%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n006.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 23:09:31 EDT 2024

% Result   : Theorem 1.94s 0.70s
% Output   : Refutation 2.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      : 2072
% Syntax   : Number of formulae    : 4698 (1097 unt; 697 typ;   0 def)
%            Number of atoms       : 10636 (3707 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 10527 (3892   ~;3948   |;1337   &)
%                                         (1029 <=>; 311  =>;   0  <=;  10 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    8 (   1 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number arithmetic     : 2917 ( 476 atm; 749 fun;1049 num; 643 var)
%            Number of types       :  127 ( 125 usr;   1 ari)
%            Number of type conns  : 1012 ( 528   >; 484   *;   0   +;   0  <<)
%            Number of predicates  :  892 ( 887 usr; 822 prp; 0-5 aty)
%            Number of functors    :  509 ( 505 usr;  46 con; 0-4 aty)
%            Number of variables   : 8443 (7911   !; 532   ?;8443   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    'Int_bool_fun$': $tType ).

tff(type_def_6,type,
    'A_iarray_a_iarray_a_iarray_prod_set_fun$': $tType ).

tff(type_def_7,type,
    'A_iarray_list_bool_fun$': $tType ).

tff(type_def_8,type,
    'A_iarray_iarray_list_a_iarray_iarray_list_prod$': $tType ).

tff(type_def_9,type,
    'Int_int_prod_a_n_vec_n_vec_prod$': $tType ).

tff(type_def_10,type,
    'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$': $tType ).

tff(type_def_11,type,
    'Int_int_int_prod_set_fun$': $tType ).

tff(type_def_12,type,
    'Nat_nat_bool_fun_fun$': $tType ).

tff(type_def_13,type,
    'Int_int_prod_set$': $tType ).

tff(type_def_14,type,
    'Int_int_prod_bool_fun$': $tType ).

tff(type_def_15,type,
    'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$': $tType ).

tff(type_def_16,type,
    'Int_a_n_vec_n_vec_prod$': $tType ).

tff(type_def_17,type,
    'Nat_a_iarray_fun$': $tType ).

tff(type_def_18,type,
    'A_iarray_a_iarray_bool_fun_fun$': $tType ).

tff(type_def_19,type,
    'A_iarray_iarray_a_iarray_iarray_prod$': $tType ).

tff(type_def_20,type,
    'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$': $tType ).

tff(type_def_21,type,
    'Nat_a_iarray_prod_list_nat_fun$': $tType ).

tff(type_def_22,type,
    'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$': $tType ).

tff(type_def_23,type,
    'A_iarray_iarray$': $tType ).

tff(type_def_24,type,
    'A_iarray_iarray_int_prod$': $tType ).

tff(type_def_25,type,
    'Int_int_prod$': $tType ).

tff(type_def_26,type,
    'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$': $tType ).

tff(type_def_27,type,
    'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$': $tType ).

tff(type_def_28,type,
    'A_n_vec_iarray$': $tType ).

tff(type_def_29,type,
    'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$': $tType ).

tff(type_def_30,type,
    'Nat_a_iarray_prod_list$': $tType ).

tff(type_def_31,type,
    'A_iarray_iarray_nat_fun$': $tType ).

tff(type_def_32,type,
    'A_n_vec_n_vec_int_int_prod_prod$': $tType ).

tff(type_def_33,type,
    'A_iarray_a_iarray_fun$': $tType ).

tff(type_def_34,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun_a_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun_fun$': $tType ).

tff(type_def_35,type,
    'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$': $tType ).

tff(type_def_36,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$': $tType ).

tff(type_def_37,type,
    'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$': $tType ).

tff(type_def_38,type,
    'A_n_vec_n_vec_bool_fun$': $tType ).

tff(type_def_39,type,
    'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$': $tType ).

tff(type_def_40,type,
    'Int_int_prod_int_int_prod_prod$': $tType ).

tff(type_def_41,type,
    'Int_set$': $tType ).

tff(type_def_42,type,
    'Int_int_fun$': $tType ).

tff(type_def_43,type,
    'Int_set_set$': $tType ).

tff(type_def_44,type,
    'A_iarray_a_iarray_prod_set$': $tType ).

tff(type_def_45,type,
    'A_n_vec_n_vec$': $tType ).

tff(type_def_46,type,
    'Int_int_prod_int_fun$': $tType ).

tff(type_def_47,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$': $tType ).

tff(type_def_48,type,
    'Nat_a_iarray_prod_nat_a_iarray_prod_prod$': $tType ).

tff(type_def_49,type,
    'A_n_vec_n_vec_option$': $tType ).

tff(type_def_50,type,
    'Int_int_prod_int_prod$': $tType ).

tff(type_def_51,type,
    'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$': $tType ).

tff(type_def_52,type,
    'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$': $tType ).

tff(type_def_53,type,
    'A_iarray_list_nat_fun$': $tType ).

tff(type_def_54,type,
    'A_iarray_list_list$': $tType ).

tff(type_def_55,type,
    'A_iarray_iarray_set$': $tType ).

tff(type_def_56,type,
    'Int_a_iarray_iarray_prod$': $tType ).

tff(type_def_57,type,
    'Int_nat_fun$': $tType ).

tff(type_def_58,type,
    'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$': $tType ).

tff(type_def_59,type,
    'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$': $tType ).

tff(type_def_60,type,
    'Int_set_int_prod$': $tType ).

tff(type_def_61,type,
    'A_iarray_list_a_iarray_list_bool_fun_fun$': $tType ).

tff(type_def_62,type,
    'Nat$': $tType ).

tff(type_def_63,type,
    'A_n_vec_n_vec_set$': $tType ).

tff(type_def_64,type,
    'N$': $tType ).

tff(type_def_65,type,
    'Int_a_iarray_fun$': $tType ).

tff(type_def_66,type,
    'Nat_a_iarray_list_prod_list$': $tType ).

tff(type_def_67,type,
    'A_iarray_list_a_iarray_list_prod_set$': $tType ).

tff(type_def_68,type,
    'A_iarray_iarray_bool_fun$': $tType ).

tff(type_def_69,type,
    'A_iarray_list_list_a_iarray_list_list_prod_set$': $tType ).

tff(type_def_70,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$': $tType ).

tff(type_def_71,type,
    'A_iarray_iarray_option_bool_fun$': $tType ).

tff(type_def_72,type,
    'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$': $tType ).

tff(type_def_73,type,
    'A_iarray_iarray_a_iarray_iarray_bool_fun_fun_a_iarray_iarray_a_iarray_iarray_prod_bool_fun_fun$': $tType ).

tff(type_def_74,type,
    'Int_int_prod_int_int_prod_prod_set$': $tType ).

tff(type_def_75,type,
    'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$': $tType ).

tff(type_def_76,type,
    'Int_int_bool_fun_fun_int_int_prod_bool_fun_fun$': $tType ).

tff(type_def_77,type,
    'Int_set_int_set_prod$': $tType ).

tff(type_def_78,type,
    'A_n_vec_n_vec_nat_fun$': $tType ).

tff(type_def_79,type,
    tlbool: $tType ).

tff(type_def_80,type,
    'A_n_vec_n_vec_int_prod$': $tType ).

tff(type_def_81,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$': $tType ).

tff(type_def_82,type,
    'Int_list_int_list_prod$': $tType ).

tff(type_def_83,type,
    'A_iarray_a_iarray_prod_bool_fun$': $tType ).

tff(type_def_84,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$': $tType ).

tff(type_def_85,type,
    'Int_int_prod_int_int_prod_fun$': $tType ).

tff(type_def_86,type,
    'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$': $tType ).

tff(type_def_87,type,
    'A_iarray_nat_fun$': $tType ).

tff(type_def_88,type,
    'Int_list$': $tType ).

tff(type_def_89,type,
    'A_iarray_bool_fun$': $tType ).

tff(type_def_90,type,
    'Nat_nat_a_iarray_prod_prod_list$': $tType ).

tff(type_def_91,type,
    'A_iarray_list_a_iarray_list_prod_bool_fun$': $tType ).

tff(type_def_92,type,
    'Int_int_set_prod$': $tType ).

tff(type_def_93,type,
    'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$': $tType ).

tff(type_def_94,type,
    'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$': $tType ).

tff(type_def_95,type,
    'Nat_a_iarray_list_fun$': $tType ).

tff(type_def_96,type,
    'A_iarray_iarray_option$': $tType ).

tff(type_def_97,type,
    'A_iarray_a_iarray_prod$': $tType ).

tff(type_def_98,type,
    'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$': $tType ).

tff(type_def_99,type,
    'A_iarray_list_a_iarray_list_prod$': $tType ).

tff(type_def_100,type,
    'Bool_bool_fun$': $tType ).

tff(type_def_101,type,
    'A_iarray_list$': $tType ).

tff(type_def_102,type,
    'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$': $tType ).

tff(type_def_103,type,
    'A_iarray_iarray_option_nat_fun$': $tType ).

tff(type_def_104,type,
    'A_n_vec_n_vec_option_nat_fun$': $tType ).

tff(type_def_105,type,
    'A_iarray_int_fun$': $tType ).

tff(type_def_106,type,
    'Nat_a_iarray_iarray_fun$': $tType ).

tff(type_def_107,type,
    'Int_a_iarray_iarray_fun$': $tType ).

tff(type_def_108,type,
    'Nat_a_iarray_prod_bool_fun$': $tType ).

tff(type_def_109,type,
    'A_iarray_set$': $tType ).

tff(type_def_110,type,
    'A_iarray_list_list_nat_fun$': $tType ).

tff(type_def_111,type,
    'Int_int_bool_fun_fun$': $tType ).

tff(type_def_112,type,
    'A_iarray$': $tType ).

tff(type_def_113,type,
    'Int_int_int_prod_prod$': $tType ).

tff(type_def_114,type,
    'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$': $tType ).

tff(type_def_115,type,
    'A_iarray_list_set$': $tType ).

tff(type_def_116,type,
    'Nat_a_iarray_prod$': $tType ).

tff(type_def_117,type,
    'A_iarray_list_a_iarray_list_fun$': $tType ).

tff(type_def_118,type,
    'Nat_bool_fun$': $tType ).

tff(type_def_119,type,
    'A_iarray_list_int_fun$': $tType ).

tff(type_def_120,type,
    'A_iarray_iarray_a_iarray_iarray_prod_set$': $tType ).

tff(type_def_121,type,
    'A_iarray_iarray_int_set_prod$': $tType ).

tff(type_def_122,type,
    'A_iarray_list_list_a_iarray_list_list_prod$': $tType ).

tff(type_def_123,type,
    'Int_list_int_list_prod_set$': $tType ).

tff(type_def_124,type,
    'Nat_set$': $tType ).

tff(type_def_125,type,
    'A_n_vec_n_vec_a_n_vec_n_vec_prod$': $tType ).

tff(type_def_126,type,
    'Nat_int_fun$': $tType ).

tff(type_def_127,type,
    'A_n_vec_n_vec_option_bool_fun$': $tType ).

tff(type_def_128,type,
    'A_iarray_iarray_list$': $tType ).

tff(type_def_129,type,
    'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$': $tType ).

tff(func_def_0,type,
    'snd$': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' ).

tff(func_def_1,type,
    'size$a': 'Nat_a_iarray_prod_list_nat_fun$' ).

tff(func_def_2,type,
    'append$': 'Nat_a_iarray_prod_list$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$' ).

tff(func_def_3,type,
    'pair$o': ( 'Int_int_prod$' * 'A_n_vec_n_vec$' ) > 'Int_int_prod_a_n_vec_n_vec_prod$' ).

tff(func_def_4,type,
    'zero$d': 'Int_int_int_prod_prod$' ).

tff(func_def_5,type,
    'collect$f': 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).

tff(func_def_6,type,
    'image2$d': ( 'Nat_set$' * 'Nat_a_iarray_fun$' * 'Nat_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).

tff(func_def_7,type,
    'fun_app$az': ( 'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).

tff(func_def_8,type,
    'fun_app$r': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_9,type,
    'image2$g': ( 'Nat_set$' * 'Nat_a_iarray_iarray_fun$' * 'Nat_a_iarray_iarray_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).

tff(func_def_10,type,
    'case_option$': ( tlbool * 'A_n_vec_n_vec_bool_fun$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).

tff(func_def_11,type,
    'gauss_Jordan_upt_k_PA$': ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_12,type,
    'lexord$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).

tff(func_def_13,type,
    'invertible$': 'A_n_vec_n_vec_bool_fun$' ).

tff(func_def_14,type,
    'listrel1$b': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).

tff(func_def_15,type,
    'fst$e': 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_16,type,
    'uug$': 'A_iarray_iarray_bool_fun$' ).

tff(func_def_17,type,
    'size$c': 'A_iarray_iarray_option$' > 'Nat$' ).

tff(func_def_18,type,
    def_3: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).

tff(func_def_19,type,
    def_1: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > tlbool ).

tff(func_def_20,type,
    'inverse_matrix_iarray$': 'A_iarray_iarray$' > 'A_iarray_iarray_option$' ).

tff(func_def_21,type,
    'same_fst$c': ( 'A_iarray_bool_fun$' * 'A_iarray_a_iarray_a_iarray_prod_set_fun$' ) > 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$' ).

tff(func_def_22,type,
    'size$f': 'A_iarray_iarray_list$' > 'Nat$' ).

tff(func_def_23,type,
    'none$': 'A_iarray_iarray_option$' ).

tff(func_def_24,type,
    'collect$e': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$' ).

tff(func_def_25,type,
    def_5: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).

tff(func_def_26,type,
    'listrel1$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).

tff(func_def_27,type,
    'lexn$b': ( 'A_iarray_a_iarray_prod_set$' * 'Nat$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_28,type,
    'enumerate$': ( 'Nat$' * 'A_iarray_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_29,type,
    'fun_app$ap': ( 'Nat_a_iarray_iarray_fun$' * 'Nat$' ) > 'A_iarray_iarray$' ).

tff(func_def_30,type,
    'fun_app$ai': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_31,type,
    'nths$': ( 'A_iarray_list$' * 'Nat_set$' ) > 'A_iarray_list$' ).

tff(func_def_32,type,
    'gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff(func_def_33,type,
    'fun_app$aa': ( 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec$' ) > 'Nat$' ).

tff(func_def_34,type,
    'pair$m': ( $int * 'A_n_vec_n_vec$' ) > 'Int_a_n_vec_n_vec_prod$' ).

tff(func_def_35,type,
    'enumerate$a': ( 'Nat$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_nat_a_iarray_prod_prod_list$' ).

tff(func_def_36,type,
    'gen_length$b': 'Nat$' > 'A_iarray_list_nat_fun$' ).

tff(func_def_37,type,
    'fun_app$av': ( 'Int_int_bool_fun_fun_int_int_prod_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_bool_fun$' ).

tff(func_def_38,type,
    'fun_app$aq': ( 'Int_a_iarray_iarray_fun$' * $int ) > 'A_iarray_iarray$' ).

tff(func_def_39,type,
    def_4: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).

tff(func_def_40,type,
    'lexord$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).

tff(func_def_41,type,
    'fst$c': 'Int_int_set_prod$' > $int ).

tff(func_def_42,type,
    'fstOp$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_int_int_prod_fun$' ).

tff(func_def_43,type,
    'fst$k': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_44,type,
    'collect$d': 'A_iarray_bool_fun$' > 'A_iarray_set$' ).

tff(func_def_45,type,
    'append$c': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_46,type,
    'sndOp$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_int_int_prod_fun$' ).

tff(func_def_47,type,
    'lex$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).

tff(func_def_48,type,
    'lexord$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).

tff(func_def_49,type,
    'plus$o': ( 'Int_int_set_prod$' * 'Int_int_set_prod$' ) > 'Int_int_set_prod$' ).

tff(func_def_50,type,
    'snd$k': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_51,type,
    'product_lists$': 'A_iarray_list_list$' > 'A_iarray_list_list$' ).

tff(func_def_52,type,
    'plus$n': ( 'Int_int_prod_set$' * 'Int_int_prod_set$' ) > 'Int_int_prod_set$' ).

tff(func_def_53,type,
    'same_fst$a': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$' ).

tff(func_def_54,type,
    'lexn$': ( 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' * 'Nat$' ) > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).

tff(func_def_55,type,
    'fun_app$ad': ( 'A_iarray_a_iarray_fun$' * 'A_iarray$' ) > 'A_iarray$' ).

tff(func_def_56,type,
    'splice$b': ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_57,type,
    'plus$s': ( 'Int_int_int_prod_prod$' * 'Int_int_int_prod_prod$' ) > 'Int_int_int_prod_prod$' ).

tff(func_def_58,type,
    'listrel1$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).

tff(func_def_59,type,
    'relcompp$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).

tff(func_def_60,type,
    'swap$b': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_61,type,
    'image2$': ( 'Nat_set$' * 'Nat_int_fun$' * 'Nat_int_fun$' ) > 'Int_int_prod_set$' ).

tff(func_def_62,type,
    'nat$': 'Int_nat_fun$' ).

tff(func_def_63,type,
    'pair$e': ( 'Int_set$' * $int ) > 'Int_set_int_prod$' ).

tff(func_def_64,type,
    'snd$h': 'A_iarray_iarray_int_prod$' > $int ).

tff(func_def_65,type,
    'fst$d': 'Int_set_int_prod$' > 'Int_set$' ).

tff(func_def_66,type,
    'size$': 'A_iarray_list_nat_fun$' ).

tff(func_def_67,type,
    'listrel1$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).

tff(func_def_68,type,
    'snd$c': 'Int_int_set_prod$' > 'Int_set$' ).

tff(func_def_69,type,
    'size$b': 'A_iarray_list_list_nat_fun$' ).

tff(func_def_70,type,
    'plus$w': ( 'A_iarray_iarray_int_set_prod$' * 'A_iarray_iarray_int_set_prod$' ) > 'A_iarray_iarray_int_set_prod$' ).

tff(func_def_71,type,
    'plus$x': ( 'A_n_vec_iarray$' * 'A_n_vec_iarray$' ) > 'A_n_vec_iarray$' ).

tff(func_def_72,type,
    'collect$': 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_73,type,
    'plus$q': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray_a_iarray_prod$' ).

tff(func_def_74,type,
    'pair$j': ( 'Int_int_prod$' * $int ) > 'Int_int_prod_int_prod$' ).

tff(func_def_75,type,
    'pair$b': ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_prod$' ).

tff(func_def_76,type,
    'cons$a': ( 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_77,type,
    'collect$c': 'Nat_bool_fun$' > 'Nat_set$' ).

tff(func_def_78,type,
    'set$a': 'A_iarray_list_list$' > 'A_iarray_list_set$' ).

tff(func_def_79,type,
    'cons$': ( 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_80,type,
    'zero$': 'Int_set$' ).

tff(func_def_81,type,
    'n_lists$': ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_82,type,
    'pick_middlep$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).

tff(func_def_83,type,
    'fun_app$ax': ( 'A_n_vec_n_vec_option_nat_fun$' * 'A_n_vec_n_vec_option$' ) > 'Nat$' ).

tff(func_def_84,type,
    'gauss_Jordan_in_ij_PA$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_85,type,
    'image2$e': ( 'Int_set$' * 'Int_a_iarray_fun$' * 'Int_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).

tff(func_def_86,type,
    'of_nat$': 'Nat_int_fun$' ).

tff(func_def_87,type,
    'sndOp$b': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ).

tff(func_def_88,type,
    'pair$x': ( 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$' ).

tff(func_def_89,type,
    'uuh$': 'A_n_vec_n_vec_bool_fun$' ).

tff(func_def_90,type,
    'snd$d': 'Int_set_int_prod$' > $int ).

tff(func_def_91,type,
    'matrix_inv$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff(func_def_92,type,
    'fun_app$bf': ( 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' ).

tff(func_def_93,type,
    'plus$e': 'A_iarray$' > 'A_iarray_a_iarray_fun$' ).

tff(func_def_94,type,
    'fst$g': 'Int_int_int_prod_prod$' > $int ).

tff(func_def_95,type,
    'fst$a': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' ).

tff(func_def_96,type,
    'nil$': 'A_iarray_list$' ).

tff(func_def_97,type,
    'fun_app$g': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_bool_fun$' ).

tff(func_def_98,type,
    'uuk$': 'A_iarray_list_set$' > 'A_iarray_list_bool_fun$' ).

tff(func_def_99,type,
    'filter$': 'A_iarray_bool_fun$' > 'A_iarray_list_a_iarray_list_fun$' ).

tff(func_def_100,type,
    'uu$': 'A_iarray_bool_fun$' ).

tff(func_def_101,type,
    'equivalent_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).

tff(func_def_102,type,
    'fun_app$k': ( 'Int_nat_fun$' * $int ) > 'Nat$' ).

tff(func_def_103,type,
    'fun_app$bc': ( 'A_iarray_nat_fun$' * 'A_iarray$' ) > 'Nat$' ).

tff(func_def_104,type,
    'image2$i': ( 'Nat_set$' * 'Nat_a_iarray_list_fun$' * 'Nat_a_iarray_list_fun$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_105,type,
    'collect$a': 'A_iarray_list_bool_fun$' > 'A_iarray_list_set$' ).

tff(func_def_106,type,
    'fun_app$as': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).

tff(func_def_107,type,
    'set$': 'A_iarray_list$' > 'A_iarray_set$' ).

tff(func_def_108,type,
    'pair$h': ( 'A_iarray_iarray$' * $int ) > 'A_iarray_iarray_int_prod$' ).

tff(func_def_109,type,
    'pair$q': ( 'A_n_vec_n_vec$' * 'Int_int_prod$' ) > 'A_n_vec_n_vec_int_int_prod_prod$' ).

tff(func_def_110,type,
    'lexord$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_111,type,
    'fun_app$w': ( 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).

tff(func_def_112,type,
    tltrue: tlbool ).

tff(func_def_113,type,
    'uuo$': 'Int_int_prod_set$' > 'Int_int_bool_fun_fun$' ).

tff(func_def_114,type,
    'cons$b': ( 'A_iarray_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_115,type,
    'zero$a': 'Int_int_prod$' ).

tff(func_def_116,type,
    'swap$a': 'A_iarray_a_iarray_prod$' > 'A_iarray_a_iarray_prod$' ).

tff(func_def_117,type,
    'image2$f': ( 'A_iarray_set$' * 'A_iarray_a_iarray_fun$' * 'A_iarray_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).

tff(func_def_118,type,
    'plus$h': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).

tff(func_def_119,type,
    'pair$t': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$' ).

tff(func_def_120,type,
    'rank$': 'A_n_vec_n_vec_nat_fun$' ).

tff(func_def_121,type,
    'gauss_Jordan_upt_k$': ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_122,type,
    'fun_app$bb': ( 'A_iarray_a_iarray_a_iarray_prod_set_fun$' * 'A_iarray$' ) > 'A_iarray_a_iarray_prod_set$' ).

tff(func_def_123,type,
    'gauss_Jordan_in_ij$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_124,type,
    'size_prod$': ( 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'Nat$' ).

tff(func_def_125,type,
    'fun_app$aj': ( 'Int_int_prod_int_int_prod_fun$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).

tff(func_def_126,type,
    'fun_app$v': ( 'A_iarray_list_list_nat_fun$' * 'A_iarray_list_list$' ) > 'Nat$' ).

tff(func_def_127,type,
    'plus$i': ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).

tff(func_def_128,type,
    'pair$y': ( 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod$' ) > 'Nat_a_iarray_prod_nat_a_iarray_prod_prod$' ).

tff(func_def_129,type,
    'filter$a': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_130,type,
    'uuj$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_prod_bool_fun$' ).

tff(func_def_131,type,
    'fun_app$h': ( 'A_iarray_a_iarray_bool_fun_fun$' * 'A_iarray$' ) > 'A_iarray_bool_fun$' ).

tff(func_def_132,type,
    'filter$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_133,type,
    'fun_app$ar': ( 'Nat_a_iarray_list_fun$' * 'Nat$' ) > 'A_iarray_list$' ).

tff(func_def_134,type,
    'relcompp$a': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ).

tff(func_def_135,type,
    'list_of$': 'A_iarray_iarray$' > 'A_iarray_list$' ).

tff(func_def_136,type,
    'fun_app$ba': ( 'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_137,type,
    'snd$e': 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_138,type,
    'a$': 'A_n_vec_n_vec$' ).

tff(func_def_139,type,
    'fun_app$ao': ( 'Int_a_iarray_fun$' * $int ) > 'A_iarray$' ).

tff(func_def_140,type,
    'uuq$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_bool_fun_fun$' ).

tff(func_def_141,type,
    'lex$d': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_142,type,
    'pair$': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_143,type,
    'sndOp$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ).

tff(func_def_144,type,
    'rank_iarray$': 'A_iarray_iarray_nat_fun$' ).

tff(func_def_145,type,
    'fun_app$ah': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_bool_fun$' ).

tff(func_def_146,type,
    'listrel1$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_147,type,
    'p_Gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff(func_def_148,type,
    'gauss_Jordan_iarrays_PA$': 'A_iarray_iarray$' > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_149,type,
    'some$a': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$' ).

tff(func_def_150,type,
    'matrix_to_iarray$': 'A_n_vec_n_vec$' > 'A_iarray_iarray$' ).

tff(func_def_151,type,
    'uuu$': ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray_bool_fun$' ).

tff(func_def_152,type,
    'reduced_row_echelon_form$': 'A_n_vec_n_vec_bool_fun$' ).

tff(func_def_153,type,
    'lexn$a': ( 'A_iarray_list_a_iarray_list_prod_set$' * 'Nat$' ) > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).

tff(func_def_154,type,
    'swap$d': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_155,type,
    'fun_app$at': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun_a_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$' ).

tff(func_def_156,type,
    'append$b': ( 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list$' ).

tff(func_def_157,type,
    'plus$l': ( 'Int_set_set$' * 'Int_set_set$' ) > 'Int_set_set$' ).

tff(func_def_158,type,
    'uua$': ( 'A_iarray_bool_fun$' * 'A_iarray_bool_fun$' ) > 'A_iarray_bool_fun$' ).

tff(func_def_159,type,
    'uur$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_a_iarray_bool_fun_fun$' ).

tff(func_def_160,type,
    'pair$n': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod_int_int_prod_prod$' ).

tff(func_def_161,type,
    'gen_length$a': 'Nat$' > 'A_iarray_list_list_nat_fun$' ).

tff(func_def_162,type,
    'size$e': 'Int_list$' > 'Nat$' ).

tff(func_def_163,type,
    'pair$p': ( 'A_n_vec_n_vec$' * $int ) > 'A_n_vec_n_vec_int_prod$' ).

tff(func_def_164,type,
    'pick_middlep$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' * $int ) > 'Int_int_fun$' ).

tff(func_def_165,type,
    'pair$d': ( $int * 'Int_set$' ) > 'Int_int_set_prod$' ).

tff(func_def_166,type,
    'snd$f': 'Int_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_167,type,
    'append$d': 'A_iarray_list$' > 'A_iarray_list_a_iarray_list_fun$' ).

tff(func_def_168,type,
    'uus$': ( 'A_iarray_list_set$' * 'A_iarray$' ) > 'A_iarray_list_bool_fun$' ).

tff(func_def_169,type,
    'gauss_Jordan_PA$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_170,type,
    'fun_app$au': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun_a_iarray_iarray_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' ).

tff(func_def_171,type,
    def_2: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).

tff(func_def_172,type,
    'plus$t': ( 'A_iarray_iarray_int_prod$' * 'A_iarray_iarray_int_prod$' ) > 'A_iarray_iarray_int_prod$' ).

tff(func_def_173,type,
    'cons$d': ( 'A_iarray_iarray$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list$' ).

tff(func_def_174,type,
    'image2$b': ( 'A_iarray_set$' * 'A_iarray_int_fun$' * 'A_iarray_int_fun$' ) > 'Int_int_prod_set$' ).

tff(func_def_175,type,
    'none$a': 'A_n_vec_n_vec_option$' ).

tff(func_def_176,type,
    'uut$': ( 'A_iarray_list$' * 'Nat_set$' ) > 'Nat_bool_fun$' ).

tff(func_def_177,type,
    'lex$c': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).

tff(func_def_178,type,
    'uue$': ( 'Bool_bool_fun$' * 'A_iarray_iarray_bool_fun$' ) > 'A_iarray_iarray_bool_fun$' ).

tff(func_def_179,type,
    'plus$m': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec_set$' ).

tff(func_def_180,type,
    'fun_app$ay': ( 'Int_int_int_prod_set_fun$' * $int ) > 'Int_int_prod_set$' ).

tff(func_def_181,type,
    'pair$k': ( 'A_iarray_iarray$' * 'Int_set$' ) > 'A_iarray_iarray_int_set_prod$' ).

tff(func_def_182,type,
    'same_fst$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$' ) > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$' ).

tff(func_def_183,type,
    'plus$a': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_184,type,
    'fun_app$bd': ( 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_185,type,
    'pair$g': ( $int * 'Int_int_prod$' ) > 'Int_int_int_prod_prod$' ).

tff(func_def_186,type,
    'collect$b': 'Int_bool_fun$' > 'Int_set$' ).

tff(func_def_187,type,
    'plus$p': ( 'Int_set_int_prod$' * 'Int_set_int_prod$' ) > 'Int_set_int_prod$' ).

tff(func_def_188,type,
    'cons$c': ( $int * 'Int_list$' ) > 'Int_list$' ).

tff(func_def_189,type,
    'fun_app$m': ( 'A_iarray_list_nat_fun$' * 'A_iarray_list$' ) > 'Nat$' ).

tff(func_def_190,type,
    'matrix_matrix_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_191,type,
    'plus$r': ( 'Int_a_iarray_iarray_prod$' * 'Int_a_iarray_iarray_prod$' ) > 'Int_a_iarray_iarray_prod$' ).

tff(func_def_192,type,
    'snd$i': 'Int_set_int_set_prod$' > 'Int_set$' ).

tff(func_def_193,type,
    'matrix_to_iarray_option$': 'A_n_vec_n_vec_option$' > 'A_iarray_iarray_option$' ).

tff(func_def_194,type,
    'plus$j': ( 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$' ) > 'A_iarray_iarray_set$' ).

tff(func_def_195,type,
    'fun_app$ab': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_196,type,
    'lenlex$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).

tff(func_def_197,type,
    'zero$i': 'A_n_vec_n_vec_int_prod$' ).

tff(func_def_198,type,
    'uul$': 'Int_set$' > 'Int_bool_fun$' ).

tff(func_def_199,type,
    'size$g': 'Nat_nat_a_iarray_prod_prod_list$' > 'Nat$' ).

tff(func_def_200,type,
    'fun_app$an': ( 'Nat_a_iarray_fun$' * 'Nat$' ) > 'A_iarray$' ).

tff(func_def_201,type,
    'fun_app$al': ( 'A_iarray_int_fun$' * 'A_iarray$' ) > $int ).

tff(func_def_202,type,
    'snd$a': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' ).

tff(func_def_203,type,
    'fst$f': 'Int_a_iarray_iarray_prod$' > $int ).

tff(func_def_204,type,
    'uuf$': 'A_n_vec_n_vec_bool_fun$' ).

tff(func_def_205,type,
    'size$h': 'Nat_a_iarray_list_prod_list$' > 'Nat$' ).

tff(func_def_206,type,
    'fstOp$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ).

tff(func_def_207,type,
    'uui$': 'A_iarray_iarray_bool_fun$' ).

tff(func_def_208,type,
    'plus$b': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).

tff(func_def_209,type,
    'zero$j': 'A_n_vec_n_vec_int_int_prod_prod$' ).

tff(func_def_210,type,
    'plus$u': ( 'Int_set_int_set_prod$' * 'Int_set_int_set_prod$' ) > 'Int_set_int_set_prod$' ).

tff(func_def_211,type,
    'shift$': ( 'A_iarray_list_set$' * 'A_iarray$' ) > 'A_iarray_list_set$' ).

tff(func_def_212,type,
    def_7: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).

tff(func_def_213,type,
    'uuc$': 'A_iarray_list_bool_fun$' > 'A_iarray_list_bool_fun$' ).

tff(func_def_214,type,
    'zero$h': 'Int_int_prod_a_n_vec_n_vec_prod$' ).

tff(func_def_215,type,
    'pair$a': ( 'A_iarray$' * 'A_iarray$' ) > 'A_iarray_a_iarray_prod$' ).

tff(func_def_216,type,
    'snd$j': 'Int_int_prod_int_prod$' > $int ).

tff(func_def_217,type,
    'gauss_Jordan_iarrays$': 'A_iarray_iarray$' > 'A_iarray_iarray$' ).

tff(func_def_218,type,
    'divides_aux$': 'Int_int_prod_bool_fun$' ).

tff(func_def_219,type,
    'same_fst$': ( 'Int_bool_fun$' * 'Int_int_int_prod_set_fun$' ) > 'Int_int_prod_int_int_prod_prod_set$' ).

tff(func_def_220,type,
    'fun_app$l': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).

tff(func_def_221,type,
    'fst$b': 'Int_int_prod_int_fun$' ).

tff(func_def_222,type,
    'plus$k': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).

tff(func_def_223,type,
    'fun_app$j': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).

tff(func_def_224,type,
    'size_prod$b': ( 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'Nat$' ).

tff(func_def_225,type,
    'image2$c': ( 'A_iarray_list_set$' * 'A_iarray_list_int_fun$' * 'A_iarray_list_int_fun$' ) > 'Int_int_prod_set$' ).

tff(func_def_226,type,
    'uum$': 'Nat_set$' > 'Nat_bool_fun$' ).

tff(func_def_227,type,
    'zero$b': 'A_n_vec_n_vec$' ).

tff(func_def_228,type,
    def_6: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).

tff(func_def_229,type,
    'plus$d': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).

tff(func_def_230,type,
    'relcompp$b': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_bool_fun_fun$' ).

tff(func_def_231,type,
    'invertible_iarray$': 'A_iarray_iarray_bool_fun$' ).

tff(func_def_232,type,
    'uud$': 'A_iarray_bool_fun$' > 'A_iarray_bool_fun$' ).

tff(func_def_233,type,
    'pair$c': ( $int * $int ) > 'Int_int_prod$' ).

tff(func_def_234,type,
    tlfalse: tlbool ).

tff(func_def_235,type,
    'fun_app$x': ( 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$' ) > 'A_iarray_iarray_option_bool_fun$' ).

tff(func_def_236,type,
    'gen_length$': 'Nat$' > 'Nat_a_iarray_prod_list_nat_fun$' ).

tff(func_def_237,type,
    'plus$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_238,type,
    'lex$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).

tff(func_def_239,type,
    'fst$h': 'A_iarray_iarray_int_prod$' > 'A_iarray_iarray$' ).

tff(func_def_240,type,
    'swap$': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list_a_iarray_list_prod$' ).

tff(func_def_241,type,
    'pair$z': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list_a_iarray_list_list_prod$' ).

tff(func_def_242,type,
    'id_upt_k$': 'A_n_vec_n_vec$' > 'Nat_bool_fun$' ).

tff(func_def_243,type,
    'fst$j': 'Int_int_prod_int_prod$' > 'Int_int_prod$' ).

tff(func_def_244,type,
    'fun_app$ak': ( 'Int_int_fun$' * $int ) > $int ).

tff(func_def_245,type,
    'collect$g': 'Int_int_prod_bool_fun$' > 'Int_int_prod_set$' ).

tff(func_def_246,type,
    'pair$s': ( 'A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod$' ) > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$' ).

tff(func_def_247,type,
    'plus$v': ( 'Int_int_prod_int_prod$' * 'Int_int_prod_int_prod$' ) > 'Int_int_prod_int_prod$' ).

tff(func_def_248,type,
    'splice$a': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_249,type,
    'pair$w': ( 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list_a_iarray_iarray_list_prod$' ).

tff(func_def_250,type,
    'lex$b': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).

tff(func_def_251,type,
    'pair$v': ( 'Int_list$' * 'Int_list$' ) > 'Int_list_int_list_prod$' ).

tff(func_def_252,type,
    'is_zero_iarray$': 'A_iarray_bool_fun$' ).

tff(func_def_253,type,
    'size_prod$a': ( 'Int_nat_fun$' * 'Int_nat_fun$' * 'Int_int_prod$' ) > 'Nat$' ).

tff(func_def_254,type,
    'fun_app$be': ( 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_bool_fun_fun$' ).

tff(func_def_255,type,
    'iarray_to_matrix$': 'A_iarray_iarray$' > 'A_n_vec_n_vec$' ).

tff(func_def_256,type,
    'fun_app$am': ( 'A_iarray_list_int_fun$' * 'A_iarray_list$' ) > $int ).

tff(func_def_257,type,
    'pair$l': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_258,type,
    'inverse_matrix$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$' ).

tff(func_def_259,type,
    'fst$i': 'Int_set_int_set_prod$' > 'Int_set$' ).

tff(func_def_260,type,
    'fst$': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' ).

tff(func_def_261,type,
    'nrows_iarray$': 'A_iarray_iarray_nat_fun$' ).

tff(func_def_262,type,
    'fun_app$z': ( 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_iarray_iarray_option$' ) > 'A_iarray_iarray_option_bool_fun$' ).

tff(func_def_263,type,
    'pair$f': ( $int * 'A_iarray_iarray$' ) > 'Int_a_iarray_iarray_prod$' ).

tff(func_def_264,type,
    'fun_app$aw': ( 'A_iarray_iarray_option_nat_fun$' * 'A_iarray_iarray_option$' ) > 'Nat$' ).

