,3,h4]) ).

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

thf(6,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1]) ).

thf(0,theorem,
    ! [X1: $i > $o] :
      ( ~ ( !! @ X1 )
     => ~ ( X1
          @ ( eps
            @ ^ [X2: $i] :
                ~ ( X1 @ X2 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYO547^1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jul  9 07:03:25 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.35  % SZS status Theorem
% 0.12/0.35  % Mode: mode213
% 0.12/0.35  % Inferences: 5
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------