TSTP Solution File: ITP178^1 by Lash---1.13

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Lash---1.13
% Problem  : ITP178^1 : 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 : n010.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 04:02:45 EDT 2023

% Result   : Theorem 120.66s 121.18s
% Output   : Proof 120.66s
% Verified : 
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)

% Comments : 
%------------------------------------------------------------------------------
thf(ty_allegorical_term_b,type,
    allegorical_term_b: $tType ).

thf(ty_produc1990145943term_b,type,
    produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).

thf(ty_restrict_b_nat,type,
    restrict_b_nat: labeled_graph_b_nat > labeled_graph_b_nat ).

thf(ty_finite1987068434at_nat,type,
    finite1987068434at_nat: set_Pr9961929at_nat > $o ).

thf(ty_finite_finite_nat,type,
    finite_finite_nat: set_nat > $o ).

thf(ty_produc1542243159_b_nat,type,
    produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(ty_v,type,
    v: allegorical_term_b ).

thf(ty_u,type,
    u: allegorical_term_b ).

thf(ty_translation_b,type,
    translation_b: allegorical_term_b > labeled_graph_b_nat ).

thf(ty_id_on_nat,type,
    id_on_nat: set_nat > set_Pr1986765409at_nat ).

thf(ty_labeled_edges_b_nat,type,
    labeled_edges_b_nat: labeled_graph_b_nat > set_Pr9961929at_nat ).

thf(ty_graph_529870330at_nat,type,
    graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).

thf(ty_allegorical_A_Int_b,type,
    allegorical_A_Int_b: allegorical_term_b > allegorical_term_b > allegorical_term_b ).

thf(ty_labele460410879_b_nat,type,
    labele460410879_b_nat: labeled_graph_b_nat > set_nat ).

thf(ty_produc194497945_b_nat,type,
    produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(ty_produc854192515term_b,type,
    produc854192515term_b: produc1478835367term_b > allegorical_term_b ).

thf(ty_produc951298923_b_nat,type,
    produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).

thf(ty_produc1223098053term_b,type,
    produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).

thf(sP1,plain,
    ( sP1
  <=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
        ~ ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
                 => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) )
                   != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
             => ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) )
         => ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X1 ) @ ( translation_b @ ( allegorical_A_Int_b @ X1 @ X2 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP1])]) ).

thf(sP2,plain,
    ( sP2
  <=> ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
             => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
               != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
         => ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
     => ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP2])]) ).

thf(sP3,plain,
    ( sP3
  <=> ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
      = ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP3])]) ).

thf(sP4,plain,
    ( sP4
  <=> ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) )
     => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
       != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP4])]) ).

thf(sP5,plain,
    ( sP5
  <=> ! [X1: allegorical_term_b] :
        ( ( produc854192515term_b @ ( produc1990145943term_b @ u @ X1 ) )
        = u ) ),
    introduced(definition,[new_symbols(definition,[sP5])]) ).

thf(sP6,plain,
    ( sP6
  <=> ( ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) )
      = ( allegorical_A_Int_b @ u @ v ) ) ),
    introduced(definition,[new_symbols(definition,[sP6])]) ).

thf(sP7,plain,
    ( sP7
  <=> ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP7])]) ).

thf(sP8,plain,
    ( sP8
  <=> ( u
      = ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP8])]) ).

thf(sP9,plain,
    ( sP9
  <=> ( ~ sP4
     => ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP9])]) ).

thf(sP10,plain,
    ( sP10
  <=> ( ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
      = ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP10])]) ).

thf(sP11,plain,
    ( sP11
  <=> ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
         => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
           != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
     => ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP11])]) ).

thf(sP12,plain,
    ( sP12
  <=> ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP12])]) ).

thf(sP13,plain,
    ( sP13
  <=> ( ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) )
      = ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP13])]) ).

thf(sP14,plain,
    ( sP14
  <=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
      = ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP14])]) ).

thf(sP15,plain,
    ( sP15
  <=> ( ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
      = ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP15])]) ).

thf(sP16,plain,
    ( sP16
  <=> ( ( allegorical_A_Int_b @ u @ v )
      = ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP16])]) ).

thf(sP17,plain,
    ( sP17
  <=> ( ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
      = ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP17])]) ).

thf(sP18,plain,
    ( sP18
  <=> ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP18])]) ).

thf(sP19,plain,
    ( sP19
  <=> ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP19])]) ).

thf(sP20,plain,
    ( sP20
  <=> ( ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
      = ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP20])]) ).

thf(sP21,plain,
    ( sP21
  <=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
        ( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
        = X2 ) ),
    introduced(definition,[new_symbols(definition,[sP21])]) ).

thf(sP22,plain,
    ( sP22
  <=> ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
      = ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP22])]) ).

thf(sP23,plain,
    ( sP23
  <=> ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) )
     => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
       != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP23])]) ).

thf(sP24,plain,
    ( sP24
  <=> ( ~ sP11
     => ~ sP19 ) ),
    introduced(definition,[new_symbols(definition,[sP24])]) ).

thf(sP25,plain,
    ( sP25
  <=> ( ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP25])]) ).

thf(sP26,plain,
    ( sP26
  <=> ( ( translation_b @ u )
      = ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP26])]) ).

thf(sP27,plain,
    ( sP27
  <=> ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP27])]) ).

thf(sP28,plain,
    ( sP28
  <=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP28])]) ).

thf(sP29,plain,
    ( sP29
  <=> ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP29])]) ).

thf(sP30,plain,
    ( sP30
  <=> ! [X1: allegorical_term_b] :
        ~ ( ~ ( ~ ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
                 => ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) )
                   != ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
             => ~ ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) )
         => ~ ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ u ) @ ( translation_b @ ( allegorical_A_Int_b @ u @ X1 ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP30])]) ).

