%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP182^1 : 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 : n026.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 04:02:46 EDT 2023

% Result   : Theorem 21.80s 22.01s
% Output   : Proof 21.80s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_name,type,
    name: $tType ).

thf(ty_set_Pr1834926343_pi_pi,type,
    set_Pr1834926343_pi_pi: $tType ).

thf(ty_pi,type,
    pi: $tType ).

thf(ty_late_subject,type,
    late_subject: $tType ).

thf(ty_x,type,
    x: name ).

thf(ty_nil_Pr743626285e_name,type,
    nil_Pr743626285e_name: list_P227219501e_name ).

thf(ty_id_pi,type,
    id_pi: set_Pr1834926343_pi_pi ).

thf(ty_strong2129052853vative,type,
    strong2129052853vative: pi > pi > late_subject > name > set_Pr1834926343_pi_pi > $o ).

thf(ty_ord_le630093991_pi_pi,type,
    ord_le630093991_pi_pi: set_Pr1834926343_pi_pi > set_Pr1834926343_pi_pi > $o ).

thf(ty_late_BoundOutputS,type,
    late_BoundOutputS: name > late_subject ).

thf(ty_produc1570949143e_name,type,
    produc1570949143e_name: name > name > produc367475239e_name ).

thf(ty_y,type,
    y: name ).

thf(ty_p2,type,
    p2: pi ).

thf(ty_cons_P1213805021e_name,type,
    cons_P1213805021e_name: produc367475239e_name > list_P227219501e_name > list_P227219501e_name ).

thf(ty_perm_name_pi,type,
    perm_name_pi: list_P227219501e_name > pi > pi ).

thf(ty_aa,type,
    aa: name ).

thf(ty_rel,type,
    rel: set_Pr1834926343_pi_pi ).

thf(sP1,plain,
    ( sP1
  <=> ( ( ord_le630093991_pi_pi @ id_pi @ rel )
     => ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: name] :
        ( ( ord_le630093991_pi_pi @ id_pi @ rel )
       => ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ X1 @ rel ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: late_subject,X2: name] :
        ( ( ord_le630093991_pi_pi @ id_pi @ rel )
       => ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ X1 @ X2 @ rel ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: pi,X2: late_subject,X3: name] :
        ( ( ord_le630093991_pi_pi @ id_pi @ rel )
       => ( strong2129052853vative @ X1 @ X1 @ X2 @ X3 @ rel ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ord_le630093991_pi_pi @ id_pi @ rel ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( strong2129052853vative @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ y @ x ) @ nil_Pr743626285e_name ) @ p2 ) @ ( late_BoundOutputS @ aa ) @ y @ rel ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: set_Pr1834926343_pi_pi,X2: pi,X3: late_subject,X4: name] :
        ( ( ord_le630093991_pi_pi @ id_pi @ X1 )
       => ( strong2129052853vative @ X2 @ X2 @ X3 @ X4 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(conj_0,conjecture,
    sP6 ).

thf(h0,negated_conjecture,
    ~ sP6,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP1
    | ~ sP5
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(5,plain,
    ( ~ sP7
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_194_derivativeReflexive,axiom,
    sP7 ).

thf(fact_0_Id,axiom,
    sP5 ).

thf(6,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,h0,fact_194_derivativeReflexive,fact_0_Id]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP182^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.17/0.33  % Computer : n026.cluster.edu
% 0.17/0.33  % Model    : x86_64 x86_64
% 0.17/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33  % Memory   : 8042.1875MB
% 0.17/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33  % CPULimit : 300
% 0.17/0.33  % WCLimit  : 300
% 0.17/0.33  % DateTime : Sun Aug 27 10:41:04 EDT 2023
% 0.17/0.34  % CPUTime  : 
% 21.80/22.01  % SZS status Theorem
% 21.80/22.01  % Mode: cade22sinegrackle2xfaf3
% 21.80/22.01  % Steps: 21637
% 21.80/22.01  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------