tff(func_def_265,type,
    'uun$': 'A_iarray_set$' > 'A_iarray_bool_fun$' ).

tff(func_def_266,type,
    'uub$': 'Nat_a_iarray_prod_bool_fun$' > 'Nat_a_iarray_prod_bool_fun$' ).

tff(func_def_267,type,
    'similar_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).

tff(func_def_268,type,
    'case_option$a': ( tlbool * 'A_iarray_iarray_bool_fun$' ) > 'A_iarray_iarray_option_bool_fun$' ).

tff(func_def_269,type,
    'zero$g': 'Int_int_prod_int_int_prod_prod$' ).

tff(func_def_270,type,
    'pair$u': ( 'Nat$' * 'A_iarray$' ) > 'Nat_a_iarray_prod$' ).

tff(func_def_271,type,
    'image2$a': ( 'Int_set$' * 'Int_int_fun$' * 'Int_int_fun$' ) > 'Int_int_prod_set$' ).

tff(func_def_272,type,
    'uup$': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ).

tff(func_def_273,type,
    'the$a': 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).

tff(func_def_274,type,
    'some$': 'A_iarray_iarray$' > 'A_iarray_iarray_option$' ).

tff(func_def_275,type,
    'size_option$': 'A_iarray_iarray_nat_fun$' > 'A_iarray_iarray_option_nat_fun$' ).

tff(func_def_276,type,
    'zero$e': 'Int_a_n_vec_n_vec_prod$' ).

tff(func_def_277,type,
    'fun_app$y': ( 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_iarray_iarray_option$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).

tff(func_def_278,type,
    'pair$r': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$' ).

tff(func_def_279,type,
    'zero$c': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).

tff(func_def_280,type,
    'image2$h': ( 'Int_set$' * 'Int_a_iarray_iarray_fun$' * 'Int_a_iarray_iarray_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).

tff(func_def_281,type,
    'fun_app$q': ( 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray$' ) > 'Nat$' ).

tff(func_def_282,type,
    'fun_app$p': ( 'A_iarray_list_a_iarray_list_fun$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_283,type,
    'fun_app$ac': ( 'Int_int_prod_int_fun$' * 'Int_int_prod$' ) > $int ).

tff(func_def_284,type,
    'swap$c': 'Int_int_prod$' > 'Int_int_prod$' ).

tff(func_def_285,type,
    'zero$f': 'Int_int_prod_int_prod$' ).

tff(func_def_286,type,
    'append$a': ( 'Int_list$' * 'Int_list$' ) > 'Int_list$' ).

tff(func_def_287,type,
    'size_option$a': 'A_n_vec_n_vec_nat_fun$' > 'A_n_vec_n_vec_option_nat_fun$' ).

tff(func_def_288,type,
    'nil$a': 'Nat_a_iarray_prod_list$' ).

tff(func_def_289,type,
    'fstOp$b': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ).

tff(func_def_290,type,
    'fun_app$i': ( 'A_iarray_list_a_iarray_list_bool_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_bool_fun$' ).

tff(func_def_291,type,
    'the$': 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$' ).

tff(func_def_292,type,
    'size$d': 'A_n_vec_n_vec_option$' > 'Nat$' ).

tff(func_def_293,type,
    'plus$g': ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_294,type,
    'enumerate$b': ( 'Nat$' * 'A_iarray_list_list$' ) > 'Nat_a_iarray_list_prod_list$' ).

tff(func_def_295,type,
    'plus$f': ( 'A_iarray_set$' * 'A_iarray_set$' ) > 'A_iarray_set$' ).

tff(func_def_296,type,
    'matrix_matrix_mult_iarray$': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).

tff(func_def_297,type,
    'splice$': ( 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_298,type,
    'fun_app$u': ( 'Nat_a_iarray_prod_list_nat_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat$' ).

tff(func_def_299,type,
    'vec_to_iarray$': 'A_n_vec_n_vec$' > 'A_n_vec_iarray$' ).

tff(func_def_300,type,
    'snd$g': 'Int_int_int_prod_prod$' > 'Int_int_prod$' ).

tff(func_def_301,type,
    'pair$i': ( 'Int_set$' * 'Int_set$' ) > 'Int_set_int_set_prod$' ).

tff(func_def_302,type,
    'lexord$b': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).

tff(func_def_303,type,
    'snd$b': 'Int_int_prod_int_fun$' ).

tff(func_def_304,type,
    'plus$c': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_305,type,
    'size_list$': ( 'A_iarray_nat_fun$' * 'A_iarray_list$' ) > 'Nat$' ).

tff(func_def_310,type,
    sK31: 'Nat$' > 'Nat$' ).

tff(func_def_311,type,
    sK32: 'Nat$' > 'Nat$' ).

tff(func_def_312,type,
    sK33: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$' ).

tff(func_def_313,type,
    sK34: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).

tff(func_def_314,type,
    sK35: 'Nat$' > 'Nat$' ).

tff(func_def_315,type,
    sK36: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_316,type,
    sK37: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_317,type,
    sK38: 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_318,type,
    sK39: 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_319,type,
    sK40: 'Int_int_prod$' > $int ).

tff(func_def_320,type,
    sK41: 'Int_int_prod$' > $int ).

tff(func_def_321,type,
    sK42: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_322,type,
    sK43: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_323,type,
    sK44: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$' ).

tff(func_def_324,type,
    sK45: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).

tff(func_def_325,type,
    sK46: 'Nat$' > 'Nat$' ).

tff(func_def_326,type,
    sK47: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec$' ).

tff(func_def_327,type,
    sK48: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec_option$' ).

tff(func_def_328,type,
    sK49: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray$' ).

tff(func_def_329,type,
    sK50: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray_option$' ).

tff(func_def_330,type,
    sK51: 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$' ).

tff(func_def_331,type,
    sK52: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).

tff(func_def_332,type,
    sK53: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec_option$' ).

tff(func_def_333,type,
    sK54: 'A_n_vec_n_vec_option_bool_fun$' > 'A_n_vec_n_vec$' ).

tff(func_def_334,type,
    sK55: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray_option$' ).

tff(func_def_335,type,
    sK56: 'A_iarray_iarray_option_bool_fun$' > 'A_iarray_iarray$' ).

tff(func_def_336,type,
    sK57: 'Nat$' > 'A_iarray_list_list$' ).

tff(func_def_337,type,
    sK58: 'Nat$' > 'Nat_a_iarray_prod_list$' ).

tff(func_def_338,type,
    sK59: 'Nat$' > 'A_iarray_list$' ).

tff(func_def_339,type,
    sK60: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff(func_def_340,type,
    sK61: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff(func_def_341,type,
    sK62: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_342,type,
    sK63: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_343,type,
    sK64: 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_344,type,
    sK65: 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_345,type,
    sK66: 'Int_int_prod$' > $int ).

tff(func_def_346,type,
    sK67: 'Int_int_prod$' > $int ).

tff(func_def_347,type,
    sK68: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_348,type,
    sK69: 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).

tff(func_def_349,type,
    sK70: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_350,type,
    sK71: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_351,type,
    sK72: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_352,type,
    sK73: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_353,type,
    sK74: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_354,type,
    sK75: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_355,type,
    sK76: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_356,type,
    sK77: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_357,type,
    sK78: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_358,type,
    sK79: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_359,type,
    sK80: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$' ).

tff(func_def_360,type,
    sK81: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$' ).

tff(func_def_361,type,
    sK82: 'Int_int_prod_set$' > $int ).

tff(func_def_362,type,
    sK83: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$' ).

tff(func_def_363,type,
    sK84: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' ) > 'A_iarray$' ).

tff(func_def_364,type,
    sK85: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' ) > 'A_iarray$' ).

tff(func_def_365,type,
    sK86: ( 'A_iarray_bool_fun$' * 'A_iarray_bool_fun$' ) > 'A_iarray$' ).

tff(func_def_366,type,
    sK87: ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_367,type,
    sK88: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$' ).

tff(func_def_368,type,
    sK89: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$' ).

tff(func_def_369,type,
    sK90: 'A_iarray_a_iarray_prod_bool_fun$' > 'A_iarray$' ).

tff(func_def_370,type,
    sK91: 'A_iarray_a_iarray_prod_bool_fun$' > 'A_iarray$' ).

tff(func_def_371,type,
    sK92: 'Int_int_prod_bool_fun$' > $int ).

tff(func_def_372,type,
    sK93: 'Int_int_prod_bool_fun$' > $int ).

tff(func_def_373,type,
    sK94: 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list$' ).

tff(func_def_374,type,
    sK95: 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list$' ).

tff(func_def_375,type,
    sK96: ( 'A_iarray_list$' * 'A_iarray_list_a_iarray_list_prod$' ) > 'A_iarray_list$' ).

tff(func_def_376,type,
    sK97: ( 'A_iarray$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray$' ).

tff(func_def_377,type,
    sK98: ( 'A_iarray_list$' * 'A_iarray_list_a_iarray_list_prod$' ) > 'A_iarray_list$' ).

tff(func_def_378,type,
    sK99: ( 'A_iarray$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray$' ).

tff(func_def_379,type,
    sK100: ( $int * 'Int_int_prod$' ) > $int ).

tff(func_def_380,type,
    sK101: ( $int * 'Int_int_prod$' ) > $int ).

tff(func_def_381,type,
    sK102: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_382,type,
    sK103: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_383,type,
    sK104: ( 'A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_384,type,
    sK105: ( 'A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_385,type,
    sK106: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_386,type,
    sK107: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_387,type,
    sK108: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_388,type,
    sK109: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_389,type,
    sK110: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_390,type,
    sK111: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_391,type,
    sK112: 'A_iarray_list$' > 'A_iarray$' ).

tff(func_def_392,type,
    sK113: 'A_iarray_list$' > 'A_iarray_list$' ).

tff(func_def_393,type,
    sK114: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_394,type,
    sK115: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_395,type,
    sK116: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_396,type,
    sK117: ( 'Nat$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod$' ).

tff(func_def_397,type,
    sK118: ( 'Nat$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_398,type,
    sK119: ( 'Nat_a_iarray_prod_list$' * 'Nat$' ) > 'Nat_a_iarray_prod$' ).

tff(func_def_399,type,
    sK120: ( 'Nat_a_iarray_prod_list$' * 'Nat$' ) > 'Nat_a_iarray_prod_list$' ).

tff(func_def_400,type,
    sK121: ( 'A_iarray_list_list$' * 'Nat$' ) > 'A_iarray_list$' ).

tff(func_def_401,type,
    sK122: ( 'A_iarray_list_list$' * 'Nat$' ) > 'A_iarray_list_list$' ).

tff(func_def_402,type,
    sK123: ( 'Nat$' * 'A_iarray_list_list$' ) > 'A_iarray_list$' ).

tff(func_def_403,type,
    sK124: ( 'Nat$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).

tff(func_def_404,type,
    sK125: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray$' ).

tff(func_def_405,type,
    sK126: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray_list$' ).

tff(func_def_406,type,
    sK127: ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_407,type,
    sK128: ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_408,type,
    sK129: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray$' ).

tff(func_def_409,type,
    sK130: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray_list$' ).

tff(func_def_410,type,
    sK131: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_411,type,
    sK132: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_412,type,
    sK133: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_413,type,
    sK134: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_414,type,
    sK135: ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_415,type,
    sK136: ( 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec_option$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_416,type,
    sK137: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > 'A_iarray_iarray$' ).

tff(func_def_417,type,
    sK138: ( 'A_iarray_iarray$' * 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$' ) > 'A_iarray_iarray$' ).

tff(func_def_418,type,
    sK139: ( 'A_iarray_iarray$' * 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$' ) > 'A_iarray_iarray$' ).

tff(func_def_419,type,
    sK140: ( 'Int_set$' * 'Int_set_set$' * 'Int_set_set$' ) > 'Int_set$' ).

tff(func_def_420,type,
    sK141: ( 'Int_set$' * 'Int_set_set$' * 'Int_set_set$' ) > 'Int_set$' ).

tff(func_def_421,type,
    sK142: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_422,type,
    sK143: ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_423,type,
    sK144: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).

tff(func_def_424,type,
    sK145: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).

tff(func_def_425,type,
    sK146: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_426,type,
    sK147: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).

tff(func_def_427,type,
    sK148: ( 'A_iarray$' * 'A_iarray_set$' * 'A_iarray_set$' ) > 'A_iarray$' ).

tff(func_def_428,type,
    sK149: ( 'A_iarray$' * 'A_iarray_set$' * 'A_iarray_set$' ) > 'A_iarray$' ).

tff(func_def_429,type,
    sK150: ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_430,type,
    sK151: ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_431,type,
    sK152: ( 'Int_int_prod$' * 'Int_int_prod_set$' * 'Int_int_prod_set$' ) > 'Int_int_prod$' ).

tff(func_def_432,type,
    sK153: ( 'Int_int_prod$' * 'Int_int_prod_set$' * 'Int_int_prod_set$' ) > 'Int_int_prod$' ).

tff(func_def_433,type,
    sK154: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_434,type,
    sK155: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_435,type,
    sK156: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_436,type,
    sK157: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_437,type,
    sK158: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_438,type,
    sK159: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_439,type,
    sK160: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray$' ).

tff(func_def_440,type,
    sK161: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_441,type,
    sK162: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray$' ).

tff(func_def_442,type,
    sK163: 'A_iarray_list_a_iarray_list_bool_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_443,type,
    sK164: ( 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_444,type,
    sK165: ( 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_445,type,
    sK166: ( 'A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_446,type,
    sK167: ( 'A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' ) > 'A_iarray_iarray$' ).

tff(func_def_447,type,
    sK168: ( 'A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > 'A_iarray_iarray$' ).

tff(func_def_448,type,
    sK169: ( 'A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > 'A_n_vec_n_vec$' ).

tff(func_def_449,type,
    sK170: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' ) > 'A_iarray_iarray$' ).

tff(func_def_450,type,
    sK171: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' ) > 'A_iarray_iarray$' ).

tff(func_def_451,type,
    sK172: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_452,type,
    sK173: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_453,type,
    sK174: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_454,type,
    sK175: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_455,type,
    sK176: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_456,type,
    sK177: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_457,type,
    sK178: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_458,type,
    sK179: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_459,type,
    sK180: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_460,type,
    sK181: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$' ).

tff(func_def_461,type,
    sK182: 'A_iarray_a_iarray_prod_set$' > 'A_iarray$' ).

tff(func_def_462,type,
    sK183: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$' ).

tff(func_def_463,type,
    sK184: 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray$' ).

tff(func_def_464,type,
    sK185: 'Int_int_prod_set$' > $int ).

tff(func_def_465,type,
    sK186: 'Int_int_prod_set$' > $int ).

tff(func_def_466,type,
    sK187: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$' ).

tff(func_def_467,type,
    sK188: 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list$' ).

tff(func_def_468,type,
    sK189: ( 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_469,type,
    sK190: ( 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_470,type,
    sK191: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_471,type,
    sK192: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_472,type,
    sK193: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray_bool_fun$' ) > 'A_iarray$' ).

tff(func_def_473,type,
    sK194: ( 'A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_list$' ).

tff(func_def_474,type,
    sK195: ( 'A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray$' ).

tff(func_def_475,type,
    sK196: ( 'Int_list$' * $int * 'Int_list$' * 'Int_int_prod_set$' ) > 'Int_list$' ).

tff(func_def_476,type,
    sK197: ( 'Int_list$' * $int * 'Int_list$' * 'Int_int_prod_set$' ) > $int ).

tff(func_def_477,type,
    sK198: ( 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_list$' ).

tff(func_def_478,type,
    sK199: ( 'A_iarray_iarray$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray$' ).

tff(func_def_479,type,
    sK200: ( $int * 'Int_list$' * 'Int_list$' * 'Int_int_prod_set$' ) > 'Int_list$' ).

tff(func_def_480,type,
    sK201: ( $int * 'Int_list$' * 'Int_list$' * 'Int_int_prod_set$' ) > $int ).

tff(func_def_481,type,
    sK202: ( 'A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > 'A_iarray_list_list$' ).

tff(func_def_482,type,
    sK203: ( 'A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > 'A_iarray_list$' ).

tff(func_def_483,type,
    sK204: ( 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > 'A_iarray_list_list$' ).

tff(func_def_484,type,
    sK205: ( 'A_iarray_list$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > 'A_iarray_list$' ).

tff(func_def_485,type,
    sK206: ( 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$' ) > 'A_iarray_list$' ).

tff(func_def_486,type,
    sK207: ( 'A_iarray_list$' * 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$' ) > 'A_iarray$' ).

tff(func_def_487,type,
    sK208: ( 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$' ) > 'A_iarray_list$' ).

tff(func_def_488,type,
    sK209: ( 'A_iarray$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_a_iarray_prod_set$' ) > 'A_iarray$' ).

tff(func_def_489,type,
    sK210: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_490,type,
    sK211: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_491,type,
    sK212: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_492,type,
    sK213: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_493,type,
    sK214: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_494,type,
    sK215: 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_495,type,
    sK216: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_496,type,
    sK217: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_497,type,
    sK218: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_498,type,
    sK219: ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray$' ).

tff(func_def_499,type,
    sK220: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_500,type,
    sK221: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).

tff(func_def_501,type,
    sK222: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_502,type,
    sK223: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_503,type,
    sK224: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_504,type,
    sK225: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_505,type,
    sK226: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_506,type,
    sK227: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$' ).

tff(func_def_507,type,
    sK228: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray$' ).

tff(func_def_508,type,
    sK229: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > 'A_iarray_list$' ).

tff(pred_def_1,type,
    'fun_app$s': ( 'A_n_vec_n_vec_option_bool_fun$' * 'A_n_vec_n_vec_option$' ) > $o ).

tff(pred_def_2,type,
    'fun_app$o': ( 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$' ) > $o ).

tff(pred_def_3,type,
    'member$q': ( 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$' * 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ) > $o ).

tff(pred_def_4,type,
    'member$p': ( 'A_iarray_iarray_list_a_iarray_iarray_list_prod$' * 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ) > $o ).

tff(pred_def_5,type,
    'fun_app$f': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > $o ).

tff(pred_def_6,type,
    'csquare$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ) > $o ).

tff(pred_def_7,type,
    'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_8,type,
    'fun_app$ae': ( 'Int_int_prod_bool_fun$' * 'Int_int_prod$' ) > $o ).

tff(pred_def_9,type,
    'member$r': ( 'Nat_a_iarray_prod_nat_a_iarray_prod_prod$' * 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' ) > $o ).

tff(pred_def_10,type,
    'member$c': ( 'Nat$' * 'Nat_set$' ) > $o ).

tff(pred_def_11,type,
    'member$a': ( 'A_iarray$' * 'A_iarray_set$' ) > $o ).

tff(pred_def_12,type,
    'member$l': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$' ) > $o ).

tff(pred_def_13,type,
    'member$e': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > $o ).

tff(pred_def_14,type,
    'fun_app$d': ( 'Int_bool_fun$' * $int ) > $o ).

tff(pred_def_15,type,
    'member$m': ( 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$' * 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$' ) > $o ).

tff(pred_def_16,type,
    'csquare$b': ( 'Int_int_prod_set$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_int_prod_fun$' * 'Int_int_prod_int_int_prod_fun$' ) > $o ).

tff(pred_def_17,type,
    'fun_app$a': ( 'A_iarray_list_a_iarray_list_prod_bool_fun$' * 'A_iarray_list_a_iarray_list_prod$' ) > $o ).

tff(pred_def_18,type,
    'member$d': ( $int * 'Int_set$' ) > $o ).

tff(pred_def_19,type,
    'fun_app$': ( 'A_iarray_bool_fun$' * 'A_iarray$' ) > $o ).

tff(pred_def_20,type,
    'fun_app$n': ( 'Bool_bool_fun$' * tlbool ) > $o ).

tff(pred_def_21,type,
    'member$b': ( 'A_iarray_list$' * 'A_iarray_list_set$' ) > $o ).

tff(pred_def_22,type,
    'fun_app$af': ( 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > $o ).

tff(pred_def_23,type,
    'member$n': ( 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$' * 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$' ) > $o ).

tff(pred_def_24,type,
    'member$k': ( 'Int_int_prod_int_int_prod_prod$' * 'Int_int_prod_int_int_prod_prod_set$' ) > $o ).

tff(pred_def_25,type,
    'fun_app$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_26,type,
    'member$s': ( 'A_iarray_list_list_a_iarray_list_list_prod$' * 'A_iarray_list_list_a_iarray_list_list_prod_set$' ) > $o ).

tff(pred_def_27,type,
    'member$i': ( 'Int_set$' * 'Int_set_set$' ) > $o ).

tff(pred_def_28,type,
    'member$j': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' ) > $o ).

tff(pred_def_29,type,
    'fun_app$e': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$' ) > $o ).

tff(pred_def_30,type,
    'member$g': ( 'Int_int_prod$' * 'Int_int_prod_set$' ) > $o ).

tff(pred_def_31,type,
    'member$o': ( 'Int_list_int_list_prod$' * 'Int_list_int_list_prod_set$' ) > $o ).

tff(pred_def_32,type,
    'fun_app$t': ( 'A_iarray_iarray_option_bool_fun$' * 'A_iarray_iarray_option$' ) > $o ).

tff(pred_def_33,type,
    'csquare$a': ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ) > $o ).

tff(pred_def_34,type,
    'member$f': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod_set$' ) > $o ).

tff(pred_def_35,type,
    'member$': ( 'A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > $o ).

tff(pred_def_36,type,
    'fun_app$ag': ( 'A_iarray_a_iarray_prod_bool_fun$' * 'A_iarray_a_iarray_prod$' ) > $o ).

tff(pred_def_37,type,
    'member$h': ( 'A_iarray_iarray$' * 'A_iarray_iarray_set$' ) > $o ).

tff(pred_def_38,type,
    'is_zero_iarray$a': 'A_n_vec_iarray$' > $o ).

tff(pred_def_43,type,
    sP2: ( 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' ) > $o ).

tff(pred_def_44,type,
    sP3: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_option$' ) > $o ).

tff(pred_def_45,type,
    sP4: ( 'Nat$' * 'Nat$' ) > $o ).

tff(pred_def_46,type,
    sP5: ( 'Nat$' * 'Nat$' ) > $o ).

tff(pred_def_47,type,
    sP6: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_48,type,
    sP7: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_49,type,
    sP8: 'Nat_nat_bool_fun_fun$' > $o ).

tff(pred_def_50,type,
    sP9: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_51,type,
    sP10: ( 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > $o ).

tff(pred_def_52,type,
    sP11: ( 'A_iarray_iarray_option$' * 'A_n_vec_n_vec_option$' * 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' ) > $o ).

tff(pred_def_53,type,
    sP12: ( 'A_n_vec_n_vec_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' ) > $o ).

tff(pred_def_54,type,
    sP13: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_option$' * 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' ) > $o ).

tff(pred_def_55,type,
    sP14: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_bool_fun$' * tlbool ) > $o ).

tff(pred_def_56,type,
    sP15: ( 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_57,type,
    sP16: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).

tff(pred_def_58,type,
    sP17: ( 'A_iarray_iarray_option$' * 'A_iarray_iarray_bool_fun$' * 'Bool_bool_fun$' * tlbool ) > $o ).

tff(pred_def_59,type,
    sP18: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_60,type,
    sP19: ( 'A_iarray_list$' * 'A_iarray_bool_fun$' * 'A_iarray$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_61,type,
    sP20: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' > $o ).

tff(pred_def_62,type,
    sP21: ( 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' * 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod$' ) > $o ).

tff(pred_def_63,type,
    sP22: ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > $o ).

tff(pred_def_64,type,
    sP23: ( 'Int_int_prod_set$' * 'Int_list$' * 'Int_list$' * $int * $int ) > $o ).

tff(pred_def_65,type,
    sP24: ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' * 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > $o ).

tff(pred_def_66,type,
    sP25: ( 'Int_int_prod_set$' * 'Int_list$' * 'Int_list$' * $int * $int ) > $o ).

tff(pred_def_67,type,
    sP26: ( 'A_iarray_list_a_iarray_list_prod_set$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_68,type,
    sP27: ( 'A_iarray_list_a_iarray_list_prod_set$' * 'A_iarray_list_list$' * 'A_iarray_list_list$' * 'A_iarray_list$' * 'A_iarray_list$' ) > $o ).

tff(pred_def_69,type,
    sP28: ( 'A_iarray_a_iarray_prod_set$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray$' ) > $o ).

tff(pred_def_70,type,
    sP29: ( 'A_iarray_a_iarray_prod_set$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray$' ) > $o ).

tff(pred_def_71,type,
    sP30: ( 'A_iarray_a_iarray_prod_set$' * 'A_iarray_list$' * 'A_iarray_list$' * 'A_iarray$' * 'A_iarray$' ) > $o ).

tff(f12470,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3509,f3513,f3518,f3522,f3526,f3530,f3534,f3539,f3543,f3547,f3551,f3555,f3559,f3563,f3567,f3571,f3576,f3580,f3584,f3588,f3593,f3598,f3603,f3608,f3613,f3618,f3623,f3628,f3633,f3638,f3643,f3648,f3653,f3657,f3661,f3665,f3669,f3673,f3677,f3681,f3685,f3689,f3693,f3697,f3701,f3705,f3709,f3713,f3717,f3721,f3726,f3731,f3736,f3740,f3744,f3750,f3757,f3761,f3766,f3771,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f3837,f3842,f3846,f3850,f3855,f3860,f3875,f3880,f3885,f3889,f3893,f3897,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4148,f4160,f4196,f4212,f4225,f4237,f4254,f4258,f4262,f4266,f4270,f4274,f4280,f4284,f4288,f4292,f4296,f4300,f4304,f4309,f4315,f4321,f4325,f4329,f4333,f4337,f4341,f4345,f4349,f4353,f4357,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4501,f4505,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4573,f4598,f4626,f4651,f4728,f4733,f4751,f4756,f4760,f4764,f4768,f4772,f4778,f4782,f4786,f4792,f4796,f4800,f4804,f4808,f4812,f4816,f4820,f4824,f4828,f4836,f4840,f4844,f4848,f4852,f4856,f4860,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4905,f4910,f4915,f4920,f4926,f4930,f5048,f5067,f5071,f5075,f5079,f5104,f5108,f5112,f5116,f5120,f5124,f5128,f5132,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5407,f5566,f5591,f5595,f5599,f5604,f5617,f5624,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5664,f5668,f5672,f5676,f5680,f5684,f5688,f5692,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f5724,f5728,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5827,f5831,f5835,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5884,f5888,f5892,f5896,f5900,f5904,f5908,f5912,f5916,f5920,f5927,f5944,f5948,f5952,f5956,f5961,f5974,f5979,f5983,f5996,f6000,f6004,f6009,f6020,f6025,f6036,f6048,f6052,f6056,f6060,f6064,f6126,f6203,f6452,f6462,f6466,f6495,f6520,f6570,f6581,f6585,f6589,f6593,f6598,f6603,f6607,f6611,f6615,f6619,f6623,f6627,f6631,f6635,f6639,f6643,f6647,f6651,f6655,f6659,f6663,f6667,f6671,f6675,f6679,f6683,f6687,f6691,f6695,f6699,f6703,f6707,f6711,f6715,f6719,f6723,f6727,f6731,f6735,f6739,f6743,f6747,f6751,f6755,f6760,f6799,f6803,f6807,f6882,f7034,f7038,f7045,f7049,f7053,f7057,f7061,f7065,f7069,f7073,f7077,f7081,f7089,f7093,f7097,f7101,f7105,f7109,f7113,f7117,f7121,f7125,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7163,f7167,f7173,f7177,f7181,f7186,f7190,f7194,f7198,f7202,f7206,f7210,f7214,f7218,f7222,f7226,f7230,f7234,f7310,f7425,f7442,f7686,f7690,f7694,f7698,f7702,f7706,f7710,f7716,f7720,f7724,f7728,f7732,f7736,f7740,f7744,f7748,f7752,f7756,f7760,f7764,f7768,f7772,f7776,f7780,f7784,f7790,f7796,f7800,f7804,f7808,f8171,f8175,f8179,f8183,f8187,f8191,f8195,f8199,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8244,f8249,f8253,f8257,f8261,f8265,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8309,f8313,f8317,f8321,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8357,f8361,f8365,f8369,f8373,f8377,f8381,f8385,f8389,f8393,f8397,f8401,f8405,f8409,f8516,f8596,f8646,f8655,f8681,f9233,f9237,f9241,f9245,f9249,f9253,f9257,f9261,f9270,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9306,f9315,f9319,f9323,f9327,f9331,f9335,f9339,f9343,f9347,f9351,f9360,f9364,f9368,f9372,f9376,f9380,f9384,f9388,f9392,f9396,f9405,f9409,f9413,f9417,f9421,f9425,f9430,f9434,f9438,f9442,f9451,f9455,f9826,f9846,f9868,f9977,f9983,f9996,f10000,f10006,f10015,f10020,f10025,f10030,f10035,f10039,f10043,f10047,f10051,f10055,f10063,f10067,f10071,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10104,f10109,f10113,f10117,f10128,f10132,f10136,f10140,f10149,f10209,f10234,f10238,f10242,f10246,f10250,f10254,f10258,f10262,f10266,f10278,f10282,f10286,f10290,f10295,f10374,f10379,f10460,f10465,f10469,f10474,f10478,f10694,f10708,f10712,f10821,f10827,f10831,f10835,f10839,f10843,f10849,f10866,f10873,f10878,f10892,f10896,f10900,f10904,f10908,f10912,f10916,f10920,f10924,f10929,f10933,f10937,f10941,f10946,f10950,f11212,f11226,f11343,f11347,f11443,f11447,f11453,f11476,f11483,f11487,f11503,f11507,f11511,f11515,f11519,f11523,f11527,f11531,f11535,f11539,f11547,f11573,f11581,f11607,f11611,f11615,f11619,f11623,f11627,f11631,f11635,f11639,f11733,f12084,f12252,f12256,f12260,f12264,f12268,f12272,f12276,f12280,f12284,f12288,f12292,f12296,f12300,f12308,f12312,f12316,f12320,f12324,f12328,f12332,f12336,f12341,f12351,f12355,f12469]) ).

tff(f12469,plain,
    ( ~ spl230_1
    | ~ spl230_58
    | ~ spl230_403
    | ~ spl230_432
    | ~ spl230_727 ),
    inference(avatar_split_clause,[],[f12344,f10293,f6579,f5925,f3754,f3502]) ).

tff(f3502,plain,
    ( spl230_1
  <=> sP0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_1])]) ).

tff(f3754,plain,
    ( spl230_58
  <=> ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_58])]) ).

tff(f5925,plain,
    ( spl230_403
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_403])]) ).

tff(f6579,plain,
    ( spl230_432
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_432])]) ).

tff(f10293,plain,
    ( spl230_727
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'(X0)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_727])]) ).

tff(f12344,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) )
    | ~ sP0
    | ~ spl230_403
    | ~ spl230_432
    | ~ spl230_727 ),
    inference(forward_demodulation,[],[f12343,f6580]) ).

tff(f6580,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) )
    | ~ spl230_432 ),
    inference(avatar_component_clause,[],[f6579]) ).

tff(f12343,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'('a$'))) )
    | ~ sP0
    | ~ spl230_403
    | ~ spl230_727 ),
    inference(forward_demodulation,[],[f12342,f10294]) ).

tff(f10294,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'(X0)))))) )
    | ~ spl230_727 ),
    inference(avatar_component_clause,[],[f10293]) ).

tff(f12342,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
    | ~ sP0
    | ~ spl230_403 ),
    inference(forward_demodulation,[],[f3312,f5926]) ).

tff(f5926,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
    | ~ spl230_403 ),
    inference(avatar_component_clause,[],[f5925]) ).

tff(f3312,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
    | ~ sP0 ),
    inference(trivial_inequality_removal,[],[f2919]) ).

tff(f2919,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
    | ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
    | ~ sP0 ),
    inference(definition_unfolding,[],[f1739,f1818]) ).

tff(f1818,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) ),
    inference(cnf_transformation,[],[f275]) ).

tff(f275,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).

tff(f1739,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
    | ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
    | ~ sP0 ),
    inference(cnf_transformation,[],[f1140]) ).

tff(f1140,plain,
    ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ~ sP0 ),
    inference(nnf_transformation,[],[f1078]) ).

tff(f1078,plain,
    ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ~ sP0 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f12355,plain,
    ( spl230_58
    | ~ spl230_403
    | ~ spl230_432
    | ~ spl230_727
    | ~ spl230_818 ),
    inference(avatar_split_clause,[],[f12354,f12338,f10293,f6579,f5925,f3754]) ).

tff(f12338,plain,
    ( spl230_818
  <=> ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_818])]) ).

tff(f12354,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) )
    | ~ spl230_403
    | ~ spl230_432
    | ~ spl230_727
    | ~ spl230_818 ),
    inference(forward_demodulation,[],[f12353,f6580]) ).

tff(f12353,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'('a$'))) )
    | ~ spl230_403
    | ~ spl230_727
    | ~ spl230_818 ),
    inference(forward_demodulation,[],[f12352,f10294]) ).

tff(f12352,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
    | ~ spl230_403
    | ~ spl230_818 ),
    inference(forward_demodulation,[],[f12340,f5926]) ).

tff(f12340,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
    | ~ spl230_818 ),
    inference(avatar_component_clause,[],[f12338]) ).

tff(f12351,plain,
    ( spl230_2
    | spl230_58
    | ~ spl230_427
    | ~ spl230_432
    | ~ spl230_727 ),
    inference(avatar_split_clause,[],[f12347,f10293,f6579,f6460,f3754,f3506]) ).

tff(f3506,plain,
    ( spl230_2
  <=> sP1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_2])]) ).

tff(f6460,plain,
    ( spl230_427
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('snd$a',X0) = sK37(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_427])]) ).

tff(f12347,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) )
    | sP1
    | ~ spl230_427
    | ~ spl230_432
    | ~ spl230_727 ),
    inference(forward_demodulation,[],[f12346,f6580]) ).

tff(f12346,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'('a$'))) )
    | sP1
    | ~ spl230_427
    | ~ spl230_727 ),
    inference(forward_demodulation,[],[f12345,f10294]) ).

tff(f12345,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
    | sP1
    | ~ spl230_427 ),
    inference(forward_demodulation,[],[f2921,f6461]) ).

tff(f6461,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('snd$a',X0) = sK37(X0) )
    | ~ spl230_427 ),
    inference(avatar_component_clause,[],[f6460]) ).

tff(f2921,plain,
    ( sP1
    | ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) ) ),
    inference(definition_unfolding,[],[f1744,f1817]) ).

tff(f1817,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) ),
    inference(cnf_transformation,[],[f206]) ).

tff(f206,axiom,
    ! [X0: 'A_iarray_iarray$'] : ( 'gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom204) ).

tff(f1744,plain,
    ( sP1
    | ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) ),
    inference(cnf_transformation,[],[f1080]) ).

tff(f1080,plain,
    ( ( sP1
      & ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
    | ( sP0
      & ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) ) ),
    inference(definition_folding,[],[f784,f1079,f1078]) ).

tff(f1079,plain,
    ( ( ( 'none$' != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ~ sP1 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f784,plain,
    ( ( ( ( ( 'none$' != 'none$' )
          & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
        | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
          & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
      & ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
    | ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
          & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
        | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
          & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
      & ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

tff(f24,negated_conjecture,
    ~ ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
       => ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
           => ( 'none$' = 'none$' ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
           => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) ) ) )
      & ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
       => ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
           => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
           => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
    inference(negated_conjecture,[],[f23]) ).

tff(f23,conjecture,
    ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
     => ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
         => ( 'none$' = 'none$' ) )
        & ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
         => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) ) ) )
    & ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
     => ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
         => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
        & ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
         => ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture22) ).

tff(f12341,plain,
    ( ~ spl230_2
    | spl230_818 ),
    inference(avatar_split_clause,[],[f3314,f12338,f3506]) ).

tff(f3314,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
    | ~ sP1 ),
    inference(trivial_inequality_removal,[],[f2915]) ).

tff(f2915,plain,
    ( ( 'none$' != 'none$' )
    | ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
    | ~ sP1 ),
    inference(definition_unfolding,[],[f1736,f1818]) ).

tff(f1736,plain,
    ( ( 'none$' != 'none$' )
    | ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
    | ~ sP1 ),
    inference(cnf_transformation,[],[f1139]) ).

tff(f1139,plain,
    ( ( ( 'none$' != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
      & ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
    | ~ sP1 ),
    inference(nnf_transformation,[],[f1079]) ).

tff(f12336,plain,
    spl230_817,
    inference(avatar_split_clause,[],[f3286,f12334]) ).

tff(f12334,plain,
    ( spl230_817
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_nat_fun$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','size_list$'(X0,'cons$'(X1,X2))) = $sum($sum('fun_app$l'('of_nat$','fun_app$bc'(X0,X1)),'fun_app$l'('of_nat$','size_list$'(X0,X2))),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_817])]) ).

tff(f3286,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_nat_fun$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','size_list$'(X0,'cons$'(X1,X2))) = $sum($sum('fun_app$l'('of_nat$','fun_app$bc'(X0,X1)),'fun_app$l'('of_nat$','size_list$'(X0,X2))),1) ),
    inference(evaluation,[],[f2382]) ).

