TSTP Solution File: ITP386_1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ITP386_1 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n018.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 : Mon May 20 22:26:51 EDT 2024

% Result   : Theorem 11.21s 4.28s
% Output   : Refutation 11.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  156
% Syntax   : Number of formulae    :  196 (  34 unt; 118 typ;   0 def)
%            Number of atoms       :  175 ( 147 equ;   0 cnn)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  667 (  22   ~;   0   |;  35   &; 548   @)
%                                         (  14 <=>;  48  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Number of types       :   92 (  91 usr)
%            Number of type conns  :   36 (  36   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   29 (  27 usr;   8 con; 0-2 aty)
%            Number of variables   :  204 (   0   ^ 180   !;  24   ?; 204   :)

% Comments : 
%------------------------------------------------------------------------------
thf('\'B_b_option_fun_b_b_option_fun_fun$\'_type',type,
    '\'B_b_option_fun_b_b_option_fun_fun$\'': $tType ).

thf('\'B_b_option_fun_b_option_fun$\'_type',type,
    '\'B_b_option_fun_b_option_fun$\'': $tType ).

thf('\'A_option_c_option_fun$\'_type',type,
    '\'A_option_c_option_fun$\'': $tType ).

thf('\'A_a_option_fun_c_c_option_fun_fun$\'_type',type,
    '\'A_a_option_fun_c_c_option_fun_fun$\'': $tType ).

thf('\'A_c_fun$\'_type',type,
    '\'A_c_fun$\'': $tType ).

thf('\'C_c_option_fun$\'_type',type,
    '\'C_c_option_fun$\'': $tType ).

thf('\'C_option$\'_type',type,
    '\'C_option$\'': $tType ).

thf('\'C_c_option_fun_a_a_option_fun_fun$\'_type',type,
    '\'C_c_option_fun_a_a_option_fun_fun$\'': $tType ).

thf('\'B_option$\'_type',type,
    '\'B_option$\'': $tType ).

thf('\'B_option_c_option_bool_fun_fun$\'_type',type,
    '\'B_option_c_option_bool_fun_fun$\'': $tType ).

thf('\'B_b_fun$\'_type',type,
    '\'B_b_fun$\'': $tType ).

thf('\'B_c_c_option_fun_fun$\'_type',type,
    '\'B_c_c_option_fun_fun$\'': $tType ).

thf('\'C_c_c_fun_fun$\'_type',type,
    '\'C_c_c_fun_fun$\'': $tType ).

thf('\'C_c_fun$\'_type',type,
    '\'C_c_fun$\'': $tType ).

thf('\'B_option_b_option_fun$\'_type',type,
    '\'B_option_b_option_fun$\'': $tType ).

thf('\'B_c_option_fun$\'_type',type,
    '\'B_c_option_fun$\'': $tType ).

thf('\'C_a_option_fun$\'_type',type,
    '\'C_a_option_fun$\'': $tType ).

thf('\'C_option_set$\'_type',type,
    '\'C_option_set$\'': $tType ).

thf('\'C_a_fun$\'_type',type,
    '\'C_a_fun$\'': $tType ).

thf('\'C_option_c_option_bool_fun_fun$\'_type',type,
    '\'C_option_c_option_bool_fun_fun$\'': $tType ).

thf('\'A_option_bool_fun$\'_type',type,
    '\'A_option_bool_fun$\'': $tType ).

thf('\'B_option_b_fun$\'_type',type,
    '\'B_option_b_fun$\'': $tType ).

thf('\'C_option_c_fun$\'_type',type,
    '\'C_option_c_fun$\'': $tType ).

thf('\'C_option_a_option_bool_fun_fun$\'_type',type,
    '\'C_option_a_option_bool_fun_fun$\'': $tType ).

thf('\'B_b_b_option_fun_fun$\'_type',type,
    '\'B_b_b_option_fun_fun$\'': $tType ).

thf('\'C_b_option_fun$\'_type',type,
    '\'C_b_option_fun$\'': $tType ).

thf('\'B$\'_type',type,
    '\'B$\'': $tType ).

thf('\'C_c_option_fun_b_b_option_fun_fun$\'_type',type,
    '\'C_c_option_fun_b_b_option_fun_fun$\'': $tType ).

