TSTP Solution File: ITP178^1 by Zipperpin---2.1.9999

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Pytpp3p78Y true

% Computer : n029.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 05:22:41 EDT 2023

% Result   : Theorem 1.75s 1.14s
% Output   : Refutation 1.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   87 (  45 unt;  24 typ;   0 def)
%            Number of atoms       :  104 (  53 equ;   0 cnn)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :  879 (   3   ~;   0   |;  24   &; 835   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Number of types       :    8 (   7 usr)
%            Number of type conns  :   20 (  20   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   21 (  17 usr;   5 con; 0-3 aty)
%                                         (  17  !!;   0  ??;   0 @@+;   0 @@-)
%            Number of variables   :  110 (  17   ^;  93   !;   0   ?; 110   :)

% Comments : 
%------------------------------------------------------------------------------
thf(labeled_graph_b_nat_type,type,
    labeled_graph_b_nat: $tType ).

thf(produc1235635379_b_nat_type,type,
    produc1235635379_b_nat: $tType ).

thf(allegorical_term_b_type,type,
    allegorical_term_b: $tType ).

thf(produc1478835367term_b_type,type,
    produc1478835367term_b: $tType ).

thf(set_Pr1986765409at_nat_type,type,
    set_Pr1986765409at_nat: $tType ).

thf(set_nat_type,type,
    set_nat: $tType ).

thf(set_Pr9961929at_nat_type,type,
    set_Pr9961929at_nat: $tType ).

thf(graph_529870330at_nat_type,type,
    graph_529870330at_nat: labeled_graph_b_nat > labeled_graph_b_nat > set_Pr1986765409at_nat > $o ).

thf(labele460410879_b_nat_type,type,
    labele460410879_b_nat: labeled_graph_b_nat > set_nat ).

thf(produc951298923_b_nat_type,type,
    produc951298923_b_nat: labeled_graph_b_nat > labeled_graph_b_nat > produc1235635379_b_nat ).

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

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

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

thf(produc1542243159_b_nat_type,type,
    produc1542243159_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(v_type,type,
    v: allegorical_term_b ).

thf(u_type,type,
    u: allegorical_term_b ).

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

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

thf(produc1223098053term_b_type,type,
    produc1223098053term_b: produc1478835367term_b > allegorical_term_b ).

thf(produc1990145943term_b_type,type,
    produc1990145943term_b: allegorical_term_b > allegorical_term_b > produc1478835367term_b ).

thf(finite1987068434at_nat_type,type,
    finite1987068434at_nat: set_Pr9961929at_nat > $o ).

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

thf(produc854192515term_b_type,type,
    produc854192515term_b: produc1478835367term_b > allegorical_term_b ).

thf(produc194497945_b_nat_type,type,
    produc194497945_b_nat: produc1235635379_b_nat > labeled_graph_b_nat ).

thf(conj_0,conjecture,
    ( ( 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 ) ) ) ) ) ) ) )
    & ( 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 ) ) ) ) ) ) ) )
    & ( ( 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 ) ) ) ) ) ) ) )
    & ( 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 ) ) ) ) ) ) ) ) ) ) ).

thf(zf_stmt_0,negated_conjecture,
    ~ ( ( 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 ) ) ) ) ) ) ) )
      & ( 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 ) ) ) ) ) ) ) )
      & ( ( 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 ) ) ) ) ) ) ) )
      & ( 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 ) ) ) ) ) ) ) ) ) ),
    inference('cnf.neg',[status(esa)],[conj_0]) ).

thf(zip_derived_cl164,plain,
    ~ ( ( 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 ) ) ) ) ) ) ) )
      & ( 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 ) ) ) ) ) ) ) )
      & ( ( 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 ) ) ) ) ) ) ) )
      & ( 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 ) ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[zf_stmt_0]) ).

thf(fact_76_fst__conv,axiom,
    ! [X1: allegorical_term_b,X22: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
      = X1 ) ).

thf(zip_derived_cl33,plain,
    ( !!
    @ ^ [Y0: allegorical_term_b] :
        ( !!
        @ ^ [Y1: allegorical_term_b] :
            ( ( produc854192515term_b @ ( produc1990145943term_b @ Y0 @ Y1 ) )
            = Y0 ) ) ),
    inference(cnf,[status(esa)],[fact_76_fst__conv]) ).

thf(zip_derived_cl224,plain,
    ! [X2: allegorical_term_b] :
      ( !!
      @ ^ [Y0: allegorical_term_b] :
          ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ Y0 ) )
          = X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).

thf(zip_derived_cl225,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl224]) ).

