%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP165^1 : 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 : n006.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 04:02:40 EDT 2023

% Result   : Theorem 20.57s 20.82s
% Output   : Proof 20.57s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

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

thf(ty_if_Ref1724547303nres_a,type,
    if_Ref1724547303nres_a: $o > refine424419629nres_a > refine424419629nres_a > refine424419629nres_a ).

thf(ty_ord_le519537037nres_a,type,
    ord_le519537037nres_a: refine424419629nres_a > refine424419629nres_a > $o ).

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

thf(ty_s1,type,
    s1: refine424419629nres_a ).

thf(ty_s2,type,
    s2: refine424419629nres_a ).

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

thf(ty_b,type,
    b: $o ).

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

thf(sP1,plain,
    ( sP1
  <=> $false ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ b
     => ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ! [X1: refine424419629nres_a] :
        ( ( if_Ref1724547303nres_a @ ~ sP1 @ s1 @ X1 )
        = s1 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( if_Ref1724547303nres_a @ ~ sP1 @ s1 @ s2 )
      = s1 ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( s1
      = ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: refine424419629nres_a] :
        ( ( if_Ref1724547303nres_a @ sP1 @ s1 @ X1 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ! [X1: refine424419629nres_a,X2: refine424419629nres_a] :
        ( ( if_Ref1724547303nres_a @ ~ sP1 @ X1 @ X2 )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( ord_le519537037nres_a @ s1 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( b
     => sP8 ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( if_Ref1724547303nres_a @ ~ sP1 @ s1 @ s2 )
      = ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ord_le519537037nres_a @ s2 @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( ord_le519537037nres_a @ ( if_Ref1724547303nres_a @ b @ s1 @ s2 ) @ ( refine1198353288_RES_a @ ( collect_a @ phi ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> b ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( if_Ref1724547303nres_a @ sP13 @ s1 @ s2 )
      = s2 ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( s2
      = ( if_Ref1724547303nres_a @ sP13 @ s1 @ s2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ! [X1: refine424419629nres_a,X2: refine424419629nres_a] :
        ( ( if_Ref1724547303nres_a @ sP1 @ X1 @ X2 )
        = X2 ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( if_Ref1724547303nres_a @ sP1 @ s1 @ s2 )
      = s2 ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( ( if_Ref1724547303nres_a @ sP1 @ s1 @ s2 )
      = ( if_Ref1724547303nres_a @ sP13 @ s1 @ s2 ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( ~ sP1 = sP13 ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(conj_2,conjecture,
    sP12 ).

thf(h0,negated_conjecture,
    ~ sP12,
    inference(assume_negation,[status(cth)],[conj_2]) ).

thf(1,plain,
    ( sP19
    | sP1
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP17
    | sP14
    | ~ sP18
    | sP1 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(3,plain,
    ( sP10
    | sP1
    | sP1
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(4,plain,
    ( sP18
    | sP1
    | sP1
    | sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP4
    | sP5
    | sP1
    | ~ sP10 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP14
    | sP15 ),
    inference(symeq,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP11
    | sP12
    | sP1
    | ~ sP15 ),
    inference(mating_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP8
    | sP12
    | sP1
    | ~ sP5 ),
    inference(mating_rule,[status(thm)],]) ).

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

thf(10,plain,
    ( ~ sP6
    | sP17 ),
    inference(all_rule,[status(thm)],]) ).

thf(11,plain,
    ( ~ sP3
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(12,plain,
    ( ~ sP2
    | sP13
    | sP11 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( ~ sP16
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP7
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(15,plain,
    ( ~ sP9
    | ~ sP13
    | sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(conj_1,axiom,
    sP2 ).

thf(conj_0,axiom,
    sP9 ).

thf(help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
    sP7 ).

thf(help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,axiom,
    sP16 ).

thf(16,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,h0,conj_1,conj_0,help_If_1_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T,help_If_2_1_If_001t__Refine____Basic____Mirabelle____kwjuvthmas__Onres_Itf__a_J_T]) ).

thf(0,theorem,
    sP12,
    inference(contra,[status(thm),contra(discharge,[h0])],[16,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : ITP165^1 : 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 : n006.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 12:01:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 20.57/20.82  % SZS status Theorem
% 20.57/20.82  % Mode: cade22sinegrackle2xfaf3
% 20.57/20.82  % Steps: 5974
% 20.57/20.82  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------