thf('\'C_option_b_option_bool_fun_fun$\'_type',type,
    '\'C_option_b_option_bool_fun_fun$\'': $tType ).

thf('\'A_a_option_fun_b_b_option_fun_fun$\'_type',type,
    '\'A_a_option_fun_b_b_option_fun_fun$\'': $tType ).

thf('\'A_a_sum_a_fun$\'_type',type,
    '\'A_a_sum_a_fun$\'': $tType ).

thf('\'C$\'_type',type,
    '\'C$\'': $tType ).

thf('\'A_option_b_option_fun$\'_type',type,
    '\'A_option_b_option_fun$\'': $tType ).

thf('\'B_option_c_option_fun$\'_type',type,
    '\'B_option_c_option_fun$\'': $tType ).

thf('\'C_b_b_fun_fun$\'_type',type,
    '\'C_b_b_fun_fun$\'': $tType ).

thf('\'C_c_c_option_fun_fun$\'_type',type,
    '\'C_c_c_option_fun_fun$\'': $tType ).

thf('\'C_b_fun$\'_type',type,
    '\'C_b_fun$\'': $tType ).

thf('\'B_b_sum_c_option_fun$\'_type',type,
    '\'B_b_sum_c_option_fun$\'': $tType ).

thf('\'A_option$\'_type',type,
    '\'A_option$\'': $tType ).

thf('\'A_a_option_fun_a_a_option_fun_fun$\'_type',type,
    '\'A_a_option_fun_a_a_option_fun_fun$\'': $tType ).

thf('\'A_option_c_option_bool_fun_fun$\'_type',type,
    '\'A_option_c_option_bool_fun_fun$\'': $tType ).

thf('\'B_a_fun$\'_type',type,
    '\'B_a_fun$\'': $tType ).

thf('\'C_option_b_option_fun$\'_type',type,
    '\'C_option_b_option_fun$\'': $tType ).

thf(tlbool_type,type,
    tlbool: $tType ).

thf('\'A_option_a_fun$\'_type',type,
    '\'A_option_a_fun$\'': $tType ).

thf('\'A_a_option_fun$\'_type',type,
    '\'A_a_option_fun$\'': $tType ).

thf('\'A_option_a_option_fun$\'_type',type,
    '\'A_option_a_option_fun$\'': $tType ).

thf('\'A_bool_fun$\'_type',type,
    '\'A_bool_fun$\'': $tType ).

thf('\'C_option_a_option_fun$\'_type',type,
    '\'C_option_a_option_fun$\'': $tType ).

thf('\'A_set$\'_type',type,
    '\'A_set$\'': $tType ).

thf('\'B_b_option_fun_c_c_option_fun_fun$\'_type',type,
    '\'B_b_option_fun_c_c_option_fun_fun$\'': $tType ).

thf('\'C_bool_fun$\'_type',type,
    '\'C_bool_fun$\'': $tType ).

thf('\'A_b_fun$\'_type',type,
    '\'A_b_fun$\'': $tType ).

thf('\'B_c_c_fun_fun$\'_type',type,
    '\'B_c_c_fun_fun$\'': $tType ).

thf('\'B_set$\'_type',type,
    '\'B_set$\'': $tType ).

thf('\'B_option_a_option_bool_fun_fun$\'_type',type,
    '\'B_option_a_option_bool_fun_fun$\'': $tType ).

thf('\'Bool_c_option_fun$\'_type',type,
    '\'Bool_c_option_fun$\'': $tType ).

thf('\'A$\'_type',type,
    '\'A$\'': $tType ).

thf('\'B_option_option$\'_type',type,
    '\'B_option_option$\'': $tType ).

thf('\'Bool_b_option_fun$\'_type',type,
    '\'Bool_b_option_fun$\'': $tType ).

thf('\'A_b_b_option_fun_fun$\'_type',type,
    '\'A_b_b_option_fun_fun$\'': $tType ).

thf('\'A_b_option_fun$\'_type',type,
    '\'A_b_option_fun$\'': $tType ).

thf('\'C_c_sum_c_option_fun$\'_type',type,
    '\'C_c_sum_c_option_fun$\'': $tType ).

thf('\'Bool_bool_fun$\'_type',type,
    '\'Bool_bool_fun$\'': $tType ).

