%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP189^1 : 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 : n011.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 20.27s 20.55s
% Output   : Proof 20.27s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_late_freeRes,type,
    late_freeRes: $tType ).

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

thf(ty_name,type,
    name: $tType ).

thf(ty_q,type,
    q: pi ).

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

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

thf(ty_par,type,
    par: pi > pi > pi ).

thf(ty_p2,type,
    p2: pi ).

thf(ty_fresh_1641682979reeRes,type,
    fresh_1641682979reeRes: name > late_freeRes > $o ).

thf(ty_alpha,type,
    alpha: late_freeRes ).

thf(ty_x,type,
    x: name ).

thf(ty_res,type,
    res: name > pi > pi ).

thf(ty_p,type,
    p: pi ).

thf(sP1,plain,
    ( sP1
  <=> ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ ( par @ p2 @ q ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: late_freeRes,X2: pi,X3: name] :
        ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ X1 @ X2 ) )
       => ( ( fresh_1641682979reeRes @ X3 @ X1 )
         => ( late_transitions @ ( res @ X3 @ ( par @ p @ q ) ) @ ( late_FreeR @ X1 @ ( res @ X3 @ X2 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: name] :
        ( sP1
       => ( ( fresh_1641682979reeRes @ X1 @ alpha )
         => ( late_transitions @ ( res @ X1 @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ X1 @ ( par @ p2 @ q ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( fresh_1641682979reeRes @ x @ alpha )
     => ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( sP1
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( late_transitions @ ( res @ x @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ x @ ( par @ p2 @ q ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( fresh_1641682979reeRes @ x @ alpha ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: pi,X2: late_freeRes,X3: pi,X4: name] :
        ( ( late_transitions @ X1 @ ( late_FreeR @ X2 @ X3 ) )
       => ( ( fresh_1641682979reeRes @ X4 @ X2 )
         => ( late_transitions @ ( res @ X4 @ X1 ) @ ( late_FreeR @ X2 @ ( res @ X4 @ X3 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: pi,X2: name] :
        ( ( late_transitions @ ( par @ p @ q ) @ ( late_FreeR @ alpha @ X1 ) )
       => ( ( fresh_1641682979reeRes @ X2 @ alpha )
         => ( late_transitions @ ( res @ X2 @ ( par @ p @ q ) ) @ ( late_FreeR @ alpha @ ( res @ X2 @ X1 ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    sP6 ).

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

thf(1,plain,
    ( ~ sP4
    | ~ sP7
    | sP6 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | ~ sP1
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP3
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP9
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP8
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_11_ResF,axiom,
    sP8 ).

thf(fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,axiom,
    sP1 ).

thf(fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062,axiom,
    sP7 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,h0,fact_11_ResF,fact_1__092_060open_062P_A_092_060parallel_062_AQ_A_092_060longmapsto_062_A_092_060alpha_062_A_092_060prec_062_AP_H_A_092_060parallel_062_AQ_092_060close_062,fact_0__092_060open_062x_A_092_060sharp_062_A_092_060alpha_062_092_060close_062]) ).

thf(0,theorem,
    sP6,
    inference(contra,[status(thm),contra(discharge,[h0])],[7,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP189^1 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n011.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 : Sun Aug 27 14:42:40 EDT 2023
% 0.20/0.34  % CPUTime  : 
% 20.27/20.55  % SZS status Theorem
% 20.27/20.55  % Mode: cade22sinegrackle2xfaf3
% 20.27/20.55  % Steps: 1469
% 20.27/20.55  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------