tff(f2382,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_nat_fun$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','size_list$'(X0,'cons$'(X1,X2))) = $sum($sum('fun_app$l'('of_nat$','fun_app$bc'(X0,X1)),'fun_app$l'('of_nat$','size_list$'(X0,X2))),$sum(0,1)) ),
    inference(cnf_transformation,[],[f494]) ).

tff(f494,axiom,
    ! [X0: 'A_iarray_nat_fun$',X1: 'A_iarray$',X2: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','size_list$'(X0,'cons$'(X1,X2))) = $sum($sum('fun_app$l'('of_nat$','fun_app$bc'(X0,X1)),'fun_app$l'('of_nat$','size_list$'(X0,X2))),$sum(0,1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom492) ).

tff(f12332,plain,
    spl230_816,
    inference(avatar_split_clause,[],[f3262,f12330]) ).

tff(f12330,plain,
    ( spl230_816
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray$',X5: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
        ( 'member$'('pair$b'('fun_app$p'('append$d'(X4),'cons$'(X0,X5)),'fun_app$p'('append$d'(X4),'cons$'(X1,X5))),'listrel1$c'(X2))
        | ~ 'member$f'('pair$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_816])]) ).

tff(f3262,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X1: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$'('pair$b'('fun_app$p'('append$d'(X4),'cons$'(X0,X5)),'fun_app$p'('append$d'(X4),'cons$'(X1,X5))),'listrel1$c'(X2))
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(equality_resolution,[],[f3261]) ).

tff(f3261,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X3,'fun_app$p'('append$d'(X4),'cons$'(X1,X5))),'listrel1$c'(X2))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) != X3 )
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(equality_resolution,[],[f2909]) ).

tff(f2909,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray$',X6: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X3,X6),'listrel1$c'(X2))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X1,X5)) != X6 )
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) != X3 )
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1071]) ).

tff(f1071,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$',X6: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X3,X6),'listrel1$c'(X2))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X1,X5)) != X6 )
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) != X3 )
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(flattening,[],[f1070]) ).

tff(f1070,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$',X6: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X3,X6),'listrel1$c'(X2))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X1,X5)) != X6 )
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) != X3 )
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f553]) ).

tff(f553,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$',X6: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X4),'cons$'(X1,X5)) = X6 )
        & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 )
        & 'member$f'('pair$a'(X0,X1),X2) )
     => 'member$'('pair$b'(X3,X6),'listrel1$c'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom551) ).

tff(f12328,plain,
    ( spl230_815
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_225 ),
    inference(avatar_split_clause,[],[f4747,f4556,f3895,f3857,f12326]) ).

tff(f12326,plain,
    ( spl230_815
  <=> ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 'size$d'('none$a') = 'fun_app$ax'('size_option$a'(X0),'none$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_815])]) ).

tff(f3857,plain,
    ( spl230_82
  <=> ( 1 = 'fun_app$l'('of_nat$','size$d'('none$a')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_82])]) ).

tff(f3895,plain,
    ( spl230_88
  <=> ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_88])]) ).

tff(f4556,plain,
    ( spl230_225
  <=> ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$ax'('size_option$a'(X0),'none$a')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_225])]) ).

tff(f4747,plain,
    ( ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 'size$d'('none$a') = 'fun_app$ax'('size_option$a'(X0),'none$a') )
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_225 ),
    inference(forward_demodulation,[],[f4744,f4138]) ).

tff(f4138,plain,
    ( ( 'size$d'('none$a') = 'fun_app$k'('nat$',1) )
    | ~ spl230_82
    | ~ spl230_88 ),
    inference(superposition,[],[f3896,f3859]) ).

tff(f3859,plain,
    ( ( 1 = 'fun_app$l'('of_nat$','size$d'('none$a')) )
    | ~ spl230_82 ),
    inference(avatar_component_clause,[],[f3857]) ).

tff(f3896,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = X0 )
    | ~ spl230_88 ),
    inference(avatar_component_clause,[],[f3895]) ).

tff(f4744,plain,
    ( ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 'fun_app$ax'('size_option$a'(X0),'none$a') = 'fun_app$k'('nat$',1) )
    | ~ spl230_88
    | ~ spl230_225 ),
    inference(superposition,[],[f3896,f4557]) ).

tff(f4557,plain,
    ( ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$ax'('size_option$a'(X0),'none$a')) )
    | ~ spl230_225 ),
    inference(avatar_component_clause,[],[f4556]) ).

tff(f12324,plain,
    spl230_814,
    inference(avatar_split_clause,[],[f3260,f12322]) ).

tff(f12322,plain,
    ( spl230_814
  <=> ! [X4: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod$'] :
        ( 'member$q'('pair$x'('fun_app$bd'('append$'(X4),'cons$a'(X0,X5)),'fun_app$bd'('append$'(X4),'cons$a'(X1,X5))),'listrel1$d'(X2))
        | ~ 'member$r'('pair$y'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_814])]) ).

tff(f3260,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'('fun_app$bd'('append$'(X4),'cons$a'(X0,X5)),'fun_app$bd'('append$'(X4),'cons$a'(X1,X5))),'listrel1$d'(X2))
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(equality_resolution,[],[f3259]) ).

tff(f3259,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'(X3,'fun_app$bd'('append$'(X4),'cons$a'(X1,X5))),'listrel1$d'(X2))
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X0,X5)) != X3 )
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(equality_resolution,[],[f2908]) ).

tff(f2908,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X6: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'(X3,X6),'listrel1$d'(X2))
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X1,X5)) != X6 )
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X0,X5)) != X3 )
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1069]) ).

tff(f1069,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$',X6: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'(X3,X6),'listrel1$d'(X2))
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X1,X5)) != X6 )
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X0,X5)) != X3 )
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(flattening,[],[f1068]) ).

tff(f1068,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$',X6: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'(X3,X6),'listrel1$d'(X2))
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X1,X5)) != X6 )
      | ( 'fun_app$bd'('append$'(X4),'cons$a'(X0,X5)) != X3 )
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f549]) ).

tff(f549,axiom,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$',X6: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X4),'cons$a'(X1,X5)) = X6 )
        & ( 'fun_app$bd'('append$'(X4),'cons$a'(X0,X5)) = X3 )
        & 'member$r'('pair$y'(X0,X1),X2) )
     => 'member$q'('pair$x'(X3,X6),'listrel1$d'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom547) ).

tff(f12320,plain,
    spl230_813,
    inference(avatar_split_clause,[],[f3202,f12318]) ).

tff(f12318,plain,
    ( spl230_813
  <=> ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( sP19('fun_app$p'('filter$'(X1),X5),X1,X2,'fun_app$p'('append$d'(X4),'cons$'(X2,X5)))
        | ~ 'fun_app$'(X1,X2)
        | 'fun_app$'(X1,sK219(X1,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_813])]) ).

tff(f3202,plain,
    ! [X2: 'A_iarray$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP19('fun_app$p'('filter$'(X1),X5),X1,X2,'fun_app$p'('append$d'(X4),'cons$'(X2,X5)))
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK219(X1,X4)) ),
    inference(equality_resolution,[],[f3201]) ).

tff(f3201,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP19('fun_app$p'('filter$'(X1),X5),X1,X2,X3)
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK219(X1,X4))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ),
    inference(equality_resolution,[],[f2763]) ).

tff(f2763,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP19(X0,X1,X2,X3)
      | ( 'fun_app$p'('filter$'(X1),X5) != X0 )
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK219(X1,X4))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ),
    inference(cnf_transformation,[],[f1680]) ).

tff(f1680,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( sP19(X0,X1,X2,X3)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X5) != X0 )
            | ~ 'fun_app$'(X1,X2)
            | ( 'fun_app$'(X1,sK219(X1,X4))
              & 'member$a'(sK219(X1,X4),'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ) )
      & ( ( ( 'fun_app$p'('filter$'(X1),sK221(X0,X1,X2,X3)) = X0 )
          & 'fun_app$'(X1,X2)
          & ! [X9: 'A_iarray$'] :
              ( ~ 'fun_app$'(X1,X9)
              | ~ 'member$a'(X9,'set$'(sK220(X0,X1,X2,X3))) )
          & ( 'fun_app$p'('append$d'(sK220(X0,X1,X2,X3)),'cons$'(X2,sK221(X0,X1,X2,X3))) = X3 ) )
        | ~ sP19(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK219,sK220,sK221])],[f1677,f1679,f1678]) ).

tff(f1678,plain,
    ! [X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$'] :
      ( ? [X6: 'A_iarray$'] :
          ( 'fun_app$'(X1,X6)
          & 'member$a'(X6,'set$'(X4)) )
     => ( 'fun_app$'(X1,sK219(X1,X4))
        & 'member$a'(sK219(X1,X4),'set$'(X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1679,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ? [X7: 'A_iarray_list$',X8: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X1),X8) = X0 )
          & 'fun_app$'(X1,X2)
          & ! [X9: 'A_iarray$'] :
              ( ~ 'fun_app$'(X1,X9)
              | ~ 'member$a'(X9,'set$'(X7)) )
          & ( 'fun_app$p'('append$d'(X7),'cons$'(X2,X8)) = X3 ) )
     => ( ( 'fun_app$p'('filter$'(X1),sK221(X0,X1,X2,X3)) = X0 )
        & 'fun_app$'(X1,X2)
        & ! [X9: 'A_iarray$'] :
            ( ~ 'fun_app$'(X1,X9)
            | ~ 'member$a'(X9,'set$'(sK220(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK220(X0,X1,X2,X3)),'cons$'(X2,sK221(X0,X1,X2,X3))) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1677,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( sP19(X0,X1,X2,X3)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X5) != X0 )
            | ~ 'fun_app$'(X1,X2)
            | ? [X6: 'A_iarray$'] :
                ( 'fun_app$'(X1,X6)
                & 'member$a'(X6,'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ) )
      & ( ? [X7: 'A_iarray_list$',X8: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X8) = X0 )
            & 'fun_app$'(X1,X2)
            & ! [X9: 'A_iarray$'] :
                ( ~ 'fun_app$'(X1,X9)
                | ~ 'member$a'(X9,'set$'(X7)) )
            & ( 'fun_app$p'('append$d'(X7),'cons$'(X2,X8)) = X3 ) )
        | ~ sP19(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f1676]) ).

tff(f1676,plain,
    ! [X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( ( sP19(X3,X0,X2,X1)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X0),X5) != X3 )
            | ~ 'fun_app$'(X0,X2)
            | ? [X6: 'A_iarray$'] :
                ( 'fun_app$'(X0,X6)
                & 'member$a'(X6,'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X1 ) ) )
      & ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
            & 'fun_app$'(X0,X2)
            & ! [X6: 'A_iarray$'] :
                ( ~ 'fun_app$'(X0,X6)
                | ~ 'member$a'(X6,'set$'(X4)) )
            & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) )
        | ~ sP19(X3,X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f1115]) ).

tff(f1115,plain,
    ! [X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( sP19(X3,X0,X2,X1)
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X0,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).

tff(f12316,plain,
    spl230_812,
    inference(avatar_split_clause,[],[f3198,f12314]) ).

tff(f12314,plain,
    ( spl230_812
  <=> ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( sP18('fun_app$p'('filter$'(X1),X5),X1,X2,'fun_app$p'('append$d'(X4),'cons$'(X2,X5)))
        | ~ 'fun_app$'(X1,X2)
        | 'fun_app$'(X1,sK216(X1,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_812])]) ).

tff(f3198,plain,
    ! [X2: 'A_iarray$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP18('fun_app$p'('filter$'(X1),X5),X1,X2,'fun_app$p'('append$d'(X4),'cons$'(X2,X5)))
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK216(X1,X4)) ),
    inference(equality_resolution,[],[f3197]) ).

tff(f3197,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP18('fun_app$p'('filter$'(X1),X5),X1,X2,X3)
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK216(X1,X4))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ),
    inference(equality_resolution,[],[f2755]) ).

tff(f2755,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( sP18(X0,X1,X2,X3)
      | ( 'fun_app$p'('filter$'(X1),X5) != X0 )
      | ~ 'fun_app$'(X1,X2)
      | 'fun_app$'(X1,sK216(X1,X4))
      | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ),
    inference(cnf_transformation,[],[f1674]) ).

tff(f1674,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( sP18(X0,X1,X2,X3)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X5) != X0 )
            | ~ 'fun_app$'(X1,X2)
            | ( 'fun_app$'(X1,sK216(X1,X4))
              & 'member$a'(sK216(X1,X4),'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ) )
      & ( ( ( 'fun_app$p'('filter$'(X1),sK218(X0,X1,X2,X3)) = X0 )
          & 'fun_app$'(X1,X2)
          & ! [X9: 'A_iarray$'] :
              ( ~ 'fun_app$'(X1,X9)
              | ~ 'member$a'(X9,'set$'(sK217(X0,X1,X2,X3))) )
          & ( 'fun_app$p'('append$d'(sK217(X0,X1,X2,X3)),'cons$'(X2,sK218(X0,X1,X2,X3))) = X3 ) )
        | ~ sP18(X0,X1,X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK216,sK217,sK218])],[f1671,f1673,f1672]) ).

tff(f1672,plain,
    ! [X1: 'A_iarray_bool_fun$',X4: 'A_iarray_list$'] :
      ( ? [X6: 'A_iarray$'] :
          ( 'fun_app$'(X1,X6)
          & 'member$a'(X6,'set$'(X4)) )
     => ( 'fun_app$'(X1,sK216(X1,X4))
        & 'member$a'(sK216(X1,X4),'set$'(X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1673,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ? [X7: 'A_iarray_list$',X8: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X1),X8) = X0 )
          & 'fun_app$'(X1,X2)
          & ! [X9: 'A_iarray$'] :
              ( ~ 'fun_app$'(X1,X9)
              | ~ 'member$a'(X9,'set$'(X7)) )
          & ( 'fun_app$p'('append$d'(X7),'cons$'(X2,X8)) = X3 ) )
     => ( ( 'fun_app$p'('filter$'(X1),sK218(X0,X1,X2,X3)) = X0 )
        & 'fun_app$'(X1,X2)
        & ! [X9: 'A_iarray$'] :
            ( ~ 'fun_app$'(X1,X9)
            | ~ 'member$a'(X9,'set$'(sK217(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK217(X0,X1,X2,X3)),'cons$'(X2,sK218(X0,X1,X2,X3))) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1671,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( sP18(X0,X1,X2,X3)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X5) != X0 )
            | ~ 'fun_app$'(X1,X2)
            | ? [X6: 'A_iarray$'] :
                ( 'fun_app$'(X1,X6)
                & 'member$a'(X6,'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) != X3 ) ) )
      & ( ? [X7: 'A_iarray_list$',X8: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X1),X8) = X0 )
            & 'fun_app$'(X1,X2)
            & ! [X9: 'A_iarray$'] :
                ( ~ 'fun_app$'(X1,X9)
                | ~ 'member$a'(X9,'set$'(X7)) )
            & ( 'fun_app$p'('append$d'(X7),'cons$'(X2,X8)) = X3 ) )
        | ~ sP18(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f1670]) ).

tff(f1670,plain,
    ! [X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X0: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( sP18(X1,X2,X0,X3)
        | ! [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X2),X5) != X1 )
            | ~ 'fun_app$'(X2,X0)
            | ? [X6: 'A_iarray$'] :
                ( 'fun_app$'(X2,X6)
                & 'member$a'(X6,'set$'(X4)) )
            | ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) != X3 ) ) )
      & ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
            & 'fun_app$'(X2,X0)
            & ! [X6: 'A_iarray$'] :
                ( ~ 'fun_app$'(X2,X6)
                | ~ 'member$a'(X6,'set$'(X4)) )
            & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) )
        | ~ sP18(X1,X2,X0,X3) ) ),
    inference(nnf_transformation,[],[f1113]) ).

tff(f1113,plain,
    ! [X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X0: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( sP18(X1,X2,X0,X3)
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X2,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).

tff(f12312,plain,
    spl230_811,
    inference(avatar_split_clause,[],[f3167,f12310]) ).

tff(f12310,plain,
    ( spl230_811
  <=> ! [X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X3: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
        | 'fun_app$'(X3,sK193(X1,X2,X3))
        | 'fun_app$'(X2,sK193(X1,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_811])]) ).

tff(f3167,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
      | 'fun_app$'(X3,sK193(X1,X2,X3))
      | 'fun_app$'(X2,sK193(X1,X2,X3)) ),
    inference(equality_resolution,[],[f2640]) ).

tff(f2640,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | 'fun_app$'(X3,sK193(X1,X2,X3))
      | 'fun_app$'(X2,sK193(X1,X2,X3))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1613]) ).

tff(f1613,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ( ( ~ 'fun_app$'(X3,sK193(X1,X2,X3))
          | ~ 'fun_app$'(X2,sK193(X1,X2,X3)) )
        & ( 'fun_app$'(X3,sK193(X1,X2,X3))
          | 'fun_app$'(X2,sK193(X1,X2,X3)) )
        & 'member$a'(sK193(X1,X2,X3),'set$'(X1)) )
      | ( X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK193])],[f1611,f1612]) ).

tff(f1612,plain,
    ! [X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ? [X4: 'A_iarray$'] :
          ( ( ~ 'fun_app$'(X3,X4)
            | ~ 'fun_app$'(X2,X4) )
          & ( 'fun_app$'(X3,X4)
            | 'fun_app$'(X2,X4) )
          & 'member$a'(X4,'set$'(X1)) )
     => ( ( ~ 'fun_app$'(X3,sK193(X1,X2,X3))
          | ~ 'fun_app$'(X2,sK193(X1,X2,X3)) )
        & ( 'fun_app$'(X3,sK193(X1,X2,X3))
          | 'fun_app$'(X2,sK193(X1,X2,X3)) )
        & 'member$a'(sK193(X1,X2,X3),'set$'(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1611,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ? [X4: 'A_iarray$'] :
          ( ( ~ 'fun_app$'(X3,X4)
            | ~ 'fun_app$'(X2,X4) )
          & ( 'fun_app$'(X3,X4)
            | 'fun_app$'(X2,X4) )
          & 'member$a'(X4,'set$'(X1)) )
      | ( X0 != X1 ) ),
    inference(flattening,[],[f1610]) ).

tff(f1610,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ? [X4: 'A_iarray$'] :
          ( ( ~ 'fun_app$'(X3,X4)
            | ~ 'fun_app$'(X2,X4) )
          & ( 'fun_app$'(X3,X4)
            | 'fun_app$'(X2,X4) )
          & 'member$a'(X4,'set$'(X1)) )
      | ( X0 != X1 ) ),
    inference(nnf_transformation,[],[f981]) ).

tff(f981,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ? [X4: 'A_iarray$'] :
          ( ( 'fun_app$'(X2,X4)
          <~> 'fun_app$'(X3,X4) )
          & 'member$a'(X4,'set$'(X1)) )
      | ( X0 != X1 ) ),
    inference(flattening,[],[f980]) ).

tff(f980,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ? [X4: 'A_iarray$'] :
          ( ( 'fun_app$'(X2,X4)
          <~> 'fun_app$'(X3,X4) )
          & 'member$a'(X4,'set$'(X1)) )
      | ( X0 != X1 ) ),
    inference(ennf_transformation,[],[f600]) ).

tff(f600,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$'] :
      ( ( ! [X4: 'A_iarray$'] :
            ( 'member$a'(X4,'set$'(X1))
           => ( 'fun_app$'(X2,X4)
            <=> 'fun_app$'(X3,X4) ) )
        & ( X0 = X1 ) )
     => ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom598) ).

tff(f12308,plain,
    spl230_810,
    inference(avatar_split_clause,[],[f3166,f12306]) ).

tff(f12306,plain,
    ( spl230_810
  <=> ! [X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X3: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
        | ~ 'fun_app$'(X3,sK193(X1,X2,X3))
        | ~ 'fun_app$'(X2,sK193(X1,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_810])]) ).

tff(f3166,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
      | ~ 'fun_app$'(X3,sK193(X1,X2,X3))
      | ~ 'fun_app$'(X2,sK193(X1,X2,X3)) ),
    inference(equality_resolution,[],[f2641]) ).

tff(f2641,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | ~ 'fun_app$'(X3,sK193(X1,X2,X3))
      | ~ 'fun_app$'(X2,sK193(X1,X2,X3))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1613]) ).

tff(f12300,plain,
    spl230_809,
    inference(avatar_split_clause,[],[f2925,f12298]) ).

tff(f12298,plain,
    ( spl230_809
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('snd$a','pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0))),'fun_app$r'('fst$','pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0)))) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_809])]) ).

tff(f2925,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('snd$a','pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0))),'fun_app$r'('fst$','pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0)))) = X0 ),
    inference(definition_unfolding,[],[f1779,f1848,f1848]) ).

tff(f1848,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'swap$d'(X0) = 'pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0)) ),
    inference(cnf_transformation,[],[f338]) ).

tff(f338,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'swap$d'(X0) = 'pair$'('fun_app$r'('snd$a',X0),'fun_app$r'('fst$',X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom336) ).

tff(f1779,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'swap$d'('swap$d'(X0)) = X0 ),
    inference(cnf_transformation,[],[f339]) ).

tff(f339,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'swap$d'('swap$d'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom337) ).

tff(f12296,plain,
    spl230_808,
    inference(avatar_split_clause,[],[f2894,f12294]) ).

tff(f12294,plain,
    ( spl230_808
  <=> ! [X3: 'A_iarray_list$',X4: 'A_iarray_list$',X0: 'A_iarray$',X5: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
        ( 'member$'('pair$b'('fun_app$p'('append$d'(X3),'cons$'(X0,X4)),'fun_app$p'('append$d'(X3),'cons$'(X1,X5))),'lexord$c'(X2))
        | ~ 'member$f'('pair$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_808])]) ).

tff(f2894,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$'('pair$b'('fun_app$p'('append$d'(X3),'cons$'(X0,X4)),'fun_app$p'('append$d'(X3),'cons$'(X1,X5))),'lexord$c'(X2))
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1044]) ).

tff(f1044,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$'('pair$b'('fun_app$p'('append$d'(X3),'cons$'(X0,X4)),'fun_app$p'('append$d'(X3),'cons$'(X1,X5))),'lexord$c'(X2))
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f548]) ).

tff(f548,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
      ( 'member$f'('pair$a'(X0,X1),X2)
     => 'member$'('pair$b'('fun_app$p'('append$d'(X3),'cons$'(X0,X4)),'fun_app$p'('append$d'(X3),'cons$'(X1,X5))),'lexord$c'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom546) ).

tff(f12292,plain,
    spl230_807,
    inference(avatar_split_clause,[],[f2893,f12290]) ).

tff(f12290,plain,
    ( spl230_807
  <=> ! [X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod$'] :
        ( 'member$q'('pair$x'('fun_app$bd'('append$'(X3),'cons$a'(X0,X4)),'fun_app$bd'('append$'(X3),'cons$a'(X1,X5))),'lexord$d'(X2))
        | ~ 'member$r'('pair$y'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_807])]) ).

tff(f2893,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'('fun_app$bd'('append$'(X3),'cons$a'(X0,X4)),'fun_app$bd'('append$'(X3),'cons$a'(X1,X5))),'lexord$d'(X2))
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1043]) ).

tff(f1043,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'('fun_app$bd'('append$'(X3),'cons$a'(X0,X4)),'fun_app$bd'('append$'(X3),'cons$a'(X1,X5))),'lexord$d'(X2))
      | ~ 'member$r'('pair$y'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f544]) ).

tff(f544,axiom,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_list$',X5: 'Nat_a_iarray_prod_list$'] :
      ( 'member$r'('pair$y'(X0,X1),X2)
     => 'member$q'('pair$x'('fun_app$bd'('append$'(X3),'cons$a'(X0,X4)),'fun_app$bd'('append$'(X3),'cons$a'(X1,X5))),'lexord$d'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom542) ).

tff(f12288,plain,
    spl230_806,
    inference(avatar_split_clause,[],[f2882,f12286]) ).

tff(f12286,plain,
    ( spl230_806
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
        | 'member$f'('pair$a'(X0,X2),X4)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_806])]) ).

tff(f2882,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
      | 'member$f'('pair$a'(X0,X2),X4)
      | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ),
    inference(cnf_transformation,[],[f1729]) ).

tff(f1729,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$f'('pair$a'(X0,X2),X4) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
          & ( X0 = X2 ) )
        | 'member$f'('pair$a'(X0,X2),X4)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ) ),
    inference(flattening,[],[f1728]) ).

tff(f1728,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$f'('pair$a'(X0,X2),X4) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
          & ( X0 = X2 ) )
        | 'member$f'('pair$a'(X0,X2),X4)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ) ),
    inference(nnf_transformation,[],[f508]) ).

tff(f508,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
    <=> ( ( 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
          & ( X0 = X2 ) )
        | 'member$f'('pair$a'(X0,X2),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom506) ).

tff(f12284,plain,
    spl230_805,
    inference(avatar_split_clause,[],[f2853,f12282]) ).

tff(f12282,plain,
    ( spl230_805
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
        | 'member$'('pair$b'(X0,X2),X4)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_805])]) ).

tff(f2853,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
      | 'member$'('pair$b'(X0,X2),X4)
      | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ),
    inference(cnf_transformation,[],[f1715]) ).

tff(f1715,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$'('pair$b'(X0,X2),X4) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
          & ( X0 = X2 ) )
        | 'member$'('pair$b'(X0,X2),X4)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ) ),
    inference(flattening,[],[f1714]) ).

tff(f1714,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$'('pair$b'(X0,X2),X4) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
          & ( X0 = X2 ) )
        | 'member$'('pair$b'(X0,X2),X4)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ) ),
    inference(nnf_transformation,[],[f507]) ).

tff(f507,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
    <=> ( ( 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
          & ( X0 = X2 ) )
        | 'member$'('pair$b'(X0,X2),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom505) ).

tff(f12280,plain,
    ( spl230_804
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_224 ),
    inference(avatar_split_clause,[],[f4742,f4552,f3895,f3857,f12278]) ).

tff(f12278,plain,
    ( spl230_804
  <=> ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 'size$d'('none$a') = 'fun_app$aw'('size_option$'(X0),'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_804])]) ).

tff(f4552,plain,
    ( spl230_224
  <=> ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'none$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_224])]) ).

tff(f4742,plain,
    ( ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 'size$d'('none$a') = 'fun_app$aw'('size_option$'(X0),'none$') )
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_224 ),
    inference(forward_demodulation,[],[f4739,f4138]) ).

tff(f4739,plain,
    ( ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 'fun_app$aw'('size_option$'(X0),'none$') = 'fun_app$k'('nat$',1) )
    | ~ spl230_88
    | ~ spl230_224 ),
    inference(superposition,[],[f3896,f4553]) ).

tff(f4553,plain,
    ( ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'none$')) )
    | ~ spl230_224 ),
    inference(avatar_component_clause,[],[f4552]) ).

tff(f12276,plain,
    spl230_803,
    inference(avatar_split_clause,[],[f2825,f12274]) ).

tff(f12274,plain,
    ( spl230_803
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
        | 'member$g'('pair$c'(X0,X2),X4)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_803])]) ).

tff(f2825,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
      | 'member$g'('pair$c'(X0,X2),X4)
      | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ),
    inference(cnf_transformation,[],[f1701]) ).

tff(f1701,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$g'('pair$c'(X0,X2),X4) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
          & ( X0 = X2 ) )
        | 'member$g'('pair$c'(X0,X2),X4)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ) ),
    inference(flattening,[],[f1700]) ).

tff(f1700,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$g'('pair$c'(X0,X2),X4) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
          & ( X0 = X2 ) )
        | 'member$g'('pair$c'(X0,X2),X4)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ) ),
    inference(nnf_transformation,[],[f505]) ).

tff(f505,axiom,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
    <=> ( ( 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
          & ( X0 = X2 ) )
        | 'member$g'('pair$c'(X0,X2),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom503) ).

tff(f12272,plain,
    spl230_802,
    inference(avatar_split_clause,[],[f2821,f12270]) ).

tff(f12270,plain,
    ( spl230_802
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
        | 'member$e'('pair$'(X0,X2),X4)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_802])]) ).

tff(f2821,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
      | 'member$e'('pair$'(X0,X2),X4)
      | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ),
    inference(cnf_transformation,[],[f1699]) ).

tff(f1699,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$e'('pair$'(X0,X2),X4) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
          & ( X0 = X2 ) )
        | 'member$e'('pair$'(X0,X2),X4)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ) ),
    inference(flattening,[],[f1698]) ).

tff(f1698,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
            | ( X0 != X2 ) )
          & ~ 'member$e'('pair$'(X0,X2),X4) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
          & ( X0 = X2 ) )
        | 'member$e'('pair$'(X0,X2),X4)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ) ),
    inference(nnf_transformation,[],[f506]) ).

tff(f506,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
    <=> ( ( 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
          & ( X0 = X2 ) )
        | 'member$e'('pair$'(X0,X2),X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom504) ).

tff(f12268,plain,
    spl230_801,
    inference(avatar_split_clause,[],[f2815,f12266]) ).

tff(f12266,plain,
    ( spl230_801
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X2,X1),'lex$'(X0))
        | ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X2)) )
        | ~ sP23(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_801])]) ).

tff(f2815,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( 'member$o'('pair$v'(X2,X1),'lex$'(X0))
      | ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X2)) )
      | ~ sP23(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f1696,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$',X3: $int,X4: $int] :
      ( ( sP23(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$o'('pair$v'(X2,X1),'lex$'(X0))
            | ( X3 != X4 ) )
          & ( ( 'fun_app$l'('of_nat$','size$e'(X1)) != 'fun_app$l'('of_nat$','size$e'(X2)) )
            | ~ 'member$g'('pair$c'(X4,X3),X0) ) ) )
      & ( ( 'member$o'('pair$v'(X2,X1),'lex$'(X0))
          & ( X3 = X4 ) )
        | ( ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X2)) )
          & 'member$g'('pair$c'(X4,X3),X0) )
        | ~ sP23(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1695]) ).

tff(f1695,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( ( sP23(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'lex$'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','size$e'(X1)) != 'fun_app$l'('of_nat$','size$e'(X3)) )
            | ~ 'member$g'('pair$c'(X0,X2),X4) ) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'lex$'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X3)) )
          & 'member$g'('pair$c'(X0,X2),X4) )
        | ~ sP23(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1694]) ).

tff(f1694,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( ( sP23(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'lex$'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','size$e'(X1)) != 'fun_app$l'('of_nat$','size$e'(X3)) )
            | ~ 'member$g'('pair$c'(X0,X2),X4) ) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'lex$'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X3)) )
          & 'member$g'('pair$c'(X0,X2),X4) )
        | ~ sP23(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1123]) ).

tff(f1123,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( sP23(X4,X3,X1,X2,X0)
    <=> ( ( 'member$o'('pair$v'(X1,X3),'lex$'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X3)) )
          & 'member$g'('pair$c'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).

tff(f12264,plain,
    spl230_800,
    inference(avatar_split_clause,[],[f2807,f12262]) ).

tff(f12262,plain,
    ( spl230_800
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
        | ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X2)) )
        | ~ sP22(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_800])]) ).

tff(f2807,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
      | ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X2)) )
      | ~ sP22(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f1692,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
      ( ( sP22(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
            | ( X3 != X4 ) )
          & ( ( 'fun_app$l'('of_nat$','size$f'(X1)) != 'fun_app$l'('of_nat$','size$f'(X2)) )
            | ~ 'member$e'('pair$'(X4,X3),X0) ) ) )
      & ( ( 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
          & ( X3 = X4 ) )
        | ( ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X2)) )
          & 'member$e'('pair$'(X4,X3),X0) )
        | ~ sP22(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1691]) ).

tff(f1691,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( ( sP22(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','size$f'(X1)) != 'fun_app$l'('of_nat$','size$f'(X3)) )
            | ~ 'member$e'('pair$'(X0,X2),X4) ) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X3)) )
          & 'member$e'('pair$'(X0,X2),X4) )
        | ~ sP22(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1690]) ).

tff(f1690,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( ( sP22(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','size$f'(X1)) != 'fun_app$l'('of_nat$','size$f'(X3)) )
            | ~ 'member$e'('pair$'(X0,X2),X4) ) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X3)) )
          & 'member$e'('pair$'(X0,X2),X4) )
        | ~ sP22(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1121]) ).

tff(f1121,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( sP22(X4,X3,X1,X2,X0)
    <=> ( ( 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X3)) )
          & 'member$e'('pair$'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).

tff(f12260,plain,
    spl230_799,
    inference(avatar_split_clause,[],[f2758,f12258]) ).

tff(f12258,plain,
    ( spl230_799
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('append$d'(sK220(X0,X1,X2,X3)),'cons$'(X2,sK221(X0,X1,X2,X3))) = X3 )
        | ~ sP19(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_799])]) ).

tff(f2758,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('append$d'(sK220(X0,X1,X2,X3)),'cons$'(X2,sK221(X0,X1,X2,X3))) = X3 )
      | ~ sP19(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1680]) ).

tff(f12256,plain,
    spl230_798,
    inference(avatar_split_clause,[],[f2750,f12254]) ).

tff(f12254,plain,
    ( spl230_798
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('append$d'(sK217(X0,X1,X2,X3)),'cons$'(X2,sK218(X0,X1,X2,X3))) = X3 )
        | ~ sP18(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_798])]) ).

tff(f2750,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('append$d'(sK217(X0,X1,X2,X3)),'cons$'(X2,sK218(X0,X1,X2,X3))) = X3 )
      | ~ sP18(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1674]) ).

tff(f12252,plain,
    spl230_797,
    inference(avatar_split_clause,[],[f2070,f12250]) ).

tff(f12250,plain,
    ( spl230_797
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( sK73(X0,X1) != sK75(X0,X1) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_797])]) ).

tff(f2070,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( sK73(X0,X1) != sK75(X0,X1) )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ( X0 = X1 ) ),
    inference(cnf_transformation,[],[f1248]) ).

tff(f1248,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(sK72(X0,X1)),'fun_app$p'('append$d'('cons$'(sK75(X0,X1),'nil$')),sK76(X0,X1))) = X1 )
        & ( 'fun_app$p'('append$d'(sK72(X0,X1)),'fun_app$p'('append$d'('cons$'(sK73(X0,X1),'nil$')),sK74(X0,X1))) = X0 )
        & ( sK73(X0,X1) != sK75(X0,X1) ) )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ( X0 = X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74,sK75,sK76])],[f833,f1247]) ).

tff(f1247,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X5,'nil$')),X6)) = X1 )
          & ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X3,'nil$')),X4)) = X0 )
          & ( X3 != X5 ) )
     => ( ( 'fun_app$p'('append$d'(sK72(X0,X1)),'fun_app$p'('append$d'('cons$'(sK75(X0,X1),'nil$')),sK76(X0,X1))) = X1 )
        & ( 'fun_app$p'('append$d'(sK72(X0,X1)),'fun_app$p'('append$d'('cons$'(sK73(X0,X1),'nil$')),sK74(X0,X1))) = X0 )
        & ( sK73(X0,X1) != sK75(X0,X1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f833,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X5,'nil$')),X6)) = X1 )
          & ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X3,'nil$')),X4)) = X0 )
          & ( X3 != X5 ) )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ( X0 = X1 ) ),
    inference(flattening,[],[f832]) ).

tff(f832,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X5,'nil$')),X6)) = X1 )
          & ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X3,'nil$')),X4)) = X0 )
          & ( X3 != X5 ) )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ( X0 = X1 ) ),
    inference(ennf_transformation,[],[f582]) ).

tff(f582,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        & ( X0 != X1 ) )
     => ? [X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X5,'nil$')),X6)) = X1 )
          & ( 'fun_app$p'('append$d'(X2),'fun_app$p'('append$d'('cons$'(X3,'nil$')),X4)) = X0 )
          & ( X3 != X5 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom580) ).

tff(f12084,plain,
    ( spl230_796
    | ~ spl230_59
    | ~ spl230_203 ),
    inference(avatar_split_clause,[],[f4694,f4466,f3759,f12082]) ).

tff(f12082,plain,
    ( spl230_796
  <=> ! [X0: $int] :
        ( $less(X0,0)
        | ~ $less(0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_796])]) ).

tff(f3759,plain,
    ( spl230_59
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_59])]) ).

tff(f4466,plain,
    ( spl230_203
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,$sum(X0,X1))
        | ~ $less(0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_203])]) ).

tff(f4694,plain,
    ( ! [X0: $int] :
        ( $less(X0,0)
        | ~ $less(0,$uminus(X0)) )
    | ~ spl230_59
    | ~ spl230_203 ),
    inference(superposition,[],[f4467,f3760]) ).

tff(f3760,plain,
    ( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
    | ~ spl230_59 ),
    inference(avatar_component_clause,[],[f3759]) ).

tff(f4467,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X0,$sum(X0,X1))
        | ~ $less(0,X1) )
    | ~ spl230_203 ),
    inference(avatar_component_clause,[],[f4466]) ).

tff(f11733,plain,
    ( spl230_795
    | ~ spl230_59
    | ~ spl230_202 ),
    inference(avatar_split_clause,[],[f4687,f4462,f3759,f11731]) ).

tff(f11731,plain,
    ( spl230_795
  <=> ! [X0: $int] :
        ( ~ $less(X0,0)
        | $less(0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_795])]) ).

tff(f4462,plain,
    ( spl230_202
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X1)
        | ~ $less(X0,$sum(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_202])]) ).

tff(f4687,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,0)
        | $less(0,$uminus(X0)) )
    | ~ spl230_59
    | ~ spl230_202 ),
    inference(superposition,[],[f4463,f3760]) ).

