%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : CSR153^1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n022.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 : Wed Aug 30 21:33:45 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_brother_THFTYPE_IiioI,type,
    brother_THFTYPE_IiioI: $i > $i > $o ).

thf(ty_sister_THFTYPE_IiioI,type,
    sister_THFTYPE_IiioI: $i > $i > $o ).

thf(ty_lMary_THFTYPE_i,type,
    lMary_THFTYPE_i: $i ).

thf(ty_lSue_THFTYPE_i,type,
    lSue_THFTYPE_i: $i ).

thf(ty_lBill_THFTYPE_i,type,
    lBill_THFTYPE_i: $i ).

thf(ty_lBob_THFTYPE_i,type,
    lBob_THFTYPE_i: $i ).

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

thf(sP2,plain,
    ( sP2
  <=> ( ( lBob_THFTYPE_i != lBill_THFTYPE_i )
     => sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ~ sP2
     => ! [X1: $i,X2: $i] : ( X1 != X2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: $i,X2: $i] : ( X1 != X2 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: $i] : ( lMary_THFTYPE_i != X1 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: $i > $i > $o] :
        ( ~ ( ( X1 @ lBob_THFTYPE_i @ lBill_THFTYPE_i )
           => ~ ( X1 @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) )
       => ! [X2: $i,X3: $i] : ( X1 @ X2 @ X3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( lBob_THFTYPE_i = lBill_THFTYPE_i ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(con,conjecture,
    ~ sP6 ).

thf(h0,negated_conjecture,
    sP6,
    inference(assume_negation,[status(cth)],[con]) ).

thf(h1,assumption,
    ~ ( ~ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i )
     => ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ~ ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lMary_THFTYPE_i ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ),
    introduced(assumption,[]) ).

thf(h5,assumption,
    lSue_THFTYPE_i != lBill_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h6,assumption,
    ~ sP1,
    introduced(assumption,[]) ).

thf(h7,assumption,
    ~ ( ( lMary_THFTYPE_i != lSue_THFTYPE_i )
     => ( lMary_THFTYPE_i = lBill_THFTYPE_i ) ),
    introduced(assumption,[]) ).

thf(h8,assumption,
    lBob_THFTYPE_i != lMary_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h9,assumption,
    lMary_THFTYPE_i != lSue_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h10,assumption,
    lMary_THFTYPE_i != lBill_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h11,assumption,
    ~ ( ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
     => ~ ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) ),
    introduced(assumption,[]) ).

thf(h12,assumption,
    brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h13,assumption,
    sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i,
    introduced(assumption,[]) ).

thf(h14,assumption,
    sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP5
    | sP8 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP2
    | sP7
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | sP2
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP6
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ~ sP8,
    inference(prop_rule,[status(thm)],]) ).

thf(ax_004,axiom,
    ~ sP7 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h13,h14,h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0])],[1,2,3,4,5,6,h0,ax_004,h6]) ).

thf(8,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h11,h12,h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h13,h14])],[h11,7,h13,h14]) ).

thf(ax,axiom,
    ~ ( ~ ( ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBill_THFTYPE_i )
         => ~ ( sister_THFTYPE_IiioI @ lSue_THFTYPE_i @ lBob_THFTYPE_i ) )
     => ~ ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lBill_THFTYPE_i ) ) ).

thf(9,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h9,h10,h7,h8,h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h11,h12])],[ax,8,h11,h12]) ).

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

thf(ax_001,axiom,
    ~ ( ~ ( ( lMary_THFTYPE_i != lSue_THFTYPE_i )
         => ( lMary_THFTYPE_i = lBill_THFTYPE_i ) )
     => ( lBob_THFTYPE_i = lMary_THFTYPE_i ) ) ).

thf(11,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h5,h6,h3,h4,h1,h2,h0]),tab_negimp(discharge,[h7,h8])],[ax_001,10,h7,h8]) ).

thf(ax_002,axiom,
    ~ ( ( lSue_THFTYPE_i != lBill_THFTYPE_i )
     => sP1 ) ).

thf(12,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h2,h0]),tab_negimp(discharge,[h5,h6])],[ax_002,11,h5,h6]) ).

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

thf(ax_003,axiom,
    ~ ( ~ ( ~ ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lSue_THFTYPE_i )
         => ( sister_THFTYPE_IiioI @ lMary_THFTYPE_i @ lBill_THFTYPE_i ) )
     => ( brother_THFTYPE_IiioI @ lBob_THFTYPE_i @ lMary_THFTYPE_i ) ) ).

thf(14,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[ax_003,13,h1,h2]) ).

thf(0,theorem,
    ~ sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[14,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : CSR153^1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n022.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  : 300
% 0.13/0.34  % DateTime : Mon Aug 28 07:32:54 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  % Mode: cade22grackle2xfee4
% 0.19/0.45  % Steps: 8087
% 0.19/0.45  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------