thf('\'B_a_option_fun$\'_type',type,
    '\'B_a_option_fun$\'': $tType ).

thf('\'A_a_a_fun_fun$\'_type',type,
    '\'A_a_a_fun_fun$\'': $tType ).

thf('\'B_b_option_fun_a_a_option_fun_fun$\'_type',type,
    '\'B_b_option_fun_a_a_option_fun_fun$\'': $tType ).

thf('\'C_option_c_option_fun$\'_type',type,
    '\'C_option_c_option_fun$\'': $tType ).

thf('\'A_a_fun$\'_type',type,
    '\'A_a_fun$\'': $tType ).

thf('\'B_b_sum_b_option_fun$\'_type',type,
    '\'B_b_sum_b_option_fun$\'': $tType ).

thf('\'B_b_b_fun_fun$\'_type',type,
    '\'B_b_b_fun_fun$\'': $tType ).

thf('\'B_b_option_fun$\'_type',type,
    '\'B_b_option_fun$\'': $tType ).

thf('\'C_option_option$\'_type',type,
    '\'C_option_option$\'': $tType ).

thf('\'A_option_b_option_bool_fun_fun$\'_type',type,
    '\'A_option_b_option_bool_fun_fun$\'': $tType ).

thf('\'C_c_sum_c_fun$\'_type',type,
    '\'C_c_sum_c_fun$\'': $tType ).

thf('\'A_a_sum_b_option_fun$\'_type',type,
    '\'A_a_sum_b_option_fun$\'': $tType ).

thf('\'A_a_option_fun_a_option_fun$\'_type',type,
    '\'A_a_option_fun_a_option_fun$\'': $tType ).

thf('\'C_option_bool_fun$\'_type',type,
    '\'C_option_bool_fun$\'': $tType ).

thf('\'A_option_a_option_bool_fun_fun$\'_type',type,
    '\'A_option_a_option_bool_fun_fun$\'': $tType ).

thf('\'C_c_option_fun_c_option_fun$\'_type',type,
    '\'C_c_option_fun_c_option_fun$\'': $tType ).

thf('\'A_b_b_fun_fun$\'_type',type,
    '\'A_b_b_fun_fun$\'': $tType ).

thf('\'C_c_option_fun_c_c_option_fun_fun$\'_type',type,
    '\'C_c_option_fun_c_c_option_fun_fun$\'': $tType ).

thf('\'B_option_bool_fun$\'_type',type,
    '\'B_option_bool_fun$\'': $tType ).

thf('\'B_option_a_option_fun$\'_type',type,
    '\'B_option_a_option_fun$\'': $tType ).

thf('\'B_c_fun$\'_type',type,
    '\'B_c_fun$\'': $tType ).

thf('\'C_set$\'_type',type,
    '\'C_set$\'': $tType ).

thf('\'B_option_b_option_bool_fun_fun$\'_type',type,
    '\'B_option_b_option_bool_fun_fun$\'': $tType ).

thf('\'B_bool_fun$\'_type',type,
    '\'B_bool_fun$\'': $tType ).

thf('\'A_c_option_fun$\'_type',type,
    '\'A_c_option_fun$\'': $tType ).

thf('\'B_option_set$\'_type',type,
    '\'B_option_set$\'': $tType ).

thf('\'B_b_sum_b_fun$\'_type',type,
    '\'B_b_sum_b_fun$\'': $tType ).

thf('\'none$a\'_type',type,
    '\'none$a\'': '\'B_option$\'' ).

thf('\'some$a\'_type',type,
    '\'some$a\'': '\'C_c_option_fun$\'' ).

thf('\'bind$b\'_type',type,
    '\'bind$b\'': '\'B_option$\'' > '\'B_c_option_fun$\'' > '\'C_option$\'' ).

thf('\'g$\'_type',type,
    '\'g$\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' ).

thf('\'none$\'_type',type,
    '\'none$\'': '\'C_option$\'' ).

thf('\'map_option$d\'_type',type,
    '\'map_option$d\'': '\'B_c_fun$\'' > '\'B_option_c_option_fun$\'' ).

thf('\'fun_app$an\'_type',type,
    '\'fun_app$an\'': '\'B_option_c_option_fun$\'' > '\'B_option$\'' > '\'C_option$\'' ).

thf('\'some$\'_type',type,
    '\'some$\'': '\'B_b_option_fun$\'' ).

