%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP175^1 : 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 : n026.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 04:02:44 EDT 2023

% Result   : Theorem 0.20s 0.39s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_product_prod_b_b,type,
    product_prod_b_b: $tType ).

thf(ty_labeled_graph_a_b,type,
    labeled_graph_a_b: $tType ).

thf(ty_set_Product_prod_b_b,type,
    set_Product_prod_b_b: $tType ).

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

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

thf(ty_set_b,type,
    set_b: $tType ).

thf(ty_getRel_a_b,type,
    getRel_a_b: a > labeled_graph_a_b > set_Product_prod_b_b ).

thf(ty_z,type,
    z: b ).

thf(ty_y,type,
    y: b ).

thf(ty_i,type,
    i: a ).

thf(ty_member1285940496od_b_b,type,
    member1285940496od_b_b: product_prod_b_b > set_Product_prod_b_b > $o ).

thf(ty_trans_b,type,
    trans_b: set_Product_prod_b_b > $o ).

thf(ty_g,type,
    g: labeled_graph_a_b ).

thf(ty_refl_on_b,type,
    refl_on_b: set_b > set_Product_prod_b_b > $o ).

thf(ty_product_Pair_b_b,type,
    product_Pair_b_b: b > b > product_prod_b_b ).

thf(ty_labeled_vertices_a_b,type,
    labeled_vertices_a_b: labeled_graph_a_b > set_b ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: b,X2: b] :
        ( ( member1285940496od_b_b @ ( product_Pair_b_b @ X1 @ X2 ) @ ( getRel_a_b @ i @ g ) )
       => ( member1285940496od_b_b @ ( product_Pair_b_b @ X2 @ X1 ) @ ( getRel_a_b @ i @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( member1285940496od_b_b @ ( product_Pair_b_b @ z @ y ) @ ( getRel_a_b @ i @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( member1285940496od_b_b @ ( product_Pair_b_b @ y @ z ) @ ( getRel_a_b @ i @ g ) )
     => sP2 ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ! [X1: b] :
        ( ( member1285940496od_b_b @ ( product_Pair_b_b @ y @ X1 ) @ ( getRel_a_b @ i @ g ) )
       => ( member1285940496od_b_b @ ( product_Pair_b_b @ X1 @ y ) @ ( getRel_a_b @ i @ g ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ( member1285940496od_b_b @ ( product_Pair_b_b @ y @ z ) @ ( getRel_a_b @ i @ g ) ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(conj_0,conjecture,
    sP2 ).

thf(h0,negated_conjecture,
    ~ sP2,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(h1,assumption,
    ~ ( ( refl_on_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ) )
     => ~ sP1 ),
    introduced(assumption,[]) ).

thf(h2,assumption,
    trans_b @ ( getRel_a_b @ i @ g ),
    introduced(assumption,[]) ).

thf(h3,assumption,
    refl_on_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ),
    introduced(assumption,[]) ).

thf(h4,assumption,
    sP1,
    introduced(assumption,[]) ).

thf(1,plain,
    ( ~ sP3
    | ~ sP5
    | sP2 ),
    inference(prop_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP4
    | sP3 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP1
    | sP4 ),
    inference(all_rule,[status(thm)],]) ).

thf(fact_1_aI,axiom,
    sP5 ).

thf(4,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h3,h4,h1,h2,h0])],[1,2,3,h0,fact_1_aI,h4]) ).

thf(5,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h1,h2,h0]),tab_negimp(discharge,[h3,h4])],[h1,4,h3,h4]) ).

thf(fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062,axiom,
    ~ ( ~ ( ( refl_on_b @ ( labeled_vertices_a_b @ g ) @ ( getRel_a_b @ i @ g ) )
         => ~ sP1 )
     => ~ ( trans_b @ ( getRel_a_b @ i @ g ) ) ) ).

thf(6,plain,
    $false,
    inference(tab_negimp,[status(thm),assumptions([h0]),tab_negimp(discharge,[h1,h2])],[fact_0__092_060open_062refl__on_A_Ivertices_AG_J_A_IgetRel_AI_AG_J_A_092_060and_062_A_I_092_060forall_062x_Ay_O_A_Ix_M_Ay_J_A_092_060in_062_AgetRel_AI_AG_A_092_060longrightarrow_062_A_Iy_M_Ax_J_A_092_060in_062_AgetRel_AI_AG_J_A_092_060and_062_Atrans_A_IgetRel_AI_AG_J_092_060close_062,5,h1,h2]) ).

thf(0,theorem,
    sP2,
    inference(contra,[status(thm),contra(discharge,[h0])],[6,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP175^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.12  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n026.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 14:15:19 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.39  % SZS status Theorem
% 0.20/0.39  % Mode: cade22sinegrackle2x6978
% 0.20/0.39  % Steps: 167
% 0.20/0.39  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------