%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEU697^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s

% Computer : n003.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 13:57:22 EDT 2022

% Result   : Theorem 0.11s 0.35s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

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

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

thf(ty_in,type,
    in: $i > $i > $o ).

thf(ty_dpsetconstr,type,
    dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).

thf(def_lam,definition,
    ( lam
    = ( ^ [X1: $i,X2: $i,X3: $i > $i] :
          ( dpsetconstr @ X1 @ X2
          @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ) ).

thf(lam2lamEq,conjecture,
    ! [X1: $i,X2: $i,X3: $i > $i] :
      ( ! [X4: $i] :
          ( ( in @ X4 @ X1 )
         => ( in @ ( X3 @ X4 ) @ X2 ) )
     => ( ( dpsetconstr @ X1 @ X2
          @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
        = ( dpsetconstr @ X1 @ X2
          @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ) ).

thf(h0,negated_conjecture,
    ~ ! [X1: $i,X2: $i,X3: $i > $i] :
        ( ! [X4: $i] :
            ( ( in @ X4 @ X1 )
           => ( in @ ( X3 @ X4 ) @ X2 ) )
       => ( ( dpsetconstr @ X1 @ X2
            @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
          = ( dpsetconstr @ X1 @ X2
            @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ),
    inference(assume_negation,[status(cth)],[lam2lamEq]) ).

thf(h1,assumption,
    ~ ! [X1: $i,X2: $i > $i] :
        ( ! [X3: $i] :
            ( ( in @ X3 @ eigen__0 )
           => ( in @ ( X2 @ X3 ) @ X1 ) )
       => ( ( dpsetconstr @ eigen__0 @ X1
            @ ^ [X3: $i] : ( (=) @ ( X2 @ X3 ) ) )
          = ( dpsetconstr @ eigen__0 @ X1
            @ ^ [X3: $i] : ( (=) @ ( X2 @ X3 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ! [X1: $i > $i] :
        ( ! [X2: $i] :
            ( ( in @ X2 @ eigen__0 )
           => ( in @ ( X1 @ X2 ) @ eigen__1 ) )
       => ( ( dpsetconstr @ eigen__0 @ eigen__1
            @ ^ [X2: $i] : ( (=) @ ( X1 @ X2 ) ) )
          = ( dpsetconstr @ eigen__0 @ eigen__1
            @ ^ [X2: $i] : ( (=) @ ( X1 @ X2 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( ! [X1: $i] :
          ( ( in @ X1 @ eigen__0 )
         => ( in @ ( eigen__2 @ X1 ) @ eigen__1 ) )
     => ( ( dpsetconstr @ eigen__0 @ eigen__1
          @ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) )
        = ( dpsetconstr @ eigen__0 @ eigen__1
          @ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ) ) ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ! [X1: $i] :
      ( ( in @ X1 @ eigen__0 )
     => ( in @ ( eigen__2 @ X1 ) @ eigen__1 ) ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( dpsetconstr @ eigen__0 @ eigen__1
    @ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) )
 != ( dpsetconstr @ eigen__0 @ eigen__1
    @ ^ [X1: $i] : ( (=) @ ( eigen__2 @ X1 ) ) ),
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_negrefl,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[h5]) ).

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

thf(3,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,2,h3]) ).

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

thf(5,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1]) ).

thf(0,theorem,
    ! [X1: $i,X2: $i,X3: $i > $i] :
      ( ! [X4: $i] :
          ( ( in @ X4 @ X1 )
         => ( in @ ( X3 @ X4 ) @ X2 ) )
     => ( ( dpsetconstr @ X1 @ X2
          @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) )
        = ( dpsetconstr @ X1 @ X2
          @ ^ [X4: $i] : ( (=) @ ( X3 @ X4 ) ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[5,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU697^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Mon Jun 20 05:35:59 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.11/0.35  % SZS status Theorem
% 0.11/0.35  % Mode: mode213
% 0.11/0.35  % Inferences: 0
% 0.11/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------