thf('\'uvg$\'_type',type,
    '\'uvg$\'': '\'B_c_fun$\'' > '\'B_c_option_fun$\'' ).

thf('\'thesis$\'_type',type,
    '\'thesis$\'': $o ).

thf('\'uwc$\'_type',type,
    '\'uwc$\'': '\'C_c_option_fun$\'' ).

thf('\'preregister$b\'_type',type,
    '\'preregister$b\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > $o ).

thf('\'fun_app$k\'_type',type,
    '\'fun_app$k\'': '\'C_c_fun$\'' > '\'C$\'' > '\'C$\'' ).

thf('\'fun_app$n\'_type',type,
    '\'fun_app$n\'': '\'B_c_option_fun$\'' > '\'B$\'' > '\'C_option$\'' ).

thf('\'fun_app$am\'_type',type,
    '\'fun_app$am\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > '\'B_b_option_fun$\'' > '\'C_c_option_fun$\'' ).

thf('\'valid_getter_setter$\'_type',type,
    '\'valid_getter_setter$\'': '\'C_b_fun$\'' > '\'B_c_c_fun_fun$\'' > $o ).

thf('\'case_option$c\'_type',type,
    '\'case_option$c\'': '\'C_option$\'' > '\'B_c_option_fun$\'' > '\'B_option_c_option_fun$\'' ).

thf('\'register_from_getter_setter$a\'_type',type,
    '\'register_from_getter_setter$a\'': '\'C_b_fun$\'' > '\'B_c_c_fun_fun$\'' > '\'B_b_option_fun_c_c_option_fun_fun$\'' ).

thf('\'register$a\'_type',type,
    '\'register$a\'': '\'B_b_option_fun_c_c_option_fun_fun$\'' > $o ).

thf('\'fun_app$y\'_type',type,
    '\'fun_app$y\'': '\'B_c_c_fun_fun$\'' > '\'B$\'' > '\'C_c_fun$\'' ).

thf('\'fun_app$m\'_type',type,
    '\'fun_app$m\'': '\'C_b_fun$\'' > '\'C$\'' > '\'B$\'' ).

thf('\'uuu$\'_type',type,
    '\'uuu$\'': '\'B_c_c_option_fun_fun$\'' > '\'C$\'' > '\'B_c_option_fun$\'' ).

thf('\'uu$\'_type',type,
    '\'uu$\'': '\'B_c_c_fun_fun$\'' > '\'C$\'' > '\'B_c_option_fun$\'' ).

thf('\'fun_app$w\'_type',type,
    '\'fun_app$w\'': '\'B_c_c_option_fun_fun$\'' > '\'B$\'' > '\'C_c_option_fun$\'' ).

thf('\'fun_app$j\'_type',type,
    '\'fun_app$j\'': '\'C_c_option_fun$\'' > '\'C$\'' > '\'C_option$\'' ).

thf('\'fun_app$g\'_type',type,
    '\'fun_app$g\'': '\'B_b_option_fun$\'' > '\'B$\'' > '\'B_option$\'' ).

thf('\'fun_app$o\'_type',type,
    '\'fun_app$o\'': '\'B_c_fun$\'' > '\'B$\'' > '\'C$\'' ).

thf(28,axiom,
    ! [A: '\'C$\''] :
      ( ( '\'fun_app$j\'' @ '\'uwc$\'' @ A )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom60) ).

thf(174,plain,
    ! [A: '\'C$\''] :
      ( ( '\'fun_app$j\'' @ '\'uwc$\'' @ A )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(10,axiom,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'register$a\'' @ A )
    <=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
          ( ( A
            = ( '\'register_from_getter_setter$a\'' @ B @ C ) )
          & ( '\'valid_getter_setter$\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom136) ).

thf(78,plain,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( ( '\'register$a\'' @ A )
       => ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
            ( ( A
              = ( '\'register_from_getter_setter$a\'' @ B @ C ) )
            & ( '\'valid_getter_setter$\'' @ B @ C ) ) )
      & ( ? [B: '\'C_b_fun$\'',C: '\'B_c_c_fun_fun$\''] :
            ( ( A
              = ( '\'register_from_getter_setter$a\'' @ B @ C ) )
            & ( '\'valid_getter_setter$\'' @ B @ C ) )
       => ( '\'register$a\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(16,axiom,
    ! [A: '\'B_option$\''] :
      ( ! [B: '\'B$\''] :
          ( A
         != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
    <=> ( A = '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).

