%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SEV232^5 : TPTP v8.1.0. Released v4.0.0.
% 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 18:05:28 EDT 2022

% Result   : Theorem 0.13s 0.35s
% Output   : Proof 0.13s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cS,type,
    cS: ( ( $i > $o ) > $o ) > ( $i > $o ) > $o ).

thf(ty_c0,type,
    c0: ( $i > $o ) > $o ).

thf(cX6007_pme,conjecture,
    ( ( ^ [X1: ( $i > $o ) > $o] :
        ! [X2: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ( ( X2 @ c0 )
             => ~ ! [X3: ( $i > $o ) > $o] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( cS @ X3 ) ) ) )
         => ( X2 @ X1 ) ) )
    = ( ^ [X1: ( $i > $o ) > $o] :
        ! [X2: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ( ( X2 @ c0 )
             => ~ ! [X3: ( $i > $o ) > $o] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( cS @ X3 ) ) ) )
         => ( X2 @ X1 ) ) ) ) ).

thf(h0,negated_conjecture,
    ( ^ [X1: ( $i > $o ) > $o] :
      ! [X2: ( ( $i > $o ) > $o ) > $o] :
        ( ~ ( ( X2 @ c0 )
           => ~ ! [X3: ( $i > $o ) > $o] :
                  ( ( X2 @ X3 )
                 => ( X2 @ ( cS @ X3 ) ) ) )
       => ( X2 @ X1 ) ) )
 != ( ^ [X1: ( $i > $o ) > $o] :
      ! [X2: ( ( $i > $o ) > $o ) > $o] :
        ( ~ ( ( X2 @ c0 )
           => ~ ! [X3: ( $i > $o ) > $o] :
                  ( ( X2 @ X3 )
                 => ( X2 @ ( cS @ X3 ) ) ) )
       => ( X2 @ X1 ) ) ),
    inference(assume_negation,[status(cth)],[cX6007_pme]) ).

thf(1,plain,
    $false,
    inference(tab_negrefl,[status(thm),assumptions([h0])],[h0]) ).

thf(0,theorem,
    ( ( ^ [X1: ( $i > $o ) > $o] :
        ! [X2: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ( ( X2 @ c0 )
             => ~ ! [X3: ( $i > $o ) > $o] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( cS @ X3 ) ) ) )
         => ( X2 @ X1 ) ) )
    = ( ^ [X1: ( $i > $o ) > $o] :
        ! [X2: ( ( $i > $o ) > $o ) > $o] :
          ( ~ ( ( X2 @ c0 )
             => ~ ! [X3: ( $i > $o ) > $o] :
                    ( ( X2 @ X3 )
                   => ( X2 @ ( cS @ X3 ) ) ) )
         => ( X2 @ X1 ) ) ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEV232^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun 28 14:42:35 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % SZS status Theorem
% 0.13/0.35  % Mode: mode213
% 0.13/0.35  % Inferences: 0
% 0.13/0.35  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------