tff(f4463,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X0,$sum(X0,X1))
        | $less(0,X1) )
    | ~ spl230_202 ),
    inference(avatar_component_clause,[],[f4462]) ).

tff(f11639,plain,
    spl230_794,
    inference(avatar_split_clause,[],[f3427,f11637]) ).

tff(f11637,plain,
    ( spl230_794
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
        | ( 'cons$'(sK127(X0,X1),sK128(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_794])]) ).

tff(f3427,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
      | ( 'cons$'(sK127(X0,X1),sK128(X0,X1)) = X1 ) ),
    inference(forward_demodulation,[],[f2312,f664]) ).

tff(f664,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f2312,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( 'cons$'(sK127(X0,X1),sK128(X0,X1)) = X1 )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ),
    inference(cnf_transformation,[],[f1459]) ).

tff(f1459,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X1 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK128(X0,X1))) )
          & ( 'cons$'(sK127(X0,X1),sK128(X0,X1)) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK127,sK128])],[f1457,f1458]) ).

tff(f1458,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X5)) )
          & ( 'cons$'(X4,X5) = X1 ) )
     => ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK128(X0,X1))) )
        & ( 'cons$'(sK127(X0,X1),sK128(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1457,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X1 ) ) )
      & ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X5)) )
            & ( 'cons$'(X4,X5) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(rectify,[],[f1456]) ).

tff(f1456,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X1 ) ) )
      & ( ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            & ( 'cons$'(X2,X3) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(nnf_transformation,[],[f489]) ).

tff(f489,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
    <=> ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & ( 'cons$'(X2,X3) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom487) ).

tff(f11635,plain,
    spl230_793,
    inference(avatar_split_clause,[],[f3425,f11633]) ).

tff(f11633,plain,
    ( spl230_793
  <=> ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
        | ( 'cons$'(sK125(X0,X1),sK126(X0,X1)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_793])]) ).

tff(f3425,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
      | ( 'cons$'(sK125(X0,X1),sK126(X0,X1)) = X0 ) ),
    inference(forward_demodulation,[],[f2309,f664]) ).

tff(f2309,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( 'cons$'(sK125(X0,X1),sK126(X0,X1)) = X0 )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ),
    inference(cnf_transformation,[],[f1455]) ).

tff(f1455,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X0 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK126(X0,X1))) )
          & ( 'cons$'(sK125(X0,X1),sK126(X0,X1)) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126])],[f1453,f1454]) ).

tff(f1454,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X5)) )
          & ( 'cons$'(X4,X5) = X0 ) )
     => ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK126(X0,X1))) )
        & ( 'cons$'(sK125(X0,X1),sK126(X0,X1)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1453,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X0 ) ) )
      & ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X5)) )
            & ( 'cons$'(X4,X5) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(rectify,[],[f1452]) ).

tff(f1452,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ( 'cons$'(X2,X3) != X0 ) ) )
      & ( ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            & ( 'cons$'(X2,X3) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(nnf_transformation,[],[f486]) ).

tff(f486,axiom,
    ! [X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
    <=> ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & ( 'cons$'(X2,X3) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom484) ).

tff(f11631,plain,
    spl230_792,
    inference(avatar_split_clause,[],[f3423,f11629]) ).

tff(f11629,plain,
    ( spl230_792
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
        | ( 'cons$b'(sK123(X0,X1),sK124(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_792])]) ).

tff(f3423,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
      | ( 'cons$b'(sK123(X0,X1),sK124(X0,X1)) = X1 ) ),
    inference(forward_demodulation,[],[f2306,f664]) ).

tff(f2306,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( 'cons$b'(sK123(X0,X1),sK124(X0,X1)) = X1 )
      | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ),
    inference(cnf_transformation,[],[f1451]) ).

tff(f1451,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X1 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK124(X0,X1))) )
          & ( 'cons$b'(sK123(X0,X1),sK124(X0,X1)) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK123,sK124])],[f1449,f1450]) ).

tff(f1450,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X5)) )
          & ( 'cons$b'(X4,X5) = X1 ) )
     => ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK124(X0,X1))) )
        & ( 'cons$b'(sK123(X0,X1),sK124(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1449,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X1 ) ) )
      & ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X5)) )
            & ( 'cons$b'(X4,X5) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(rectify,[],[f1448]) ).

tff(f1448,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X1 ) ) )
      & ( ? [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            & ( 'cons$b'(X2,X3) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(nnf_transformation,[],[f488]) ).

tff(f488,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
    <=> ? [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & ( 'cons$b'(X2,X3) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom486) ).

tff(f11627,plain,
    spl230_791,
    inference(avatar_split_clause,[],[f3421,f11625]) ).

tff(f11625,plain,
    ( spl230_791
  <=> ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
        | ( 'cons$b'(sK121(X0,X1),sK122(X0,X1)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_791])]) ).

tff(f3421,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
      | ( 'cons$b'(sK121(X0,X1),sK122(X0,X1)) = X0 ) ),
    inference(forward_demodulation,[],[f2303,f664]) ).

tff(f2303,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( 'cons$b'(sK121(X0,X1),sK122(X0,X1)) = X0 )
      | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ),
    inference(cnf_transformation,[],[f1447]) ).

tff(f1447,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X0 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK122(X0,X1))) )
          & ( 'cons$b'(sK121(X0,X1),sK122(X0,X1)) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK121,sK122])],[f1445,f1446]) ).

tff(f1446,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X5)) )
          & ( 'cons$b'(X4,X5) = X0 ) )
     => ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK122(X0,X1))) )
        & ( 'cons$b'(sK121(X0,X1),sK122(X0,X1)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1445,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X0 ) ) )
      & ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X5)) )
            & ( 'cons$b'(X4,X5) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(rectify,[],[f1444]) ).

tff(f1444,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ( 'cons$b'(X2,X3) != X0 ) ) )
      & ( ? [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            & ( 'cons$b'(X2,X3) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(nnf_transformation,[],[f485]) ).

tff(f485,axiom,
    ! [X0: 'A_iarray_list_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
    <=> ? [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & ( 'cons$b'(X2,X3) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom483) ).

tff(f11623,plain,
    spl230_790,
    inference(avatar_split_clause,[],[f3419,f11621]) ).

tff(f11621,plain,
    ( spl230_790
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
        | ( 'cons$a'(sK119(X0,X1),sK120(X0,X1)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_790])]) ).

tff(f3419,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum(1,'fun_app$l'('of_nat$',X1)) )
      | ( 'cons$a'(sK119(X0,X1),sK120(X0,X1)) = X0 ) ),
    inference(forward_demodulation,[],[f2300,f664]) ).

tff(f2300,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( 'cons$a'(sK119(X0,X1),sK120(X0,X1)) = X0 )
      | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ),
    inference(cnf_transformation,[],[f1443]) ).

tff(f1443,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X0 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK120(X0,X1))) )
          & ( 'cons$a'(sK119(X0,X1),sK120(X0,X1)) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK119,sK120])],[f1441,f1442]) ).

tff(f1442,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ? [X4: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X5)) )
          & ( 'cons$a'(X4,X5) = X0 ) )
     => ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK120(X0,X1))) )
        & ( 'cons$a'(sK119(X0,X1),sK120(X0,X1)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1441,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X0 ) ) )
      & ( ? [X4: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X5)) )
            & ( 'cons$a'(X4,X5) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(rectify,[],[f1440]) ).

tff(f1440,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X0 ) ) )
      & ( ? [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            & ( 'cons$a'(X2,X3) = X0 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(nnf_transformation,[],[f484]) ).

tff(f484,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = $sum('fun_app$l'('of_nat$',X1),1) )
    <=> ? [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & ( 'cons$a'(X2,X3) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom482) ).

tff(f11619,plain,
    ( spl230_789
    | ~ spl230_59
    | ~ spl230_201 ),
    inference(avatar_split_clause,[],[f4681,f4458,f3759,f11617]) ).

tff(f11617,plain,
    ( spl230_789
  <=> ! [X0: $int] :
        ( $less($uminus(X0),0)
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_789])]) ).

tff(f4458,plain,
    ( spl230_201
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,$sum(X1,X0))
        | ~ $less(0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_201])]) ).

tff(f4681,plain,
    ( ! [X0: $int] :
        ( $less($uminus(X0),0)
        | ~ $less(0,X0) )
    | ~ spl230_59
    | ~ spl230_201 ),
    inference(superposition,[],[f4459,f3760]) ).

tff(f4459,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X0,$sum(X1,X0))
        | ~ $less(0,X1) )
    | ~ spl230_201 ),
    inference(avatar_component_clause,[],[f4458]) ).

tff(f11615,plain,
    spl230_788,
    inference(avatar_split_clause,[],[f3417,f11613]) ).

tff(f11613,plain,
    ( spl230_788
  <=> ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
        | ( 'cons$a'(sK117(X0,X1),sK118(X0,X1)) = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_788])]) ).

tff(f3417,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum(1,'fun_app$l'('of_nat$',X0)) )
      | ( 'cons$a'(sK117(X0,X1),sK118(X0,X1)) = X1 ) ),
    inference(forward_demodulation,[],[f2297,f664]) ).

tff(f2297,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'cons$a'(sK117(X0,X1),sK118(X0,X1)) = X1 )
      | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ),
    inference(cnf_transformation,[],[f1439]) ).

tff(f1439,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X1 ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK118(X0,X1))) )
          & ( 'cons$a'(sK117(X0,X1),sK118(X0,X1)) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK117,sK118])],[f1437,f1438]) ).

tff(f1438,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ? [X4: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X5)) )
          & ( 'cons$a'(X4,X5) = X1 ) )
     => ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK118(X0,X1))) )
        & ( 'cons$a'(sK117(X0,X1),sK118(X0,X1)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1437,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X1 ) ) )
      & ( ? [X4: 'Nat_a_iarray_prod$',X5: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X5)) )
            & ( 'cons$a'(X4,X5) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(rectify,[],[f1436]) ).

tff(f1436,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
        | ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ( 'cons$a'(X2,X3) != X1 ) ) )
      & ( ? [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            & ( 'cons$a'(X2,X3) = X1 ) )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != $sum('fun_app$l'('of_nat$',X0),1) ) ) ),
    inference(nnf_transformation,[],[f487]) ).

tff(f487,axiom,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = $sum('fun_app$l'('of_nat$',X0),1) )
    <=> ? [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$'] :
          ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & ( 'cons$a'(X2,X3) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom485) ).

tff(f11611,plain,
    spl230_787,
    inference(avatar_split_clause,[],[f3415,f11609]) ).

tff(f11609,plain,
    ( spl230_787
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ~ $less($sum(1,'fun_app$l'('of_nat$',X0)),'fun_app$l'('of_nat$',X1))
        | ( 'fun_app$l'('of_nat$',X1) = $sum(1,'fun_app$l'('of_nat$',sK116(X0,X1))) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_787])]) ).

tff(f3415,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less($sum(1,'fun_app$l'('of_nat$',X0)),'fun_app$l'('of_nat$',X1))
      | ( 'fun_app$l'('of_nat$',X1) = $sum(1,'fun_app$l'('of_nat$',sK116(X0,X1))) ) ),
    inference(forward_demodulation,[],[f3414,f664]) ).

tff(f3414,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X1) = $sum(1,'fun_app$l'('of_nat$',sK116(X0,X1))) )
      | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ),
    inference(forward_demodulation,[],[f2290,f664]) ).

tff(f2290,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',sK116(X0,X1)),1) )
      | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1433]) ).

tff(f1433,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] :
            ( ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))
            | ( 'fun_app$l'('of_nat$',X1) != $sum('fun_app$l'('of_nat$',X2),1) ) ) )
      & ( ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK116(X0,X1)))
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',sK116(X0,X1)),1) ) )
        | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK116])],[f1431,f1432]) ).

tff(f1432,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X3))
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X3),1) ) )
     => ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK116(X0,X1)))
        & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',sK116(X0,X1)),1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1431,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] :
            ( ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))
            | ( 'fun_app$l'('of_nat$',X1) != $sum('fun_app$l'('of_nat$',X2),1) ) ) )
      & ( ? [X3: 'Nat$'] :
            ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X3))
            & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X3),1) ) )
        | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ) ),
    inference(rectify,[],[f1430]) ).

tff(f1430,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] :
            ( ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))
            | ( 'fun_app$l'('of_nat$',X1) != $sum('fun_app$l'('of_nat$',X2),1) ) ) )
      & ( ? [X2: 'Nat$'] :
            ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))
            & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X2),1) ) )
        | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ) ),
    inference(nnf_transformation,[],[f649]) ).

tff(f649,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1))
    <=> ? [X2: 'Nat$'] :
          ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X2),1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom647) ).

tff(f11607,plain,
    spl230_786,
    inference(avatar_split_clause,[],[f3400,f11605]) ).

tff(f11605,plain,
    ( spl230_786
  <=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X1) != $sum(1,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))) )
        | $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_786])]) ).

tff(f3400,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X1) != $sum(1,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2))) )
      | $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(forward_demodulation,[],[f2279,f664]) ).

tff(f2279,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
      | ( 'fun_app$l'('of_nat$',X1) != $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) ) ),
    inference(cnf_transformation,[],[f1420]) ).

tff(f1420,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) != $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) ) )
      & ( ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK114(X0,X1))),1) )
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK114])],[f1418,f1419]) ).

tff(f1419,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ? [X3: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X3)),1) )
     => ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK114(X0,X1))),1) ) ),
    introduced(choice_axiom,[]) ).

tff(f1418,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) != $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) ) )
      & ( ? [X3: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X3)),1) )
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    inference(rectify,[],[f1417]) ).

tff(f1417,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
        | ! [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) != $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) ) )
      & ( ? [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) )
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    inference(nnf_transformation,[],[f638]) ).

tff(f638,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
    <=> ? [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X1) = $sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom636) ).

tff(f11581,plain,
    ( spl230_785
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_784 ),
    inference(avatar_split_clause,[],[f11577,f11571,f6450,f6201,f11579]) ).

tff(f11579,plain,
    ( spl230_785
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum(sK40(X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X0 )
        | ( 'zero$a' = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_785])]) ).

tff(f6201,plain,
    ( spl230_425
  <=> ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('fst$b',X0) = sK40(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_425])]) ).

tff(f6450,plain,
    ( spl230_426
  <=> ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('snd$b',X0) = sK41(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_426])]) ).

tff(f11571,plain,
    ( spl230_784
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'zero$a' = X1 )
        | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_784])]) ).

tff(f11577,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum(sK40(X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X0 )
        | ( 'zero$a' = X1 ) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_784 ),
    inference(forward_demodulation,[],[f11576,f6202]) ).

tff(f6202,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('fst$b',X0) = sK40(X0) )
    | ~ spl230_425 ),
    inference(avatar_component_clause,[],[f6201]) ).

tff(f11576,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X0 )
        | ( 'zero$a' = X1 ) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_784 ),
    inference(forward_demodulation,[],[f11575,f6202]) ).

tff(f11575,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum(sK41(X0),sK41(X1))) != X0 )
        | ( 'zero$a' = X1 ) )
    | ~ spl230_426
    | ~ spl230_784 ),
    inference(forward_demodulation,[],[f11574,f6451]) ).

tff(f6451,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('snd$b',X0) = sK41(X0) )
    | ~ spl230_426 ),
    inference(avatar_component_clause,[],[f6450]) ).

tff(f11574,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),sK41(X1))) != X0 )
        | ( 'zero$a' = X1 ) )
    | ~ spl230_426
    | ~ spl230_784 ),
    inference(forward_demodulation,[],[f11572,f6451]) ).

tff(f11572,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'zero$a' = X1 )
        | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X0 ) )
    | ~ spl230_784 ),
    inference(avatar_component_clause,[],[f11571]) ).

tff(f11573,plain,
    spl230_784,
    inference(avatar_split_clause,[],[f2962,f11571]) ).

tff(f2962,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'zero$a' = X1 )
      | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X0 ) ),
    inference(definition_unfolding,[],[f2192,f2036]) ).

tff(f2036,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] : ( 'plus$b'(X0,X1) = 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) ),
    inference(cnf_transformation,[],[f196]) ).

tff(f196,axiom,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] : ( 'plus$b'(X0,X1) = 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom194) ).

tff(f2192,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'zero$a' = X1 )
      | ( 'plus$b'(X0,X1) != X0 ) ),
    inference(cnf_transformation,[],[f1357]) ).

tff(f1357,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( ( 'plus$b'(X0,X1) = X0 )
        | ( 'zero$a' != X1 ) )
      & ( ( 'zero$a' = X1 )
        | ( 'plus$b'(X0,X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f380]) ).

tff(f380,axiom,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'plus$b'(X0,X1) = X0 )
    <=> ( 'zero$a' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom378) ).

tff(f11547,plain,
    ( spl230_783
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_782 ),
    inference(avatar_split_clause,[],[f11543,f11537,f6450,f6201,f11545]) ).

tff(f11545,plain,
    ( spl230_783
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum(sK40(X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X1 )
        | ( 'zero$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_783])]) ).

tff(f11537,plain,
    ( spl230_782
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'zero$a' = X0 )
        | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_782])]) ).

tff(f11543,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum(sK40(X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X1 )
        | ( 'zero$a' = X0 ) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_782 ),
    inference(forward_demodulation,[],[f11542,f6202]) ).

tff(f11542,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),sK40(X1)),$sum(sK41(X0),sK41(X1))) != X1 )
        | ( 'zero$a' = X0 ) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_782 ),
    inference(forward_demodulation,[],[f11541,f6202]) ).

tff(f11541,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum(sK41(X0),sK41(X1))) != X1 )
        | ( 'zero$a' = X0 ) )
    | ~ spl230_426
    | ~ spl230_782 ),
    inference(forward_demodulation,[],[f11540,f6451]) ).

tff(f11540,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),sK41(X1))) != X1 )
        | ( 'zero$a' = X0 ) )
    | ~ spl230_426
    | ~ spl230_782 ),
    inference(forward_demodulation,[],[f11538,f6451]) ).

tff(f11538,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'zero$a' = X0 )
        | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X1 ) )
    | ~ spl230_782 ),
    inference(avatar_component_clause,[],[f11537]) ).

tff(f11539,plain,
    spl230_782,
    inference(avatar_split_clause,[],[f2960,f11537]) ).

tff(f2960,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'zero$a' = X0 )
      | ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b',X1)),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b',X1))) != X1 ) ),
    inference(definition_unfolding,[],[f2190,f2036]) ).

tff(f2190,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'zero$a' = X0 )
      | ( 'plus$b'(X0,X1) != X1 ) ),
    inference(cnf_transformation,[],[f1356]) ).

tff(f1356,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( ( 'plus$b'(X0,X1) = X1 )
        | ( 'zero$a' != X0 ) )
      & ( ( 'zero$a' = X0 )
        | ( 'plus$b'(X0,X1) != X1 ) ) ),
    inference(nnf_transformation,[],[f371]) ).

tff(f371,axiom,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( 'plus$b'(X0,X1) = X1 )
    <=> ( 'zero$a' = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom369) ).

tff(f11535,plain,
    spl230_781,
    inference(avatar_split_clause,[],[f2874,f11533]) ).

tff(f11533,plain,
    ( spl230_781
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X3 = X4 )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
        | ~ sP29(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_781])]) ).

tff(f2874,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( ( X3 = X4 )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
      | ~ sP29(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1726]) ).

tff(f1726,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray$'] :
      ( ( sP29(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$'('pair$b'(X2,X1),'lex$d'(X0))
            | ( X3 != X4 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
            | ~ 'member$f'('pair$a'(X4,X3),X0) ) ) )
      & ( ( 'member$'('pair$b'(X2,X1),'lex$d'(X0))
          & ( X3 = X4 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
          & 'member$f'('pair$a'(X4,X3),X0) )
        | ~ sP29(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1725]) ).

tff(f1725,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP29(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lex$d'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ~ 'member$f'('pair$a'(X0,X2),X4) ) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lex$d'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & 'member$f'('pair$a'(X0,X2),X4) )
        | ~ sP29(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1724]) ).

tff(f1724,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP29(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lex$d'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
            | ~ 'member$f'('pair$a'(X0,X2),X4) ) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lex$d'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & 'member$f'('pair$a'(X0,X2),X4) )
        | ~ sP29(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1135]) ).

tff(f1135,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( sP29(X4,X3,X1,X2,X0)
    <=> ( ( 'member$'('pair$b'(X1,X3),'lex$d'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & 'member$f'('pair$a'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).

tff(f11531,plain,
    spl230_780,
    inference(avatar_split_clause,[],[f2845,f11529]) ).

tff(f11529,plain,
    ( spl230_780
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( X3 = X4 )
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X2)) )
        | ~ sP26(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_780])]) ).

tff(f2845,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( ( X3 = X4 )
      | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X2)) )
      | ~ sP26(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1712]) ).

tff(f1712,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
      ( ( sP26(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$s'('pair$z'(X2,X1),'lex$c'(X0))
            | ( X3 != X4 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X2)) )
            | ~ 'member$'('pair$b'(X4,X3),X0) ) ) )
      & ( ( 'member$s'('pair$z'(X2,X1),'lex$c'(X0))
          & ( X3 = X4 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X2)) )
          & 'member$'('pair$b'(X4,X3),X0) )
        | ~ sP26(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1711]) ).

tff(f1711,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( sP26(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ~ 'member$'('pair$b'(X0,X2),X4) ) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & 'member$'('pair$b'(X0,X2),X4) )
        | ~ sP26(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1710]) ).

tff(f1710,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( sP26(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
            | ~ 'member$'('pair$b'(X0,X2),X4) ) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & 'member$'('pair$b'(X0,X2),X4) )
        | ~ sP26(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1129]) ).

tff(f1129,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( sP26(X4,X3,X1,X2,X0)
    <=> ( ( 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & 'member$'('pair$b'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).

tff(f11527,plain,
    spl230_779,
    inference(avatar_split_clause,[],[f2816,f11525]) ).

tff(f11525,plain,
    ( spl230_779
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( sP23(X0,X1,X2,X3,X4)
        | ( 'fun_app$l'('of_nat$','size$e'(X1)) != 'fun_app$l'('of_nat$','size$e'(X2)) )
        | ~ 'member$g'('pair$c'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_779])]) ).

tff(f2816,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP23(X0,X1,X2,X3,X4)
      | ( 'fun_app$l'('of_nat$','size$e'(X1)) != 'fun_app$l'('of_nat$','size$e'(X2)) )
      | ~ 'member$g'('pair$c'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f11523,plain,
    spl230_778,
    inference(avatar_split_clause,[],[f2808,f11521]) ).

tff(f11521,plain,
    ( spl230_778
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( sP22(X0,X1,X2,X3,X4)
        | ( 'fun_app$l'('of_nat$','size$f'(X1)) != 'fun_app$l'('of_nat$','size$f'(X2)) )
        | ~ 'member$e'('pair$'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_778])]) ).

tff(f2808,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP22(X0,X1,X2,X3,X4)
      | ( 'fun_app$l'('of_nat$','size$f'(X1)) != 'fun_app$l'('of_nat$','size$f'(X2)) )
      | ~ 'member$e'('pair$'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f11519,plain,
    spl230_777,
    inference(avatar_split_clause,[],[f2797,f11517]) ).

tff(f11517,plain,
    ( spl230_777
  <=> ! [X4: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( X3 = X4 )
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X2)) )
        | ~ sP21(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_777])]) ).

tff(f2797,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X3: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod$'] :
      ( ( X3 = X4 )
      | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X2)) )
      | ~ sP21(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1688]) ).

tff(f1688,plain,
    ! [X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$',X3: 'Nat_a_iarray_prod$',X4: 'Nat_a_iarray_prod$'] :
      ( ( sP21(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$q'('pair$x'(X2,X1),'lex$b'(X0))
            | ( X3 != X4 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X2)) )
            | ~ 'member$r'('pair$y'(X4,X3),X0) ) ) )
      & ( ( 'member$q'('pair$x'(X2,X1),'lex$b'(X0))
          & ( X3 = X4 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X2)) )
          & 'member$r'('pair$y'(X4,X3),X0) )
        | ~ sP21(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1687]) ).

tff(f1687,plain,
    ! [X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod$'] :
      ( ( sP21(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ~ 'member$r'('pair$y'(X0,X2),X4) ) ) )
      & ( ( 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & 'member$r'('pair$y'(X0,X2),X4) )
        | ~ sP21(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1686]) ).

tff(f1686,plain,
    ! [X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod$'] :
      ( ( sP21(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
            | ( X0 != X2 ) )
          & ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
            | ~ 'member$r'('pair$y'(X0,X2),X4) ) ) )
      & ( ( 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & 'member$r'('pair$y'(X0,X2),X4) )
        | ~ sP21(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1119]) ).

tff(f1119,plain,
    ! [X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod$'] :
      ( sP21(X4,X3,X1,X2,X0)
    <=> ( ( 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & 'member$r'('pair$y'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).

tff(f11515,plain,
    spl230_776,
    inference(avatar_split_clause,[],[f2515,f11513]) ).

tff(f11513,plain,
    ( spl230_776
  <=> ! [X2: 'A_iarray_list_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
        | ( X1 = X2 )
        | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0))
        | ( sK187(X0) != sK188(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_776])]) ).

tff(f2515,plain,
    ! [X2: 'A_iarray_list_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
      | ( X1 = X2 )
      | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0))
      | ( sK187(X0) != sK188(X0) ) ),
    inference(cnf_transformation,[],[f1561]) ).

tff(f1561,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
      | ( X1 = X2 )
      | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0))
      | ( ~ 'member$'('pair$b'(sK188(X0),sK187(X0)),X0)
        & ( sK187(X0) != sK188(X0) )
        & ~ 'member$'('pair$b'(sK187(X0),sK188(X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK187,sK188])],[f958,f1560]) ).

tff(f1560,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ? [X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
          ( ~ 'member$'('pair$b'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$'('pair$b'(X3,X4),X0) )
     => ( ~ 'member$'('pair$b'(sK188(X0),sK187(X0)),X0)
        & ( sK187(X0) != sK188(X0) )
        & ~ 'member$'('pair$b'(sK187(X0),sK188(X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f958,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
      | ( X1 = X2 )
      | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0))
      | ? [X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
          ( ~ 'member$'('pair$b'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$'('pair$b'(X3,X4),X0) ) ),
    inference(flattening,[],[f957]) ).

tff(f957,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
      | ( X1 = X2 )
      | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0))
      | ? [X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
          ( ~ 'member$'('pair$b'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$'('pair$b'(X3,X4),X0) ) ),
    inference(ennf_transformation,[],[f526]) ).

tff(f526,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$'] :
      ( ! [X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
          ( 'member$'('pair$b'(X4,X3),X0)
          | ( X3 = X4 )
          | 'member$'('pair$b'(X3,X4),X0) )
     => ( 'member$s'('pair$z'(X2,X1),'lexord$b'(X0))
        | ( X1 = X2 )
        | 'member$s'('pair$z'(X1,X2),'lexord$b'(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom524) ).

tff(f11511,plain,
    spl230_775,
    inference(avatar_split_clause,[],[f2512,f11509]) ).

tff(f11509,plain,
    ( spl230_775
  <=> ! [X2: 'Int_list$',X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
        | ( X1 = X2 )
        | 'member$o'('pair$v'(X1,X2),'lexord$'(X0))
        | ( sK185(X0) != sK186(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_775])]) ).

tff(f2512,plain,
    ! [X2: 'Int_list$',X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
      ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
      | ( X1 = X2 )
      | 'member$o'('pair$v'(X1,X2),'lexord$'(X0))
      | ( sK185(X0) != sK186(X0) ) ),
    inference(cnf_transformation,[],[f1559]) ).

tff(f1559,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$'] :
      ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
      | ( X1 = X2 )
      | 'member$o'('pair$v'(X1,X2),'lexord$'(X0))
      | ( ~ 'member$g'('pair$c'(sK186(X0),sK185(X0)),X0)
        & ( sK185(X0) != sK186(X0) )
        & ~ 'member$g'('pair$c'(sK185(X0),sK186(X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK185,sK186])],[f956,f1558]) ).

tff(f1558,plain,
    ! [X0: 'Int_int_prod_set$'] :
      ( ? [X3: $int,X4: $int] :
          ( ~ 'member$g'('pair$c'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$g'('pair$c'(X3,X4),X0) )
     => ( ~ 'member$g'('pair$c'(sK186(X0),sK185(X0)),X0)
        & ( sK185(X0) != sK186(X0) )
        & ~ 'member$g'('pair$c'(sK185(X0),sK186(X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f956,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$'] :
      ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
      | ( X1 = X2 )
      | 'member$o'('pair$v'(X1,X2),'lexord$'(X0))
      | ? [X3: $int,X4: $int] :
          ( ~ 'member$g'('pair$c'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$g'('pair$c'(X3,X4),X0) ) ),
    inference(flattening,[],[f955]) ).

tff(f955,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$'] :
      ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
      | ( X1 = X2 )
      | 'member$o'('pair$v'(X1,X2),'lexord$'(X0))
      | ? [X3: $int,X4: $int] :
          ( ~ 'member$g'('pair$c'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$g'('pair$c'(X3,X4),X0) ) ),
    inference(ennf_transformation,[],[f524]) ).

tff(f524,axiom,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$'] :
      ( ! [X3: $int,X4: $int] :
          ( 'member$g'('pair$c'(X4,X3),X0)
          | ( X3 = X4 )
          | 'member$g'('pair$c'(X3,X4),X0) )
     => ( 'member$o'('pair$v'(X2,X1),'lexord$'(X0))
        | ( X1 = X2 )
        | 'member$o'('pair$v'(X1,X2),'lexord$'(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom522) ).

tff(f11507,plain,
    spl230_774,
    inference(avatar_split_clause,[],[f2509,f11505]) ).

tff(f11505,plain,
    ( spl230_774
  <=> ! [X2: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
        | ( X1 = X2 )
        | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0))
        | ( sK183(X0) != sK184(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_774])]) ).

tff(f2509,plain,
    ! [X2: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
      | ( X1 = X2 )
      | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0))
      | ( sK183(X0) != sK184(X0) ) ),
    inference(cnf_transformation,[],[f1557]) ).

tff(f1557,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
      | ( X1 = X2 )
      | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0))
      | ( ~ 'member$e'('pair$'(sK184(X0),sK183(X0)),X0)
        & ( sK183(X0) != sK184(X0) )
        & ~ 'member$e'('pair$'(sK183(X0),sK184(X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK183,sK184])],[f954,f1556]) ).

tff(f1556,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'member$e'('pair$'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$e'('pair$'(X3,X4),X0) )
     => ( ~ 'member$e'('pair$'(sK184(X0),sK183(X0)),X0)
        & ( sK183(X0) != sK184(X0) )
        & ~ 'member$e'('pair$'(sK183(X0),sK184(X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f954,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
      | ( X1 = X2 )
      | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0))
      | ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'member$e'('pair$'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$e'('pair$'(X3,X4),X0) ) ),
    inference(flattening,[],[f953]) ).

tff(f953,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
      | ( X1 = X2 )
      | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0))
      | ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'member$e'('pair$'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$e'('pair$'(X3,X4),X0) ) ),
    inference(ennf_transformation,[],[f525]) ).

tff(f525,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$'] :
      ( ! [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( 'member$e'('pair$'(X4,X3),X0)
          | ( X3 = X4 )
          | 'member$e'('pair$'(X3,X4),X0) )
     => ( 'member$p'('pair$w'(X2,X1),'lexord$a'(X0))
        | ( X1 = X2 )
        | 'member$p'('pair$w'(X1,X2),'lexord$a'(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom523) ).

tff(f11503,plain,
    spl230_773,
    inference(avatar_split_clause,[],[f2506,f11501]) ).

tff(f11501,plain,
    ( spl230_773
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
        | ( X1 = X2 )
        | 'member$'('pair$b'(X1,X2),'lexord$c'(X0))
        | ( sK181(X0) != sK182(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_773])]) ).

tff(f2506,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
      | ( X1 = X2 )
      | 'member$'('pair$b'(X1,X2),'lexord$c'(X0))
      | ( sK181(X0) != sK182(X0) ) ),
    inference(cnf_transformation,[],[f1555]) ).

tff(f1555,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
      | ( X1 = X2 )
      | 'member$'('pair$b'(X1,X2),'lexord$c'(X0))
      | ( ~ 'member$f'('pair$a'(sK182(X0),sK181(X0)),X0)
        & ( sK181(X0) != sK182(X0) )
        & ~ 'member$f'('pair$a'(sK181(X0),sK182(X0)),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK181,sK182])],[f952,f1554]) ).

tff(f1554,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$'] :
      ( ? [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( ~ 'member$f'('pair$a'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$f'('pair$a'(X3,X4),X0) )
     => ( ~ 'member$f'('pair$a'(sK182(X0),sK181(X0)),X0)
        & ( sK181(X0) != sK182(X0) )
        & ~ 'member$f'('pair$a'(sK181(X0),sK182(X0)),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f952,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
      | ( X1 = X2 )
      | 'member$'('pair$b'(X1,X2),'lexord$c'(X0))
      | ? [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( ~ 'member$f'('pair$a'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$f'('pair$a'(X3,X4),X0) ) ),
    inference(flattening,[],[f951]) ).

tff(f951,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
      | ( X1 = X2 )
      | 'member$'('pair$b'(X1,X2),'lexord$c'(X0))
      | ? [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( ~ 'member$f'('pair$a'(X4,X3),X0)
          & ( X3 != X4 )
          & ~ 'member$f'('pair$a'(X3,X4),X0) ) ),
    inference(ennf_transformation,[],[f527]) ).

tff(f527,axiom,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ! [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( 'member$f'('pair$a'(X4,X3),X0)
          | ( X3 = X4 )
          | 'member$f'('pair$a'(X3,X4),X0) )
     => ( 'member$'('pair$b'(X2,X1),'lexord$c'(X0))
        | ( X1 = X2 )
        | 'member$'('pair$b'(X1,X2),'lexord$c'(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom525) ).

tff(f11487,plain,
    ( spl230_772
    | ~ spl230_111
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_769
    | ~ spl230_770 ),
    inference(avatar_split_clause,[],[f11479,f11474,f11451,f6450,f6201,f3988,f11485]) ).

tff(f11485,plain,
    ( spl230_772
  <=> ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'(sK41('fun_app$aj'('fstOp$a'(X0,X1),X2)),sK41(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_772])]) ).

tff(f3988,plain,
    ( spl230_111
  <=> ! [X0: $int,X1: $int] : ( 'fun_app$ac'('snd$b','pair$c'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_111])]) ).

tff(f11451,plain,
    ( spl230_769
  <=> ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'(sK40(X2),'fun_app$ak'('pick_middlep$a'(X0,X1,sK40(X2)),sK41(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_769])]) ).

tff(f11474,plain,
    ( spl230_770
  <=> ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2)),'fun_app$ac'('snd$b',X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_770])]) ).

tff(f11479,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'(sK41('fun_app$aj'('fstOp$a'(X0,X1),X2)),sK41(X2)) )
    | ~ spl230_111
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_769
    | ~ spl230_770 ),
    inference(forward_demodulation,[],[f11478,f11471]) ).

tff(f11471,plain,
    ( ! [X2: 'Int_int_bool_fun_fun$',X0: 'Int_int_prod$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$ak'('pick_middlep$a'(X1,X2,sK40(X0)),sK41(X0)) = sK41('fun_app$aj'('fstOp$a'(X1,X2),X0)) )
    | ~ spl230_111
    | ~ spl230_426
    | ~ spl230_769 ),
    inference(forward_demodulation,[],[f11459,f6451]) ).

tff(f11459,plain,
    ( ! [X2: 'Int_int_bool_fun_fun$',X0: 'Int_int_prod$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$ak'('pick_middlep$a'(X1,X2,sK40(X0)),sK41(X0)) = 'fun_app$ac'('snd$b','fun_app$aj'('fstOp$a'(X1,X2),X0)) )
    | ~ spl230_111
    | ~ spl230_769 ),
    inference(superposition,[],[f3989,f11452]) ).

tff(f11452,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'(sK40(X2),'fun_app$ak'('pick_middlep$a'(X0,X1,sK40(X2)),sK41(X2))) )
    | ~ spl230_769 ),
    inference(avatar_component_clause,[],[f11451]) ).

tff(f3989,plain,
    ( ! [X0: $int,X1: $int] : ( 'fun_app$ac'('snd$b','pair$c'(X0,X1)) = X1 )
    | ~ spl230_111 ),
    inference(avatar_component_clause,[],[f3988]) ).

tff(f11478,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,sK40(X2)),sK41(X2)),sK41(X2)) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_770 ),
    inference(forward_demodulation,[],[f11477,f6202]) ).

tff(f11477,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),sK41(X2)),sK41(X2)) )
    | ~ spl230_426
    | ~ spl230_770 ),
    inference(forward_demodulation,[],[f11475,f6451]) ).

tff(f11475,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2)),'fun_app$ac'('snd$b',X2)) )
    | ~ spl230_770 ),
    inference(avatar_component_clause,[],[f11474]) ).

tff(f11483,plain,
    ( spl230_771
    | ~ spl230_35
    | ~ spl230_762 ),
    inference(avatar_split_clause,[],[f11425,f10948,f3655,f11481]) ).

tff(f11481,plain,
    ( spl230_771
  <=> ! [X2: 'N$',X1: 'N$'] : ( 'zero$b' = 'gauss_Jordan_in_ij$'('zero$b',X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_771])]) ).

tff(f3655,plain,
    ( spl230_35
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'(X0,'zero$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_35])]) ).

