%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO058^4 : 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 : Fri Sep  1 04:44:57 EDT 2023

% Result   : Theorem 0.12s 0.39s
% Output   : Proof 0.12s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__0,type,
    eigen__0: $i ).

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

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

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

thf(def_mnot,definition,
    ( mnot
    = ( ^ [X1: $i > $o,X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_mor,definition,
    ( mor
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          | ( X2 @ X3 ) ) ) ) ).

thf(def_mand,definition,
    ( mand
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          & ( X2 @ X3 ) ) ) ) ).

thf(def_mimplies,definition,
    ( mimplies
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).

thf(def_mbox_s4,definition,
    ( mbox_s4
    = ( ^ [X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( irel @ X2 @ X3 )
          @ ( X1 @ X3 ) ) ) ) ).

thf(def_iatom,definition,
    ( iatom
    = ( ^ [X1: $i > $o] : X1 ) ) ).

thf(def_inot,definition,
    ( inot
    = ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ X1 ) ) ) ) ).

thf(def_itrue,definition,
    ( itrue
    = ( ^ [X1: $i] : $true ) ) ).

thf(def_ifalse,definition,
    ( ifalse
    = ( inot @ itrue ) ) ).

thf(def_iand,definition,
    ( iand
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ X1 @ X2 ) ) ) ).

thf(def_ior,definition,
    ( ior
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).

thf(def_iimplies,definition,
    ( iimplies
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mimplies @ ( mbox_s4 @ X1 ) @ ( mbox_s4 @ X2 ) ) ) ) ).

thf(def_iimplied,definition,
    ( iimplied
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( iimplies @ X2 @ X1 ) ) ) ).

thf(def_iequiv,definition,
    ( iequiv
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( iand @ ( iimplies @ X1 @ X2 ) @ ( iimplies @ X2 @ X1 ) ) ) ) ).

thf(def_ixor,definition,
    ( ixor
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( inot @ ( iequiv @ X1 @ X2 ) ) ) ) ).

thf(def_ivalid,definition,
    ( ivalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] : ( X1 @ X2 ) ) ) ).

thf(def_isatisfiable,definition,
    ( isatisfiable
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] : ( X1 @ X2 ) ) ) ).

thf(def_icountersatisfiable,definition,
    ( icountersatisfiable
    = ( ^ [X1: $i > $o] :
        ? [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(def_iinvalid,definition,
    ( iinvalid
    = ( ^ [X1: $i > $o] :
        ! [X2: $i] : ( (~) @ ( X1 @ X2 ) ) ) ) ).

thf(con,conjecture,
    sP1 ).

thf(h0,negated_conjecture,
    ~ sP1,
    inference(assume_negation,[status(cth)],[con]) ).

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

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

thf(axiom1,axiom,
    sP1 ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,h1,axiom1]) ).

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,2,h1]) ).

thf(0,theorem,
    sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO058^4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n025.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sat Aug 26 05:30:22 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.39  % SZS status Theorem
% 0.12/0.39  % Mode: cade22grackle2xfee4
% 0.12/0.39  % Steps: 7
% 0.12/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------