%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP161^1 : 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 : n008.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 04:02:36 EDT 2023

% Result   : Theorem 0.20s 0.46s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_a,type,
    a: $tType ).

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

thf(ty_refine432681134nres_b,type,
    refine432681134nres_b: $tType ).

thf(ty_ord_le527798542nres_b,type,
    ord_le527798542nres_b: refine432681134nres_b > refine432681134nres_b > $o ).

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(ty_f,type,
    f: a > refine432681134nres_b ).

thf(ty_x,type,
    x: a ).

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

thf(ty_m,type,
    m: refine432681134nres_b ).

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

thf(ty_refine436832839nd_a_b,type,
    refine436832839nd_a_b: refine424419629nres_a > ( a > refine432681134nres_b ) > refine432681134nres_b ).

thf(sP1,plain,
    ( sP1
  <=> ( ord_le527798542nres_b @ m @ ( f @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ( member_a @ x @ ( collect_a @ phi ) )
      = ( phi @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ f ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( member_a @ x @ ( collect_a @ phi ) )
     => ( sP1
       => sP3 ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: a > refine432681134nres_b] :
        ( ( member_a @ x @ ( collect_a @ phi ) )
       => ( ( ord_le527798542nres_b @ m @ ( X1 @ x ) )
         => ( ord_le527798542nres_b @ m @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: a,X2: set_a,X3: refine432681134nres_b,X4: a > refine432681134nres_b] :
        ( ( member_a @ X1 @ X2 )
       => ( ( ord_le527798542nres_b @ X3 @ ( X4 @ X1 ) )
         => ( ord_le527798542nres_b @ X3 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X2 ) @ X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: a > $o] :
        ( ( member_a @ x @ ( collect_a @ X1 ) )
        = ( X1 @ x ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( phi @ x ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: a,X2: a > $o] :
        ( ( member_a @ X1 @ ( collect_a @ X2 ) )
        = ( X2 @ X1 ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: set_a,X2: refine432681134nres_b,X3: a > refine432681134nres_b] :
        ( ( member_a @ x @ X1 )
       => ( ( ord_le527798542nres_b @ X2 @ ( X3 @ x ) )
         => ( ord_le527798542nres_b @ X2 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ X1 ) @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( sP1
     => sP3 ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( member_a @ x @ ( collect_a @ phi ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ! [X1: refine432681134nres_b,X2: a > refine432681134nres_b] :
        ( sP12
       => ( ( ord_le527798542nres_b @ X1 @ ( X2 @ x ) )
         => ( ord_le527798542nres_b @ X1 @ ( refine436832839nd_a_b @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(conj_0,conjecture,
    sP3 ).

thf(h0,negated_conjecture,
    ~ sP3,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP11
    | ~ sP1
    | sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | ~ sP12
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP5
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP13
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP10
    | sP13 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP2
    | sP12
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP7
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP9
    | sP7 ),
    inference(all_rule,[status(thm)],]) ).

thf(9,plain,
    ( ~ sP6
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_107_mem__Collect__eq,axiom,
    sP9 ).

thf(fact_35_RES__bind__choose,axiom,
    sP6 ).

thf(fact_1_assms_I2_J,axiom,
    sP1 ).

thf(fact_0_assms_I1_J,axiom,
    sP8 ).

thf(10,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,h0,fact_107_mem__Collect__eq,fact_35_RES__bind__choose,fact_1_assms_I2_J,fact_0_assms_I1_J]) ).

thf(0,theorem,
    sP3,
    inference(contra,[status(thm),contra(discharge,[h0])],[10,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP161^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Sun Aug 27 11:56:32 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  % Mode: cade22sinegrackle2x6978
% 0.20/0.46  % Steps: 334
% 0.20/0.46  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------