tff(f10948,plain,
    ( spl230_762
  <=> ! [X4: 'N$',X0: 'A_n_vec_n_vec$',X3: 'N$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'matrix_matrix_mult$'(X0,X1)),X3,X4)),X1) = 'gauss_Jordan_in_ij$'('matrix_matrix_mult$'(X0,X1),X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_762])]) ).

tff(f11425,plain,
    ( ! [X2: 'N$',X1: 'N$'] : ( 'zero$b' = 'gauss_Jordan_in_ij$'('zero$b',X1,X2) )
    | ~ spl230_35
    | ~ spl230_762 ),
    inference(forward_demodulation,[],[f11407,f3656]) ).

tff(f3656,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'(X0,'zero$b') )
    | ~ spl230_35 ),
    inference(avatar_component_clause,[],[f3655]) ).

tff(f11407,plain,
    ( ! [X2: 'N$',X0: 'A_n_vec_n_vec$',X1: 'N$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'zero$b'),X1,X2)),'zero$b') = 'gauss_Jordan_in_ij$'('zero$b',X1,X2) )
    | ~ spl230_35
    | ~ spl230_762 ),
    inference(superposition,[],[f10949,f3656]) ).

tff(f10949,plain,
    ( ! [X3: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X4: 'N$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'matrix_matrix_mult$'(X0,X1)),X3,X4)),X1) = 'gauss_Jordan_in_ij$'('matrix_matrix_mult$'(X0,X1),X3,X4) )
    | ~ spl230_762 ),
    inference(avatar_component_clause,[],[f10948]) ).

tff(f11476,plain,
    spl230_770,
    inference(avatar_split_clause,[],[f2380,f11474]) ).

tff(f2380,plain,
    ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2)),'fun_app$ac'('snd$b',X2)) ),
    inference(cnf_transformation,[],[f352]) ).

tff(f352,axiom,
    ! [X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$',X2: 'Int_int_prod$'] : ( 'fun_app$aj'('sndOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2)),'fun_app$ac'('snd$b',X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom350) ).

tff(f11453,plain,
    ( spl230_769
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_768 ),
    inference(avatar_split_clause,[],[f11449,f11445,f6450,f6201,f11451]) ).

tff(f11445,plain,
    ( spl230_768
  <=> ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ac'('fst$b',X2),'fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_768])]) ).

tff(f11449,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'(sK40(X2),'fun_app$ak'('pick_middlep$a'(X0,X1,sK40(X2)),sK41(X2))) )
    | ~ spl230_425
    | ~ spl230_426
    | ~ spl230_768 ),
    inference(forward_demodulation,[],[f11448,f6202]) ).

tff(f11448,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ac'('fst$b',X2),'fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),sK41(X2))) )
    | ~ spl230_426
    | ~ spl230_768 ),
    inference(forward_demodulation,[],[f11446,f6451]) ).

tff(f11446,plain,
    ( ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ac'('fst$b',X2),'fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2))) )
    | ~ spl230_768 ),
    inference(avatar_component_clause,[],[f11445]) ).

tff(f11447,plain,
    spl230_768,
    inference(avatar_split_clause,[],[f2379,f11445]) ).

tff(f2379,plain,
    ! [X2: 'Int_int_prod$',X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ac'('fst$b',X2),'fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2))) ),
    inference(cnf_transformation,[],[f354]) ).

tff(f354,axiom,
    ! [X0: 'Int_int_bool_fun_fun$',X1: 'Int_int_bool_fun_fun$',X2: 'Int_int_prod$'] : ( 'fun_app$aj'('fstOp$a'(X0,X1),X2) = 'pair$c'('fun_app$ac'('fst$b',X2),'fun_app$ak'('pick_middlep$a'(X0,X1,'fun_app$ac'('fst$b',X2)),'fun_app$ac'('snd$b',X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom352) ).

tff(f11443,plain,
    spl230_767,
    inference(avatar_split_clause,[],[f2058,f11441]) ).

tff(f11441,plain,
    ( spl230_767
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK71(X0,X1))) )
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_767])]) ).

tff(f2058,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK71(X0,X1))) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1246]) ).

tff(f1246,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK71(X0,X1))) )
        & $less(0,'fun_app$l'('of_nat$',sK71(X0,X1))) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f820,f1245]) ).

tff(f1245,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)) )
          & $less(0,'fun_app$l'('of_nat$',X2)) )
     => ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK71(X0,X1))) )
        & $less(0,'fun_app$l'('of_nat$',sK71(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f820,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)) )
          & $less(0,'fun_app$l'('of_nat$',X2)) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(ennf_transformation,[],[f636]) ).

tff(f636,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))
     => ? [X2: 'Nat$'] :
          ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X2)) )
          & $less(0,'fun_app$l'('of_nat$',X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom634) ).

tff(f11347,plain,
    ( spl230_766
    | ~ spl230_738
    | ~ spl230_760 ),
    inference(avatar_split_clause,[],[f10942,f10939,f10818,f11345]) ).

tff(f11345,plain,
    ( spl230_766
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK134(X0,X1)))))
        | ~ sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_766])]) ).

tff(f10818,plain,
    ( spl230_738
  <=> ( 'fun_app$k'('nat$',0) = 'fun_app$aa'('rank$','zero$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_738])]) ).

tff(f10939,plain,
    ( spl230_760
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK134(X0,X1)))))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_760])]) ).

tff(f10942,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK134(X0,X1)))))
        | ~ sP7(X1,X0) )
    | ~ spl230_738
    | ~ spl230_760 ),
    inference(forward_demodulation,[],[f10940,f10820]) ).

tff(f10820,plain,
    ( ( 'fun_app$k'('nat$',0) = 'fun_app$aa'('rank$','zero$b') )
    | ~ spl230_738 ),
    inference(avatar_component_clause,[],[f10818]) ).

tff(f10940,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK134(X0,X1)))))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) )
    | ~ spl230_760 ),
    inference(avatar_component_clause,[],[f10939]) ).

tff(f11343,plain,
    ( spl230_765
    | ~ spl230_59
    | ~ spl230_200 ),
    inference(avatar_split_clause,[],[f4675,f4454,f3759,f11341]) ).

tff(f11341,plain,
    ( spl230_765
  <=> ! [X0: $int] :
        ( ~ $less($uminus(X0),0)
        | $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_765])]) ).

tff(f4454,plain,
    ( spl230_200
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X1)
        | ~ $less(X0,$sum(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_200])]) ).

tff(f4675,plain,
    ( ! [X0: $int] :
        ( ~ $less($uminus(X0),0)
        | $less(0,X0) )
    | ~ spl230_59
    | ~ spl230_200 ),
    inference(superposition,[],[f4455,f3760]) ).

tff(f4455,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X0,$sum(X1,X0))
        | $less(0,X1) )
    | ~ spl230_200 ),
    inference(avatar_component_clause,[],[f4454]) ).

tff(f11226,plain,
    ( spl230_764
    | ~ spl230_738
    | ~ spl230_756 ),
    inference(avatar_split_clause,[],[f10925,f10922,f10818,f11224]) ).

tff(f11224,plain,
    ( spl230_764
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK132(X0,X1)))))
        | sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_764])]) ).

tff(f10922,plain,
    ( spl230_756
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK132(X0,X1)))))
        | sP6(X1,X0)
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_756])]) ).

tff(f10925,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK132(X0,X1)))))
        | sP6(X1,X0) )
    | ~ spl230_738
    | ~ spl230_756 ),
    inference(forward_demodulation,[],[f10923,f10820]) ).

tff(f10923,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK132(X0,X1)))))
        | sP6(X1,X0)
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
    | ~ spl230_756 ),
    inference(avatar_component_clause,[],[f10922]) ).

tff(f11212,plain,
    ( spl230_763
    | ~ spl230_59
    | ~ spl230_196 ),
    inference(avatar_split_clause,[],[f4663,f4438,f3759,f11210]) ).

tff(f11210,plain,
    ( spl230_763
  <=> ! [X0: $int] :
        ( ( 0 != $uminus(X0) )
        | ( 0 = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_763])]) ).

tff(f4438,plain,
    ( spl230_196
  <=> ! [X0: $int,X1: $int] :
        ( ( 0 = X0 )
        | ( $sum(X0,X1) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_196])]) ).

tff(f4663,plain,
    ( ! [X0: $int] :
        ( ( 0 != $uminus(X0) )
        | ( 0 = X0 ) )
    | ~ spl230_59
    | ~ spl230_196 ),
    inference(superposition,[],[f4439,f3760]) ).

tff(f4439,plain,
    ( ! [X0: $int,X1: $int] :
        ( ( $sum(X0,X1) != X1 )
        | ( 0 = X0 ) )
    | ~ spl230_196 ),
    inference(avatar_component_clause,[],[f4438]) ).

tff(f10950,plain,
    spl230_762,
    inference(avatar_split_clause,[],[f3500,f10948]) ).

tff(f3500,plain,
    ! [X3: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X4: 'N$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'matrix_matrix_mult$'(X0,X1)),X3,X4)),X1) = 'gauss_Jordan_in_ij$'('matrix_matrix_mult$'(X0,X1),X3,X4) ),
    inference(forward_demodulation,[],[f3220,f2600]) ).

tff(f2600,plain,
    ! [X2: 'N$',X3: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X1),X2,X3)) = 'gauss_Jordan_in_ij$'(X1,X2,X3) ),
    inference(cnf_transformation,[],[f328]) ).

tff(f328,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'N$',X3: 'N$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X1),X2,X3)) = 'gauss_Jordan_in_ij$'(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom326) ).

tff(f3220,plain,
    ! [X3: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X4: 'N$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'matrix_matrix_mult$'(X0,X1)),X3,X4)),X1) = 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,'matrix_matrix_mult$'(X0,X1)),X3,X4)) ),
    inference(equality_resolution,[],[f2786]) ).

tff(f2786,plain,
    ! [X2: 'A_n_vec_n_vec$',X3: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X4: 'N$'] :
      ( ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)),X1) = 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)) )
      | ( 'matrix_matrix_mult$'(X0,X1) != X2 ) ),
    inference(cnf_transformation,[],[f1034]) ).

tff(f1034,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$',X3: 'N$',X4: 'N$'] :
      ( ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)),X1) = 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)) )
      | ( 'matrix_matrix_mult$'(X0,X1) != X2 ) ),
    inference(ennf_transformation,[],[f325]) ).

tff(f325,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$',X3: 'N$',X4: 'N$'] :
      ( ( 'matrix_matrix_mult$'(X0,X1) = X2 )
     => ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)),X1) = 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X2),X3,X4)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom323) ).

tff(f10946,plain,
    spl230_761,
    inference(avatar_split_clause,[],[f3454,f10944]) ).

tff(f10944,plain,
    ( spl230_761
  <=> ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray$'] : ( 'enumerate$'(X0,'cons$'(X1,X2)) = 'cons$a'('pair$u'(X0,X1),'enumerate$'('fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X0))),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_761])]) ).

tff(f3454,plain,
    ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray$'] : ( 'enumerate$'(X0,'cons$'(X1,X2)) = 'cons$a'('pair$u'(X0,X1),'enumerate$'('fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X0))),X2)) ),
    inference(forward_demodulation,[],[f2378,f664]) ).

tff(f2378,plain,
    ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray$'] : ( 'enumerate$'(X0,'cons$'(X1,X2)) = 'cons$a'('pair$u'(X0,X1),'enumerate$'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X0),1)),X2)) ),
    inference(cnf_transformation,[],[f495]) ).

tff(f495,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray$',X2: 'A_iarray_list$'] : ( 'enumerate$'(X0,'cons$'(X1,X2)) = 'cons$a'('pair$u'(X0,X1),'enumerate$'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X0),1)),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom493) ).

tff(f10941,plain,
    spl230_760,
    inference(avatar_split_clause,[],[f3439,f10939]) ).

tff(f3439,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK134(X0,X1)))))
      | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
      | ~ sP7(X1,X0) ),
    inference(forward_demodulation,[],[f2347,f664]) ).

tff(f2347,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK134(X0,X1)),1)))
      | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
      | ~ sP7(X1,X0) ),
    inference(cnf_transformation,[],[f1490]) ).

tff(f1490,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP7(X1,X0)
        | ( ! [X2: 'Nat$'] :
              ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
              | ~ $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) )
          & ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) )
      & ( ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK134(X0,X1)),1)))
          & $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f1488,f1489]) ).

tff(f1489,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ? [X3: 'Nat$'] :
          ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
     => ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK134(X0,X1)),1)))
        & $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1488,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP7(X1,X0)
        | ( ! [X2: 'Nat$'] :
              ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
              | ~ $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) )
          & ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) )
      & ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    inference(rectify,[],[f1487]) ).

tff(f1487,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP7(X1,X0)
        | ( ! [X3: 'Nat$'] :
              ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) )
      & ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    inference(flattening,[],[f1486]) ).

tff(f1486,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP7(X1,X0)
        | ( ! [X3: 'Nat$'] :
              ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) )
      & ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    inference(nnf_transformation,[],[f1092]) ).

tff(f1092,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP7(X1,X0)
    <=> ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    inference(definition_folding,[],[f739,f1091]) ).

tff(f1091,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( sP7(X1,X0)
    <=> ? [X2: 'Nat$'] :
          ( 'fun_app$c'(X1,X2)
          & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

tff(f739,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( 'fun_app$c'(X1,X2)
          & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) )
    <=> ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    inference(rectify,[],[f635]) ).

tff(f635,axiom,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( 'fun_app$c'(X1,X2)
          & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) )
    <=> ( ? [X2: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
            & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) )
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom633) ).

tff(f10937,plain,
    spl230_759,
    inference(avatar_split_clause,[],[f3438,f10935]) ).

tff(f10935,plain,
    ( spl230_759
  <=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X2))))
        | sP7(X1,X0)
        | ~ $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_759])]) ).

tff(f3438,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X2))))
      | sP7(X1,X0)
      | ~ $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) ),
    inference(forward_demodulation,[],[f2349,f664]) ).

tff(f2349,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP7(X1,X0)
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
      | ~ $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) ),
    inference(cnf_transformation,[],[f1490]) ).

tff(f10933,plain,
    spl230_758,
    inference(avatar_split_clause,[],[f3435,f10931]) ).

tff(f10931,plain,
    ( spl230_758
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X3: 'Nat$'] :
        ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X3))))
        | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0))
        | ~ sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_758])]) ).

tff(f3435,plain,
    ! [X3: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',X3))))
      | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0))
      | ~ sP6(X1,X0) ),
    inference(forward_demodulation,[],[f2340,f664]) ).

tff(f2340,plain,
    ! [X3: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
      | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0))
      | ~ sP6(X1,X0) ),
    inference(cnf_transformation,[],[f1481]) ).

tff(f1481,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP6(X1,X0)
        | ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK132(X0,X1)),1)))
          & $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0)) )
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
      & ( ( ! [X3: 'Nat$'] :
              ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
        | ~ sP6(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK132])],[f1479,f1480]) ).

tff(f1480,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) )
     => ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK132(X0,X1)),1)))
        & $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1479,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP6(X1,X0)
        | ? [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
            & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0)) )
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
      & ( ( ! [X3: 'Nat$'] :
              ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
        | ~ sP6(X1,X0) ) ),
    inference(rectify,[],[f1478]) ).

tff(f1478,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP6(X1,X0)
        | ? [X3: 'Nat$'] :
            ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
      & ( ( ! [X3: 'Nat$'] :
              ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
        | ~ sP6(X1,X0) ) ),
    inference(flattening,[],[f1477]) ).

tff(f1477,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( sP6(X1,X0)
        | ? [X3: 'Nat$'] :
            ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
      & ( ( ! [X3: 'Nat$'] :
              ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
          & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
        | ~ sP6(X1,X0) ) ),
    inference(nnf_transformation,[],[f1090]) ).

tff(f1090,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP6(X1,X0)
    <=> ( ! [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    inference(definition_folding,[],[f880,f1089]) ).

tff(f1089,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( sP6(X1,X0)
    <=> ! [X2: 'Nat$'] :
          ( 'fun_app$c'(X1,X2)
          | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

tff(f880,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ! [X2: 'Nat$'] :
          ( 'fun_app$c'(X1,X2)
          | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) )
    <=> ( ! [X3: 'Nat$'] :
            ( 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
            | ~ $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0)) )
        & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    inference(ennf_transformation,[],[f738]) ).

tff(f738,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ! [X2: 'Nat$'] :
          ( $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1))
         => 'fun_app$c'(X1,X2) )
    <=> ( ! [X3: 'Nat$'] :
            ( $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X0))
           => 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1))) )
        & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    inference(rectify,[],[f633]) ).

tff(f633,axiom,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ! [X2: 'Nat$'] :
          ( $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1))
         => 'fun_app$c'(X1,X2) )
    <=> ( ! [X2: 'Nat$'] :
            ( $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X0))
           => 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1))) )
        & 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom631) ).

tff(f10929,plain,
    ( spl230_757
    | ~ spl230_59
    | ~ spl230_195 ),
    inference(avatar_split_clause,[],[f4660,f4434,f3759,f10927]) ).

tff(f10927,plain,
    ( spl230_757
  <=> ! [X0: $int] :
        ( ( 0 != X0 )
        | ( 0 = $uminus(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_757])]) ).

tff(f4434,plain,
    ( spl230_195
  <=> ! [X0: $int,X1: $int] :
        ( ( 0 = X1 )
        | ( $sum(X0,X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_195])]) ).

tff(f4660,plain,
    ( ! [X0: $int] :
        ( ( 0 != X0 )
        | ( 0 = $uminus(X0) ) )
    | ~ spl230_59
    | ~ spl230_195 ),
    inference(superposition,[],[f4435,f3760]) ).

tff(f4435,plain,
    ( ! [X0: $int,X1: $int] :
        ( ( $sum(X0,X1) != X0 )
        | ( 0 = X1 ) )
    | ~ spl230_195 ),
    inference(avatar_component_clause,[],[f4434]) ).

tff(f10924,plain,
    spl230_756,
    inference(avatar_split_clause,[],[f3434,f10922]) ).

tff(f3434,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK132(X0,X1)))))
      | sP6(X1,X0)
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ),
    inference(forward_demodulation,[],[f2342,f664]) ).

tff(f2342,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP6(X1,X0)
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK132(X0,X1)),1)))
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ),
    inference(cnf_transformation,[],[f1481]) ).

tff(f10920,plain,
    spl230_755,
    inference(avatar_split_clause,[],[f3268,f10918]) ).

tff(f10918,plain,
    ( spl230_755
  <=> ! [X4: 'A_iarray_list_list$',X0: 'A_iarray_list$',X5: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$s'('pair$z'('append$c'(X4,'cons$b'(X0,X5)),'append$c'(X4,'cons$b'(X1,X5))),'listrel1$b'(X2))
        | ~ 'member$'('pair$b'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_755])]) ).

tff(f3268,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'('append$c'(X4,'cons$b'(X0,X5)),'append$c'(X4,'cons$b'(X1,X5))),'listrel1$b'(X2))
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(equality_resolution,[],[f3267]) ).

tff(f3267,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X3,'append$c'(X4,'cons$b'(X1,X5))),'listrel1$b'(X2))
      | ( 'append$c'(X4,'cons$b'(X0,X5)) != X3 )
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(equality_resolution,[],[f2912]) ).

tff(f2912,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X6: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X3,X6),'listrel1$b'(X2))
      | ( 'append$c'(X4,'cons$b'(X1,X5)) != X6 )
      | ( 'append$c'(X4,'cons$b'(X0,X5)) != X3 )
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1077]) ).

tff(f1077,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$',X6: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X3,X6),'listrel1$b'(X2))
      | ( 'append$c'(X4,'cons$b'(X1,X5)) != X6 )
      | ( 'append$c'(X4,'cons$b'(X0,X5)) != X3 )
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(flattening,[],[f1076]) ).

tff(f1076,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$',X6: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X3,X6),'listrel1$b'(X2))
      | ( 'append$c'(X4,'cons$b'(X1,X5)) != X6 )
      | ( 'append$c'(X4,'cons$b'(X0,X5)) != X3 )
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f552]) ).

tff(f552,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$',X6: 'A_iarray_list_list$'] :
      ( ( ( 'append$c'(X4,'cons$b'(X1,X5)) = X6 )
        & ( 'append$c'(X4,'cons$b'(X0,X5)) = X3 )
        & 'member$'('pair$b'(X0,X1),X2) )
     => 'member$s'('pair$z'(X3,X6),'listrel1$b'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom550) ).

tff(f10916,plain,
    spl230_754,
    inference(avatar_split_clause,[],[f3266,f10914]) ).

tff(f10914,plain,
    ( spl230_754
  <=> ! [X4: 'Int_list$',X0: $int,X5: 'Int_list$',X2: 'Int_int_prod_set$',X1: $int] :
        ( 'member$o'('pair$v'('append$a'(X4,'cons$c'(X0,X5)),'append$a'(X4,'cons$c'(X1,X5))),'listrel1$'(X2))
        | ~ 'member$g'('pair$c'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_754])]) ).

tff(f3266,plain,
    ! [X2: 'Int_int_prod_set$',X0: $int,X1: $int,X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$o'('pair$v'('append$a'(X4,'cons$c'(X0,X5)),'append$a'(X4,'cons$c'(X1,X5))),'listrel1$'(X2))
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(equality_resolution,[],[f3265]) ).

tff(f3265,plain,
    ! [X2: 'Int_int_prod_set$',X3: 'Int_list$',X0: $int,X1: $int,X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$o'('pair$v'(X3,'append$a'(X4,'cons$c'(X1,X5))),'listrel1$'(X2))
      | ( 'append$a'(X4,'cons$c'(X0,X5)) != X3 )
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(equality_resolution,[],[f2911]) ).

tff(f2911,plain,
    ! [X2: 'Int_int_prod_set$',X3: 'Int_list$',X0: $int,X1: $int,X6: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$o'('pair$v'(X3,X6),'listrel1$'(X2))
      | ( 'append$a'(X4,'cons$c'(X1,X5)) != X6 )
      | ( 'append$a'(X4,'cons$c'(X0,X5)) != X3 )
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1075]) ).

tff(f1075,plain,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$',X6: 'Int_list$'] :
      ( 'member$o'('pair$v'(X3,X6),'listrel1$'(X2))
      | ( 'append$a'(X4,'cons$c'(X1,X5)) != X6 )
      | ( 'append$a'(X4,'cons$c'(X0,X5)) != X3 )
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(flattening,[],[f1074]) ).

tff(f1074,plain,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$',X6: 'Int_list$'] :
      ( 'member$o'('pair$v'(X3,X6),'listrel1$'(X2))
      | ( 'append$a'(X4,'cons$c'(X1,X5)) != X6 )
      | ( 'append$a'(X4,'cons$c'(X0,X5)) != X3 )
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f550]) ).

tff(f550,axiom,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$',X6: 'Int_list$'] :
      ( ( ( 'append$a'(X4,'cons$c'(X1,X5)) = X6 )
        & ( 'append$a'(X4,'cons$c'(X0,X5)) = X3 )
        & 'member$g'('pair$c'(X0,X1),X2) )
     => 'member$o'('pair$v'(X3,X6),'listrel1$'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom548) ).

tff(f10912,plain,
    spl230_753,
    inference(avatar_split_clause,[],[f3264,f10910]) ).

tff(f10910,plain,
    ( spl230_753
  <=> ! [X4: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X5: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
        ( 'member$p'('pair$w'('append$b'(X4,'cons$d'(X0,X5)),'append$b'(X4,'cons$d'(X1,X5))),'listrel1$a'(X2))
        | ~ 'member$e'('pair$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_753])]) ).

tff(f3264,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'('append$b'(X4,'cons$d'(X0,X5)),'append$b'(X4,'cons$d'(X1,X5))),'listrel1$a'(X2))
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(equality_resolution,[],[f3263]) ).

tff(f3263,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X3,'append$b'(X4,'cons$d'(X1,X5))),'listrel1$a'(X2))
      | ( 'append$b'(X4,'cons$d'(X0,X5)) != X3 )
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(equality_resolution,[],[f2910]) ).

tff(f2910,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X6: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X3,X6),'listrel1$a'(X2))
      | ( 'append$b'(X4,'cons$d'(X1,X5)) != X6 )
      | ( 'append$b'(X4,'cons$d'(X0,X5)) != X3 )
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1073]) ).

tff(f1073,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$',X6: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X3,X6),'listrel1$a'(X2))
      | ( 'append$b'(X4,'cons$d'(X1,X5)) != X6 )
      | ( 'append$b'(X4,'cons$d'(X0,X5)) != X3 )
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(flattening,[],[f1072]) ).

tff(f1072,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$',X6: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'(X3,X6),'listrel1$a'(X2))
      | ( 'append$b'(X4,'cons$d'(X1,X5)) != X6 )
      | ( 'append$b'(X4,'cons$d'(X0,X5)) != X3 )
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f551]) ).

tff(f551,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$',X6: 'A_iarray_iarray_list$'] :
      ( ( ( 'append$b'(X4,'cons$d'(X1,X5)) = X6 )
        & ( 'append$b'(X4,'cons$d'(X0,X5)) = X3 )
        & 'member$e'('pair$'(X0,X1),X2) )
     => 'member$p'('pair$w'(X3,X6),'listrel1$a'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom549) ).

tff(f10908,plain,
    spl230_752,
    inference(avatar_split_clause,[],[f2897,f10906]) ).

tff(f10906,plain,
    ( spl230_752
  <=> ! [X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X0: 'A_iarray_list$',X5: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$s'('pair$z'('append$c'(X3,'cons$b'(X0,X4)),'append$c'(X3,'cons$b'(X1,X5))),'lexord$b'(X2))
        | ~ 'member$'('pair$b'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_752])]) ).

tff(f2897,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'('append$c'(X3,'cons$b'(X0,X4)),'append$c'(X3,'cons$b'(X1,X5))),'lexord$b'(X2))
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1047]) ).

tff(f1047,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'('append$c'(X3,'cons$b'(X0,X4)),'append$c'(X3,'cons$b'(X1,X5))),'lexord$b'(X2))
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f547]) ).

tff(f547,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_list$',X5: 'A_iarray_list_list$'] :
      ( 'member$'('pair$b'(X0,X1),X2)
     => 'member$s'('pair$z'('append$c'(X3,'cons$b'(X0,X4)),'append$c'(X3,'cons$b'(X1,X5))),'lexord$b'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom545) ).

tff(f10904,plain,
    spl230_751,
    inference(avatar_split_clause,[],[f2896,f10902]) ).

tff(f10902,plain,
    ( spl230_751
  <=> ! [X3: 'Int_list$',X4: 'Int_list$',X0: $int,X5: 'Int_list$',X2: 'Int_int_prod_set$',X1: $int] :
        ( 'member$o'('pair$v'('append$a'(X3,'cons$c'(X0,X4)),'append$a'(X3,'cons$c'(X1,X5))),'lexord$'(X2))
        | ~ 'member$g'('pair$c'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_751])]) ).

tff(f2896,plain,
    ! [X2: 'Int_int_prod_set$',X3: 'Int_list$',X0: $int,X1: $int,X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$o'('pair$v'('append$a'(X3,'cons$c'(X0,X4)),'append$a'(X3,'cons$c'(X1,X5))),'lexord$'(X2))
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1046]) ).

tff(f1046,plain,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$o'('pair$v'('append$a'(X3,'cons$c'(X0,X4)),'append$a'(X3,'cons$c'(X1,X5))),'lexord$'(X2))
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f545]) ).

tff(f545,axiom,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$',X4: 'Int_list$',X5: 'Int_list$'] :
      ( 'member$g'('pair$c'(X0,X1),X2)
     => 'member$o'('pair$v'('append$a'(X3,'cons$c'(X0,X4)),'append$a'(X3,'cons$c'(X1,X5))),'lexord$'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom543) ).

tff(f10900,plain,
    spl230_750,
    inference(avatar_split_clause,[],[f2895,f10898]) ).

tff(f10898,plain,
    ( spl230_750
  <=> ! [X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X5: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
        ( 'member$p'('pair$w'('append$b'(X3,'cons$d'(X0,X4)),'append$b'(X3,'cons$d'(X1,X5))),'lexord$a'(X2))
        | ~ 'member$e'('pair$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_750])]) ).

tff(f2895,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'('append$b'(X3,'cons$d'(X0,X4)),'append$b'(X3,'cons$d'(X1,X5))),'lexord$a'(X2))
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1045]) ).

tff(f1045,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'('append$b'(X3,'cons$d'(X0,X4)),'append$b'(X3,'cons$d'(X1,X5))),'lexord$a'(X2))
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f546]) ).

tff(f546,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_list$',X5: 'A_iarray_iarray_list$'] :
      ( 'member$e'('pair$'(X0,X1),X2)
     => 'member$p'('pair$w'('append$b'(X3,'cons$d'(X0,X4)),'append$b'(X3,'cons$d'(X1,X5))),'lexord$a'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom544) ).

tff(f10896,plain,
    spl230_749,
    inference(avatar_split_clause,[],[f2635,f10894]) ).

tff(f10894,plain,
    ( spl230_749
  <=> ! [X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X6: 'A_iarray$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( ~ 'fun_app$'(X0,X6)
        | ~ 'member$a'(X6,'set$'(sK191(X0,X1,X2,X3)))
        | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_749])]) ).

tff(f2635,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X6: 'A_iarray$'] :
      ( ~ 'fun_app$'(X0,X6)
      | ~ 'member$a'(X6,'set$'(sK191(X0,X1,X2,X3)))
      | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1609]) ).

tff(f1609,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),sK192(X0,X1,X2,X3)) = X3 )
        & 'fun_app$'(X0,X2)
        & ! [X6: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X6)
            | ~ 'member$a'(X6,'set$'(sK191(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK191(X0,X1,X2,X3)),'cons$'(X2,sK192(X0,X1,X2,X3))) = X1 ) )
      | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK191,sK192])],[f977,f1608]) ).

tff(f1608,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X0,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) )
     => ( ( 'fun_app$p'('filter$'(X0),sK192(X0,X1,X2,X3)) = X3 )
        & 'fun_app$'(X0,X2)
        & ! [X6: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X6)
            | ~ 'member$a'(X6,'set$'(sK191(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK191(X0,X1,X2,X3)),'cons$'(X2,sK192(X0,X1,X2,X3))) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f977,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X0,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) )
      | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ),
    inference(ennf_transformation,[],[f603]) ).

tff(f603,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
     => ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( 'member$a'(X6,'set$'(X4))
             => ~ 'fun_app$'(X0,X6) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom601) ).

tff(f10892,plain,
    spl230_748,
    inference(avatar_split_clause,[],[f2631,f10890]) ).

tff(f10890,plain,
    ( spl230_748
  <=> ! [X3: 'A_iarray_list$',X0: 'A_iarray$',X6: 'A_iarray$',X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ~ 'fun_app$'(X2,X6)
        | ~ 'member$a'(X6,'set$'(sK189(X0,X1,X2,X3)))
        | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_748])]) ).

tff(f2631,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X6: 'A_iarray$'] :
      ( ~ 'fun_app$'(X2,X6)
      | ~ 'member$a'(X6,'set$'(sK189(X0,X1,X2,X3)))
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f1607,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X2),sK190(X0,X1,X2,X3)) = X1 )
        & 'fun_app$'(X2,X0)
        & ! [X6: 'A_iarray$'] :
            ( ~ 'fun_app$'(X2,X6)
            | ~ 'member$a'(X6,'set$'(sK189(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK189(X0,X1,X2,X3)),'cons$'(X0,sK190(X0,X1,X2,X3))) = X3 ) )
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK189,sK190])],[f976,f1606]) ).

tff(f1606,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X2,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) )
     => ( ( 'fun_app$p'('filter$'(X2),sK190(X0,X1,X2,X3)) = X1 )
        & 'fun_app$'(X2,X0)
        & ! [X6: 'A_iarray$'] :
            ( ~ 'fun_app$'(X2,X6)
            | ~ 'member$a'(X6,'set$'(sK189(X0,X1,X2,X3))) )
        & ( 'fun_app$p'('append$d'(sK189(X0,X1,X2,X3)),'cons$'(X0,sK190(X0,X1,X2,X3))) = X3 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f976,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X2,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) )
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(ennf_transformation,[],[f602]) ).

tff(f602,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
     => ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( 'member$a'(X6,'set$'(X4))
             => ~ 'fun_app$'(X2,X6) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom600) ).

tff(f10878,plain,
    ( spl230_747
    | ~ spl230_84
    | ~ spl230_85
    | ~ spl230_88 ),
    inference(avatar_split_clause,[],[f4139,f3895,f3882,f3877,f10875]) ).

tff(f10875,plain,
    ( spl230_747
  <=> ( 'fun_app$aa'('rank$','zero$b') = 'fun_app$m'('size$','nil$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_747])]) ).

tff(f3877,plain,
    ( spl230_84
  <=> ( 0 = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','zero$b')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_84])]) ).

tff(f3882,plain,
    ( spl230_85
  <=> ( 0 = 'fun_app$l'('of_nat$','fun_app$m'('size$','nil$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_85])]) ).

tff(f4139,plain,
    ( ( 'fun_app$aa'('rank$','zero$b') = 'fun_app$m'('size$','nil$') )
    | ~ spl230_84
    | ~ spl230_85
    | ~ spl230_88 ),
    inference(forward_demodulation,[],[f4137,f4136]) ).

tff(f4136,plain,
    ( ( 'fun_app$k'('nat$',0) = 'fun_app$aa'('rank$','zero$b') )
    | ~ spl230_84
    | ~ spl230_88 ),
    inference(superposition,[],[f3896,f3879]) ).

tff(f3879,plain,
    ( ( 0 = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','zero$b')) )
    | ~ spl230_84 ),
    inference(avatar_component_clause,[],[f3877]) ).

tff(f4137,plain,
    ( ( 'fun_app$k'('nat$',0) = 'fun_app$m'('size$','nil$') )
    | ~ spl230_85
    | ~ spl230_88 ),
    inference(superposition,[],[f3896,f3884]) ).

tff(f3884,plain,
    ( ( 0 = 'fun_app$l'('of_nat$','fun_app$m'('size$','nil$')) )
    | ~ spl230_85 ),
    inference(avatar_component_clause,[],[f3882]) ).

tff(f10873,plain,
    ( spl230_746
    | ~ spl230_114
    | ~ spl230_427
    | ~ spl230_428
    | ~ spl230_744
    | ~ spl230_745 ),
    inference(avatar_split_clause,[],[f10869,f10864,f10847,f6464,f6460,f4000,f10871]) ).

tff(f10871,plain,
    ( spl230_746
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'(sK37('fun_app$ai'('fstOp$'(X0,X1),X2)),sK37(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_746])]) ).

tff(f4000,plain,
    ( spl230_114
  <=> ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_114])]) ).

tff(f6464,plain,
    ( spl230_428
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('fst$',X0) = sK36(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_428])]) ).

tff(f10847,plain,
    ( spl230_744
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'(sK36(X2),'pick_middlep$'(X0,X1,sK36(X2),sK37(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_744])]) ).

tff(f10864,plain,
    ( spl230_745
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2)),'fun_app$r'('snd$a',X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_745])]) ).

tff(f10869,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'(sK37('fun_app$ai'('fstOp$'(X0,X1),X2)),sK37(X2)) )
    | ~ spl230_114
    | ~ spl230_427
    | ~ spl230_428
    | ~ spl230_744
    | ~ spl230_745 ),
    inference(forward_demodulation,[],[f10868,f10862]) ).

tff(f10862,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'pick_middlep$'(X1,X2,sK36(X0),sK37(X0)) = sK37('fun_app$ai'('fstOp$'(X1,X2),X0)) )
    | ~ spl230_114
    | ~ spl230_427
    | ~ spl230_744 ),
    inference(forward_demodulation,[],[f10852,f6461]) ).

tff(f10852,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'pick_middlep$'(X1,X2,sK36(X0),sK37(X0)) = 'fun_app$r'('snd$a','fun_app$ai'('fstOp$'(X1,X2),X0)) )
    | ~ spl230_114
    | ~ spl230_744 ),
    inference(superposition,[],[f4001,f10848]) ).

tff(f10848,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'(sK36(X2),'pick_middlep$'(X0,X1,sK36(X2),sK37(X2))) )
    | ~ spl230_744 ),
    inference(avatar_component_clause,[],[f10847]) ).

tff(f4001,plain,
    ( ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 )
    | ~ spl230_114 ),
    inference(avatar_component_clause,[],[f4000]) ).

tff(f10868,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,sK36(X2),sK37(X2)),sK37(X2)) )
    | ~ spl230_427
    | ~ spl230_428
    | ~ spl230_745 ),
    inference(forward_demodulation,[],[f10867,f6465]) ).

tff(f6465,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('fst$',X0) = sK36(X0) )
    | ~ spl230_428 ),
    inference(avatar_component_clause,[],[f6464]) ).

tff(f10867,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),sK37(X2)),sK37(X2)) )
    | ~ spl230_427
    | ~ spl230_745 ),
    inference(forward_demodulation,[],[f10865,f6461]) ).

tff(f10865,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2)),'fun_app$r'('snd$a',X2)) )
    | ~ spl230_745 ),
    inference(avatar_component_clause,[],[f10864]) ).

tff(f10866,plain,
    spl230_745,
    inference(avatar_split_clause,[],[f2377,f10864]) ).

tff(f2377,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2)),'fun_app$r'('snd$a',X2)) ),
    inference(cnf_transformation,[],[f351]) ).

