%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SWV435^4 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n024.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 22:49:13 EDT 2023

% Result   : Theorem 0.22s 0.42s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__1,type,
    eigen__1: $i ).

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

thf(ty_rel,type,
    rel: $i > $i > $o ).

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

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

thf(sP2,plain,
    ( sP2
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( a @ eigen__1 )
      = ~ sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( a
      = ( ^ [X1: $i] : ~ sP2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

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

thf(def_mfalse,definition,
    ( mfalse
    = ( ^ [X1: $i] : sP2 ) ) ).

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

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_mimpl,definition,
    ( mimpl
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ ( mnot @ X1 ) @ X2 ) ) ) ).

thf(def_miff,definition,
    ( miff
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mand @ ( mimpl @ X1 @ X2 ) @ ( mimpl @ X2 @ X1 ) ) ) ) ).

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

thf(def_mdia,definition,
    ( mdia
    = ( ^ [X1: $i > $i > $o,X2: $i > $o,X3: $i] :
        ? [X4: $i] :
          ( ( X1 @ X3 @ X4 )
          & ( X2 @ X4 ) ) ) ) ).

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

thf(def_mexists,definition,
    ( mexists
    = ( ^ [X1: individuals > $i > $o,X2: $i] :
        ? [X3: individuals] : ( X1 @ X3 @ X2 ) ) ) ).

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_icl_atom,definition,
    ( icl_atom
    = ( ^ [X1: $i > $o] : ( mbox @ rel @ X1 ) ) ) ).

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

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

thf(def_icl_or,definition,
    ( icl_or
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mor @ X1 @ X2 ) ) ) ).

thf(def_icl_impl,definition,
    ( icl_impl
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mimpl @ X1 @ X2 ) ) ) ) ).

thf(def_icl_true,definition,
    icl_true = mtrue ).

thf(def_icl_false,definition,
    icl_false = mfalse ).

thf(def_icl_says,definition,
    ( icl_says
    = ( ^ [X1: $i > $o,X2: $i > $o] : ( mbox @ rel @ ( mor @ X1 @ X2 ) ) ) ) ).

thf(def_iclval,definition,
    ( iclval
    = ( ^ [X1: $i > $o] : ( mvalid @ X1 ) ) ) ).

thf(untrust,conjecture,
    ! [X1: $i,X2: $i] :
      ( ( rel @ X1 @ X2 )
     => ( a @ X2 ) ) ).

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

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

thf(h2,assumption,
    ~ ( ( rel @ eigen__0 @ eigen__1 )
     => sP5 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    rel @ eigen__0 @ eigen__1,
    introduced(assumption,[]) ).

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

thf(1,plain,
    ~ sP2,
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP3
    | sP5
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP4
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(ax1,axiom,
    sP4 ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h2,h1,h0])],[1,2,3,4,h4,ax1]) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,5,h3,h4]) ).

thf(7,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,6,h2]) ).

thf(8,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i] :
      ( ( rel @ X1 @ X2 )
     => ( a @ X2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[8,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWV435^4 : TPTP v8.1.2. Released v3.6.0.
% 0.08/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35  % Computer : n024.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Tue Aug 29 04:10:23 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.22/0.42  % SZS status Theorem
% 0.22/0.42  % Mode: cade22grackle2xfee4
% 0.22/0.42  % Steps: 15
% 0.22/0.42  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------