TSTP Solution File: SET583^7 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SET583^7 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n029.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 15:17:35 EDT 2023

% Result   : Theorem 0.21s 0.44s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mu,type,
    mu: $tType ).

thf(ty_qmltpeq,type,
    qmltpeq: mu > mu > $i > $o ).

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

thf(ty_eigen__2,type,
    eigen__2: mu ).

thf(ty_subset,type,
    subset: mu > mu > $i > $o ).

thf(ty_eigen__1,type,
    eigen__1: mu ).

thf(ty_exists_in_world,type,
    exists_in_world: mu > $i > $o ).

thf(sP1,plain,
    ( sP1
  <=> ( ( exists_in_world @ eigen__2 @ eigen__0 )
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ~ ( ( ( qmltpeq @ eigen__2 @ X1 @ eigen__0 )
               => ~ ( ( subset @ eigen__2 @ X1 @ eigen__0 )
                   => ~ ( subset @ X1 @ eigen__2 @ eigen__0 ) ) )
             => ~ ( ~ ( ( subset @ eigen__2 @ X1 @ eigen__0 )
                     => ~ ( subset @ X1 @ eigen__2 @ eigen__0 ) )
                 => ( qmltpeq @ eigen__2 @ X1 @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( ( qmltpeq @ eigen__2 @ eigen__1 @ eigen__0 )
       => ~ ( ( subset @ eigen__2 @ eigen__1 @ eigen__0 )
           => ~ ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) ) )
     => ~ ( ~ ( ( subset @ eigen__2 @ eigen__1 @ eigen__0 )
             => ~ ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) )
         => ( qmltpeq @ eigen__2 @ eigen__1 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( exists_in_world @ eigen__1 @ eigen__0 )
     => ( ( qmltpeq @ eigen__2 @ eigen__1 @ eigen__0 )
       => ( qmltpeq @ eigen__1 @ eigen__2 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

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

thf(sP5,plain,
    ( sP5
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ( ( qmltpeq @ eigen__2 @ X1 @ eigen__0 )
         => ( qmltpeq @ X1 @ eigen__2 @ eigen__0 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( subset @ eigen__2 @ eigen__1 @ eigen__0 )
     => ~ ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( exists_in_world @ eigen__2 @ eigen__0 )
     => sP5 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ( ( qmltpeq @ X2 @ X3 @ X1 )
             => ( qmltpeq @ X3 @ X2 @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( subset @ eigen__1 @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( exists_in_world @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ sP6
     => ( qmltpeq @ eigen__2 @ eigen__1 @ eigen__0 ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ~ ( ( ( qmltpeq @ eigen__2 @ X1 @ eigen__0 )
             => ~ ( ( subset @ eigen__2 @ X1 @ eigen__0 )
                 => ~ ( subset @ X1 @ eigen__2 @ eigen__0 ) ) )
           => ~ ( ~ ( ( subset @ eigen__2 @ X1 @ eigen__0 )
                   => ~ ( subset @ X1 @ eigen__2 @ eigen__0 ) )
               => ( qmltpeq @ eigen__2 @ X1 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( subset @ eigen__2 @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP10
     => ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ~ ( ( ( qmltpeq @ X2 @ X3 @ X1 )
                 => ~ ( ( subset @ X2 @ X3 @ X1 )
                     => ~ ( subset @ X3 @ X2 @ X1 ) ) )
               => ~ ( ~ ( ( subset @ X2 @ X3 @ X1 )
                       => ~ ( subset @ X3 @ X2 @ X1 ) )
                   => ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ( ( qmltpeq @ X1 @ X2 @ eigen__0 )
             => ( qmltpeq @ X2 @ X1 @ eigen__0 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( qmltpeq @ eigen__2 @ eigen__1 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( qmltpeq @ eigen__1 @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ~ ( ( ( qmltpeq @ X1 @ X2 @ eigen__0 )
                 => ~ ( ( subset @ X1 @ X2 @ eigen__0 )
                     => ~ ( subset @ X2 @ X1 @ eigen__0 ) ) )
               => ~ ( ~ ( ( subset @ X1 @ X2 @ eigen__0 )
                       => ~ ( subset @ X2 @ X1 @ eigen__0 ) )
                   => ( qmltpeq @ X1 @ X2 @ eigen__0 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( exists_in_world @ eigen__2 @ eigen__0 ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(def_meq_prop,definition,
    ( meq_prop
    = ( ^ [X1: $i > $o,X2: $i > $o,X3: $i] :
          ( ( X1 @ X3 )
          = ( X2 @ X3 ) ) ) ) ).