thf(121,plain,
    ! [A: '\'B_option$\''] :
      ( ( ! [B: '\'B$\''] :
            ( A
           != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A = '\'none$a\'' ) )
      & ( ( A = '\'none$a\'' )
       => ! [B: '\'B$\''] :
            ( A
           != ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(24,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uvg$\'' @ A ) @ B )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).

thf(160,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uvg$\'' @ A ) @ B )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(39,axiom,
    ! [A: '\'B_c_c_fun_fun$\'',B: '\'C_b_fun$\''] :
      ( ( ! [C: '\'B_b_option_fun$\'',D: '\'C$\''] :
            ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ '\'g$\'' @ C ) @ D )
            = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ A @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ B @ D ) ) ) )
        & ( '\'valid_getter_setter$\'' @ B @ A ) )
     => '\'thesis$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis73) ).

thf(229,plain,
    ! [A: '\'B_c_c_fun_fun$\'',B: '\'C_b_fun$\''] :
      ( ( ! [C: '\'B_b_option_fun$\'',D: '\'C$\''] :
            ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ '\'g$\'' @ C ) @ D )
            = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ A @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ B @ D ) ) ) )
        & ( '\'valid_getter_setter$\'' @ B @ A ) )
     => '\'thesis$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(20,axiom,
    ! [A: '\'B_option$\''] :
      ( ( A != '\'none$a\'' )
    <=> ? [B: '\'B$\''] :
          ( A
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).

thf(141,plain,
    ! [A: '\'B_option$\''] :
      ( ( ( A != '\'none$a\'' )
       => ? [B: '\'B$\''] :
            ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) )
      & ( ? [B: '\'B$\''] :
            ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A != '\'none$a\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(3,axiom,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\'',D: '\'B_c_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$n\'' @ C @ E )
              = ( '\'fun_app$n\'' @ D @ E ) ) ) )
     => ( ( '\'bind$b\'' @ A @ C )
        = ( '\'bind$b\'' @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).

thf(41,plain,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\'',D: '\'B_c_option_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$n\'' @ C @ E )
              = ( '\'fun_app$n\'' @ D @ E ) ) ) )
     => ( ( '\'bind$b\'' @ A @ C )
        = ( '\'bind$b\'' @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(7,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( '\'none$\''
        = ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) )
    <=> ( B = '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom223) ).

thf(59,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( ( '\'none$\''
          = ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) )
       => ( B = '\'none$a\'' ) )
      & ( ( B = '\'none$a\'' )
       => ( '\'none$\''
          = ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(31,axiom,
    ! [A: '\'C_option$\'',B: '\'B_c_option_fun$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ '\'none$a\'' )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).

thf(187,plain,
    ! [A: '\'C_option$\'',B: '\'B_c_option_fun$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ '\'none$a\'' )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(29,axiom,
    ! [A: '\'C_option$\'',B: '\'B_c_option_fun$\'',C: '\'B$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
      = ( '\'fun_app$n\'' @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).

thf(177,plain,
    ! [A: '\'C_option$\'',B: '\'B_c_option_fun$\'',C: '\'B$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ A @ B ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ C ) )
      = ( '\'fun_app$n\'' @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(38,axiom,
    ! [A: '\'C_option$\''] :
      ( ( A != '\'none$\'' )
    <=> ? [B: '\'C$\''] :
          ( A
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).

thf(222,plain,
    ! [A: '\'C_option$\''] :
      ( ( ( A != '\'none$\'' )
       => ? [B: '\'C$\''] :
            ( A
            = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) )
      & ( ? [B: '\'C$\''] :
            ( A
            = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
       => ( A != '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(27,axiom,
    ! [A: '\'C$\''] :
      ( '\'none$\''
     != ( '\'fun_app$j\'' @ '\'some$a\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).

thf(170,plain,
    ! [A: '\'C$\''] :
      ( '\'none$\''
     != ( '\'fun_app$j\'' @ '\'some$a\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(36,axiom,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'preregister$b\'' @ A )
    <=> ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
        ! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
          ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
          = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).