tff(f351,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X2: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$ai'('sndOp$'(X0,X1),X2) = 'pair$'('pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2)),'fun_app$r'('snd$a',X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom349) ).

tff(f10849,plain,
    ( spl230_744
    | ~ spl230_427
    | ~ spl230_428
    | ~ spl230_743 ),
    inference(avatar_split_clause,[],[f10845,f10841,f6464,f6460,f10847]) ).

tff(f10841,plain,
    ( spl230_743
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'('fun_app$r'('fst$',X2),'pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_743])]) ).

tff(f10845,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'(sK36(X2),'pick_middlep$'(X0,X1,sK36(X2),sK37(X2))) )
    | ~ spl230_427
    | ~ spl230_428
    | ~ spl230_743 ),
    inference(forward_demodulation,[],[f10844,f6465]) ).

tff(f10844,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'('fun_app$r'('fst$',X2),'pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),sK37(X2))) )
    | ~ spl230_427
    | ~ spl230_743 ),
    inference(forward_demodulation,[],[f10842,f6461]) ).

tff(f10842,plain,
    ( ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'('fun_app$r'('fst$',X2),'pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2))) )
    | ~ spl230_743 ),
    inference(avatar_component_clause,[],[f10841]) ).

tff(f10843,plain,
    spl230_743,
    inference(avatar_split_clause,[],[f2376,f10841]) ).

tff(f2376,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod$',X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'('fun_app$r'('fst$',X2),'pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2))) ),
    inference(cnf_transformation,[],[f353]) ).

tff(f353,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$',X2: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$ai'('fstOp$'(X0,X1),X2) = 'pair$'('fun_app$r'('fst$',X2),'pick_middlep$'(X0,X1,'fun_app$r'('fst$',X2),'fun_app$r'('snd$a',X2))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom351) ).

tff(f10839,plain,
    spl230_742,
    inference(avatar_split_clause,[],[f2283,f10837]) ).

tff(f10837,plain,
    ( spl230_742
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( $less(0,'fun_app$l'('of_nat$',X1))
        | $less(0,'fun_app$l'('of_nat$',X0))
        | ~ $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_742])]) ).

tff(f2283,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',X1))
      | $less(0,'fun_app$l'('of_nat$',X0))
      | ~ $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))) ),
    inference(cnf_transformation,[],[f1424]) ).

tff(f1424,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
        | ( ~ $less(0,'fun_app$l'('of_nat$',X1))
          & ~ $less(0,'fun_app$l'('of_nat$',X0)) ) )
      & ( $less(0,'fun_app$l'('of_nat$',X1))
        | $less(0,'fun_app$l'('of_nat$',X0))
        | ~ $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))) ) ),
    inference(flattening,[],[f1423]) ).

tff(f1423,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
        | ( ~ $less(0,'fun_app$l'('of_nat$',X1))
          & ~ $less(0,'fun_app$l'('of_nat$',X0)) ) )
      & ( $less(0,'fun_app$l'('of_nat$',X1))
        | $less(0,'fun_app$l'('of_nat$',X0))
        | ~ $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1))) ) ),
    inference(nnf_transformation,[],[f626]) ).

tff(f626,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
    <=> ( $less(0,'fun_app$l'('of_nat$',X1))
        | $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom624) ).

tff(f10835,plain,
    spl230_741,
    inference(avatar_split_clause,[],[f2039,f10833]) ).

tff(f10833,plain,
    ( spl230_741
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_741])]) ).

tff(f2039,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    inference(cnf_transformation,[],[f178]) ).

tff(f178,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom176) ).

tff(f10831,plain,
    spl230_740,
    inference(avatar_split_clause,[],[f2038,f10829]) ).

tff(f10829,plain,
    ( spl230_740
  <=> ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','splice$a'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$v'('size$b',X0)),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_740])]) ).

tff(f2038,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','splice$a'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$v'('size$b',X0)),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ),
    inference(cnf_transformation,[],[f177]) ).

tff(f177,axiom,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','splice$a'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$v'('size$b',X0)),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom175) ).

tff(f10827,plain,
    spl230_739,
    inference(avatar_split_clause,[],[f2037,f10825]) ).

tff(f10825,plain,
    ( spl230_739
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','splice$'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$u'('size$a',X0)),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_739])]) ).

tff(f2037,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','splice$'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$u'('size$a',X0)),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','splice$'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$u'('size$a',X0)),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom174) ).

tff(f10821,plain,
    ( spl230_738
    | ~ spl230_84
    | ~ spl230_88 ),
    inference(avatar_split_clause,[],[f4136,f3895,f3877,f10818]) ).

tff(f10712,plain,
    ( spl230_737
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_732 ),
    inference(avatar_split_clause,[],[f10470,f10467,f3895,f3877,f10710]) ).

tff(f10710,plain,
    ( spl230_737
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK78(X0)))))
        | 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_737])]) ).

tff(f10467,plain,
    ( spl230_732
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK78(X0)))))
        | 'fun_app$c'(X0,X1)
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_732])]) ).

tff(f10470,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK78(X0)))))
        | 'fun_app$c'(X0,X1) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_732 ),
    inference(forward_demodulation,[],[f10468,f4136]) ).

tff(f10468,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK78(X0)))))
        | 'fun_app$c'(X0,X1)
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) )
    | ~ spl230_732 ),
    inference(avatar_component_clause,[],[f10467]) ).

tff(f10708,plain,
    ( spl230_736
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_730 ),
    inference(avatar_split_clause,[],[f10461,f10458,f3895,f3877,f10706]) ).

tff(f10706,plain,
    ( spl230_736
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK77(X0)))))
        | ~ 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_736])]) ).

tff(f10458,plain,
    ( spl230_730
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK77(X0)))))
        | 'fun_app$c'(X0,'fun_app$k'('nat$',0))
        | ~ 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_730])]) ).

tff(f10461,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK77(X0)))))
        | ~ 'fun_app$c'(X0,X1) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_730 ),
    inference(forward_demodulation,[],[f10459,f4136]) ).

tff(f10459,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK77(X0)))))
        | 'fun_app$c'(X0,'fun_app$k'('nat$',0))
        | ~ 'fun_app$c'(X0,X1) )
    | ~ spl230_730 ),
    inference(avatar_component_clause,[],[f10458]) ).

tff(f10694,plain,
    ( spl230_735
    | ~ spl230_83
    | ~ spl230_86 ),
    inference(avatar_split_clause,[],[f4133,f3887,f3873,f10692]) ).

tff(f10692,plain,
    ( spl230_735
  <=> ! [X0: 'Nat$'] : ( 0 != $sum(1,'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_735])]) ).

tff(f3873,plain,
    ( spl230_83
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_83])]) ).

tff(f3887,plain,
    ( spl230_86
  <=> ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$l'('of_nat$',X0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_86])]) ).

tff(f4133,plain,
    ( ! [X0: 'Nat$'] : ( 0 != $sum(1,'fun_app$l'('of_nat$',X0)) )
    | ~ spl230_83
    | ~ spl230_86 ),
    inference(superposition,[],[f3888,f3874]) ).

tff(f3874,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl230_83 ),
    inference(avatar_component_clause,[],[f3873]) ).

tff(f3888,plain,
    ( ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$l'('of_nat$',X0),1) )
    | ~ spl230_86 ),
    inference(avatar_component_clause,[],[f3887]) ).

tff(f10478,plain,
    spl230_734,
    inference(avatar_split_clause,[],[f3457,f10476]) ).

tff(f10476,plain,
    ( spl230_734
  <=> ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'enumerate$'(X0,'fun_app$p'('append$d'(X1),X2)) = 'fun_app$bd'('append$'('enumerate$'(X0,X1)),'enumerate$'('fun_app$m'('gen_length$b'(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_734])]) ).

tff(f3457,plain,
    ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'enumerate$'(X0,'fun_app$p'('append$d'(X1),X2)) = 'fun_app$bd'('append$'('enumerate$'(X0,X1)),'enumerate$'('fun_app$m'('gen_length$b'(X0),X1),X2)) ),
    inference(forward_demodulation,[],[f3456,f1821]) ).

tff(f1821,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = X0 ),
    inference(cnf_transformation,[],[f651]) ).

tff(f651,axiom,
    ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom649) ).

tff(f3456,plain,
    ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'enumerate$'(X0,'fun_app$p'('append$d'(X1),X2)) = 'fun_app$bd'('append$'('enumerate$'(X0,X1)),'enumerate$'('fun_app$k'('nat$','fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X0),X1))),X2)) ),
    inference(forward_demodulation,[],[f2383,f2028]) ).

tff(f2028,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    inference(cnf_transformation,[],[f173]) ).

tff(f173,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom171) ).

tff(f2383,plain,
    ! [X2: 'A_iarray_list$',X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'enumerate$'(X0,'fun_app$p'('append$d'(X1),X2)) = 'fun_app$bd'('append$'('enumerate$'(X0,X1)),'enumerate$'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$m'('size$',X1)))),X2)) ),
    inference(cnf_transformation,[],[f585]) ).

tff(f585,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'enumerate$'(X0,'fun_app$p'('append$d'(X1),X2)) = 'fun_app$bd'('append$'('enumerate$'(X0,X1)),'enumerate$'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$m'('size$',X1)))),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom583) ).

tff(f10474,plain,
    spl230_733,
    inference(avatar_split_clause,[],[f3413,f10472]) ).

tff(f10472,plain,
    ( spl230_733
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ~ $less($sum(1,'fun_app$l'('of_nat$',X0)),'fun_app$l'('of_nat$',X1))
        | $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK116(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_733])]) ).

tff(f3413,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less($sum(1,'fun_app$l'('of_nat$',X0)),'fun_app$l'('of_nat$',X1))
      | $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK116(X0,X1))) ),
    inference(forward_demodulation,[],[f2291,f664]) ).

tff(f2291,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',sK116(X0,X1)))
      | ~ $less($sum('fun_app$l'('of_nat$',X0),1),'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1433]) ).

tff(f10469,plain,
    spl230_732,
    inference(avatar_split_clause,[],[f3377,f10467]) ).

tff(f3377,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK78(X0)))))
      | 'fun_app$c'(X0,X1)
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(forward_demodulation,[],[f2080,f664]) ).

tff(f2080,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X1)
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK78(X0)),1)))
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(cnf_transformation,[],[f1252]) ).

tff(f1252,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X1)
      | ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK78(X0)),1)))
        & 'fun_app$c'(X0,sK78(X0)) )
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f845,f1251]) ).

tff(f1251,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & 'fun_app$c'(X0,X2) )
     => ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK78(X0)),1)))
        & 'fun_app$c'(X0,sK78(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f845,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & 'fun_app$c'(X0,X2) )
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(flattening,[],[f844]) ).

tff(f844,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & 'fun_app$c'(X0,X2) )
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(ennf_transformation,[],[f455]) ).

tff(f455,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ! [X2: 'Nat$'] :
            ( 'fun_app$c'(X0,X2)
           => 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1))) )
        & 'fun_app$c'(X0,'fun_app$k'('nat$',0)) )
     => 'fun_app$c'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom453) ).

tff(f10465,plain,
    ( spl230_731
    | ~ spl230_19
    | ~ spl230_68 ),
    inference(avatar_split_clause,[],[f3864,f3798,f3578,f10463]) ).

tff(f10463,plain,
    ( spl230_731
  <=> ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP14('none$',X1,X0)
        | ( tlfalse = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_731])]) ).

tff(f3578,plain,
    ( spl230_19
  <=> ! [X1: 'A_iarray_iarray_bool_fun$'] : sP14('none$',X1,tltrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_19])]) ).

tff(f3798,plain,
    ( spl230_68
  <=> ! [X0: tlbool] :
        ( ( tlfalse = X0 )
        | ( tltrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_68])]) ).

tff(f3864,plain,
    ( ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP14('none$',X1,X0)
        | ( tlfalse = X0 ) )
    | ~ spl230_19
    | ~ spl230_68 ),
    inference(superposition,[],[f3579,f3799]) ).

tff(f3799,plain,
    ( ! [X0: tlbool] :
        ( ( tltrue = X0 )
        | ( tlfalse = X0 ) )
    | ~ spl230_68 ),
    inference(avatar_component_clause,[],[f3798]) ).

tff(f3579,plain,
    ( ! [X1: 'A_iarray_iarray_bool_fun$'] : sP14('none$',X1,tltrue)
    | ~ spl230_19 ),
    inference(avatar_component_clause,[],[f3578]) ).

tff(f10460,plain,
    spl230_730,
    inference(avatar_split_clause,[],[f3376,f10458]) ).

tff(f3376,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK77(X0)))))
      | 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | ~ 'fun_app$c'(X0,X1) ),
    inference(forward_demodulation,[],[f2077,f664]) ).

tff(f2077,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK77(X0)),1)))
      | ~ 'fun_app$c'(X0,X1) ),
    inference(cnf_transformation,[],[f1250]) ).

tff(f1250,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | ( ~ 'fun_app$c'(X0,sK77(X0))
        & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK77(X0)),1))) )
      | ~ 'fun_app$c'(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f843,f1249]) ).

tff(f1249,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1))) )
     => ( ~ 'fun_app$c'(X0,sK77(X0))
        & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK77(X0)),1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f843,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1))) )
      | ~ 'fun_app$c'(X0,X1) ),
    inference(flattening,[],[f842]) ).

tff(f842,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1))) )
      | ~ 'fun_app$c'(X0,X1) ),
    inference(ennf_transformation,[],[f453]) ).

tff(f453,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ! [X2: 'Nat$'] :
            ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
           => 'fun_app$c'(X0,X2) )
        & 'fun_app$c'(X0,X1) )
     => 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom451) ).

tff(f10379,plain,
    ( spl230_729
    | ~ spl230_88
    | ~ spl230_675
    | ~ spl230_728 ),
    inference(avatar_split_clause,[],[f10375,f10372,f9453,f3895,f10377]) ).

tff(f10377,plain,
    ( spl230_729
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,'cons$'(X1,'nil$')))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_729])]) ).

tff(f9453,plain,
    ( spl230_675
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_675])]) ).

tff(f10372,plain,
    ( spl230_728
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),'cons$'(X1,'nil$')))) = $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_728])]) ).

tff(f10375,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,'cons$'(X1,'nil$')))) )
    | ~ spl230_88
    | ~ spl230_675
    | ~ spl230_728 ),
    inference(forward_demodulation,[],[f10373,f9934]) ).

tff(f9934,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$m'('size$','splice$b'(X0,X1)) = 'fun_app$m'('size$','fun_app$p'('append$d'(X0),X1)) )
    | ~ spl230_88
    | ~ spl230_675 ),
    inference(forward_demodulation,[],[f9892,f3896]) ).

tff(f9892,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$m'('size$','fun_app$p'('append$d'(X0),X1)) = 'fun_app$k'('nat$','fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1)))) )
    | ~ spl230_88
    | ~ spl230_675 ),
    inference(superposition,[],[f3896,f9454]) ).

tff(f9454,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),X1))) )
    | ~ spl230_675 ),
    inference(avatar_component_clause,[],[f9453]) ).

tff(f10373,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),'cons$'(X1,'nil$')))) = $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) )
    | ~ spl230_728 ),
    inference(avatar_component_clause,[],[f10372]) ).

tff(f10374,plain,
    spl230_728,
    inference(avatar_split_clause,[],[f3365,f10372]) ).

tff(f3365,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),'cons$'(X1,'nil$')))) = $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) ),
    inference(forward_demodulation,[],[f2034,f664]) ).

tff(f2034,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),'cons$'(X1,'nil$')))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),1) ),
    inference(cnf_transformation,[],[f583]) ).

tff(f583,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),'cons$'(X1,'nil$')))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom581) ).

tff(f10295,plain,
    ( spl230_727
    | ~ spl230_427
    | ~ spl230_726 ),
    inference(avatar_split_clause,[],[f10291,f10288,f6460,f10293]) ).

tff(f10288,plain,
    ( spl230_726
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_726])]) ).

tff(f10291,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK37('gauss_Jordan_iarrays_PA$'(X0)))))) )
    | ~ spl230_427
    | ~ spl230_726 ),
    inference(forward_demodulation,[],[f10289,f6461]) ).

tff(f10289,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)))))) )
    | ~ spl230_726 ),
    inference(avatar_component_clause,[],[f10288]) ).

tff(f10290,plain,
    spl230_726,
    inference(avatar_split_clause,[],[f2940,f10288]) ).

tff(f2940,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)))))) ),
    inference(definition_unfolding,[],[f1857,f1817]) ).

tff(f1857,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'(X0))))) ),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,axiom,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'(X0))))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom27) ).

tff(f10286,plain,
    spl230_725,
    inference(avatar_split_clause,[],[f2881,f10284]) ).

tff(f10284,plain,
    ( spl230_725
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( ( X0 = X2 )
        | 'member$f'('pair$a'(X0,X2),X4)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_725])]) ).

tff(f2881,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( X0 = X2 )
      | 'member$f'('pair$a'(X0,X2),X4)
      | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4)) ),
    inference(cnf_transformation,[],[f1729]) ).

tff(f10282,plain,
    spl230_724,
    inference(avatar_split_clause,[],[f2852,f10280]) ).

tff(f10280,plain,
    ( spl230_724
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( ( X0 = X2 )
        | 'member$'('pair$b'(X0,X2),X4)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_724])]) ).

tff(f2852,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( X0 = X2 )
      | 'member$'('pair$b'(X0,X2),X4)
      | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4)) ),
    inference(cnf_transformation,[],[f1715]) ).

tff(f10278,plain,
    spl230_723,
    inference(avatar_split_clause,[],[f2824,f10276]) ).

tff(f10276,plain,
    ( spl230_723
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( ( X0 = X2 )
        | 'member$g'('pair$c'(X0,X2),X4)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_723])]) ).

tff(f2824,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( ( X0 = X2 )
      | 'member$g'('pair$c'(X0,X2),X4)
      | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4)) ),
    inference(cnf_transformation,[],[f1701]) ).

tff(f10266,plain,
    spl230_722,
    inference(avatar_split_clause,[],[f2820,f10264]) ).

tff(f10264,plain,
    ( spl230_722
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( ( X0 = X2 )
        | 'member$e'('pair$'(X0,X2),X4)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_722])]) ).

tff(f2820,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( X0 = X2 )
      | 'member$e'('pair$'(X0,X2),X4)
      | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4)) ),
    inference(cnf_transformation,[],[f1699]) ).

tff(f10262,plain,
    spl230_721,
    inference(avatar_split_clause,[],[f2813,f10260]) ).

tff(f10260,plain,
    ( spl230_721
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( ( X3 = X4 )
        | ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X2)) )
        | ~ sP23(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_721])]) ).

tff(f2813,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( ( X3 = X4 )
      | ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X2)) )
      | ~ sP23(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f10258,plain,
    spl230_720,
    inference(avatar_split_clause,[],[f2805,f10256]) ).

tff(f10256,plain,
    ( spl230_720
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( ( X3 = X4 )
        | ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X2)) )
        | ~ sP22(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_720])]) ).

tff(f2805,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( ( X3 = X4 )
      | ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X2)) )
      | ~ sP22(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f10254,plain,
    spl230_719,
    inference(avatar_split_clause,[],[f2637,f10252]) ).

tff(f10252,plain,
    ( spl230_719
  <=> ! [X0: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),sK192(X0,X1,X2,X3)) = X3 )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_719])]) ).

tff(f2637,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),sK192(X0,X1,X2,X3)) = X3 )
      | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1609]) ).

tff(f10250,plain,
    spl230_718,
    inference(avatar_split_clause,[],[f2633,f10248]) ).

tff(f10248,plain,
    ( spl230_718
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X2),sK190(X0,X1,X2,X3)) = X1 )
        | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_718])]) ).

tff(f2633,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X2),sK190(X0,X1,X2,X3)) = X1 )
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f10246,plain,
    spl230_717,
    inference(avatar_split_clause,[],[f2467,f10244]) ).

tff(f10244,plain,
    ( spl230_717
  <=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
        ( 'fun_app$c'(X2,X0)
        | sP9(X2,X1)
        | ~ 'fun_app$c'(X2,sK159(X1,X2))
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_717])]) ).

tff(f2467,plain,
    ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
      ( 'fun_app$c'(X2,X0)
      | sP9(X2,X1)
      | ~ 'fun_app$c'(X2,sK159(X1,X2))
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1526]) ).

tff(f1526,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X2,X0)
      | sP9(X2,X1)
      | ( ~ 'fun_app$c'(X2,sK159(X1,X2))
        & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',sK159(X1,X2)),1) ) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK159])],[f1524,f1525]) ).

tff(f1525,plain,
    ! [X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X3),1) ) )
     => ( ~ 'fun_app$c'(X2,sK159(X1,X2))
        & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',sK159(X1,X2)),1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1524,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X2,X0)
      | sP9(X2,X1)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X3),1) ) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(rectify,[],[f1096]) ).

tff(f1096,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X2,X0)
      | sP9(X2,X1)
      | ? [X4: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X4)
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X4),1) ) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(definition_folding,[],[f936,f1095]) ).

tff(f1095,plain,
    ! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
      | ~ sP9(X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

tff(f936,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X2,X0)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
      | ? [X4: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X4)
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X4),1) ) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(flattening,[],[f935]) ).

tff(f935,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X2,X0)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
      | ? [X4: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X4)
          & ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X4),1) ) )
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(ennf_transformation,[],[f751]) ).

tff(f751,plain,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( ( ! [X3: 'Nat$'] :
            ( ( 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
           => 'fun_app$c'(X2,X3) )
        & ! [X4: 'Nat$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X4),1) )
           => 'fun_app$c'(X2,X4) )
        & $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) )
     => 'fun_app$c'(X2,X0) ),
    inference(rectify,[],[f644]) ).

tff(f644,axiom,
    ! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
      ( ( ! [X3: 'Nat$'] :
            ( ( 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
              & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
           => 'fun_app$c'(X2,X3) )
        & ! [X3: 'Nat$'] :
            ( ( 'fun_app$l'('of_nat$',X1) = $sum('fun_app$l'('of_nat$',X3),1) )
           => 'fun_app$c'(X2,X3) )
        & $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) )
     => 'fun_app$c'(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom642) ).

tff(f10242,plain,
    spl230_716,
    inference(avatar_split_clause,[],[f2375,f10240]) ).

tff(f10240,plain,
    ( spl230_716
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('append$d'(X1),X2)) = 'fun_app$p'('append$d'('fun_app$p'('filter$'(X0),X1)),'fun_app$p'('filter$'(X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_716])]) ).

tff(f2375,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('append$d'(X1),X2)) = 'fun_app$p'('append$d'('fun_app$p'('filter$'(X0),X1)),'fun_app$p'('filter$'(X0),X2)) ),
    inference(cnf_transformation,[],[f579]) ).

tff(f579,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('append$d'(X1),X2)) = 'fun_app$p'('append$d'('fun_app$p'('filter$'(X0),X1)),'fun_app$p'('filter$'(X0),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom577) ).

tff(f10238,plain,
    spl230_715,
    inference(avatar_split_clause,[],[f2374,f10236]) ).

tff(f10236,plain,
    ( spl230_715
  <=> ! [X2: 'Nat_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'nths$'('fun_app$p'('append$d'(X0),X1),X2) = 'fun_app$p'('append$d'('nths$'(X0,X2)),'nths$'(X1,'collect$c'('uut$'(X0,X2)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_715])]) ).

tff(f2374,plain,
    ! [X2: 'Nat_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'nths$'('fun_app$p'('append$d'(X0),X1),X2) = 'fun_app$p'('append$d'('nths$'(X0,X2)),'nths$'(X1,'collect$c'('uut$'(X0,X2)))) ),
    inference(cnf_transformation,[],[f593]) ).

tff(f593,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'Nat_set$'] : ( 'nths$'('fun_app$p'('append$d'(X0),X1),X2) = 'fun_app$p'('append$d'('nths$'(X0,X2)),'nths$'(X1,'collect$c'('uut$'(X0,X2)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom591) ).

tff(f10234,plain,
    spl230_714,
    inference(avatar_split_clause,[],[f2294,f10232]) ).

tff(f10232,plain,
    ( spl230_714
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( $sum('fun_app$l'('of_nat$',X0),1) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_714])]) ).

tff(f2294,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),1) = $sum('fun_app$l'('of_nat$',X1),1) )
      | ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$',X1) ) ),
    inference(cnf_transformation,[],[f1434]) ).

tff(f1434,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( $sum('fun_app$l'('of_nat$',X0),1) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ( 'fun_app$l'('of_nat$',X0) != 'fun_app$l'('of_nat$',X1) ) )
      & ( ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$',X1) )
        | ( $sum('fun_app$l'('of_nat$',X0),1) != $sum('fun_app$l'('of_nat$',X1),1) ) ) ),
    inference(nnf_transformation,[],[f444]) ).

tff(f444,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),1) = $sum('fun_app$l'('of_nat$',X1),1) )
    <=> ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$',X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom442) ).

tff(f10209,plain,
    ( spl230_713
    | ~ spl230_411
    | ~ spl230_620 ),
    inference(avatar_split_clause,[],[f9148,f8407,f5981,f10207]) ).

tff(f10207,plain,
    ( spl230_713
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( sP7(X0,X1)
        | ~ 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_713])]) ).

tff(f5981,plain,
    ( spl230_411
  <=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_411])]) ).

tff(f8407,plain,
    ( spl230_620
  <=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ $less('fun_app$l'('of_nat$',X2),$sum(1,'fun_app$l'('of_nat$',X1)))
        | sP7(X0,X1)
        | ~ 'fun_app$c'(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_620])]) ).

tff(f9148,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( sP7(X0,X1)
        | ~ 'fun_app$c'(X0,X1) )
    | ~ spl230_411
    | ~ spl230_620 ),
    inference(resolution,[],[f8408,f5982]) ).

tff(f5982,plain,
    ( ! [X0: $int] : $less(X0,$sum(1,X0))
    | ~ spl230_411 ),
    inference(avatar_component_clause,[],[f5981]) ).

tff(f8408,plain,
    ( ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ $less('fun_app$l'('of_nat$',X2),$sum(1,'fun_app$l'('of_nat$',X1)))
        | sP7(X0,X1)
        | ~ 'fun_app$c'(X0,X2) )
    | ~ spl230_620 ),
    inference(avatar_component_clause,[],[f8407]) ).

tff(f10149,plain,
    ( spl230_712
    | ~ spl230_411
    | ~ spl230_619 ),
    inference(avatar_split_clause,[],[f9066,f8403,f5981,f10147]) ).

tff(f10147,plain,
    ( spl230_712
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,X1)
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_712])]) ).

tff(f8403,plain,
    ( spl230_619
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
        ( ~ $less('fun_app$l'('of_nat$',X3),$sum(1,'fun_app$l'('of_nat$',X1)))
        | 'fun_app$c'(X0,X3)
        | ~ sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_619])]) ).

tff(f9066,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,X1)
        | ~ sP6(X0,X1) )
    | ~ spl230_411
    | ~ spl230_619 ),
    inference(resolution,[],[f8404,f5982]) ).

tff(f8404,plain,
    ( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ $less('fun_app$l'('of_nat$',X3),$sum(1,'fun_app$l'('of_nat$',X1)))
        | 'fun_app$c'(X0,X3)
        | ~ sP6(X0,X1) )
    | ~ spl230_619 ),
    inference(avatar_component_clause,[],[f8403]) ).

tff(f10140,plain,
    ( spl230_711
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_687 ),
    inference(avatar_split_clause,[],[f10031,f10028,f3895,f3877,f10138]) ).

tff(f10138,plain,
    ( spl230_711
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0))
        | ~ sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_711])]) ).

tff(f10028,plain,
    ( spl230_687
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_687])]) ).

tff(f10031,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0))
        | ~ sP7(X1,X0) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_687 ),
    inference(forward_demodulation,[],[f10029,f4136]) ).

tff(f10029,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0))
        | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP7(X1,X0) )
    | ~ spl230_687 ),
    inference(avatar_component_clause,[],[f10028]) ).

tff(f10136,plain,
    ( spl230_710
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_686 ),
    inference(avatar_split_clause,[],[f10026,f10023,f3895,f3877,f10134]) ).

tff(f10134,plain,
    ( spl230_710
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | sP6(X1,X0)
        | $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_710])]) ).

tff(f10023,plain,
    ( spl230_686
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( sP6(X1,X0)
        | $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0))
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_686])]) ).

tff(f10026,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | sP6(X1,X0)
        | $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0)) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_686 ),
    inference(forward_demodulation,[],[f10024,f4136]) ).

tff(f10024,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( sP6(X1,X0)
        | $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0))
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
    | ~ spl230_686 ),
    inference(avatar_component_clause,[],[f10023]) ).

tff(f10132,plain,
    ( spl230_709
    | ~ spl230_345
    | ~ spl230_685 ),
    inference(avatar_split_clause,[],[f10021,f10018,f5678,f10130]) ).

tff(f10130,plain,
    ( spl230_709
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),'matrix_matrix_mult$'(X0,sK108(X0,X1))) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_709])]) ).

tff(f5678,plain,
    ( spl230_345
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_345])]) ).

tff(f10018,plain,
    ( spl230_685
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),X0),sK108(X0,X1)) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_685])]) ).

tff(f10021,plain,
    ( ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),'matrix_matrix_mult$'(X0,sK108(X0,X1))) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) )
    | ~ spl230_345
    | ~ spl230_685 ),
    inference(forward_demodulation,[],[f10019,f5679]) ).

tff(f5679,plain,
    ( ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$'(X0,X1),X2) )
    | ~ spl230_345 ),
    inference(avatar_component_clause,[],[f5678]) ).

tff(f10019,plain,
    ( ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),X0),sK108(X0,X1)) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) )
    | ~ spl230_685 ),
    inference(avatar_component_clause,[],[f10018]) ).

tff(f10128,plain,
    ( spl230_708
    | ~ spl230_345
    | ~ spl230_684 ),
    inference(avatar_split_clause,[],[f10016,f10013,f5678,f10126]) ).

tff(f10126,plain,
    ( spl230_708
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),'matrix_matrix_mult$'(X0,sK106(X0,X1))) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_708])]) ).

tff(f10013,plain,
    ( spl230_684
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),X0),sK106(X0,X1)) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_684])]) ).

tff(f10016,plain,
    ( ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),'matrix_matrix_mult$'(X0,sK106(X0,X1))) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) )
    | ~ spl230_345
    | ~ spl230_684 ),
    inference(forward_demodulation,[],[f10014,f5679]) ).

tff(f10014,plain,
    ( ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),X0),sK106(X0,X1)) = X1 )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) )
    | ~ spl230_684 ),
    inference(avatar_component_clause,[],[f10013]) ).

tff(f10117,plain,
    spl230_707,
    inference(avatar_split_clause,[],[f2887,f10115]) ).

tff(f10115,plain,
    ( spl230_707
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
        | 'member$f'('pair$a'(X4,X3),X0)
        | ~ sP30(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_707])]) ).

tff(f2887,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
      | 'member$f'('pair$a'(X4,X3),X0)
      | ~ sP30(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f1732,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray$'] :
      ( ( sP30(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
            | ( X3 != X4 ) )
          & ( ( X1 != X2 )
            | ~ 'member$f'('pair$a'(X4,X3),X0) ) ) )
      & ( ( 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
          & ( X3 = X4 ) )
        | ( ( X1 = X2 )
          & 'member$f'('pair$a'(X4,X3),X0) )
        | ~ sP30(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1731]) ).

tff(f1731,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP30(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$f'('pair$a'(X0,X2),X4) ) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$f'('pair$a'(X0,X2),X4) )
        | ~ sP30(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1730]) ).

tff(f1730,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP30(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$f'('pair$a'(X0,X2),X4) ) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$f'('pair$a'(X0,X2),X4) )
        | ~ sP30(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1137]) ).

tff(f1137,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( sP30(X4,X3,X1,X2,X0)
    <=> ( ( 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$f'('pair$a'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).

tff(f10113,plain,
    spl230_706,
    inference(avatar_split_clause,[],[f2875,f10111]) ).

tff(f10111,plain,
    ( spl230_706
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X2,X1),'lex$d'(X0))
        | 'member$f'('pair$a'(X4,X3),X0)
        | ~ sP29(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_706])]) ).

tff(f2875,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( 'member$'('pair$b'(X2,X1),'lex$d'(X0))
      | 'member$f'('pair$a'(X4,X3),X0)
      | ~ sP29(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1726]) ).

tff(f10109,plain,
    spl230_705,
    inference(avatar_split_clause,[],[f2868,f10107]) ).

tff(f10107,plain,
    ( spl230_705
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP28(X0,X1,X2,X3,X4)
        | ~ $less('fun_app$l'('of_nat$','fun_app$m'('size$',X2)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_705])]) ).

tff(f2868,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP28(X0,X1,X2,X3,X4)
      | ~ $less('fun_app$l'('of_nat$','fun_app$m'('size$',X2)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    inference(cnf_transformation,[],[f1722]) ).

tff(f1722,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray$'] :
      ( ( sP28(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$'('pair$b'(X2,X1),'lenlex$'(X0))
            | ( X3 != X4 ) )
          & ( ~ 'member$f'('pair$a'(X4,X3),X0)
            | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) ) )
          & ~ $less('fun_app$l'('of_nat$','fun_app$m'('size$',X2)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ) )
      & ( ( 'member$'('pair$b'(X2,X1),'lenlex$'(X0))
          & ( X3 = X4 ) )
        | ( 'member$f'('pair$a'(X4,X3),X0)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) ) )
        | $less('fun_app$l'('of_nat$','fun_app$m'('size$',X2)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1)))
        | ~ sP28(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1721]) ).

tff(f1721,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP28(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
            | ( X0 != X2 ) )
          & ( ~ 'member$f'('pair$a'(X0,X2),X4)
            | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
          & ~ $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3))) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
          & ( X0 = X2 ) )
        | ( 'member$f'('pair$a'(X0,X2),X4)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
        | $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3)))
        | ~ sP28(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1720]) ).

tff(f1720,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( ( sP28(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
            | ( X0 != X2 ) )
          & ( ~ 'member$f'('pair$a'(X0,X2),X4)
            | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
          & ~ $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3))) ) )
      & ( ( 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
          & ( X0 = X2 ) )
        | ( 'member$f'('pair$a'(X0,X2),X4)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
        | $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3)))
        | ~ sP28(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1133]) ).

tff(f1133,plain,
    ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray$',X0: 'A_iarray$'] :
      ( sP28(X4,X3,X1,X2,X0)
    <=> ( ( 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
          & ( X0 = X2 ) )
        | ( 'member$f'('pair$a'(X0,X2),X4)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
        | $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3))) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).

tff(f10104,plain,
    ( spl230_704
    | ~ spl230_96
    | ~ spl230_167 ),
    inference(avatar_split_clause,[],[f4359,f4318,f3928,f10101]) ).

tff(f10101,plain,
    ( spl230_704
  <=> ( 'zero$a' = 'pair$c'(sK40('zero$a'),0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_704])]) ).

tff(f3928,plain,
    ( spl230_96
  <=> ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK40(X0),sK41(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_96])]) ).

tff(f4318,plain,
    ( spl230_167
  <=> ( 0 = sK41('zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_167])]) ).

tff(f4359,plain,
    ( ( 'zero$a' = 'pair$c'(sK40('zero$a'),0) )
    | ~ spl230_96
    | ~ spl230_167 ),
    inference(superposition,[],[f3929,f4320]) ).

tff(f4320,plain,
    ( ( 0 = sK41('zero$a') )
    | ~ spl230_167 ),
    inference(avatar_component_clause,[],[f4318]) ).

tff(f3929,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK40(X0),sK41(X0)) = X0 )
    | ~ spl230_96 ),
    inference(avatar_component_clause,[],[f3928]) ).

tff(f10099,plain,
    spl230_703,
    inference(avatar_split_clause,[],[f2858,f10097]) ).

tff(f10097,plain,
    ( spl230_703
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
        | 'member$'('pair$b'(X4,X3),X0)
        | ~ sP27(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_703])]) ).

tff(f2858,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
      | 'member$'('pair$b'(X4,X3),X0)
      | ~ sP27(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f1718,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X4: 'A_iarray_list$'] :
      ( ( sP27(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
            | ( X3 != X4 ) )
          & ( ( X1 != X2 )
            | ~ 'member$'('pair$b'(X4,X3),X0) ) ) )
      & ( ( 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
          & ( X3 = X4 ) )
        | ( ( X1 = X2 )
          & 'member$'('pair$b'(X4,X3),X0) )
        | ~ sP27(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1717]) ).

tff(f1717,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( sP27(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$'('pair$b'(X0,X2),X4) ) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$'('pair$b'(X0,X2),X4) )
        | ~ sP27(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1716]) ).

tff(f1716,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( sP27(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$'('pair$b'(X0,X2),X4) ) ) )
      & ( ( 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$'('pair$b'(X0,X2),X4) )
        | ~ sP27(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1131]) ).

tff(f1131,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( sP27(X4,X3,X1,X2,X0)
    <=> ( ( 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$'('pair$b'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).

tff(f10095,plain,
    spl230_702,
    inference(avatar_split_clause,[],[f2846,f10093]) ).

tff(f10093,plain,
    ( spl230_702
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X2,X1),'lex$c'(X0))
        | 'member$'('pair$b'(X4,X3),X0)
        | ~ sP26(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_702])]) ).

tff(f2846,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'lex$c'(X0))
      | 'member$'('pair$b'(X4,X3),X0)
      | ~ sP26(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1712]) ).

