%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : SYO088^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n004.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  : 300s
% DateTime : Fri Sep  1 04:45:10 EDT 2023

% Result   : Theorem 0.21s 0.39s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_s,type,
    s: $o ).

thf(ty_a,type,
    a: $o ).

thf(ty_c,type,
    c: $o ).

thf(ty_b,type,
    b: $o ).

thf(ty_p,type,
    p: $o ).

thf(ty_t,type,
    t: $o ).

thf(ty_d,type,
    d: $o ).

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

thf(sP2,plain,
    ( sP2
  <=> ( a
     => ~ b ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ sP2
     => ( c
       => ~ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> p ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP4
     => ~ ( ~ ( ~ sP2
             => ~ c )
         => ~ d ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> c ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ~ sP2
     => ~ sP6 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( sP3
     => ~ sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> t ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( sP6
     => ~ d ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> d ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ~ sP7
     => ~ sP11 ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( sP1
     => sP9 ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( sP5
     => sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(cARR_COM_DMG5,conjecture,
    ( sP14
   => ( sP8
     => sP13 ) ) ).

thf(h0,negated_conjecture,
    ~ ( sP14
     => ( sP8
       => sP13 ) ),
    inference(assume_negation,[status(cth)],[cARR_COM_DMG5]) ).

thf(h1,assumption,
    sP14,
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( sP8
     => sP13 ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP8,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP13,
    introduced(assumption,[]) ).

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

thf(h6,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | sP2
    | ~ sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP12
    | sP7
    | ~ sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP5
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP5
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP13
    | ~ sP1
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP14
    | ~ sP5
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP10
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( sP10
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP3
    | ~ sP10 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( sP3
    | ~ sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP8
    | ~ sP3
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,7,8,9,10,11,h1,h3,h5,h6]) ).

thf(13,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[h4,12,h5,h6]) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h2,13,h3,h4]) ).

thf(15,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[h0,14,h1,h2]) ).

thf(0,theorem,
    ( sP14
   => ( sP8
     => sP13 ) ),
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SYO088^5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n004.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sat Aug 26 06:58:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.21/0.39  % SZS status Theorem
% 0.21/0.39  % Mode: cade22grackle2xfee4
% 0.21/0.39  % Steps: 20
% 0.21/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------