thf(202,plain,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( ( '\'preregister$b\'' @ A )
       => ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
          ! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
            ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
            = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) ) )
      & ( ? [B: '\'C_b_fun$\'',C: '\'B_c_c_option_fun_fun$\''] :
          ! [D: '\'B_b_option_fun$\'',E: '\'C$\''] :
            ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ A @ D ) @ E )
            = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uuu$\'' @ C @ E ) ) @ ( '\'fun_app$g\'' @ D @ ( '\'fun_app$m\'' @ B @ E ) ) ) )
       => ( '\'preregister$b\'' @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(35,axiom,
    '\'register$a\'' @ '\'g$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).

thf(201,plain,
    '\'register$a\'' @ '\'g$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(13,axiom,
    ! [A: '\'B$\'',B: '\'B$\''] :
      ( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).

thf(102,plain,
    ! [A: '\'B$\'',B: '\'B$\''] :
      ( ( ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$g\'' @ '\'some$\'' @ A )
          = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(14,axiom,
    ! [A: '\'B_c_fun$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ '\'none$a\'' )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom278) ).

thf(109,plain,
    ! [A: '\'B_c_fun$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ '\'none$a\'' )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(33,axiom,
    ! [A: '\'C_option$\'',B: '\'C$\''] :
      ( ( A
        = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
     => ( A != '\'none$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom114) ).

thf(193,plain,
    ! [A: '\'C_option$\'',B: '\'C$\''] :
      ( ( A
        = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
     => ( A != '\'none$\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(19,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
        = '\'none$\'' )
    <=> ( B = '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).

thf(134,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = '\'none$\'' )
       => ( B = '\'none$a\'' ) )
      & ( ( B = '\'none$a\'' )
       => ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(17,axiom,
    ! [A: '\'B_c_c_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uu$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ A @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).

thf(128,plain,
    ! [A: '\'B_c_c_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uu$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ A @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(26,axiom,
    ! [A: '\'B$\''] :
      ( '\'none$a\''
     != ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom112) ).

thf(166,plain,
    ! [A: '\'B$\''] :
      ( '\'none$a\''
     != ( '\'fun_app$g\'' @ '\'some$\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(21,axiom,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_fun$\'',D: '\'B_c_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$o\'' @ C @ E )
              = ( '\'fun_app$o\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ C ) @ A )
        = ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom290) ).

thf(148,plain,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_fun$\'',D: '\'B_c_fun$\''] :
      ( ( ( A = B )
        & ! [E: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ E ) )
           => ( ( '\'fun_app$o\'' @ C @ E )
              = ( '\'fun_app$o\'' @ D @ E ) ) ) )
     => ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ C ) @ A )
        = ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(30,axiom,
    ! [A: '\'C_option$\''] :
      ( ! [B: '\'C$\''] :
          ( A
         != ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
    <=> ( A = '\'none$\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).

thf(180,plain,
    ! [A: '\'C_option$\''] :
      ( ( ! [B: '\'C$\''] :
            ( A
           != ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
       => ( A = '\'none$\'' ) )
      & ( ( A = '\'none$\'' )
       => ! [B: '\'C$\''] :
            ( A
           != ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(9,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
        = '\'none$\'' )
    <=> ( B = '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).

thf(71,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = '\'none$\'' )
       => ( B = '\'none$a\'' ) )
      & ( ( B = '\'none$a\'' )
       => ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = '\'none$\'' ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(6,axiom,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$b\'' @ A @ C )
        = ( '\'bind$b\'' @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).

thf(54,plain,
    ! [A: '\'B_option$\'',B: '\'B_option$\'',C: '\'B_c_option_fun$\''] :
      ( ( A = B )
     => ( ( '\'bind$b\'' @ A @ C )
        = ( '\'bind$b\'' @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(11,axiom,
    ! [A: '\'B_option$\'',B: '\'B_c_option_fun$\'',C: '\'C$\''] :
      ( ( ( '\'bind$b\'' @ A @ B )
        = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
    <=> ? [D: '\'B$\''] :
          ( ( A
            = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
          & ( ( '\'fun_app$n\'' @ B @ D )
            = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom414) ).

