%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP163^1 : 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 : n024.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 04:02:39 EDT 2023

% Result   : Theorem 0.20s 0.44s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_refine424419629nres_a,type,
    refine424419629nres_a: $tType ).

thf(ty_set_a,type,
    set_a: $tType ).

thf(ty_a,type,
    a: $tType ).

thf(ty_phi,type,
    phi: a > $o ).

thf(ty_refine1312857699nres_a,type,
    refine1312857699nres_a: refine424419629nres_a > a > $o ).

thf(ty_x,type,
    x: a ).

thf(ty_collect_a,type,
    collect_a: ( a > $o ) > set_a ).

thf(ty_member_a,type,
    member_a: a > set_a > $o ).

thf(ty_refine1198353288_RES_a,type,
    refine1198353288_RES_a: set_a > refine424419629nres_a ).

thf(sP1,plain,
    ( sP1
  <=> ( member_a @ x @ ( collect_a @ phi ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: a > $o] :
        ( ( member_a @ x @ ( collect_a @ X1 ) )
        = ( X1 @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

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

thf(sP4,plain,
    ( sP4
  <=> ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x )
      = sP1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a] :
        ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X1 )
        = ( member_a @ X1 @ ( collect_a @ phi ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( refine1312857699nres_a @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ x ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: set_a,X2: a] :
        ( ( refine1312857699nres_a @ ( refine1198353288_RES_a @ X1 ) @ X2 )
        = ( member_a @ X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ! [X1: a,X2: a > $o] :
        ( ( member_a @ X1 @ ( collect_a @ X2 ) )
        = ( X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( phi @ x ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(conj_0,conjecture,
    sP6 = sP9 ).

thf(h0,negated_conjecture,
    sP6 != sP9,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    sP6,
    introduced(assumption,[]) ).

thf(h2,assumption,
    sP9,
    introduced(assumption,[]) ).

thf(h3,assumption,
    ~ sP6,
    introduced(assumption,[]) ).

thf(h4,assumption,
    ~ sP9,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP4
    | ~ sP6
    | sP1 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(3,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP3
    | ~ sP1
    | sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

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

thf(fact_41_mem__Collect__eq,axiom,
    sP8 ).

thf(fact_2_nf__inres__RES,axiom,
    sP7 ).

thf(7,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h1,h2,h0])],[1,2,3,4,5,6,h1,h2,fact_41_mem__Collect__eq,fact_2_nf__inres__RES]) ).

thf(8,plain,
    ( ~ sP3
    | sP1
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP4
    | sP6
    | ~ sP1 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP2
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP8
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP7
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h0])],[8,9,10,11,12,13,h3,h4,fact_41_mem__Collect__eq,fact_2_nf__inres__RES]) ).

thf(15,plain,
    $false,
    inference(tab_be,[status(thm),assumptions([h0]),tab_be(discharge,[h1,h2]),tab_be(discharge,[h3,h4])],[h0,7,14,h1,h2,h3,h4]) ).

thf(0,theorem,
    sP6 = sP9,
    inference(contra,[status(thm),contra(discharge,[h0])],[15,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem  : ITP163^1 : TPTP v8.1.2. Released v7.5.0.
% 0.07/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Sun Aug 27 10:32:53 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  % Mode: cade22sinegrackle2x6978
% 0.20/0.44  % Steps: 120
% 0.20/0.44  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------