%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP190^1 : 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 : 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 : Thu Aug 31 04:02:49 EDT 2023

% Result   : Theorem 121.10s 121.36s
% Output   : Proof 121.10s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_pi,type,
    pi: $tType ).

thf(ty_late_residual,type,
    late_residual: $tType ).

thf(ty_list_P227219501e_name,type,
    list_P227219501e_name: $tType ).

thf(ty_z,type,
    z: name ).

thf(ty_x,type,
    x: name ).

thf(ty_aa,type,
    aa: name ).

thf(ty_q,type,
    q: pi ).

thf(ty_perm_n414416632sidual,type,
    perm_n414416632sidual: list_P227219501e_name > late_residual > late_residual ).

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

thf(ty_late_transitions,type,
    late_transitions: pi > late_residual > $o ).

thf(ty_late_FreeR,type,
    late_FreeR: late_freeRes > pi > late_residual ).

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

thf(ty_q_a,type,
    q_a: pi ).

thf(ty_b,type,
    b: name ).

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

thf(ty_nil_Pr743626285e_name,type,
    nil_Pr743626285e_name: list_P227219501e_name ).

thf(ty_late_OutputR,type,
    late_OutputR: name > name > late_freeRes ).

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

thf(sP2,plain,
    ( sP2
  <=> ( ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a )
      = ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: late_residual,X2: list_P227219501e_name] :
        ( ( late_transitions @ q @ X1 )
       => ( late_transitions @ ( perm_name_pi @ X2 @ q ) @ ( perm_n414416632sidual @ X2 @ X1 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: list_P227219501e_name] :
        ( ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) )
       => ( late_transitions @ ( perm_name_pi @ X1 @ q ) @ ( perm_n414416632sidual @ X1 @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) )
     => ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

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

thf(sP7,plain,
    ( sP7
  <=> ( late_transitions @ ( perm_name_pi @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ q ) @ ( perm_n414416632sidual @ ( cons_P1213805021e_name @ ( produc1570949143e_name @ z @ x ) @ nil_Pr743626285e_name ) @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( b = aa ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ b @ x ) @ q_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( late_transitions @ q @ ( late_FreeR @ ( late_OutputR @ aa @ x ) @ q_a ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ! [X1: pi,X2: late_residual,X3: list_P227219501e_name] :
        ( ( late_transitions @ X1 @ X2 )
       => ( late_transitions @ ( perm_name_pi @ X3 @ X1 ) @ ( perm_n414416632sidual @ X3 @ X2 ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ( late_OutputR @ b @ x )
      = ( late_OutputR @ aa @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(conj_0,conjecture,
    sP7 ).

thf(h0,negated_conjecture,
    ~ sP7,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP5
    | ~ sP10
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( sP12
    | sP6
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP2
    | sP6
    | ~ sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | sP10
    | ~ sP2
    | sP6 ),
    inference(mating_rule,[status(thm)],]) ).

thf(5,plain,
    ~ sP6,
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP4
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP11
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP1
    | sP8 ),
    inference(symeq,[status(thm)],]) ).

thf(fact_41_eqvt,axiom,
    sP11 ).

thf(fact_6_cOpen_Ohyps_I1_J,axiom,
    sP9 ).

thf(fact_0__092_060open_062a_A_061_Ab_092_060close_062,axiom,
    sP1 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,fact_41_eqvt,fact_6_cOpen_Ohyps_I1_J,fact_0__092_060open_062a_A_061_Ab_092_060close_062,h0]) ).

thf(0,theorem,
    sP7,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ITP190^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.11  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.31  % Computer : n022.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit : 300
% 0.12/0.31  % WCLimit  : 300
% 0.12/0.31  % DateTime : Sun Aug 27 12:17:54 EDT 2023
% 0.12/0.31  % CPUTime  : 
% 121.10/121.36  % SZS status Theorem
% 121.10/121.36  % Mode: cade22sinegrackle2xec37
% 121.10/121.36  % Steps: 146
% 121.10/121.36  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------