%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP177^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : lash -P picomus -M modes -p tstp -t %d %s

% Computer : n014.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 04:02:45 EDT 2023

% Result   : Theorem 0.21s 0.44s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_b,type,
    b: $tType ).

thf(ty_member_b,type,
    member_b: b > set_b > $o ).

thf(ty_x,type,
    x: b ).

thf(ty_labele1424214014nt_a_b,type,
    labele1424214014nt_a_b: labele1159362096nt_a_b > set_b ).

thf(ty_g,type,
    g: labele1159362096nt_a_b ).

thf(ty_f,type,
    f: b > b ).

thf(sP1,plain,
    ( sP1
  <=> ( member_b @ ( f @ x ) @ ( labele1424214014nt_a_b @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: b] :
        ( ( member_b @ ( f @ X1 ) @ ( labele1424214014nt_a_b @ g ) )
       => ( member_b @ X1 @ ( labele1424214014nt_a_b @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( member_b @ x @ ( labele1424214014nt_a_b @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(conj_0,conjecture,
    sP3 ).

thf(h0,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_2_fv_I1_J,axiom,
    sP1 ).

thf(fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062,axiom,
    sP2 ).

thf(3,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,h0,fact_2_fv_I1_J,fact_0__092_060open_062_092_060And_062xa_O_A_092_060lbrakk_062f_Axa_A_092_060in_062_Avertices_AG_059_Axa_A_092_060notin_062_Avertices_AG_092_060rbrakk_062_A_092_060Longrightarrow_062_AFalse_092_060close_062]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[3,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP177^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 16:21:01 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.21/0.44  % SZS status Theorem
% 0.21/0.44  % Mode: cade22sinegrackle2x6978
% 0.21/0.44  % Steps: 186
% 0.21/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------