tff(f10091,plain,
    spl230_701,
    inference(avatar_split_clause,[],[f2838,f10089]) ).

tff(f10089,plain,
    ( spl230_701
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
        | 'member$g'('pair$c'(X4,X3),X0)
        | ~ sP25(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_701])]) ).

tff(f2838,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
      | 'member$g'('pair$c'(X4,X3),X0)
      | ~ sP25(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f1708,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$',X2: 'Int_list$',X3: $int,X4: $int] :
      ( ( sP25(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
            | ( X3 != X4 ) )
          & ( ( X1 != X2 )
            | ~ 'member$g'('pair$c'(X4,X3),X0) ) ) )
      & ( ( 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
          & ( X3 = X4 ) )
        | ( ( X1 = X2 )
          & 'member$g'('pair$c'(X4,X3),X0) )
        | ~ sP25(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1707]) ).

tff(f1707,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( ( sP25(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$g'('pair$c'(X0,X2),X4) ) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$g'('pair$c'(X0,X2),X4) )
        | ~ sP25(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1706]) ).

tff(f1706,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( ( sP25(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$g'('pair$c'(X0,X2),X4) ) ) )
      & ( ( 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$g'('pair$c'(X0,X2),X4) )
        | ~ sP25(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1127]) ).

tff(f1127,plain,
    ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X1: 'Int_list$',X2: $int,X0: $int] :
      ( sP25(X4,X3,X1,X2,X0)
    <=> ( ( 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$g'('pair$c'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).

tff(f10087,plain,
    spl230_700,
    inference(avatar_split_clause,[],[f2830,f10085]) ).

tff(f10085,plain,
    ( spl230_700
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
        | 'member$e'('pair$'(X4,X3),X0)
        | ~ sP24(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_700])]) ).

tff(f2830,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
      | 'member$e'('pair$'(X4,X3),X0)
      | ~ sP24(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f1704,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
      ( ( sP24(X0,X1,X2,X3,X4)
        | ( ( ~ 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
            | ( X3 != X4 ) )
          & ( ( X1 != X2 )
            | ~ 'member$e'('pair$'(X4,X3),X0) ) ) )
      & ( ( 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
          & ( X3 = X4 ) )
        | ( ( X1 = X2 )
          & 'member$e'('pair$'(X4,X3),X0) )
        | ~ sP24(X0,X1,X2,X3,X4) ) ),
    inference(rectify,[],[f1703]) ).

tff(f1703,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( ( sP24(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$e'('pair$'(X0,X2),X4) ) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$e'('pair$'(X0,X2),X4) )
        | ~ sP24(X4,X3,X1,X2,X0) ) ),
    inference(flattening,[],[f1702]) ).

tff(f1702,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( ( sP24(X4,X3,X1,X2,X0)
        | ( ( ~ 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
            | ( X0 != X2 ) )
          & ( ( X1 != X3 )
            | ~ 'member$e'('pair$'(X0,X2),X4) ) ) )
      & ( ( 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$e'('pair$'(X0,X2),X4) )
        | ~ sP24(X4,X3,X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1125]) ).

tff(f1125,plain,
    ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] :
      ( sP24(X4,X3,X1,X2,X0)
    <=> ( ( 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$e'('pair$'(X0,X2),X4) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).

tff(f10083,plain,
    spl230_699,
    inference(avatar_split_clause,[],[f2814,f10081]) ).

tff(f10081,plain,
    ( spl230_699
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X2,X1),'lex$'(X0))
        | 'member$g'('pair$c'(X4,X3),X0)
        | ~ sP23(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_699])]) ).

tff(f2814,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( 'member$o'('pair$v'(X2,X1),'lex$'(X0))
      | 'member$g'('pair$c'(X4,X3),X0)
      | ~ sP23(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f10079,plain,
    spl230_698,
    inference(avatar_split_clause,[],[f2806,f10077]) ).

tff(f10077,plain,
    ( spl230_698
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
        | 'member$e'('pair$'(X4,X3),X0)
        | ~ sP22(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_698])]) ).

tff(f2806,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
      | 'member$e'('pair$'(X4,X3),X0)
      | ~ sP22(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f10075,plain,
    spl230_697,
    inference(avatar_split_clause,[],[f2798,f10073]) ).

tff(f10073,plain,
    ( spl230_697
  <=> ! [X4: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( 'member$q'('pair$x'(X2,X1),'lex$b'(X0))
        | 'member$r'('pair$y'(X4,X3),X0)
        | ~ sP21(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_697])]) ).

tff(f2798,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X3: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod$'] :
      ( 'member$q'('pair$x'(X2,X1),'lex$b'(X0))
      | 'member$r'('pair$y'(X4,X3),X0)
      | ~ sP21(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1688]) ).

tff(f10071,plain,
    spl230_696,
    inference(avatar_split_clause,[],[f2701,f10069]) ).

tff(f10069,plain,
    ( spl230_696
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$p'('append$d'(X3),X1) != 'fun_app$p'('append$d'(X2),X0) )
        | ~ sP15(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_696])]) ).

tff(f2701,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$p'('append$d'(X3),X1) != 'fun_app$p'('append$d'(X2),X0) )
      | ~ sP15(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1642]) ).

tff(f1642,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( ( ( ( 'fun_app$p'('append$d'(X3),X1) = 'fun_app$p'('append$d'(X2),X0) )
          | ( X0 != X1 )
          | ( X2 != X3 ) )
        & ( ( ( X0 = X1 )
            & ( X2 = X3 ) )
          | ( 'fun_app$p'('append$d'(X3),X1) != 'fun_app$p'('append$d'(X2),X0) ) ) )
      | ~ sP15(X0,X1,X2,X3) ),
    inference(rectify,[],[f1641]) ).

tff(f1641,plain,
    ! [X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( ( ( 'fun_app$p'('append$d'(X0),X2) = 'fun_app$p'('append$d'(X1),X3) )
          | ( X2 != X3 )
          | ( X0 != X1 ) )
        & ( ( ( X2 = X3 )
            & ( X0 = X1 ) )
          | ( 'fun_app$p'('append$d'(X0),X2) != 'fun_app$p'('append$d'(X1),X3) ) ) )
      | ~ sP15(X3,X2,X1,X0) ),
    inference(flattening,[],[f1640]) ).

tff(f1640,plain,
    ! [X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( ( ( 'fun_app$p'('append$d'(X0),X2) = 'fun_app$p'('append$d'(X1),X3) )
          | ( X2 != X3 )
          | ( X0 != X1 ) )
        & ( ( ( X2 = X3 )
            & ( X0 = X1 ) )
          | ( 'fun_app$p'('append$d'(X0),X2) != 'fun_app$p'('append$d'(X1),X3) ) ) )
      | ~ sP15(X3,X2,X1,X0) ),
    inference(nnf_transformation,[],[f1107]) ).

tff(f1107,plain,
    ! [X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$',X0: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X0),X2) = 'fun_app$p'('append$d'(X1),X3) )
      <=> ( ( X2 = X3 )
          & ( X0 = X1 ) ) )
      | ~ sP15(X3,X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

tff(f10067,plain,
    spl230_695,
    inference(avatar_split_clause,[],[f2700,f10065]) ).

tff(f10065,plain,
    ( spl230_695
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X2 = X3 )
        | ( 'fun_app$p'('append$d'(X3),X1) != 'fun_app$p'('append$d'(X2),X0) )
        | ~ sP15(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_695])]) ).

tff(f2700,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X2 = X3 )
      | ( 'fun_app$p'('append$d'(X3),X1) != 'fun_app$p'('append$d'(X2),X0) )
      | ~ sP15(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1642]) ).

tff(f10063,plain,
    spl230_694,
    inference(avatar_split_clause,[],[f2560,f10061]) ).

tff(f10061,plain,
    ( spl230_694
  <=> ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_694])]) ).

tff(f2560,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ),
    inference(cnf_transformation,[],[f1586]) ).

tff(f1586,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'(X0,X1),'lex$d'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | ~ 'member$'('pair$b'(X0,X1),'lexord$c'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
          & 'member$'('pair$b'(X0,X1),'lexord$c'(X2)) )
        | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ) ),
    inference(flattening,[],[f1585]) ).

tff(f1585,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'(X0,X1),'lex$d'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | ~ 'member$'('pair$b'(X0,X1),'lexord$c'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
          & 'member$'('pair$b'(X0,X1),'lexord$c'(X2)) )
        | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ) ),
    inference(nnf_transformation,[],[f542]) ).

tff(f542,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'(X0,X1),'lex$d'(X2))
    <=> ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        & 'member$'('pair$b'(X0,X1),'lexord$c'(X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom540) ).

tff(f10055,plain,
    spl230_693,
    inference(avatar_split_clause,[],[f2555,f10053]) ).

tff(f10053,plain,
    ( spl230_693
  <=> ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_693])]) ).

tff(f2555,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
      | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ),
    inference(cnf_transformation,[],[f1583]) ).

tff(f1583,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'(X0,X1),'lex$c'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        | ~ 'member$s'('pair$z'(X0,X1),'lexord$b'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
          & 'member$s'('pair$z'(X0,X1),'lexord$b'(X2)) )
        | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ) ),
    inference(flattening,[],[f1582]) ).

tff(f1582,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'(X0,X1),'lex$c'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) != 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        | ~ 'member$s'('pair$z'(X0,X1),'lexord$b'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
          & 'member$s'('pair$z'(X0,X1),'lexord$b'(X2)) )
        | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ) ),
    inference(nnf_transformation,[],[f541]) ).

tff(f541,axiom,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'(X0,X1),'lex$c'(X2))
    <=> ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        & 'member$s'('pair$z'(X0,X1),'lexord$b'(X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom539) ).

tff(f10051,plain,
    spl230_692,
    inference(avatar_split_clause,[],[f2546,f10049]) ).

tff(f10049,plain,
    ( spl230_692
  <=> ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
        | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_692])]) ).

tff(f2546,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
      | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ),
    inference(cnf_transformation,[],[f1578]) ).

tff(f1578,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( ( 'member$q'('pair$x'(X0,X1),'lex$b'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
        | ~ 'member$q'('pair$x'(X0,X1),'lexord$d'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
          & 'member$q'('pair$x'(X0,X1),'lexord$d'(X2)) )
        | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ) ),
    inference(flattening,[],[f1577]) ).

tff(f1577,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( ( 'member$q'('pair$x'(X0,X1),'lex$b'(X2))
        | ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) != 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
        | ~ 'member$q'('pair$x'(X0,X1),'lexord$d'(X2)) )
      & ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
          & 'member$q'('pair$x'(X0,X1),'lexord$d'(X2)) )
        | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ) ),
    inference(nnf_transformation,[],[f540]) ).

tff(f540,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( 'member$q'('pair$x'(X0,X1),'lex$b'(X2))
    <=> ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
        & 'member$q'('pair$x'(X0,X1),'lexord$d'(X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom538) ).

tff(f10047,plain,
    spl230_691,
    inference(avatar_split_clause,[],[f2447,f10045]) ).

tff(f10045,plain,
    ( spl230_691
  <=> ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
        ( ( 'fun_app$ad'('plus$e'(sK148(X0,X1,X2)),sK149(X0,X1,X2)) = X0 )
        | ~ 'member$a'(X0,'plus$f'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_691])]) ).

tff(f2447,plain,
    ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
      ( ( 'fun_app$ad'('plus$e'(sK148(X0,X1,X2)),sK149(X0,X1,X2)) = X0 )
      | ~ 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(cnf_transformation,[],[f1508]) ).

tff(f1508,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray_set$'] :
      ( ( 'member$a'(sK149(X0,X1,X2),X2)
        & 'member$a'(sK148(X0,X1,X2),X1)
        & ( 'fun_app$ad'('plus$e'(sK148(X0,X1,X2)),sK149(X0,X1,X2)) = X0 ) )
      | ~ 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK148,sK149])],[f928,f1507]) ).

tff(f1507,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray_set$'] :
      ( ? [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( 'member$a'(X4,X2)
          & 'member$a'(X3,X1)
          & ( 'fun_app$ad'('plus$e'(X3),X4) = X0 ) )
     => ( 'member$a'(sK149(X0,X1,X2),X2)
        & 'member$a'(sK148(X0,X1,X2),X1)
        & ( 'fun_app$ad'('plus$e'(sK148(X0,X1,X2)),sK149(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f928,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray_set$'] :
      ( ? [X3: 'A_iarray$',X4: 'A_iarray$'] :
          ( 'member$a'(X4,X2)
          & 'member$a'(X3,X1)
          & ( 'fun_app$ad'('plus$e'(X3),X4) = X0 ) )
      | ~ 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(ennf_transformation,[],[f747]) ).

tff(f747,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray_set$'] :
      ~ ( ! [X3: 'A_iarray$',X4: 'A_iarray$'] :
            ~ ( 'member$a'(X4,X2)
              & 'member$a'(X3,X1)
              & ( 'fun_app$ad'('plus$e'(X3),X4) = X0 ) )
        & 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f161]) ).

tff(f161,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray_set$'] :
      ( ( ! [X3: 'A_iarray$',X4: 'A_iarray$'] :
            ( ( 'member$a'(X4,X2)
              & 'member$a'(X3,X1)
              & ( 'fun_app$ad'('plus$e'(X3),X4) = X0 ) )
           => $false )
        & 'member$a'(X0,'plus$f'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom159) ).

tff(f10043,plain,
    spl230_690,
    inference(avatar_split_clause,[],[f2406,f10041]) ).

tff(f10041,plain,
    ( spl230_690
  <=> ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_690])]) ).

tff(f2406,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ),
    inference(cnf_transformation,[],[f899]) ).

tff(f899,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
      | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ),
    inference(ennf_transformation,[],[f519]) ).

tff(f519,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'(X0,X1),'listrel1$c'(X2))
     => ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom517) ).

tff(f10039,plain,
    spl230_689,
    inference(avatar_split_clause,[],[f2405,f10037]) ).

tff(f10037,plain,
    ( spl230_689
  <=> ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        | ~ 'member$s'('pair$z'(X0,X1),'listrel1$b'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_689])]) ).

tff(f2405,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
      | ~ 'member$s'('pair$z'(X0,X1),'listrel1$b'(X2)) ),
    inference(cnf_transformation,[],[f898]) ).

tff(f898,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
      | ~ 'member$s'('pair$z'(X0,X1),'listrel1$b'(X2)) ),
    inference(ennf_transformation,[],[f518]) ).

tff(f518,axiom,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'(X0,X1),'listrel1$b'(X2))
     => ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom516) ).

tff(f10035,plain,
    spl230_688,
    inference(avatar_split_clause,[],[f2404,f10033]) ).

tff(f10033,plain,
    ( spl230_688
  <=> ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
        | ~ 'member$q'('pair$x'(X0,X1),'listrel1$d'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_688])]) ).

tff(f2404,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
      | ~ 'member$q'('pair$x'(X0,X1),'listrel1$d'(X2)) ),
    inference(cnf_transformation,[],[f897]) ).

tff(f897,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) )
      | ~ 'member$q'('pair$x'(X0,X1),'listrel1$d'(X2)) ),
    inference(ennf_transformation,[],[f517]) ).

tff(f517,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( 'member$q'('pair$x'(X0,X1),'listrel1$d'(X2))
     => ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom515) ).

tff(f10030,plain,
    spl230_687,
    inference(avatar_split_clause,[],[f2346,f10028]) ).

tff(f2346,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( $less('fun_app$l'('of_nat$',sK134(X0,X1)),'fun_app$l'('of_nat$',X0))
      | 'fun_app$c'(X1,'fun_app$k'('nat$',0))
      | ~ sP7(X1,X0) ),
    inference(cnf_transformation,[],[f1490]) ).

tff(f10025,plain,
    spl230_686,
    inference(avatar_split_clause,[],[f2341,f10023]) ).

tff(f2341,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP6(X1,X0)
      | $less('fun_app$l'('of_nat$',sK132(X0,X1)),'fun_app$l'('of_nat$',X0))
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ),
    inference(cnf_transformation,[],[f1481]) ).

tff(f10020,plain,
    spl230_685,
    inference(avatar_split_clause,[],[f2229,f10018]) ).

tff(f2229,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),X0),sK108(X0,X1)) = X1 )
      | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ),
    inference(cnf_transformation,[],[f1380]) ).

tff(f1380,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) != X1 )
            | ~ 'fun_app$o'('invertible$',X3)
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),X0),sK108(X0,X1)) = X1 )
          & 'fun_app$o'('invertible$',sK108(X0,X1))
          & 'fun_app$o'('invertible$',sK107(X0,X1)) )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK107,sK108])],[f1378,f1379]) ).

tff(f1379,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ? [X4: 'A_n_vec_n_vec$',X5: 'A_n_vec_n_vec$'] :
          ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X4),X0),X5) = X1 )
          & 'fun_app$o'('invertible$',X5)
          & 'fun_app$o'('invertible$',X4) )
     => ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK107(X0,X1)),X0),sK108(X0,X1)) = X1 )
        & 'fun_app$o'('invertible$',sK108(X0,X1))
        & 'fun_app$o'('invertible$',sK107(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1378,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) != X1 )
            | ~ 'fun_app$o'('invertible$',X3)
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ? [X4: 'A_n_vec_n_vec$',X5: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X4),X0),X5) = X1 )
            & 'fun_app$o'('invertible$',X5)
            & 'fun_app$o'('invertible$',X4) )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    inference(rectify,[],[f1377]) ).

tff(f1377,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) != X1 )
            | ~ 'fun_app$o'('invertible$',X3)
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ? [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) = X1 )
            & 'fun_app$o'('invertible$',X3)
            & 'fun_app$o'('invertible$',X2) )
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    inference(nnf_transformation,[],[f293]) ).

tff(f293,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1)
    <=> ? [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
          ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) = X1 )
          & 'fun_app$o'('invertible$',X3)
          & 'fun_app$o'('invertible$',X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom291) ).

tff(f10015,plain,
    spl230_684,
    inference(avatar_split_clause,[],[f2225,f10013]) ).

tff(f2225,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),X0),sK106(X0,X1)) = X1 )
      | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ),
    inference(cnf_transformation,[],[f1376]) ).

tff(f1376,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) != X1 )
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),X0),sK106(X0,X1)) = X1 )
          & 'fun_app$o'('invertible$',sK106(X0,X1)) )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK106])],[f1374,f1375]) ).

tff(f1375,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] :
          ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X3),X0),X3) = X1 )
          & 'fun_app$o'('invertible$',X3) )
     => ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(sK106(X0,X1)),X0),sK106(X0,X1)) = X1 )
        & 'fun_app$o'('invertible$',sK106(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1374,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) != X1 )
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ? [X3: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X3),X0),X3) = X1 )
            & 'fun_app$o'('invertible$',X3) )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    inference(rectify,[],[f1373]) ).

tff(f1373,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1)
        | ! [X2: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) != X1 )
            | ~ 'fun_app$o'('invertible$',X2) ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] :
            ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) = X1 )
            & 'fun_app$o'('invertible$',X2) )
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    inference(nnf_transformation,[],[f294]) ).

tff(f294,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1)
    <=> ? [X2: 'A_n_vec_n_vec$'] :
          ( ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) = X1 )
          & 'fun_app$o'('invertible$',X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom292) ).

tff(f10006,plain,
    ( spl230_683
    | ~ spl230_427
    | ~ spl230_682 ),
    inference(avatar_split_clause,[],[f10002,f9998,f6460,f10004]) ).

tff(f10004,plain,
    ( spl230_683
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( ( sK37(X0) != sK37(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_683])]) ).

tff(f9998,plain,
    ( spl230_682
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$r'('snd$a',X0) != 'fun_app$r'('snd$a',X1) )
        | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_682])]) ).

tff(f10002,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( ( sK37(X0) != sK37(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) )
    | ~ spl230_427
    | ~ spl230_682 ),
    inference(forward_demodulation,[],[f10001,f6461]) ).

tff(f10001,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( ( 'fun_app$r'('snd$a',X0) != sK37(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) )
    | ~ spl230_427
    | ~ spl230_682 ),
    inference(forward_demodulation,[],[f9999,f6461]) ).

tff(f9999,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$r'('snd$a',X0) != 'fun_app$r'('snd$a',X1) )
        | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) )
    | ~ spl230_682 ),
    inference(avatar_component_clause,[],[f9998]) ).

tff(f10000,plain,
    spl230_682,
    inference(avatar_split_clause,[],[f2086,f9998]) ).

tff(f2086,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$r'('snd$a',X0) != 'fun_app$r'('snd$a',X1) )
      | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) ),
    inference(cnf_transformation,[],[f857]) ).

tff(f857,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$r'('snd$a',X0) != 'fun_app$r'('snd$a',X1) )
      | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) ),
    inference(flattening,[],[f856]) ).

tff(f856,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$r'('snd$a',X0) != 'fun_app$r'('snd$a',X1) )
      | ( 'fun_app$r'('fst$',X0) != 'fun_app$r'('fst$',X1) ) ),
    inference(ennf_transformation,[],[f270]) ).

tff(f270,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('snd$a',X0) = 'fun_app$r'('snd$a',X1) )
        & ( 'fun_app$r'('fst$',X0) = 'fun_app$r'('fst$',X1) ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom268) ).

tff(f9996,plain,
    spl230_681,
    inference(avatar_split_clause,[],[f2084,f9994]) ).

tff(f9994,plain,
    ( spl230_681
  <=> ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$ab'('snd$',X0) != 'fun_app$ab'('snd$',X1) )
        | ( 'fun_app$ab'('fst$a',X0) != 'fun_app$ab'('fst$a',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_681])]) ).

tff(f2084,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ab'('snd$',X0) != 'fun_app$ab'('snd$',X1) )
      | ( 'fun_app$ab'('fst$a',X0) != 'fun_app$ab'('fst$a',X1) ) ),
    inference(cnf_transformation,[],[f853]) ).

tff(f853,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ab'('snd$',X0) != 'fun_app$ab'('snd$',X1) )
      | ( 'fun_app$ab'('fst$a',X0) != 'fun_app$ab'('fst$a',X1) ) ),
    inference(flattening,[],[f852]) ).

tff(f852,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ab'('snd$',X0) != 'fun_app$ab'('snd$',X1) )
      | ( 'fun_app$ab'('fst$a',X0) != 'fun_app$ab'('fst$a',X1) ) ),
    inference(ennf_transformation,[],[f271]) ).

tff(f271,axiom,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('snd$',X0) = 'fun_app$ab'('snd$',X1) )
        & ( 'fun_app$ab'('fst$a',X0) = 'fun_app$ab'('fst$a',X1) ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom269) ).

tff(f9983,plain,
    ( spl230_680
    | ~ spl230_425
    | ~ spl230_679 ),
    inference(avatar_split_clause,[],[f9979,f9975,f6201,f9981]) ).

tff(f9981,plain,
    ( spl230_680
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( sK40(X0) != sK40(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_680])]) ).

tff(f9975,plain,
    ( spl230_679
  <=> ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) )
        | ( 'fun_app$ac'('fst$b',X0) != 'fun_app$ac'('fst$b',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_679])]) ).

tff(f9979,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( sK40(X0) != sK40(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) ) )
    | ~ spl230_425
    | ~ spl230_679 ),
    inference(forward_demodulation,[],[f9978,f6202]) ).

tff(f9978,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( 'fun_app$ac'('fst$b',X0) != sK40(X1) )
        | ( X0 = X1 )
        | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) ) )
    | ~ spl230_425
    | ~ spl230_679 ),
    inference(forward_demodulation,[],[f9976,f6202]) ).

tff(f9976,plain,
    ( ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
        ( ( X0 = X1 )
        | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) )
        | ( 'fun_app$ac'('fst$b',X0) != 'fun_app$ac'('fst$b',X1) ) )
    | ~ spl230_679 ),
    inference(avatar_component_clause,[],[f9975]) ).

tff(f9977,plain,
    spl230_679,
    inference(avatar_split_clause,[],[f2082,f9975]) ).

tff(f2082,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) )
      | ( 'fun_app$ac'('fst$b',X0) != 'fun_app$ac'('fst$b',X1) ) ),
    inference(cnf_transformation,[],[f849]) ).

tff(f849,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) )
      | ( 'fun_app$ac'('fst$b',X0) != 'fun_app$ac'('fst$b',X1) ) ),
    inference(flattening,[],[f848]) ).

tff(f848,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( X0 = X1 )
      | ( 'fun_app$ac'('snd$b',X0) != 'fun_app$ac'('snd$b',X1) )
      | ( 'fun_app$ac'('fst$b',X0) != 'fun_app$ac'('fst$b',X1) ) ),
    inference(ennf_transformation,[],[f272]) ).

tff(f272,axiom,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('snd$b',X0) = 'fun_app$ac'('snd$b',X1) )
        & ( 'fun_app$ac'('fst$b',X0) = 'fun_app$ac'('fst$b',X1) ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom270) ).

tff(f9868,plain,
    ( spl230_678
    | ~ spl230_345
    | ~ spl230_669 ),
    inference(avatar_split_clause,[],[f9426,f9423,f5678,f9866]) ).

tff(f9866,plain,
    ( spl230_678
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),'matrix_matrix_mult$'('matrix_inv$'(X2),'matrix_matrix_mult$'(X0,X3)))
        | ~ 'fun_app$o'('invertible$',X3)
        | ~ 'fun_app$o'('invertible$',X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_678])]) ).

tff(f9423,plain,
    ( spl230_669
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3))
        | ~ 'fun_app$o'('invertible$',X3)
        | ~ 'fun_app$o'('invertible$',X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_669])]) ).

tff(f9426,plain,
    ( ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),'matrix_matrix_mult$'('matrix_inv$'(X2),'matrix_matrix_mult$'(X0,X3)))
        | ~ 'fun_app$o'('invertible$',X3)
        | ~ 'fun_app$o'('invertible$',X2) )
    | ~ spl230_345
    | ~ spl230_669 ),
    inference(forward_demodulation,[],[f9424,f5679]) ).

tff(f9424,plain,
    ( ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3))
        | ~ 'fun_app$o'('invertible$',X3)
        | ~ 'fun_app$o'('invertible$',X2) )
    | ~ spl230_669 ),
    inference(avatar_component_clause,[],[f9423]) ).

tff(f9846,plain,
    ( spl230_677
    | ~ spl230_646 ),
    inference(avatar_split_clause,[],[f9803,f9321,f9844]) ).

tff(f9844,plain,
    ( spl230_677
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : sP15(X0,X0,X1,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_677])]) ).

tff(f9321,plain,
    ( spl230_646
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP15(X3,X2,X1,X0)
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_646])]) ).

tff(f9803,plain,
    ( ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : sP15(X0,X0,X1,X2)
    | ~ spl230_646 ),
    inference(equality_resolution,[],[f9322]) ).

tff(f9322,plain,
    ( ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
        | sP15(X3,X2,X1,X0) )
    | ~ spl230_646 ),
    inference(avatar_component_clause,[],[f9321]) ).

tff(f9826,plain,
    ( spl230_676
    | ~ spl230_645 ),
    inference(avatar_split_clause,[],[f9794,f9317,f9824]) ).

tff(f9824,plain,
    ( spl230_676
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : sP15(X0,X1,X2,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_676])]) ).

tff(f9317,plain,
    ( spl230_645
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP15(X3,X2,X1,X0)
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_645])]) ).

tff(f9794,plain,
    ( ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : sP15(X0,X1,X2,X2)
    | ~ spl230_645 ),
    inference(equality_resolution,[],[f9318]) ).

tff(f9318,plain,
    ( ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) )
        | sP15(X3,X2,X1,X0) )
    | ~ spl230_645 ),
    inference(avatar_component_clause,[],[f9317]) ).

tff(f9455,plain,
    spl230_675,
    inference(avatar_split_clause,[],[f3369,f9453]) ).

tff(f3369,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','splice$b'(X0,X1))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),X1))) ),
    inference(forward_demodulation,[],[f2043,f2039]) ).

tff(f2043,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),X1))) ),
    inference(cnf_transformation,[],[f581]) ).

tff(f581,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X0)),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('append$d'(X0),X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom579) ).

tff(f9451,plain,
    spl230_674,
    inference(avatar_split_clause,[],[f3236,f9449]) ).

tff(f9449,plain,
    ( spl230_674
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X2,X1),'cons$'(X2,X3)),'lexord$c'(X4))
        | ~ 'member$'('pair$b'(X1,X3),'lexord$c'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_674])]) ).

tff(f3236,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X2,X1),'cons$'(X2,X3)),'lexord$c'(X4))
      | ~ 'member$'('pair$b'(X1,X3),'lexord$c'(X4)) ),
    inference(equality_resolution,[],[f2884]) ).

tff(f2884,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
      | ~ 'member$'('pair$b'(X1,X3),'lexord$c'(X4))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f1729]) ).

tff(f9442,plain,
    spl230_673,
    inference(avatar_split_clause,[],[f3231,f9440]) ).

tff(f9440,plain,
    ( spl230_673
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'('cons$b'(X2,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
        | ~ 'member$s'('pair$z'(X1,X3),'lexord$b'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_673])]) ).

tff(f3231,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X2,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
      | ~ 'member$s'('pair$z'(X1,X3),'lexord$b'(X4)) ),
    inference(equality_resolution,[],[f2855]) ).

tff(f2855,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
      | ~ 'member$s'('pair$z'(X1,X3),'lexord$b'(X4))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f1715]) ).

tff(f9438,plain,
    spl230_672,
    inference(avatar_split_clause,[],[f3225,f9436]) ).

tff(f9436,plain,
    ( spl230_672
  <=> ! [X4: 'Int_int_prod_set$',X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( 'member$o'('pair$v'('cons$c'(X2,X1),'cons$c'(X2,X3)),'lexord$'(X4))
        | ~ 'member$o'('pair$v'(X1,X3),'lexord$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_672])]) ).

tff(f3225,plain,
    ! [X2: $int,X3: 'Int_list$',X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X2,X1),'cons$c'(X2,X3)),'lexord$'(X4))
      | ~ 'member$o'('pair$v'(X1,X3),'lexord$'(X4)) ),
    inference(equality_resolution,[],[f2827]) ).

tff(f2827,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
      | ~ 'member$o'('pair$v'(X1,X3),'lexord$'(X4))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f1701]) ).

tff(f9434,plain,
    spl230_671,
    inference(avatar_split_clause,[],[f3224,f9432]) ).

tff(f9432,plain,
    ( spl230_671
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'('cons$d'(X2,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
        | ~ 'member$p'('pair$w'(X1,X3),'lexord$a'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_671])]) ).

tff(f3224,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X2,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
      | ~ 'member$p'('pair$w'(X1,X3),'lexord$a'(X4)) ),
    inference(equality_resolution,[],[f2823]) ).

tff(f2823,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
      | ~ 'member$p'('pair$w'(X1,X3),'lexord$a'(X4))
      | ( X0 != X2 ) ),
    inference(cnf_transformation,[],[f1699]) ).

tff(f9430,plain,
    spl230_670,
    inference(avatar_split_clause,[],[f3168,f9428]) ).

tff(f9428,plain,
    ( spl230_670
  <=> ! [X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X3: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
        | 'member$a'(sK193(X1,X2,X3),'set$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_670])]) ).

tff(f3168,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X3),X1) = 'fun_app$p'('filter$'(X2),X1) )
      | 'member$a'(sK193(X1,X2,X3),'set$'(X1)) ),
    inference(equality_resolution,[],[f2639]) ).

tff(f2639,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_bool_fun$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X2),X0) = 'fun_app$p'('filter$'(X3),X1) )
      | 'member$a'(sK193(X1,X2,X3),'set$'(X1))
      | ( X0 != X1 ) ),
    inference(cnf_transformation,[],[f1613]) ).

tff(f9425,plain,
    spl230_669,
    inference(avatar_split_clause,[],[f3088,f9423]) ).

tff(f3088,plain,
    ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3))
      | ~ 'fun_app$o'('invertible$',X3)
      | ~ 'fun_app$o'('invertible$',X2) ),
    inference(equality_resolution,[],[f2230]) ).

tff(f2230,plain,
    ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1)
      | ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X3) != X1 )
      | ~ 'fun_app$o'('invertible$',X3)
      | ~ 'fun_app$o'('invertible$',X2) ),
    inference(cnf_transformation,[],[f1380]) ).

tff(f9421,plain,
    spl230_668,
    inference(avatar_split_clause,[],[f2892,f9419]) ).

tff(f9419,plain,
    ( spl230_668
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4))
        | ~ sP30(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_668])]) ).

tff(f2892,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4))
      | ~ sP30(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1733]) ).

tff(f1733,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4))
        | ~ sP30(X4,X3,X1,X2,X0) )
      & ( sP30(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4)) ) ),
    inference(nnf_transformation,[],[f1138]) ).

tff(f1138,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4))
    <=> sP30(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f515,f1137]) ).

tff(f515,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4))
    <=> ( ( 'member$'('pair$b'(X1,X3),'listrel1$c'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$f'('pair$a'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom513) ).

tff(f9417,plain,
    spl230_667,
    inference(avatar_split_clause,[],[f2891,f9415]) ).

tff(f9415,plain,
    ( spl230_667
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( sP30(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_667])]) ).

tff(f2891,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( sP30(X4,X3,X1,X2,X0)
      | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'listrel1$c'(X4)) ),
    inference(cnf_transformation,[],[f1733]) ).

tff(f9413,plain,
    spl230_666,
    inference(avatar_split_clause,[],[f2880,f9411]) ).

tff(f9411,plain,
    ( spl230_666
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4))
        | ~ sP29(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_666])]) ).

tff(f2880,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4))
      | ~ sP29(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1727]) ).

tff(f1727,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4))
        | ~ sP29(X4,X3,X1,X2,X0) )
      & ( sP29(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4)) ) ),
    inference(nnf_transformation,[],[f1136]) ).

tff(f1136,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4))
    <=> sP29(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f500,f1135]) ).

tff(f500,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4))
    <=> ( ( 'member$'('pair$b'(X1,X3),'lex$d'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) )
          & 'member$f'('pair$a'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom498) ).

tff(f9409,plain,
    spl230_665,
    inference(avatar_split_clause,[],[f2879,f9407]) ).

tff(f9407,plain,
    ( spl230_665
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( sP29(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_665])]) ).

tff(f2879,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( sP29(X4,X3,X1,X2,X0)
      | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lex$d'(X4)) ),
    inference(cnf_transformation,[],[f1727]) ).

tff(f9405,plain,
    spl230_664,
    inference(avatar_split_clause,[],[f2872,f9403]) ).

tff(f9403,plain,
    ( spl230_664
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4))
        | ~ sP28(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_664])]) ).

tff(f2872,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4))
      | ~ sP28(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1723]) ).

tff(f1723,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4))
        | ~ sP28(X4,X3,X1,X2,X0) )
      & ( sP28(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4)) ) ),
    inference(nnf_transformation,[],[f1134]) ).

tff(f1134,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4))
    <=> sP28(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f608,f1133]) ).

tff(f608,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4))
    <=> ( ( 'member$'('pair$b'(X1,X3),'lenlex$'(X4))
          & ( X0 = X2 ) )
        | ( 'member$f'('pair$a'(X0,X2),X4)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) ) )
        | $less('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),'fun_app$l'('of_nat$','fun_app$m'('size$',X3))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom606) ).

tff(f9396,plain,
    spl230_663,
    inference(avatar_split_clause,[],[f2871,f9394]) ).

tff(f9394,plain,
    ( spl230_663
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( sP28(X4,X3,X1,X2,X0)
        | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_663])]) ).

tff(f2871,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( sP28(X4,X3,X1,X2,X0)
      | ~ 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lenlex$'(X4)) ),
    inference(cnf_transformation,[],[f1723]) ).

tff(f9392,plain,
    spl230_662,
    inference(avatar_split_clause,[],[f2863,f9390]) ).

tff(f9390,plain,
    ( spl230_662
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4))
        | ~ sP27(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_662])]) ).

tff(f2863,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4))
      | ~ sP27(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1719]) ).

tff(f1719,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4))
        | ~ sP27(X4,X3,X1,X2,X0) )
      & ( sP27(X4,X3,X1,X2,X0)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4)) ) ),
    inference(nnf_transformation,[],[f1132]) ).

tff(f1132,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4))
    <=> sP27(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f514,f1131]) ).

tff(f514,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4))
    <=> ( ( 'member$s'('pair$z'(X1,X3),'listrel1$b'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$'('pair$b'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom512) ).

tff(f9388,plain,
    spl230_661,
    inference(avatar_split_clause,[],[f2862,f9386]) ).

tff(f9386,plain,
    ( spl230_661
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( sP27(X4,X3,X1,X2,X0)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_661])]) ).

tff(f2862,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( sP27(X4,X3,X1,X2,X0)
      | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'listrel1$b'(X4)) ),
    inference(cnf_transformation,[],[f1719]) ).

tff(f9384,plain,
    spl230_660,
    inference(avatar_split_clause,[],[f2851,f9382]) ).

tff(f9382,plain,
    ( spl230_660
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4))
        | ~ sP26(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_660])]) ).

tff(f2851,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4))
      | ~ sP26(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1713]) ).

tff(f1713,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4))
        | ~ sP26(X4,X3,X1,X2,X0) )
      & ( sP26(X4,X3,X1,X2,X0)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4)) ) ),
    inference(nnf_transformation,[],[f1130]) ).

tff(f1130,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4))
    <=> sP26(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f499,f1129]) ).

