%------------------------------------------------------------------------------
% File     : Satallax---3.5
% Problem  : SYO078^5 : 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 : n023.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 19:30:11 EDT 2022

% Result   : Theorem 0.20s 0.36s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_cP,type,
    cP: $o ).

thf(ty_cR,type,
    cR: $o ).

thf(ty_cQ,type,
    cQ: $o ).

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

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

thf(sP3,plain,
    ( sP3
  <=> cR ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(cTHM49,conjecture,
    ( ~ ( ( sP1 != sP2 )
       => ( sP2 = sP3 ) )
   => ( sP1 = sP3 ) ) ).

thf(h0,negated_conjecture,
    ~ ( ~ ( ( sP1 != sP2 )
         => ( sP2 = sP3 ) )
     => ( sP1 = sP3 ) ),
    inference(assume_negation,[status(cth)],[cTHM49]) ).

thf(h1,assumption,
    ~ ( ( sP1 != sP2 )
     => ( sP2 = sP3 ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP1 != sP3,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP1 != sP2,
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP2 != sP3,
    introduced(assumption,[]) ).

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

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

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

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

thf(h9,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h10,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h5,h9,h6,h9,h5,h6,h3,h4,h1,h2,h0])],[h6,h6]) ).

thf(2,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h10,h6,h9,h5,h6,h3,h4,h1,h2,h0])],[h10,h9]) ).

thf(3,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h6,h9,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h9]),tab_be(discharge,[h7,h10])],[h2,1,2,h5,h9,h7,h10]) ).

thf(4,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h5,h9,h8,h10,h5,h6,h3,h4,h1,h2,h0])],[h10,h9]) ).

thf(5,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h10,h8,h10,h5,h6,h3,h4,h1,h2,h0])],[h5,h7]) ).

thf(6,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h8,h10,h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h9]),tab_be(discharge,[h7,h10])],[h2,4,5,h5,h9,h7,h10]) ).

thf(7,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_be(discharge,[h6,h9]),tab_be(discharge,[h8,h10])],[h4,3,6,h6,h9,h8,h10]) ).

thf(8,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h5,h9,h6,h9,h7,h8,h3,h4,h1,h2,h0])],[h5,h7]) ).

thf(9,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h10,h6,h9,h7,h8,h3,h4,h1,h2,h0])],[h10,h9]) ).

thf(10,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h6,h9,h7,h8,h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h9]),tab_be(discharge,[h7,h10])],[h2,8,9,h5,h9,h7,h10]) ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h5,h9,h8,h10,h7,h8,h3,h4,h1,h2,h0])],[h10,h9]) ).

thf(12,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h10,h8,h10,h7,h8,h3,h4,h1,h2,h0])],[h8,h8]) ).

thf(13,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h8,h10,h7,h8,h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h9]),tab_be(discharge,[h7,h10])],[h2,11,12,h5,h9,h7,h10]) ).

thf(14,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h7,h8,h3,h4,h1,h2,h0]),tab_be(discharge,[h6,h9]),tab_be(discharge,[h8,h10])],[h4,10,13,h6,h9,h8,h10]) ).

thf(15,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_be(discharge,[h5,h6]),tab_be(discharge,[h7,h8])],[h3,7,14,h5,h6,h7,h8]) ).

thf(16,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,15,h3,h4]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,16,h1,h2]) ).

thf(0,theorem,
    ( ~ ( ( sP1 != sP2 )
       => ( sP2 = sP3 ) )
   => ( sP1 = sP3 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[17,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SYO078^5 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n023.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 : Sat Jul  9 14:23:10 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.36  % SZS status Theorem
% 0.20/0.36  % Mode: mode213
% 0.20/0.36  % Inferences: 0
% 0.20/0.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------