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_mbox,definition,
    ( mbox
    = ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
        ! [X4: $i] :
          ( ( (~) @ ( X1 @ X3 @ X4 ) )
          | ( X2 @ X4 ) ) ) ) ).

thf(def_mforall_prop,definition,
    ( mforall_prop
    = ( ^ [X1: ( $i > $o ) > $i > $o,X2: $i] :
        ! [X3: $i > $o] : ( X1 @ X3 @ X2 ) ) ) ).

thf(def_mtrue,definition,
    ( mtrue
    = ( ^ [X1: $i] : $true ) ) ).

thf(def_mfalse,definition,
    ( mfalse
    = ( mnot @ mtrue ) ) ).

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

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

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

thf(def_mequiv,definition,
    ( mequiv
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimplies @ X1 @ X2 ) @ ( mimplies @ X2 @ X1 ) ) ) ) ).

thf(def_mxor,definition,
    ( mxor
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mnot @ ( mequiv @ X1 @ X2 ) ) ) ) ).

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: $i > $i > $o,X2: $i > $o] : ( mnot @ ( mbox @ X1 @ ( mnot @ X2 ) ) ) ) ) ).

thf(def_mforall_ind,definition,
    ( mforall_ind
    = ( ^ [X1: mu > $i > $o,X2: $i] :
        ! [X3: mu] :
          ( ^ [X4: $o,X5: $o] :
              ( X4
             => X5 )
          @ ( exists_in_world @ X3 @ X2 )
          @ ( X1 @ X3 @ X2 ) ) ) ) ).

thf(def_mexists_ind,definition,
    ( mexists_ind
    = ( ^ [X1: mu > $i > $o] :
          ( mnot
          @ ( mforall_ind
            @ ^ [X2: mu] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).

thf(def_mexists_prop,definition,
    ( mexists_prop
    = ( ^ [X1: ( $i > $o ) > $i > $o] :
          ( mnot
          @ ( mforall_prop
            @ ^ [X2: $i > $o] : ( mnot @ ( X1 @ X2 ) ) ) ) ) ) ).

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

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

thf(def_mserial,definition,
    ( mserial
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
        ? [X3: $i] : ( X1 @ X2 @ X3 ) ) ) ).

thf(def_mtransitive,definition,
    ( mtransitive
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X3 @ X4 ) )
          @ ( X1 @ X2 @ X4 ) ) ) ) ).

thf(def_meuclidean,definition,
    ( meuclidean
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( X1 @ X3 @ X4 ) ) ) ) ).

thf(def_mpartially_functional,definition,
    ( mpartially_functional
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( X3 = X4 ) ) ) ) ).

thf(def_mfunctional,definition,
    ( mfunctional
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
        ? [X3: $i] :
          ( ( X1 @ X2 @ X3 )
          & ! [X4: $i] :
              ( ^ [X5: $o,X6: $o] :
                  ( X5
                 => X6 )
              @ ( X1 @ X2 @ X4 )
              @ ( X3 = X4 ) ) ) ) ) ).

thf(def_mweakly_dense,definition,
    ( mweakly_dense
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( X1 @ X2 @ X3 )
          @ ? [X5: $i] :
              ( ( X1 @ X2 @ X5 )
              & ( X1 @ X5 @ X3 ) ) ) ) ) ).

thf(def_mweakly_connected,definition,
    ( mweakly_connected
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ( ( X1 @ X3 @ X4 )
            | ( X3 = X4 )
            | ( X1 @ X4 @ X3 ) ) ) ) ) ).

thf(def_mweakly_directed,definition,
    ( mweakly_directed
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ^ [X5: $o,X6: $o] :
              ( X5
             => X6 )
          @ ( ( X1 @ X2 @ X3 )
            & ( X1 @ X2 @ X4 ) )
          @ ? [X5: $i] :
              ( ( X1 @ X3 @ X5 )
              & ( X1 @ X4 @ X5 ) ) ) ) ) ).

