%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP010^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n002.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 : Thu Aug 31 04:00:59 EDT 2023

% Result   : Theorem 0.18s 0.40s
% Output   : Proof 0.18s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_mono_2Ec_2Ebool_2EF,type,
    mono_2Ec_2Ebool_2EF: $o ).

thf(ty_mono_2Ec_2Ebool_2ET,type,
    mono_2Ec_2Ebool_2ET: $o ).

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

thf(sP2,plain,
    ( sP2
  <=> mono_2Ec_2Ebool_2EF ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> mono_2Ec_2Ebool_2ET ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(thm_2Ecardinal_2ECARD__NOT__LE,conjecture,
    ~ sP1 ).

thf(h0,negated_conjecture,
    sP1,
    inference(assume_negation,[status(cth)],[thm_2Ecardinal_2ECARD__NOT__LE]) ).

thf(h1,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP3,
    introduced(assumption,[]) ).

thf(h3,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP3,
    introduced(assumption,[]) ).

thf(h5,assumption,
    ( ~ sP3 = sP2 ),
    introduced(assumption,[]) ).

thf(h6,assumption,
    ( ~ sP2 = sP3 ),
    introduced(assumption,[]) ).

thf(h7,assumption,
    sP2,
    introduced(assumption,[]) ).

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

thf(1,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h8,h2,h4,h7,h5,h6,h1,h2,h0])],[h7,h8]) ).

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

thf(3,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h4,h7,h5,h6,h1,h2,h0]),tab_bq(discharge,[h8,h2]),tab_bq(discharge,[h7,h4])],[h6,1,2,h8,h2,h7,h4]) ).

thf(4,plain,
    ~ sP1,
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h8,h2,h2,h8,h5,h6,h1,h2,h0])],[4,h0]) ).

thf(6,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h4,h2,h8,h5,h6,h1,h2,h0])],[h2,h4]) ).

thf(7,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h2,h8,h5,h6,h1,h2,h0]),tab_bq(discharge,[h8,h2]),tab_bq(discharge,[h7,h4])],[h6,5,6,h8,h2,h7,h4]) ).

thf(8,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h5,h6,h1,h2,h0]),tab_bq(discharge,[h4,h7]),tab_bq(discharge,[h2,h8])],[h5,3,7,h4,h7,h2,h8]) ).

thf(thm_2Ebool_2ENOT__CLAUSES,axiom,
    ~ ( ( ~ sP3 = sP2 )
     => ( ~ sP2 != sP3 ) ) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[thm_2Ebool_2ENOT__CLAUSES,8,h5,h6]) ).

thf(10,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h8,h2,h4,h7,h5,h6,h3,h4,h0])],[h7,h8]) ).

thf(thm_2Ebool_2ETRUTH,axiom,
    sP3 ).

thf(11,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h4,h4,h7,h5,h6,h3,h4,h0])],[thm_2Ebool_2ETRUTH,h4]) ).

thf(12,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h4,h7,h5,h6,h3,h4,h0]),tab_bq(discharge,[h8,h2]),tab_bq(discharge,[h7,h4])],[h6,10,11,h8,h2,h7,h4]) ).

thf(13,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h8,h2,h2,h8,h5,h6,h3,h4,h0])],[h2,h4]) ).

thf(14,plain,
    $false,
    inference(tab_conflict,[status(thm),assumptions([h7,h4,h2,h8,h5,h6,h3,h4,h0])],[h2,h4]) ).

thf(15,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h2,h8,h5,h6,h3,h4,h0]),tab_bq(discharge,[h8,h2]),tab_bq(discharge,[h7,h4])],[h6,13,14,h8,h2,h7,h4]) ).

thf(16,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h5,h6,h3,h4,h0]),tab_bq(discharge,[h4,h7]),tab_bq(discharge,[h2,h8])],[h5,12,15,h4,h7,h2,h8]) ).

thf(17,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h0]),tab_negimp(discharge,[h5,h6])],[thm_2Ebool_2ENOT__CLAUSES,16,h5,h6]) ).

thf(thm_2Ebool_2EREFL__CLAUSE,axiom,
    ( ~ sP1 = sP3 ) ).

thf(18,plain,
    $false,
    inference(tab_bq,[status(thm),assumptions([h0]),tab_bq(discharge,[h1,h2]),tab_bq(discharge,[h3,h4])],[thm_2Ebool_2EREFL__CLAUSE,9,17,h1,h2,h3,h4]) ).

thf(0,theorem,
    ~ sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[18,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ITP010^1 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Aug 27 16:14:49 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  % Mode: cade22grackle2xfee4
% 0.18/0.40  % Steps: 5
% 0.18/0.40  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------