thf(zip_derived_cl226,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(fact_85_snd__conv,axiom,
    ! [X1: allegorical_term_b,X22: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X1 @ X22 ) )
      = X22 ) ).

thf(zip_derived_cl36,plain,
    ( !!
    @ ^ [Y0: allegorical_term_b] :
        ( !!
        @ ^ [Y1: allegorical_term_b] :
            ( ( produc1223098053term_b @ ( produc1990145943term_b @ Y0 @ Y1 ) )
            = Y1 ) ) ),
    inference(cnf,[status(esa)],[fact_85_snd__conv]) ).

thf(zip_derived_cl229,plain,
    ! [X2: allegorical_term_b] :
      ( !!
      @ ^ [Y0: allegorical_term_b] :
          ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ Y0 ) )
          = Y0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).

thf(zip_derived_cl230,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl229]) ).

thf(zip_derived_cl231,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(fact_86_snd__conv,axiom,
    ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
      = X22 ) ).

thf(zip_derived_cl37,plain,
    ( !!
    @ ^ [Y0: labeled_graph_b_nat] :
        ( !!
        @ ^ [Y1: labeled_graph_b_nat] :
            ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ Y0 @ Y1 ) )
            = Y1 ) ) ),
    inference(cnf,[status(esa)],[fact_86_snd__conv]) ).

thf(zip_derived_cl232,plain,
    ! [X2: labeled_graph_b_nat] :
      ( !!
      @ ^ [Y0: labeled_graph_b_nat] :
          ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ Y0 ) )
          = Y0 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl37]) ).

thf(zip_derived_cl233,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl232]) ).

thf(zip_derived_cl234,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(fact_12_verts__in__translation__finite_I2_J,axiom,
    ! [X: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X ) ) ) ).

thf(zip_derived_cl4,plain,
    ( !!
    @ ^ [Y0: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_12_verts__in__translation__finite_I2_J]) ).

thf(zip_derived_cl165,plain,
    ! [X2: allegorical_term_b] : ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( translation_b @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl4]) ).

thf(zip_derived_cl226_001,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_002,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(zip_derived_cl234_003,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(fact_20_verts__in__translation__finite_I1_J,axiom,
    ! [X: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X ) ) ) ).

thf(zip_derived_cl5,plain,
    ( !!
    @ ^ [Y0: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ Y0 ) ) ) ),
    inference(cnf,[status(esa)],[fact_20_verts__in__translation__finite_I1_J]) ).

thf(zip_derived_cl166,plain,
    ! [X2: allegorical_term_b] : ( finite_finite_nat @ ( labele460410879_b_nat @ ( translation_b @ X2 ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl5]) ).

thf(zip_derived_cl226_004,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_005,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(zip_derived_cl234_006,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl226_007,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_008,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(zip_derived_cl234_009,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(fact_3_graph__rule__translation,axiom,
    ! [X: allegorical_term_b,Y: allegorical_term_b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X ) @ ( translation_b @ ( allegorical_A_Int_b @ X @ Y ) ) ) ) ) ) ) ).

thf(zip_derived_cl0,plain,
    ( !!
    @ ^ [Y0: allegorical_term_b] :
        ( !!
        @ ^ [Y1: allegorical_term_b] :
            ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) ) ) )
            & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) )
              = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) ) )
            & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) ) )
            & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ Y0 ) @ ( translation_b @ ( allegorical_A_Int_b @ Y0 @ Y1 ) ) ) ) ) ) ) ) ),
    inference(cnf,[status(esa)],[fact_3_graph__rule__translation]) ).

thf(zip_derived_cl174,plain,
    ! [X2: allegorical_term_b] :
      ( !!
      @ ^ [Y0: allegorical_term_b] :
          ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) ) ) )
          & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) )
            = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) ) )
          & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) ) )
          & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ Y0 ) ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl0]) ).

thf(zip_derived_cl175,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) ) )
      & ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) )
        = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) )
      & ( finite_finite_nat @ ( labele460410879_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) )
      & ( finite1987068434at_nat @ ( labeled_edges_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl174]) ).

thf(zip_derived_cl177,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl175]) ).

thf(zip_derived_cl180,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) )
      = ( restrict_b_nat @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl177]) ).

thf(zip_derived_cl234_010,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl234_011,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl246,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) )
      = ( restrict_b_nat @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl180,zip_derived_cl234,zip_derived_cl234]) ).

thf(zip_derived_cl226_012,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_013,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(fact_75_fst__conv,axiom,
    ! [X1: labeled_graph_b_nat,X22: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X1 @ X22 ) )
      = X1 ) ).