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

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

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

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

thf(def_mbox_s4,definition,
    ( mbox_s4
    = ( ^ [X1: $i > $o,X2: $i] :
        ! [X3: $i] :
          ( ( (~) @ ( rel_s4 @ X2 @ X3 ) )
          | ( X1 @ X3 ) ) ) ) ).

thf(def_mdia_s4,definition,
    ( mdia_s4
    = ( ^ [X1: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X1 ) ) ) ) ) ).

thf(prove_extensionality,conjecture,
    ! [X1: $i,X2: mu] :
      ( ( exists_in_world @ X2 @ X1 )
     => ! [X3: mu] :
          ( ( exists_in_world @ X3 @ X1 )
         => ( ~ ( ( subset @ X2 @ X3 @ X1 )
               => ~ ( subset @ X3 @ X2 @ X1 ) )
           => ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: mu] :
        ( ( exists_in_world @ X2 @ X1 )
       => ! [X3: mu] :
            ( ( exists_in_world @ X3 @ X1 )
           => ( ~ ( ( subset @ X2 @ X3 @ X1 )
                 => ~ ( subset @ X3 @ X2 @ X1 ) )
             => ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ),
    inference(assume_negation,[status(cth)],[prove_extensionality]) ).

thf(h1,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ! [X2: mu] :
            ( ( exists_in_world @ X2 @ eigen__0 )
           => ( ~ ( ( subset @ X1 @ X2 @ eigen__0 )
                 => ~ ( subset @ X2 @ X1 @ eigen__0 ) )
             => ( qmltpeq @ X1 @ X2 @ eigen__0 ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP10
     => ! [X1: mu] :
          ( ( exists_in_world @ X1 @ eigen__0 )
         => ( ~ ( ( subset @ eigen__1 @ X1 @ eigen__0 )
               => ~ ( subset @ X1 @ eigen__1 @ eigen__0 ) )
           => ( qmltpeq @ eigen__1 @ X1 @ eigen__0 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP10,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: mu] :
        ( ( exists_in_world @ X1 @ eigen__0 )
       => ( ~ ( ( subset @ eigen__1 @ X1 @ eigen__0 )
             => ~ ( subset @ X1 @ eigen__1 @ eigen__0 ) )
         => ( qmltpeq @ eigen__1 @ X1 @ eigen__0 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ~ ( sP20
     => ( ~ ( sP9
           => ~ sP13 )
       => sP18 ) ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP20,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( ~ ( sP9
         => ~ sP13 )
     => sP18 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( sP9
     => ~ sP13 ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ sP18,
    introduced(assumption,[]) ).

thf(h10,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP13,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP6
    | ~ sP13
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP11
    | sP6
    | sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP14
    | ~ sP10
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP12
    | sP14 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP1
    | ~ sP20
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP19
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP4
    | ~ sP17
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP3
    | ~ sP10
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP5
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP7
    | ~ sP20
    | sP5 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP16
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP8
    | sP16 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP15
    | sP19 ),
    inference(all_rule,[status(thm)],]) ).

thf(equal_defn,axiom,
    sP15 ).

thf(symmetry,axiom,
    sP8 ).

thf(15,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h3,h6,h10,h11,h9,equal_defn,symmetry]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h10,h11])],[h8,15,h10,h11]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h8,h9])],[h7,16,h8,h9]) ).

thf(18,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,17,h6,h7]) ).

thf(19,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,18,h5]) ).

thf(20,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,19,h3,h4]) ).

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,20,h2]) ).

thf(22,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,21,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: mu] :
      ( ( exists_in_world @ X2 @ X1 )
     => ! [X3: mu] :
          ( ( exists_in_world @ X3 @ X1 )
         => ( ~ ( ( subset @ X2 @ X3 @ X1 )
               => ~ ( subset @ X3 @ X2 @ X1 ) )
           => ( qmltpeq @ X2 @ X3 @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[22,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET583^7 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.35  % Computer : n029.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 : Sat Aug 26 15:35:40 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 0.21/0.44  % SZS status Theorem
% 0.21/0.44  % Mode: cade22grackle2xfee4
% 0.21/0.44  % Steps: 307
% 0.21/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------