TSTP Solution File: SEU458^1 by Satallax---3.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU458^1 : TPTP v8.1.0. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n022.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 : Tue Jul 19 13:52:16 EDT 2022

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

% Comments : 
%------------------------------------------------------------------------------
thf(ty_eigen__2,type,
    eigen__2: $i ).

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

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

thf(sP1,plain,
    ( sP1
  <=> ( eigen__0 @ eigen__2 @ eigen__1 ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

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

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

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

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

thf(def_infl,definition,
    ( infl
    = ( ^ [X1: ( $i > $i > $o ) > $i > $i > $o] :
        ! [X2: $i > $i > $o] : ( subrel @ X2 @ ( X1 @ X2 ) ) ) ) ).

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

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

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

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

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

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

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

thf(def_sc,definition,
    ( sc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ( ~ ( X1 @ X3 @ X2 )
         => ( X1 @ X2 @ X3 ) ) ) ) ).

thf(def_trans,definition,
    ( trans
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X3 )
             => ~ ( X1 @ X3 @ X4 ) )
         => ( X1 @ X2 @ X4 ) ) ) ) ).

thf(def_tc,definition,
    ( tc
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
        ! [X4: $i > $i > $o] :
          ( ~ ( ( trans @ X4 )
             => ~ ( subrel @ X1 @ X4 ) )
         => ( X4 @ X2 @ X3 ) ) ) ) ).

thf(def_trc,definition,
    ( trc
    = ( ^ [X1: $i > $i > $o] : ( rc @ ( tc @ X1 ) ) ) ) ).

thf(def_trsc,definition,
    ( trsc
    = ( ^ [X1: $i > $i > $o] : ( sc @ ( rc @ ( tc @ X1 ) ) ) ) ) ).

thf(def_po,definition,
    ( po
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ~ ( ( refl @ X1 )
               => ~ ( antisymm @ X1 ) )
           => ~ ( trans @ X1 ) ) ) ) ).

thf(def_so,definition,
    ( so
    = ( ^ [X1: $i > $i > $o] :
          ~ ( ( asymm @ X1 )
           => ~ ( trans @ X1 ) ) ) ) ).

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

thf(def_term,definition,
    ( term
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ~ ! [X3: $i] :
                ~ ( X2 @ X3 )
         => ~ ! [X3: $i] :
                ( ( X2 @ X3 )
               => ~ ! [X4: $i] :
                      ( ( X2 @ X4 )
                     => ~ ( X1 @ X3 @ X4 ) ) ) ) ) ) ).

thf(def_ind,definition,
    ( ind
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i > $o] :
          ( ! [X3: $i] :
              ( ! [X4: $i] :
                  ( ( tc @ X1 @ X3 @ X4 )
                 => ( X2 @ X4 ) )
             => ( X2 @ X3 ) )
         => ( !! @ X2 ) ) ) ) ).

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

thf(def_nfof,definition,
    ( nfof
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ~ ( ( trc @ X1 @ X3 @ X2 )
           => ~ ( innf @ X1 @ X2 ) ) ) ) ).

thf(def_norm,definition,
    ( norm
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i] :
          ~ ! [X3: $i] :
              ~ ( nfof @ X1 @ X3 @ X2 ) ) ) ).

thf(def_join,definition,
    ( join
    = ( ^ [X1: $i > $i > $o,X2: $i,X3: $i] :
          ~ ! [X4: $i] :
              ( ( trc @ X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X3 @ X4 ) ) ) ) ).

thf(def_lconfl,definition,
    ( lconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X4 )
             => ~ ( X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_sconfl,definition,
    ( sconfl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_confl,definition,
    ( confl
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i,X4: $i] :
          ( ~ ( ( trc @ X1 @ X2 @ X4 )
             => ~ ( trc @ X1 @ X2 @ X3 ) )
         => ( join @ X1 @ X4 @ X3 ) ) ) ) ).

thf(def_cr,definition,
    ( cr
    = ( ^ [X1: $i > $i > $o] :
        ! [X2: $i,X3: $i] :
          ( ( trsc @ X1 @ X2 @ X3 )
         => ( join @ X1 @ X2 @ X3 ) ) ) ) ).

thf(symmetric_closure_op_is_idempotent,conjecture,
    ! [X1: $i > $i > $o] :
      ( ( ^ [X2: $i,X3: $i] :
            ( ~ ( ~ ( X1 @ X2 @ X3 )
               => ( X1 @ X3 @ X2 ) )
           => ( ~ ( X1 @ X3 @ X2 )
             => ( X1 @ X2 @ X3 ) ) ) )
      = ( ^ [X2: $i,X3: $i] :
            ( ~ ( X1 @ X3 @ X2 )
           => ( X1 @ X2 @ X3 ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i > $i > $o] :
        ( ( ^ [X2: $i,X3: $i] :
              ( ~ ( ~ ( X1 @ X2 @ X3 )
                 => ( X1 @ X3 @ X2 ) )
             => ( ~ ( X1 @ X3 @ X2 )
               => ( X1 @ X2 @ X3 ) ) ) )
        = ( ^ [X2: $i,X3: $i] :
              ( ~ ( X1 @ X3 @ X2 )
             => ( X1 @ X2 @ X3 ) ) ) ),
    inference(assume_negation,[status(cth)],[symmetric_closure_op_is_idempotent]) ).