thf(86,plain,
    ! [A: '\'B_option$\'',B: '\'B_c_option_fun$\'',C: '\'C$\''] :
      ( ( ( ( '\'bind$b\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
       => ? [D: '\'B$\''] :
            ( ( A
              = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
            & ( ( '\'fun_app$n\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) )
      & ( ? [D: '\'B$\''] :
            ( ( A
              = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
            & ( ( '\'fun_app$n\'' @ B @ D )
              = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) )
       => ( ( '\'bind$b\'' @ A @ B )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(8,axiom,
    ! [A: '\'B_option$\'',B: '\'B$\''] :
      ( ( A
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
     => ( A != '\'none$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom115) ).

thf(66,plain,
    ! [A: '\'B_option$\'',B: '\'B$\''] :
      ( ( A
        = ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
     => ( A != '\'none$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(22,axiom,
    ! [A: '\'B_c_c_option_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ ( '\'fun_app$w\'' @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).

thf(155,plain,
    ! [A: '\'B_c_c_option_fun_fun$\'',B: '\'C$\'',C: '\'B$\''] :
      ( ( '\'fun_app$n\'' @ ( '\'uuu$\'' @ A @ B ) @ C )
      = ( '\'fun_app$j\'' @ ( '\'fun_app$w\'' @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(34,axiom,
    ! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\'',C: '\'B_b_option_fun$\'',D: '\'C$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ ( '\'register_from_getter_setter$a\'' @ A @ B ) @ C ) @ D )
      = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).

thf(198,plain,
    ! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\'',C: '\'B_b_option_fun$\'',D: '\'C$\''] :
      ( ( '\'fun_app$j\'' @ ( '\'fun_app$am\'' @ ( '\'register_from_getter_setter$a\'' @ A @ B ) @ C ) @ D )
      = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uu$\'' @ B @ D ) ) @ ( '\'fun_app$g\'' @ C @ ( '\'fun_app$m\'' @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(37,axiom,
    ! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\''] :
      ( ( '\'valid_getter_setter$\'' @ A @ B )
    <=> ( ! [C: '\'C$\''] :
            ( C
            = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
        & ! [C: '\'B$\'',D: '\'C$\''] :
            ( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
            = C )
        & ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
            ( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
            = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).

thf(209,plain,
    ! [A: '\'C_b_fun$\'',B: '\'B_c_c_fun_fun$\''] :
      ( ( ( '\'valid_getter_setter$\'' @ A @ B )
       => ( ! [C: '\'C$\''] :
              ( C
              = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
          & ! [C: '\'B$\'',D: '\'C$\''] :
              ( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
              = C )
          & ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
              ( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
              = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) ) )
      & ( ( ! [C: '\'C$\''] :
              ( C
              = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ ( '\'fun_app$m\'' @ A @ C ) ) @ C ) )
          & ! [C: '\'B$\'',D: '\'C$\''] :
              ( ( '\'fun_app$m\'' @ A @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ D ) )
              = C )
          & ! [C: '\'B$\'',D: '\'B$\'',E: '\'C$\''] :
              ( ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ D ) @ E ) )
              = ( '\'fun_app$k\'' @ ( '\'fun_app$y\'' @ B @ C ) @ E ) ) )
       => ( '\'valid_getter_setter$\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(15,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\'',C: '\'C$\''] :
      ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
        = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
    <=> ? [D: '\'B$\''] :
          ( ( B
            = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
          & ( ( '\'fun_app$o\'' @ A @ D )
            = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).

thf(112,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\'',C: '\'C$\''] :
      ( ( ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) )
       => ? [D: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
            & ( ( '\'fun_app$o\'' @ A @ D )
              = C ) ) )
      & ( ? [D: '\'B$\''] :
            ( ( B
              = ( '\'fun_app$g\'' @ '\'some$\'' @ D ) )
            & ( ( '\'fun_app$o\'' @ A @ D )
              = C ) )
       => ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(4,axiom,
    ! [A: '\'B_c_option_fun$\''] :
      ( ( '\'bind$b\'' @ '\'none$a\'' @ A )
      = '\'none$\'' ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom406) ).

thf(48,plain,
    ! [A: '\'B_c_option_fun$\''] :
      ( ( '\'bind$b\'' @ '\'none$a\'' @ A )
      = '\'none$\'' ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(12,axiom,
    ! [A: '\'C$\'',B: '\'C$\''] :
      ( ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
        = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).

