%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO232^5 : 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 : 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  : 600s
% DateTime : Thu Jul 21 19:31:00 EDT 2022

% Result   : Theorem 0.11s 0.34s
% Output   : Proof 0.11s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

thf(ty_cP,type,
    cP: a > $o ).

thf(ty_y,type,
    y: $i ).

thf(ty_cB,type,
    cB: $o ).

thf(ty_x,type,
    x: a ).

thf(sP1,plain,
    ( sP1
  <=> ( cP @ x ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a] :
        ~ ( cP @ X1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(cADDHYP4,conjecture,
    ( ( ( y = y )
     => cB )
   => ( sP1
     => ~ sP2 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ( ( y = y )
       => cB )
     => ( sP1
       => ~ sP2 ) ),
    inference(assume_negation,[status(cth)],[cADDHYP4]) ).

thf(h1,assumption,
    ( ( y = y )
   => cB ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP1
     => ~ sP2 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    y != y,
    introduced(assumption,[]) ).

thf(h4,assumption,
    cB,
    introduced(assumption,[]) ).

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

thf(h5,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h6,assumption,
    sP2,
    introduced(assumption,[]) ).

thf(2,plain,
    ( ~ sP2
    | ~ sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h4,h1,h2,h0])],[2,h5,h6]) ).

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

thf(5,plain,
    $false,
    inference(tab_imp,[status(thm),assumptions([h1,h2,h0]),tab_imp(discharge,[h3]),tab_imp(discharge,[h4])],[h1,1,4,h3,h4]) ).

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

thf(0,theorem,
    ( ( ( y = y )
     => cB )
   => ( sP1
     => ~ sP2 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYO232^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32  % Computer : n029.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Sat Jul  9 02:29:30 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.11/0.34  % SZS status Theorem
% 0.11/0.34  % Mode: mode213
% 0.11/0.34  % Inferences: 2
% 0.11/0.34  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------