%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP180^1 : 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 : n001.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 04:02:46 EDT 2023

% Result   : Theorem 24.86s 25.10s
% Output   : Proof 24.86s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_labele2115946735nt_V_V,type,
    labele2115946735nt_V_V: $tType ).

thf(ty_v,type,
    v: $tType ).

thf(ty_set_V,type,
    set_V: $tType ).

thf(ty_v2,type,
    v2: $tType ).

thf(ty_product_prod_V_V,type,
    product_prod_V_V: $tType ).

thf(ty_set_Product_prod_V_V,type,
    set_Product_prod_V_V: $tType ).

thf(ty_set_V2,type,
    set_V2: $tType ).

thf(ty_standard_Constant_V,type,
    standard_Constant_V: $tType ).

thf(ty_map_gr907434255tant_V,type,
    map_gr907434255tant_V: set_Product_prod_V_V > labele2115946735nt_V_V > labele2115946735nt_V_V ).

thf(ty_product_Pair_V_V2,type,
    product_Pair_V_V2: v > v > product_prod_V_V ).

thf(ty_c,type,
    c: set_V2 ).

thf(ty_h,type,
    h: v > v ).

thf(ty_g,type,
    g: labele2115946735nt_V_V ).

thf(ty_eigen__2,type,
    eigen__2: v ).

thf(ty_member_V2,type,
    member_V2: v > set_V > $o ).

thf(ty_m,type,
    m: v2 > v ).

thf(ty_member2015049524od_V_V,type,
    member2015049524od_V_V: product_prod_V_V > set_Product_prod_V_V > $o ).

thf(ty_eigen__1,type,
    eigen__1: v2 > v ).

thf(ty_getRel1432786916nt_V_V,type,
    getRel1432786916nt_V_V: standard_Constant_V > labele2115946735nt_V_V > set_Product_prod_V_V ).

thf(ty_id_on_V2,type,
    id_on_V2: set_V > set_Product_prod_V_V ).

thf(ty_standard_S_Const_V,type,
    standard_S_Const_V: v2 > standard_Constant_V ).

thf(ty_member_V,type,
    member_V: v2 > set_V2 > $o ).

thf(ty_y,type,
    y: v2 ).

thf(ty_graph_1808119_V_V_V,type,
    graph_1808119_V_V_V: labele2115946735nt_V_V > labele2115946735nt_V_V > set_Product_prod_V_V > $o ).

thf(ty_xa,type,
    xa: v2 ).

thf(ty_labele1134902411nt_V_V,type,
    labele1134902411nt_V_V: labele2115946735nt_V_V > set_V ).

thf(ty_bNF_Gr_V_V2,type,
    bNF_Gr_V_V2: set_V > ( v > v ) > set_Product_prod_V_V ).

thf(ty_eigen__0,type,
    eigen__0: v2 > v ).

thf(sP1,plain,
    ( sP1
  <=> ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) )
     => ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
       => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ! [X1: labele2115946735nt_V_V,X2: labele2115946735nt_V_V] :
        ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ X1 ) )
       => ( ( graph_1808119_V_V_V @ X1 @ X2 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X1 ) ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ X2 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: standard_Constant_V,X2: labele2115946735nt_V_V,X3: labele2115946735nt_V_V] :
        ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ X1 @ X2 ) )
       => ( ( graph_1808119_V_V_V @ X2 @ X3 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X2 ) ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ X1 @ X3 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ! [X1: v,X2: v,X3: standard_Constant_V,X4: labele2115946735nt_V_V,X5: labele2115946735nt_V_V] :
        ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X1 @ X2 ) @ ( getRel1432786916nt_V_V @ X3 @ X4 ) )
       => ( ( graph_1808119_V_V_V @ X4 @ X5 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X4 ) ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ X1 @ X2 ) @ ( getRel1432786916nt_V_V @ X3 @ X5 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
     => sP4 ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ g @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ! [X1: v,X2: standard_Constant_V,X3: labele2115946735nt_V_V,X4: labele2115946735nt_V_V] :
        ( ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X3 ) )
       => ( ( graph_1808119_V_V_V @ X3 @ X4 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ X3 ) ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ X1 ) @ ( getRel1432786916nt_V_V @ X2 @ X4 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ! [X1: labele2115946735nt_V_V] :
        ( sP3
       => ( ( graph_1808119_V_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) @ X1 @ ( id_on_V2 @ ( labele1134902411nt_V_V @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) )
         => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( m @ xa ) @ ( m @ xa ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ y ) @ X1 ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(conj_0,conjecture,
    sP4 ).

thf(h0,negated_conjecture,
    ~ sP4,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ! [X1: v2] :
      ( ( member_V @ X1 @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( eigen__0 @ X1 ) @ ( eigen__0 @ X1 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X1 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    ! [X1: v2] :
      ( ( member_V @ X1 @ c )
     => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( eigen__1 @ X1 ) @ ( eigen__1 @ X1 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X1 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    member_V2 @ eigen__2 @ ( labele1134902411nt_V_V @ g ),
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP7
    | ~ sP8
    | sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP1
    | ~ sP3
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

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

thf(4,plain,
    ( ~ sP2
    | sP10 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( ~ sP5
    | sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP9
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(7,plain,
    ( ~ sP6
    | sP9 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_38_getRel__subgraph,axiom,
    sP6 ).

thf(fact_8_h_I3_J,axiom,
    sP8 ).

thf(fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062,axiom,
    sP3 ).

thf(8,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,h0,fact_38_getRel__subgraph,fact_8_h_I3_J,fact_6__092_060open_062_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ay_J_A_Imap__graph__fn_AG_H_Ah_J_092_060close_062]) ).

thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [X1: v] :
        ~ ( member_V2 @ X1 @ ( labele1134902411nt_V_V @ g ) ) ).

thf(9,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_Avertices_AG_H_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,8,h3]) ).

thf(fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
    ~ ! [X1: v2 > v] :
        ~ ! [X2: v2] :
            ( ( member_V @ X2 @ c )
           => ( member2015049524od_V_V @ ( product_Pair_V_V2 @ ( X1 @ X2 ) @ ( X1 @ X2 ) ) @ ( getRel1432786916nt_V_V @ ( standard_S_Const_V @ X2 ) @ ( map_gr907434255tant_V @ ( bNF_Gr_V_V2 @ ( labele1134902411nt_V_V @ g ) @ h ) @ g ) ) ) ) ).

thf(10,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,9,h2]) ).

thf(11,plain,
    $false,
    inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_20__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062m_O_A_I_092_060And_062x_O_Ax_A_092_060in_062_AC_A_092_060Longrightarrow_062_A_Im_Ax_M_Am_Ax_J_A_092_060in_062_AgetRel_A_IS__Const_Ax_J_A_Imap__graph__fn_AG_H_Ah_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,10,h1]) ).

thf(0,theorem,
    sP4,
    inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP180^1 : TPTP v8.1.2. Released v7.5.0.
% 0.14/0.14  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Sun Aug 27 14:41:03 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 24.86/25.10  % SZS status Theorem
% 24.86/25.10  % Mode: cade22sinegrackle2xfaf3
% 24.86/25.10  % Steps: 22174
% 24.86/25.10  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------