thf(zip_derived_cl32,plain,
    ( !!
    @ ^ [Y0: labeled_graph_b_nat] :
        ( !!
        @ ^ [Y1: labeled_graph_b_nat] :
            ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ Y0 @ Y1 ) )
            = Y0 ) ) ),
    inference(cnf,[status(esa)],[fact_75_fst__conv]) ).

thf(zip_derived_cl216,plain,
    ! [X2: labeled_graph_b_nat] :
      ( !!
      @ ^ [Y0: labeled_graph_b_nat] :
          ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ Y0 ) )
          = X2 ) ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).

thf(zip_derived_cl217,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X2 ),
    inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl216]) ).

thf(zip_derived_cl218,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl217]) ).

thf(zip_derived_cl226_014,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_015,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(zip_derived_cl234_016,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl226_017,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc854192515term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl225]) ).

thf(zip_derived_cl231_018,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] :
      ( ( produc1223098053term_b @ ( produc1990145943term_b @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl230]) ).

thf(zip_derived_cl218_019,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl217]) ).

thf(zip_derived_cl176,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] : ( graph_529870330at_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( produc1542243159_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) ) ) ),
    inference(lazy_cnf_and,[status(thm)],[zip_derived_cl175]) ).

thf(zip_derived_cl218_020,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl217]) ).

thf(zip_derived_cl218_021,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc1542243159_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X2 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl217]) ).

thf(zip_derived_cl219,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] : ( graph_529870330at_nat @ ( translation_b @ X2 ) @ ( produc194497945_b_nat @ ( produc951298923_b_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X2 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl176,zip_derived_cl218,zip_derived_cl218]) ).

thf(zip_derived_cl234_022,plain,
    ! [X2: labeled_graph_b_nat,X4: labeled_graph_b_nat] :
      ( ( produc194497945_b_nat @ ( produc951298923_b_nat @ X2 @ X4 ) )
      = X4 ),
    inference('simplify nested equalities',[status(thm)],[zip_derived_cl233]) ).

thf(zip_derived_cl237,plain,
    ! [X2: allegorical_term_b,X4: allegorical_term_b] : ( graph_529870330at_nat @ ( translation_b @ X2 ) @ ( translation_b @ ( allegorical_A_Int_b @ X2 @ X4 ) ) @ ( id_on_nat @ ( labele460410879_b_nat @ ( translation_b @ X2 ) ) ) ),
    inference(demod,[status(thm)],[zip_derived_cl219,zip_derived_cl234]) ).

thf(zip_derived_cl736,plain,
    ~ ( $true
      & $true
      & ( ( translation_b @ ( allegorical_A_Int_b @ u @ v ) )
        = ( translation_b @ ( allegorical_A_Int_b @ u @ v ) ) )
      & $true ),
    inference(demod,[status(thm)],[zip_derived_cl164,zip_derived_cl226,zip_derived_cl231,zip_derived_cl234,zip_derived_cl165,zip_derived_cl226,zip_derived_cl231,zip_derived_cl234,zip_derived_cl166,zip_derived_cl226,zip_derived_cl231,zip_derived_cl234,zip_derived_cl226,zip_derived_cl231,zip_derived_cl234,zip_derived_cl246,zip_derived_cl226,zip_derived_cl231,zip_derived_cl218,zip_derived_cl226,zip_derived_cl231,zip_derived_cl234,zip_derived_cl226,zip_derived_cl231,zip_derived_cl218,zip_derived_cl237]) ).

thf(zip_derived_cl737,plain,
    $false,
    inference('simplify boolean subterms',[status(thm)],[zip_derived_cl736]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ITP178^1 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Pytpp3p78Y true
% 0.13/0.34  % Computer : n029.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 16:30:25 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  % Running portfolio for 300 s
% 0.13/0.34  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35  % Number of cores: 8
% 0.13/0.35  % Python version: Python 3.6.8
% 0.13/0.35  % Running in HO mode
% 0.20/0.63  % Total configuration time : 828
% 0.20/0.63  % Estimated wc time : 1656
% 0.20/0.63  % Estimated cpu time (8 cpus) : 207.0
% 0.20/0.73  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.20/0.75  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.20/0.76  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.20/0.80  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.20/0.83  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 1.75/1.14  % Solved by lams/30_b.l.sh.
% 1.75/1.14  % done 0 iterations in 0.246s
% 1.75/1.14  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 1.75/1.14  % SZS output start Refutation
% See solution above
% 1.75/1.14  
% 1.75/1.14  
% 1.75/1.14  % Terminating...
% 2.15/1.27  % Runner terminated.
% 2.15/1.28  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------