thf(h1,assumption,
    ( ^ [X1: $i,X2: $i] :
        ( ~ ( ~ ( eigen__0 @ X1 @ X2 )
           => ( eigen__0 @ X2 @ X1 ) )
       => ( ~ ( eigen__0 @ X2 @ X1 )
         => ( eigen__0 @ X1 @ X2 ) ) ) )
 != ( ^ [X1: $i,X2: $i] :
        ( ~ ( eigen__0 @ X2 @ X1 )
       => ( eigen__0 @ X1 @ X2 ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i] :
        ( ( ^ [X2: $i] :
              ( ~ ( ~ ( eigen__0 @ X1 @ X2 )
                 => ( eigen__0 @ X2 @ X1 ) )
             => ( ~ ( eigen__0 @ X2 @ X1 )
               => ( eigen__0 @ X1 @ X2 ) ) ) )
        = ( ^ [X2: $i] :
              ( ~ ( eigen__0 @ X2 @ X1 )
             => ( eigen__0 @ X1 @ X2 ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ( ^ [X1: $i] :
        ( ~ ( ~ ( eigen__0 @ eigen__1 @ X1 )
           => ( eigen__0 @ X1 @ eigen__1 ) )
       => ( ~ ( eigen__0 @ X1 @ eigen__1 )
         => ( eigen__0 @ eigen__1 @ X1 ) ) ) )
 != ( ^ [X1: $i] :
        ( ~ ( eigen__0 @ X1 @ eigen__1 )
       => ( eigen__0 @ eigen__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ! [X1: $i] :
        ( ( ~ ( ~ ( eigen__0 @ eigen__1 @ X1 )
             => ( eigen__0 @ X1 @ eigen__1 ) )
         => ( ~ ( eigen__0 @ X1 @ eigen__1 )
           => ( eigen__0 @ eigen__1 @ X1 ) ) )
        = ( ~ ( eigen__0 @ X1 @ eigen__1 )
         => ( eigen__0 @ eigen__1 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( ~ ( ~ sP2
       => sP1 )
   => ( ~ sP1
     => sP2 ) )
 != ( ~ sP1
   => sP2 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( ~ ( ~ sP2
       => sP1 )
   => ( ~ sP1
     => sP2 ) ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    ( ~ sP1
   => sP2 ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    ~ ( ~ ( ~ sP2
         => sP1 )
     => ( ~ sP1
       => sP2 ) ),
    introduced(assumption,[]) ).

thf(h9,assumption,
    ~ ( ~ sP1
     => sP2 ),
    introduced(assumption,[]) ).

thf(h10,assumption,
    ( ~ sP2
   => sP1 ),
    introduced(assumption,[]) ).

thf(h11,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(h12,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h13,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h14,assumption,
    ~ sP2,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h14,h11,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).

thf(2,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,1,h13,h14]) ).

thf(3,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h14,h12,h10,h6,h7,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).

thf(4,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,3,h13,h14]) ).

thf(5,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h10,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h11]),tab_imp(discharge,[h12])],[h10,2,4,h11,h12]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h14,h12,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).

thf(7,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h12,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,6,h13,h14]) ).

thf(8,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h13,h14,h11,h7,h6,h7,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h7,8,h13,h14]) ).

thf(10,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h7,h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h11])],[h7,7,9,h12,h11]) ).

thf(11,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h6,h7,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h7])],[h6,5,10,h10,h7]) ).

thf(h15,assumption,
    ~ ( ~ sP2
     => sP1 ),
    introduced(assumption,[]) ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h12,h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0])],[h12,h13]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h11,h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0])],[h11,h14]) ).

thf(14,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h13,h14,h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_imp(discharge,[h12]),tab_imp(discharge,[h11])],[h9,12,13,h12,h11]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h14,h13,h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h13,h14])],[h9,14,h13,h14]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h15,h9,h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h14,h13])],[h15,15,h14,h13]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h8,h9,h5,h4,h3,h2,h1,h0]),tab_negimp(discharge,[h15,h9])],[h8,16,h15,h9]) ).

thf(18,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h5,h4,h3,h2,h1,h0]),tab_be(discharge,[h6,h7]),tab_be(discharge,[h8,h9])],[h5,11,17,h6,h7,h8,h9]) ).

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

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

thf(21,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,20,h3]) ).

thf(22,plain,
    $false,
    inference(tab_fe,[status(thm),assumptions([h1,h0]),tab_fe(discharge,[h2])],[h1,21,h2]) ).

thf(23,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,22,h1]) ).

thf(0,theorem,
    ! [X1: $i > $i > $o] :
      ( ( ^ [X2: $i,X3: $i] :
            ( ~ ( ~ ( X1 @ X2 @ X3 )
               => ( X1 @ X3 @ X2 ) )
           => ( ~ ( X1 @ X3 @ X2 )
             => ( X1 @ X2 @ X3 ) ) ) )
      = ( ^ [X2: $i,X3: $i] :
            ( ~ ( X1 @ X3 @ X2 )
           => ( X1 @ X2 @ X3 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[23,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU458^1 : TPTP v8.1.0. Released v3.6.0.
% 0.07/0.12  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n022.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 : Sun Jun 19 19:46:31 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: 0
% 0.12/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------