thf(sP31,plain,
    ( sP31
  <=> ! [X1: allegorical_term_b] :
        ( ( produc1223098053term_b @ ( produc1990145943term_b @ u @ X1 ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP31])]) ).

thf(sP32,plain,
    ( sP32
  <=> ( ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) )
      = u ) ),
    introduced(definition,[new_symbols(definition,[sP32])]) ).

thf(sP33,plain,
    ( sP33
  <=> ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ ( produc854192515term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) @ ( translation_b @ ( produc1223098053term_b @ ( produc1990145943term_b @ u @ ( allegorical_A_Int_b @ u @ v ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbols(definition,[sP33])]) ).

thf(sP34,plain,
    ( sP34
  <=> ! [X1: allegorical_term_b,X2: allegorical_term_b] :
        ( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X2 ) )
        = X1 ) ),
    introduced(definition,[new_symbols(definition,[sP34])]) ).

thf(conj_0,conjecture,
    ~ sP24 ).

thf(h0,negated_conjecture,
    sP24,
    inference(assume_negation,[status(cth)],[conj_0]) ).

thf(1,plain,
    ( ~ sP31
    | sP6 ),
    inference(all_rule,[status(thm)],]) ).

thf(2,plain,
    ( ~ sP5
    | sP32 ),
    inference(all_rule,[status(thm)],]) ).

thf(3,plain,
    ( ~ sP21
    | sP31 ),
    inference(all_rule,[status(thm)],]) ).

thf(4,plain,
    ( ~ sP34
    | sP5 ),
    inference(all_rule,[status(thm)],]) ).

thf(5,plain,
    ( sP25
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(6,plain,
    ( ~ sP28
    | sP33
    | ~ sP14
    | ~ sP25 ),
    inference(confrontation_rule,[status(thm)],]) ).

thf(7,plain,
    ( sP10
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(8,plain,
    ( ~ sP18
    | sP27
    | ~ sP10 ),
    inference(mating_rule,[status(thm)],]) ).

thf(9,plain,
    ( sP20
    | ~ sP14 ),
    inference(prop_rule,[status(thm)],]) ).

thf(10,plain,
    ( ~ sP7
    | sP19
    | ~ sP20 ),
    inference(mating_rule,[status(thm)],]) ).

thf(11,plain,
    ( sP17
    | ~ sP3 ),
    inference(prop_rule,[status(thm)],]) ).

thf(12,plain,
    ( sP15
    | ~ sP17 ),
    inference(prop_rule,[status(thm)],]) ).

thf(13,plain,
    ( sP14
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(14,plain,
    ( ~ sP6
    | sP16 ),
    inference(symeq,[status(thm)],]) ).

thf(15,plain,
    ( sP22
    | ~ sP16 ),
    inference(prop_rule,[status(thm)],]) ).

thf(16,plain,
    ( sP13
    | ~ sP22
    | ~ sP26 ),
    inference(prop_rule,[status(thm)],]) ).

thf(17,plain,
    ( sP3
    | ~ sP13 ),
    inference(prop_rule,[status(thm)],]) ).

thf(18,plain,
    ( ~ sP12
    | sP29
    | ~ sP15
    | ~ sP14
    | ~ sP3 ),
    inference(mating_rule,[status(thm)],]) ).

thf(19,plain,
    ( sP4
    | sP28 ),
    inference(prop_rule,[status(thm)],]) ).

thf(20,plain,
    ( sP4
    | sP12 ),
    inference(prop_rule,[status(thm)],]) ).

thf(21,plain,
    ( sP9
    | sP18 ),
    inference(prop_rule,[status(thm)],]) ).

thf(22,plain,
    ( sP9
    | ~ sP4 ),
    inference(prop_rule,[status(thm)],]) ).

thf(23,plain,
    ( sP2
    | sP7 ),
    inference(prop_rule,[status(thm)],]) ).

thf(24,plain,
    ( sP2
    | ~ sP9 ),
    inference(prop_rule,[status(thm)],]) ).

thf(25,plain,
    ( ~ sP32
    | sP8 ),
    inference(symeq,[status(thm)],]) ).

thf(26,plain,
    ( sP26
    | ~ sP8 ),
    inference(prop_rule,[status(thm)],]) ).

thf(27,plain,
    ( ~ sP30
    | ~ sP2 ),
    inference(all_rule,[status(thm)],]) ).

thf(28,plain,
    ( ~ sP1
    | sP30 ),
    inference(all_rule,[status(thm)],]) ).

thf(29,plain,
    ( ~ sP23
    | ~ sP29
    | ~ sP33 ),
    inference(prop_rule,[status(thm)],]) ).

thf(30,plain,
    ( ~ sP11
    | sP23
    | ~ sP27 ),
    inference(prop_rule,[status(thm)],]) ).

thf(31,plain,
    ( ~ sP24
    | sP11
    | ~ sP19 ),
    inference(prop_rule,[status(thm)],]) ).

thf(fact_85_snd__conv,axiom,
    sP21 ).

thf(fact_76_fst__conv,axiom,
    sP34 ).

thf(fact_3_graph__rule__translation,axiom,
    sP1 ).

thf(32,plain,
    $false,
    inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,fact_85_snd__conv,fact_76_fst__conv,fact_3_graph__rule__translation,h0]) ).

thf(0,theorem,
    ~ sP24,
    inference(contra,[status(thm),contra(discharge,[h0])],[32,h0]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35  % Computer : n010.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 16:02:49 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 120.66/121.18  % SZS status Theorem
% 120.66/121.18  % Mode: cade22sinegrackle2xec37
% 120.66/121.18  % Steps: 4172
% 120.66/121.18  % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------