%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP037^1 : 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 : n009.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 04:01:40 EDT 2023

% Result   : Theorem 0.19s 0.44s
% Output   : Proof 0.19s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_c,type,
    c: $tType ).

thf(ty_dfree_a_c,type,
    dfree_a_c: trm_a_c > $o ).

thf(ty_i2,type,
    i2: c ).

thf(ty_args,type,
    args: c > trm_a_c ).

thf(sP1,plain,
    ( sP1
  <=> ( dfree_a_c @ ( args @ i2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: c] : ( dfree_a_c @ ( args @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(conj_0,conjecture,
    sP1 ).

thf(h0,negated_conjecture,
    ~ sP1,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP2
    | sP1 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_0_free,axiom,
    sP2 ).

thf(2,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,h0,fact_0_free]) ).

thf(0,theorem,
    sP1,
    inference(contra,[status(thm),contra(discharge,[h0])],[2,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : ITP037^1 : TPTP v8.1.2. Released v7.5.0.
% 0.06/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Sun Aug 27 12:15:20 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.44  % SZS status Theorem
% 0.19/0.44  % Mode: cade22sinegrackle2x6978
% 0.19/0.44  % Steps: 67
% 0.19/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------