thf(95,plain,
    ! [A: '\'C$\'',B: '\'C$\''] :
      ( ( ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( '\'fun_app$j\'' @ '\'some$a\'' @ A )
          = ( '\'fun_app$j\'' @ '\'some$a\'' @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(1,conjecture,
    '\'thesis$\'',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture72) ).

thf(2,negated_conjecture,
    ~ '\'thesis$\'',
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(40,plain,
    ~ '\'thesis$\'',
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(23,axiom,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( '\'preregister$b\'' @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom313) ).

thf(158,plain,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( '\'preregister$b\'' @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(5,axiom,
    ! [A: '\'B$\'',B: '\'B_c_option_fun$\''] :
      ( ( '\'bind$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom424) ).

thf(51,plain,
    ! [A: '\'B$\'',B: '\'B_c_option_fun$\''] :
      ( ( '\'bind$b\'' @ ( '\'fun_app$g\'' @ '\'some$\'' @ A ) @ B )
      = ( '\'fun_app$n\'' @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(32,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
      = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uvg$\'' @ A ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).

thf(190,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B_option$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ B )
      = ( '\'fun_app$an\'' @ ( '\'case_option$c\'' @ '\'none$\'' @ ( '\'uvg$\'' @ A ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(18,axiom,
    ! [A: '\'B_c_fun$\'',B: '\'B$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom287) ).

thf(131,plain,
    ! [A: '\'B_c_fun$\'',B: '\'B$\''] :
      ( ( '\'fun_app$an\'' @ ( '\'map_option$d\'' @ A ) @ ( '\'fun_app$g\'' @ '\'some$\'' @ B ) )
      = ( '\'fun_app$j\'' @ '\'some$a\'' @ ( '\'fun_app$o\'' @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(25,axiom,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$am\'' @ A @ '\'some$\'' )
        = '\'some$a\'' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).

thf(163,plain,
    ! [A: '\'B_b_option_fun_c_c_option_fun_fun$\''] :
      ( ( '\'register$a\'' @ A )
     => ( ( '\'fun_app$am\'' @ A @ '\'some$\'' )
        = '\'some$a\'' ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(233,plain,
    $false,
    inference(cvc4,[status(thm)],[174,78,121,160,229,141,41,59,187,177,222,170,202,201,102,109,193,134,128,166,148,180,71,54,86,66,155,198,209,112,48,95,40,158,51,190,131,163]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ITP386_1 : TPTP v8.2.0. Released v8.0.0.
% 0.12/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n018.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Sat May 18 15:50:23 EDT 2024
% 0.16/0.37  % CPUTime  : 
% 1.29/1.19  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 3.68/1.87  % [INFO] 	 Parsing done (675ms). 
% 3.68/1.89  % [INFO] 	 Running in sequential loop mode. 
% 4.82/2.36  % [INFO] 	 eprover registered as external prover. 
% 4.82/2.37  % [INFO] 	 cvc4 registered as external prover. 
% 4.82/2.37  % [INFO] 	 Scanning for conjecture ... 
% 5.48/2.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 734 axioms. Running axiom selection ... 
% 6.26/2.84  % [INFO] 	 Axiom selection finished. Selected 37 axioms (removed 697 axioms). 
% 6.87/2.94  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 6.87/2.95  % [INFO] 	 Type checking passed. 
% 6.87/2.96  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 11.21/4.27  % External prover 'cvc4' found a proof!
% 11.21/4.27  % [INFO] 	 Killing All external provers ... 
% 11.21/4.28  % Time passed: 3715ms (effective reasoning time: 2381ms)
% 11.21/4.28  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 11.21/4.28  % Axioms used in derivation (37): axiom76, axiom214, axiom173, axiom112, axiom82, axiom232, axiom111, axiom223, hypothesis73, axiom49, axiom92, axiom424, axiom406, axiom115, axiom278, axiom94, axiom83, axiom60, axiom290, axiom108, axiom387, axiom75, axiom80, axiom97, axiom205, axiom79, axiom96, axiom23, axiom313, axiom102, axiom15, axiom114, axiom287, axiom136, axiom414, axiom420, axiom194
% 11.21/4.28  % No. of inferences in proof: 78
% 11.21/4.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3715 ms resp. 2381 ms w/o parsing
% 11.61/4.38  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.61/4.38  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------