tff(f499,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4))
    <=> ( ( 'member$s'('pair$z'(X1,X3),'lex$c'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X3)) )
          & 'member$'('pair$b'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom497) ).

tff(f9380,plain,
    spl230_659,
    inference(avatar_split_clause,[],[f2850,f9378]) ).

tff(f9378,plain,
    ( spl230_659
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( sP26(X4,X3,X1,X2,X0)
        | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_659])]) ).

tff(f2850,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( sP26(X4,X3,X1,X2,X0)
      | ~ 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lex$c'(X4)) ),
    inference(cnf_transformation,[],[f1713]) ).

tff(f9376,plain,
    spl230_658,
    inference(avatar_split_clause,[],[f2843,f9374]) ).

tff(f9374,plain,
    ( spl230_658
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4))
        | ~ sP25(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_658])]) ).

tff(f2843,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4))
      | ~ sP25(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1709]) ).

tff(f1709,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4))
        | ~ sP25(X4,X3,X1,X2,X0) )
      & ( sP25(X4,X3,X1,X2,X0)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4)) ) ),
    inference(nnf_transformation,[],[f1128]) ).

tff(f1128,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4))
    <=> sP25(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f512,f1127]) ).

tff(f512,axiom,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4))
    <=> ( ( 'member$o'('pair$v'(X1,X3),'listrel1$'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$g'('pair$c'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom510) ).

tff(f9372,plain,
    spl230_657,
    inference(avatar_split_clause,[],[f2842,f9370]) ).

tff(f9370,plain,
    ( spl230_657
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( sP25(X4,X3,X1,X2,X0)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_657])]) ).

tff(f2842,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( sP25(X4,X3,X1,X2,X0)
      | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'listrel1$'(X4)) ),
    inference(cnf_transformation,[],[f1709]) ).

tff(f9368,plain,
    spl230_656,
    inference(avatar_split_clause,[],[f2835,f9366]) ).

tff(f9366,plain,
    ( spl230_656
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4))
        | ~ sP24(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_656])]) ).

tff(f2835,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4))
      | ~ sP24(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1705]) ).

tff(f1705,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4))
        | ~ sP24(X4,X3,X1,X2,X0) )
      & ( sP24(X4,X3,X1,X2,X0)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4)) ) ),
    inference(nnf_transformation,[],[f1126]) ).

tff(f1126,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4))
    <=> sP24(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f513,f1125]) ).

tff(f513,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4))
    <=> ( ( 'member$p'('pair$w'(X1,X3),'listrel1$a'(X4))
          & ( X0 = X2 ) )
        | ( ( X1 = X3 )
          & 'member$e'('pair$'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom511) ).

tff(f9364,plain,
    spl230_655,
    inference(avatar_split_clause,[],[f2834,f9362]) ).

tff(f9362,plain,
    ( spl230_655
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( sP24(X4,X3,X1,X2,X0)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_655])]) ).

tff(f2834,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( sP24(X4,X3,X1,X2,X0)
      | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'listrel1$a'(X4)) ),
    inference(cnf_transformation,[],[f1705]) ).

tff(f9360,plain,
    spl230_654,
    inference(avatar_split_clause,[],[f2819,f9358]) ).

tff(f9358,plain,
    ( spl230_654
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4))
        | ~ sP23(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_654])]) ).

tff(f2819,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4))
      | ~ sP23(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1697]) ).

tff(f1697,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4))
        | ~ sP23(X4,X3,X1,X2,X0) )
      & ( sP23(X4,X3,X1,X2,X0)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4)) ) ),
    inference(nnf_transformation,[],[f1124]) ).

tff(f1124,plain,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4))
    <=> sP23(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f496,f1123]) ).

tff(f496,axiom,
    ! [X0: $int,X1: 'Int_list$',X2: $int,X3: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4))
    <=> ( ( 'member$o'('pair$v'(X1,X3),'lex$'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$e'(X1)) = 'fun_app$l'('of_nat$','size$e'(X3)) )
          & 'member$g'('pair$c'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom494) ).

tff(f9351,plain,
    spl230_653,
    inference(avatar_split_clause,[],[f2818,f9349]) ).

tff(f9349,plain,
    ( spl230_653
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( sP23(X4,X3,X1,X2,X0)
        | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_653])]) ).

tff(f2818,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( sP23(X4,X3,X1,X2,X0)
      | ~ 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lex$'(X4)) ),
    inference(cnf_transformation,[],[f1697]) ).

tff(f9347,plain,
    spl230_652,
    inference(avatar_split_clause,[],[f2811,f9345]) ).

tff(f9345,plain,
    ( spl230_652
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4))
        | ~ sP22(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_652])]) ).

tff(f2811,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4))
      | ~ sP22(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1693]) ).

tff(f1693,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4))
        | ~ sP22(X4,X3,X1,X2,X0) )
      & ( sP22(X4,X3,X1,X2,X0)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4)) ) ),
    inference(nnf_transformation,[],[f1122]) ).

tff(f1122,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4))
    <=> sP22(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f497,f1121]) ).

tff(f497,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4))
    <=> ( ( 'member$p'('pair$w'(X1,X3),'lex$a'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','size$f'(X1)) = 'fun_app$l'('of_nat$','size$f'(X3)) )
          & 'member$e'('pair$'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom495) ).

tff(f9343,plain,
    spl230_651,
    inference(avatar_split_clause,[],[f2810,f9341]) ).

tff(f9341,plain,
    ( spl230_651
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( sP22(X4,X3,X1,X2,X0)
        | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_651])]) ).

tff(f2810,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( sP22(X4,X3,X1,X2,X0)
      | ~ 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lex$a'(X4)) ),
    inference(cnf_transformation,[],[f1693]) ).

tff(f9339,plain,
    spl230_650,
    inference(avatar_split_clause,[],[f2803,f9337]) ).

tff(f9337,plain,
    ( spl230_650
  <=> ! [X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] :
        ( 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4))
        | ~ sP21(X4,X3,X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_650])]) ).

tff(f2803,plain,
    ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4))
      | ~ sP21(X4,X3,X1,X2,X0) ),
    inference(cnf_transformation,[],[f1689]) ).

tff(f1689,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( ( 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4))
        | ~ sP21(X4,X3,X1,X2,X0) )
      & ( sP21(X4,X3,X1,X2,X0)
        | ~ 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4)) ) ),
    inference(nnf_transformation,[],[f1120]) ).

tff(f1120,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4))
    <=> sP21(X4,X3,X1,X2,X0) ),
    inference(definition_folding,[],[f498,f1119]) ).

tff(f498,axiom,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4))
    <=> ( ( 'member$q'('pair$x'(X1,X3),'lex$b'(X4))
          & ( X0 = X2 ) )
        | ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',X3)) )
          & 'member$r'('pair$y'(X0,X2),X4) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom496) ).

tff(f9335,plain,
    spl230_649,
    inference(avatar_split_clause,[],[f2802,f9333]) ).

tff(f9333,plain,
    ( spl230_649
  <=> ! [X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] :
        ( sP21(X4,X3,X1,X2,X0)
        | ~ 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_649])]) ).

tff(f2802,plain,
    ! [X2: 'Nat_a_iarray_prod$',X3: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$'] :
      ( sP21(X4,X3,X1,X2,X0)
      | ~ 'member$q'('pair$x'('cons$a'(X0,X1),'cons$a'(X2,X3)),'lex$b'(X4)) ),
    inference(cnf_transformation,[],[f1689]) ).

tff(f9331,plain,
    spl230_648,
    inference(avatar_split_clause,[],[f2759,f9329]) ).

tff(f9329,plain,
    ( spl230_648
  <=> ! [X3: 'A_iarray_list$',X0: 'A_iarray_list$',X9: 'A_iarray$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ~ 'fun_app$'(X1,X9)
        | ~ 'member$a'(X9,'set$'(sK220(X0,X1,X2,X3)))
        | ~ sP19(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_648])]) ).

tff(f2759,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X9: 'A_iarray$'] :
      ( ~ 'fun_app$'(X1,X9)
      | ~ 'member$a'(X9,'set$'(sK220(X0,X1,X2,X3)))
      | ~ sP19(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1680]) ).

tff(f9327,plain,
    spl230_647,
    inference(avatar_split_clause,[],[f2751,f9325]) ).

tff(f9325,plain,
    ( spl230_647
  <=> ! [X3: 'A_iarray_list$',X0: 'A_iarray_list$',X9: 'A_iarray$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ~ 'fun_app$'(X1,X9)
        | ~ 'member$a'(X9,'set$'(sK217(X0,X1,X2,X3)))
        | ~ sP18(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_647])]) ).

tff(f2751,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X9: 'A_iarray$'] :
      ( ~ 'fun_app$'(X1,X9)
      | ~ 'member$a'(X9,'set$'(sK217(X0,X1,X2,X3)))
      | ~ sP18(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1674]) ).

tff(f9323,plain,
    spl230_646,
    inference(avatar_split_clause,[],[f2704,f9321]) ).

tff(f2704,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( sP15(X3,X2,X1,X0)
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) ) ),
    inference(cnf_transformation,[],[f1108]) ).

tff(f1108,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( sP15(X3,X2,X1,X0)
      | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) ) ),
    inference(definition_folding,[],[f1024,f1107]) ).

tff(f1024,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X0),X2) = 'fun_app$p'('append$d'(X1),X3) )
      <=> ( ( X2 = X3 )
          & ( X0 = X1 ) ) )
      | ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) ) ),
    inference(ennf_transformation,[],[f578]) ).

tff(f578,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X3)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) )
     => ( ( 'fun_app$p'('append$d'(X0),X2) = 'fun_app$p'('append$d'(X1),X3) )
      <=> ( ( X2 = X3 )
          & ( X0 = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom576) ).

tff(f9319,plain,
    spl230_645,
    inference(avatar_split_clause,[],[f2703,f9317]) ).

tff(f2703,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( sP15(X3,X2,X1,X0)
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) ) ),
    inference(cnf_transformation,[],[f1108]) ).

tff(f9315,plain,
    spl230_644,
    inference(avatar_split_clause,[],[f2629,f9313]) ).

tff(f9313,plain,
    ( spl230_644
  <=> ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X3: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_644])]) ).

tff(f2629,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'Nat$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3)) ),
    inference(cnf_transformation,[],[f975]) ).

tff(f975,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X3) ) )
      | ~ 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3)) ),
    inference(ennf_transformation,[],[f511]) ).

tff(f511,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'Nat$'] :
      ( 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3))
     => ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom509) ).

tff(f9306,plain,
    spl230_643,
    inference(avatar_split_clause,[],[f2628,f9304]) ).

tff(f9304,plain,
    ( spl230_643
  <=> ! [X0: 'A_iarray_list$',X3: 'Nat$',X2: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_643])]) ).

tff(f2628,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'Nat$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$'('pair$b'(X0,X1),'lexn$b'(X2,X3)) ),
    inference(cnf_transformation,[],[f975]) ).

tff(f9302,plain,
    spl230_642,
    inference(avatar_split_clause,[],[f2627,f9300]) ).

tff(f9300,plain,
    ( spl230_642
  <=> ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X3: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_642])]) ).

tff(f2627,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'Nat$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3)) ),
    inference(cnf_transformation,[],[f974]) ).

tff(f974,plain,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$',X3) ) )
      | ~ 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3)) ),
    inference(ennf_transformation,[],[f510]) ).

tff(f510,axiom,
    ! [X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'Nat$'] :
      ( 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3))
     => ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$',X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom508) ).

tff(f9298,plain,
    spl230_641,
    inference(avatar_split_clause,[],[f2626,f9296]) ).

tff(f9296,plain,
    ( spl230_641
  <=> ! [X0: 'A_iarray_list_list$',X3: 'Nat$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_641])]) ).

tff(f2626,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'Nat$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X0)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$s'('pair$z'(X0,X1),'lexn$a'(X2,X3)) ),
    inference(cnf_transformation,[],[f974]) ).

tff(f9294,plain,
    spl230_640,
    inference(avatar_split_clause,[],[f2625,f9292]) ).

tff(f9292,plain,
    ( spl230_640
  <=> ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X3: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_640])]) ).

tff(f2625,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3)) ),
    inference(cnf_transformation,[],[f973]) ).

tff(f973,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$',X3) ) )
      | ~ 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3)) ),
    inference(ennf_transformation,[],[f509]) ).

tff(f509,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat$'] :
      ( 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3))
     => ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X3) )
        & ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$',X3) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom507) ).

tff(f9290,plain,
    spl230_639,
    inference(avatar_split_clause,[],[f2624,f9288]) ).

tff(f9288,plain,
    ( spl230_639
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X3: 'Nat$',X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$',X3) )
        | ~ 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_639])]) ).

tff(f2624,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X0)) = 'fun_app$l'('of_nat$',X3) )
      | ~ 'member$q'('pair$x'(X0,X1),'lexn$'(X2,X3)) ),
    inference(cnf_transformation,[],[f973]) ).

tff(f9286,plain,
    spl230_638,
    inference(avatar_split_clause,[],[f2623,f9284]) ).

tff(f9284,plain,
    ( spl230_638
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X3,X0),'cons$'(X3,X1)),'listrel1$c'(X2))
        | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_638])]) ).

tff(f2623,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( 'member$'('pair$b'('cons$'(X3,X0),'cons$'(X3,X1)),'listrel1$c'(X2))
      | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ),
    inference(cnf_transformation,[],[f972]) ).

tff(f972,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$'] :
      ( 'member$'('pair$b'('cons$'(X3,X0),'cons$'(X3,X1)),'listrel1$c'(X2))
      | ~ 'member$'('pair$b'(X0,X1),'listrel1$c'(X2)) ),
    inference(ennf_transformation,[],[f516]) ).

tff(f516,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$'] :
      ( 'member$'('pair$b'(X0,X1),'listrel1$c'(X2))
     => 'member$'('pair$b'('cons$'(X3,X0),'cons$'(X3,X1)),'listrel1$c'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom514) ).

tff(f9282,plain,
    spl230_637,
    inference(avatar_split_clause,[],[f2444,f9280]) ).

tff(f9280,plain,
    ( spl230_637
  <=> ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
        ( ( 'plus$g'(sK146(X0,X1,X2),sK147(X0,X1,X2)) = X0 )
        | ~ 'member$c'(X0,'plus$h'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_637])]) ).

tff(f2444,plain,
    ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
      ( ( 'plus$g'(sK146(X0,X1,X2),sK147(X0,X1,X2)) = X0 )
      | ~ 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(cnf_transformation,[],[f1506]) ).

tff(f1506,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat_set$'] :
      ( ( 'member$c'(sK147(X0,X1,X2),X2)
        & 'member$c'(sK146(X0,X1,X2),X1)
        & ( 'plus$g'(sK146(X0,X1,X2),sK147(X0,X1,X2)) = X0 ) )
      | ~ 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK146,sK147])],[f927,f1505]) ).

tff(f1505,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat_set$'] :
      ( ? [X3: 'Nat$',X4: 'Nat$'] :
          ( 'member$c'(X4,X2)
          & 'member$c'(X3,X1)
          & ( 'plus$g'(X3,X4) = X0 ) )
     => ( 'member$c'(sK147(X0,X1,X2),X2)
        & 'member$c'(sK146(X0,X1,X2),X1)
        & ( 'plus$g'(sK146(X0,X1,X2),sK147(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f927,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat_set$'] :
      ( ? [X3: 'Nat$',X4: 'Nat$'] :
          ( 'member$c'(X4,X2)
          & 'member$c'(X3,X1)
          & ( 'plus$g'(X3,X4) = X0 ) )
      | ~ 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(ennf_transformation,[],[f746]) ).

tff(f746,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat_set$'] :
      ~ ( ! [X3: 'Nat$',X4: 'Nat$'] :
            ~ ( 'member$c'(X4,X2)
              & 'member$c'(X3,X1)
              & ( 'plus$g'(X3,X4) = X0 ) )
        & 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f162]) ).

tff(f162,axiom,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat_set$'] :
      ( ( ! [X3: 'Nat$',X4: 'Nat$'] :
            ( ( 'member$c'(X4,X2)
              & 'member$c'(X3,X1)
              & ( 'plus$g'(X3,X4) = X0 ) )
           => $false )
        & 'member$c'(X0,'plus$h'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom160) ).

tff(f9278,plain,
    spl230_636,
    inference(avatar_split_clause,[],[f2441,f9276]) ).

tff(f9276,plain,
    ( spl230_636
  <=> ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
        ( ( $sum(sK144(X0,X1,X2),sK145(X0,X1,X2)) = X0 )
        | ~ 'member$d'(X0,'plus$k'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_636])]) ).

tff(f2441,plain,
    ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
      ( ( $sum(sK144(X0,X1,X2),sK145(X0,X1,X2)) = X0 )
      | ~ 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(cnf_transformation,[],[f1504]) ).

tff(f1504,plain,
    ! [X0: $int,X1: 'Int_set$',X2: 'Int_set$'] :
      ( ( 'member$d'(sK145(X0,X1,X2),X2)
        & 'member$d'(sK144(X0,X1,X2),X1)
        & ( $sum(sK144(X0,X1,X2),sK145(X0,X1,X2)) = X0 ) )
      | ~ 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK144,sK145])],[f926,f1503]) ).

tff(f1503,plain,
    ! [X0: $int,X1: 'Int_set$',X2: 'Int_set$'] :
      ( ? [X3: $int,X4: $int] :
          ( 'member$d'(X4,X2)
          & 'member$d'(X3,X1)
          & ( $sum(X3,X4) = X0 ) )
     => ( 'member$d'(sK145(X0,X1,X2),X2)
        & 'member$d'(sK144(X0,X1,X2),X1)
        & ( $sum(sK144(X0,X1,X2),sK145(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f926,plain,
    ! [X0: $int,X1: 'Int_set$',X2: 'Int_set$'] :
      ( ? [X3: $int,X4: $int] :
          ( 'member$d'(X4,X2)
          & 'member$d'(X3,X1)
          & ( $sum(X3,X4) = X0 ) )
      | ~ 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(ennf_transformation,[],[f745]) ).

tff(f745,plain,
    ! [X0: $int,X1: 'Int_set$',X2: 'Int_set$'] :
      ~ ( ! [X3: $int,X4: $int] :
            ~ ( 'member$d'(X4,X2)
              & 'member$d'(X3,X1)
              & ( $sum(X3,X4) = X0 ) )
        & 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f168]) ).

tff(f168,axiom,
    ! [X0: $int,X1: 'Int_set$',X2: 'Int_set$'] :
      ( ( ! [X3: $int,X4: $int] :
            ( ( 'member$d'(X4,X2)
              & 'member$d'(X3,X1)
              & ( $sum(X3,X4) = X0 ) )
           => $false )
        & 'member$d'(X0,'plus$k'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom166) ).

tff(f9274,plain,
    spl230_635,
    inference(avatar_split_clause,[],[f2438,f9272]) ).

tff(f9272,plain,
    ( spl230_635
  <=> ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
        ( ( 'plus$a'(sK142(X0,X1,X2),sK143(X0,X1,X2)) = X0 )
        | ~ 'member$j'(X0,'plus$m'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_635])]) ).

tff(f2438,plain,
    ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
      ( ( 'plus$a'(sK142(X0,X1,X2),sK143(X0,X1,X2)) = X0 )
      | ~ 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(cnf_transformation,[],[f1502]) ).

tff(f1502,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec_set$'] :
      ( ( 'member$j'(sK143(X0,X1,X2),X2)
        & 'member$j'(sK142(X0,X1,X2),X1)
        & ( 'plus$a'(sK142(X0,X1,X2),sK143(X0,X1,X2)) = X0 ) )
      | ~ 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143])],[f925,f1501]) ).

tff(f1501,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec_set$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( 'member$j'(X4,X2)
          & 'member$j'(X3,X1)
          & ( 'plus$a'(X3,X4) = X0 ) )
     => ( 'member$j'(sK143(X0,X1,X2),X2)
        & 'member$j'(sK142(X0,X1,X2),X1)
        & ( 'plus$a'(sK142(X0,X1,X2),sK143(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f925,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec_set$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( 'member$j'(X4,X2)
          & 'member$j'(X3,X1)
          & ( 'plus$a'(X3,X4) = X0 ) )
      | ~ 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(ennf_transformation,[],[f744]) ).

tff(f744,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec_set$'] :
      ~ ( ! [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
            ~ ( 'member$j'(X4,X2)
              & 'member$j'(X3,X1)
              & ( 'plus$a'(X3,X4) = X0 ) )
        & 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f166]) ).

tff(f166,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec_set$'] :
      ( ( ! [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
            ( ( 'member$j'(X4,X2)
              & 'member$j'(X3,X1)
              & ( 'plus$a'(X3,X4) = X0 ) )
           => $false )
        & 'member$j'(X0,'plus$m'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom164) ).

tff(f9270,plain,
    spl230_634,
    inference(avatar_split_clause,[],[f2435,f9268]) ).

tff(f9268,plain,
    ( spl230_634
  <=> ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
        ( ( 'plus$k'(sK140(X0,X1,X2),sK141(X0,X1,X2)) = X0 )
        | ~ 'member$i'(X0,'plus$l'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_634])]) ).

tff(f2435,plain,
    ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
      ( ( 'plus$k'(sK140(X0,X1,X2),sK141(X0,X1,X2)) = X0 )
      | ~ 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(cnf_transformation,[],[f1500]) ).

tff(f1500,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] :
      ( ( 'member$i'(sK141(X0,X1,X2),X2)
        & 'member$i'(sK140(X0,X1,X2),X1)
        & ( 'plus$k'(sK140(X0,X1,X2),sK141(X0,X1,X2)) = X0 ) )
      | ~ 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK140,sK141])],[f924,f1499]) ).

tff(f1499,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] :
      ( ? [X3: 'Int_set$',X4: 'Int_set$'] :
          ( 'member$i'(X4,X2)
          & 'member$i'(X3,X1)
          & ( 'plus$k'(X3,X4) = X0 ) )
     => ( 'member$i'(sK141(X0,X1,X2),X2)
        & 'member$i'(sK140(X0,X1,X2),X1)
        & ( 'plus$k'(sK140(X0,X1,X2),sK141(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f924,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] :
      ( ? [X3: 'Int_set$',X4: 'Int_set$'] :
          ( 'member$i'(X4,X2)
          & 'member$i'(X3,X1)
          & ( 'plus$k'(X3,X4) = X0 ) )
      | ~ 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(ennf_transformation,[],[f743]) ).

tff(f743,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] :
      ~ ( ! [X3: 'Int_set$',X4: 'Int_set$'] :
            ~ ( 'member$i'(X4,X2)
              & 'member$i'(X3,X1)
              & ( 'plus$k'(X3,X4) = X0 ) )
        & 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f165]) ).

tff(f165,axiom,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set_set$'] :
      ( ( ! [X3: 'Int_set$',X4: 'Int_set$'] :
            ( ( 'member$i'(X4,X2)
              & 'member$i'(X3,X1)
              & ( 'plus$k'(X3,X4) = X0 ) )
           => $false )
        & 'member$i'(X0,'plus$l'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom163) ).

tff(f9261,plain,
    spl230_633,
    inference(avatar_split_clause,[],[f2432,f9259]) ).

tff(f9259,plain,
    ( spl230_633
  <=> ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
        ( ( 'plus$d'(sK138(X0,X1,X2),sK139(X0,X1,X2)) = X0 )
        | ~ 'member$h'(X0,'plus$j'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_633])]) ).

tff(f2432,plain,
    ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
      ( ( 'plus$d'(sK138(X0,X1,X2),sK139(X0,X1,X2)) = X0 )
      | ~ 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(cnf_transformation,[],[f1498]) ).

tff(f1498,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray_set$'] :
      ( ( 'member$h'(sK139(X0,X1,X2),X2)
        & 'member$h'(sK138(X0,X1,X2),X1)
        & ( 'plus$d'(sK138(X0,X1,X2),sK139(X0,X1,X2)) = X0 ) )
      | ~ 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK138,sK139])],[f923,f1497]) ).

tff(f1497,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray_set$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( 'member$h'(X4,X2)
          & 'member$h'(X3,X1)
          & ( 'plus$d'(X3,X4) = X0 ) )
     => ( 'member$h'(sK139(X0,X1,X2),X2)
        & 'member$h'(sK138(X0,X1,X2),X1)
        & ( 'plus$d'(sK138(X0,X1,X2),sK139(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f923,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray_set$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( 'member$h'(X4,X2)
          & 'member$h'(X3,X1)
          & ( 'plus$d'(X3,X4) = X0 ) )
      | ~ 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(ennf_transformation,[],[f742]) ).

tff(f742,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray_set$'] :
      ~ ( ! [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
            ~ ( 'member$h'(X4,X2)
              & 'member$h'(X3,X1)
              & ( 'plus$d'(X3,X4) = X0 ) )
        & 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f164]) ).

tff(f164,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray_set$'] :
      ( ( ! [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
            ( ( 'member$h'(X4,X2)
              & 'member$h'(X3,X1)
              & ( 'plus$d'(X3,X4) = X0 ) )
           => $false )
        & 'member$h'(X0,'plus$j'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom162) ).

tff(f9257,plain,
    spl230_632,
    inference(avatar_split_clause,[],[f2387,f9255]) ).

tff(f9255,plain,
    ( spl230_632
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
        ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'cons$'(X1,'fun_app$p'('filter$'(X0),X2)) )
        | ~ 'fun_app$'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_632])]) ).

tff(f2387,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'cons$'(X1,'fun_app$p'('filter$'(X0),X2)) )
      | ~ 'fun_app$'(X0,X1) ),
    inference(cnf_transformation,[],[f881]) ).

tff(f881,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$',X2: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'fun_app$p'('filter$'(X0),X2) )
        | 'fun_app$'(X0,X1) )
      & ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'cons$'(X1,'fun_app$p'('filter$'(X0),X2)) )
        | ~ 'fun_app$'(X0,X1) ) ),
    inference(ennf_transformation,[],[f482]) ).

tff(f482,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$',X2: 'A_iarray_list$'] :
      ( ( ~ 'fun_app$'(X0,X1)
       => ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'fun_app$p'('filter$'(X0),X2) ) )
      & ( 'fun_app$'(X0,X1)
       => ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'cons$'(X1,'fun_app$p'('filter$'(X0),X2)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom480) ).

tff(f9253,plain,
    spl230_631,
    inference(avatar_split_clause,[],[f2052,f9251]) ).

tff(f9251,plain,
    ( spl230_631
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
        | ~ 'member$b'(X0,'set$a'('product_lists$'(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_631])]) ).

tff(f2052,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
      | ~ 'member$b'(X0,'set$a'('product_lists$'(X1))) ),
    inference(cnf_transformation,[],[f816]) ).

tff(f816,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) )
      | ~ 'member$b'(X0,'set$a'('product_lists$'(X1))) ),
    inference(ennf_transformation,[],[f606]) ).

tff(f606,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
      ( 'member$b'(X0,'set$a'('product_lists$'(X1)))
     => ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom604) ).

tff(f9249,plain,
    spl230_630,
    inference(avatar_split_clause,[],[f2049,f9247]) ).

tff(f9247,plain,
    ( spl230_630
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X0,X1))) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_630])]) ).

tff(f2049,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X0,X1))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f813]) ).

tff(f813,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X0,X1))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f220]) ).

tff(f220,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
     => ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X0,X1))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom218) ).

tff(f9245,plain,
    spl230_629,
    inference(avatar_split_clause,[],[f2048,f9243]) ).

tff(f9243,plain,
    ( spl230_629
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X1,X0))) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_629])]) ).

tff(f2048,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X1,X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f812]) ).

tff(f812,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X1,X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f218]) ).

tff(f218,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
     => ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X1)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','matrix_matrix_mult$'(X1,X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom216) ).

tff(f9241,plain,
    spl230_628,
    inference(avatar_split_clause,[],[f2028,f9239]) ).

tff(f9239,plain,
    ( spl230_628
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_628])]) ).

tff(f9237,plain,
    spl230_627,
    inference(avatar_split_clause,[],[f2027,f9235]) ).

tff(f9235,plain,
    ( spl230_627
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('gen_length$a'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_627])]) ).

tff(f2027,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('gen_length$a'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ),
    inference(cnf_transformation,[],[f172]) ).

tff(f172,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('gen_length$a'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom170) ).

tff(f9233,plain,
    spl230_626,
    inference(avatar_split_clause,[],[f2026,f9231]) ).

tff(f9231,plain,
    ( spl230_626
  <=> ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('gen_length$'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_626])]) ).

tff(f2026,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('gen_length$'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,axiom,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('gen_length$'(X0),X1)) = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom169) ).

tff(f8681,plain,
    ( spl230_625
    | ~ spl230_115
    | ~ spl230_428 ),
    inference(avatar_split_clause,[],[f7168,f6464,f4004,f8679]) ).

tff(f8679,plain,
    ( spl230_625
  <=> ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( sK36('pair$'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_625])]) ).

tff(f4004,plain,
    ( spl230_115
  <=> ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('fst$','pair$'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_115])]) ).

tff(f7168,plain,
    ( ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( sK36('pair$'(X0,X1)) = X0 )
    | ~ spl230_115
    | ~ spl230_428 ),
    inference(superposition,[],[f6465,f4005]) ).

tff(f4005,plain,
    ( ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('fst$','pair$'(X0,X1)) = X0 )
    | ~ spl230_115 ),
    inference(avatar_component_clause,[],[f4004]) ).

tff(f8655,plain,
    ( spl230_624
    | ~ spl230_114
    | ~ spl230_427 ),
    inference(avatar_split_clause,[],[f7126,f6460,f4000,f8653]) ).

tff(f8653,plain,
    ( spl230_624
  <=> ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( sK37('pair$'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_624])]) ).

tff(f7126,plain,
    ( ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( sK37('pair$'(X0,X1)) = X1 )
    | ~ spl230_114
    | ~ spl230_427 ),
    inference(superposition,[],[f6461,f4001]) ).

tff(f8646,plain,
    ( spl230_623
    | ~ spl230_111
    | ~ spl230_426 ),
    inference(avatar_split_clause,[],[f7083,f6450,f3988,f8644]) ).

tff(f8644,plain,
    ( spl230_623
  <=> ! [X0: $int,X1: $int] : ( sK41('pair$c'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_623])]) ).

tff(f7083,plain,
    ( ! [X0: $int,X1: $int] : ( sK41('pair$c'(X0,X1)) = X1 )
    | ~ spl230_111
    | ~ spl230_426 ),
    inference(superposition,[],[f6451,f3989]) ).

tff(f8596,plain,
    ( spl230_622
    | ~ spl230_110
    | ~ spl230_425 ),
    inference(avatar_split_clause,[],[f6862,f6201,f3984,f8594]) ).

tff(f8594,plain,
    ( spl230_622
  <=> ! [X0: $int,X1: $int] : ( sK40('pair$c'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_622])]) ).

tff(f3984,plain,
    ( spl230_110
  <=> ! [X0: $int,X1: $int] : ( 'fun_app$ac'('fst$b','pair$c'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_110])]) ).

tff(f6862,plain,
    ( ! [X0: $int,X1: $int] : ( sK40('pair$c'(X0,X1)) = X0 )
    | ~ spl230_110
    | ~ spl230_425 ),
    inference(superposition,[],[f6202,f3985]) ).

tff(f3985,plain,
    ( ! [X0: $int,X1: $int] : ( 'fun_app$ac'('fst$b','pair$c'(X0,X1)) = X0 )
    | ~ spl230_110 ),
    inference(avatar_component_clause,[],[f3984]) ).

tff(f8516,plain,
    ( spl230_621
    | ~ spl230_73
    | ~ spl230_151 ),
    inference(avatar_split_clause,[],[f5133,f4235,f3819,f8514]) ).

tff(f8514,plain,
    ( spl230_621
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( sK42('pair$b'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_621])]) ).

tff(f3819,plain,
    ( spl230_73
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fst$k'('pair$b'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_73])]) ).

tff(f4235,plain,
    ( spl230_151
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'fst$k'(X0) = sK42(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_151])]) ).

tff(f5133,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( sK42('pair$b'(X0,X1)) = X0 )
    | ~ spl230_73
    | ~ spl230_151 ),
    inference(superposition,[],[f4236,f3820]) ).

tff(f3820,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fst$k'('pair$b'(X0,X1)) = X0 )
    | ~ spl230_73 ),
    inference(avatar_component_clause,[],[f3819]) ).

tff(f4236,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'fst$k'(X0) = sK42(X0) )
    | ~ spl230_151 ),
    inference(avatar_component_clause,[],[f4235]) ).

tff(f8409,plain,
    spl230_620,
    inference(avatar_split_clause,[],[f3436,f8407]) ).

tff(f3436,plain,
    ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ $less('fun_app$l'('of_nat$',X2),$sum(1,'fun_app$l'('of_nat$',X1)))
      | sP7(X0,X1)
      | ~ 'fun_app$c'(X0,X2) ),
    inference(forward_demodulation,[],[f2345,f664]) ).

tff(f2345,plain,
    ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( sP7(X0,X1)
      | ~ 'fun_app$c'(X0,X2)
      | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X1),1)) ),
    inference(cnf_transformation,[],[f1485]) ).

tff(f1485,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( sP7(X0,X1)
        | ! [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X0,X2)
            | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X1),1)) ) )
      & ( ( 'fun_app$c'(X0,sK133(X0,X1))
          & $less('fun_app$l'('of_nat$',sK133(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1)) )
        | ~ sP7(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f1483,f1484]) ).

tff(f1484,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( 'fun_app$c'(X0,X3)
          & $less('fun_app$l'('of_nat$',X3),$sum('fun_app$l'('of_nat$',X1),1)) )
     => ( 'fun_app$c'(X0,sK133(X0,X1))
        & $less('fun_app$l'('of_nat$',sK133(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1483,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( sP7(X0,X1)
        | ! [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X0,X2)
            | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X1),1)) ) )
      & ( ? [X3: 'Nat$'] :
            ( 'fun_app$c'(X0,X3)
            & $less('fun_app$l'('of_nat$',X3),$sum('fun_app$l'('of_nat$',X1),1)) )
        | ~ sP7(X0,X1) ) ),
    inference(rectify,[],[f1482]) ).

tff(f1482,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( ( sP7(X1,X0)
        | ! [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X1,X2)
            | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) ) )
      & ( ? [X2: 'Nat$'] :
            ( 'fun_app$c'(X1,X2)
            & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) )
        | ~ sP7(X1,X0) ) ),
    inference(nnf_transformation,[],[f1091]) ).

tff(f8405,plain,
    spl230_619,
    inference(avatar_split_clause,[],[f3433,f8403]) ).

tff(f3433,plain,
    ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ $less('fun_app$l'('of_nat$',X3),$sum(1,'fun_app$l'('of_nat$',X1)))
      | 'fun_app$c'(X0,X3)
      | ~ sP6(X0,X1) ),
    inference(forward_demodulation,[],[f2336,f664]) ).

tff(f2336,plain,
    ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X3)
      | ~ $less('fun_app$l'('of_nat$',X3),$sum('fun_app$l'('of_nat$',X1),1))
      | ~ sP6(X0,X1) ),
    inference(cnf_transformation,[],[f1476]) ).

tff(f1476,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( sP6(X0,X1)
        | ( ~ 'fun_app$c'(X0,sK131(X0,X1))
          & $less('fun_app$l'('of_nat$',sK131(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1)) ) )
      & ( ! [X3: 'Nat$'] :
            ( 'fun_app$c'(X0,X3)
            | ~ $less('fun_app$l'('of_nat$',X3),$sum('fun_app$l'('of_nat$',X1),1)) )
        | ~ sP6(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK131])],[f1474,f1475]) ).

tff(f1475,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X1),1)) )
     => ( ~ 'fun_app$c'(X0,sK131(X0,X1))
        & $less('fun_app$l'('of_nat$',sK131(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1474,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( sP6(X0,X1)
        | ? [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X0,X2)
            & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X1),1)) ) )
      & ( ! [X3: 'Nat$'] :
            ( 'fun_app$c'(X0,X3)
            | ~ $less('fun_app$l'('of_nat$',X3),$sum('fun_app$l'('of_nat$',X1),1)) )
        | ~ sP6(X0,X1) ) ),
    inference(rectify,[],[f1473]) ).

tff(f1473,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( ( sP6(X1,X0)
        | ? [X2: 'Nat$'] :
            ( ~ 'fun_app$c'(X1,X2)
            & $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) ) )
      & ( ! [X2: 'Nat$'] :
            ( 'fun_app$c'(X1,X2)
            | ~ $less('fun_app$l'('of_nat$',X2),$sum('fun_app$l'('of_nat$',X0),1)) )
        | ~ sP6(X1,X0) ) ),
    inference(nnf_transformation,[],[f1089]) ).

tff(f8401,plain,
    spl230_618,
    inference(avatar_split_clause,[],[f3361,f8399]) ).

tff(f8399,plain,
    ( spl230_618
  <=> ! [X0: 'A_iarray_iarray_nat_fun$',X1: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'some$'(X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$q'(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_618])]) ).

tff(f3361,plain,
    ! [X0: 'A_iarray_iarray_nat_fun$',X1: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'some$'(X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$q'(X0,X1))) ),
    inference(forward_demodulation,[],[f3304,f664]) ).

tff(f3304,plain,
    ! [X0: 'A_iarray_iarray_nat_fun$',X1: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'some$'(X1))) = $sum('fun_app$l'('of_nat$','fun_app$q'(X0,X1)),1) ),
    inference(evaluation,[],[f2030]) ).

tff(f2030,plain,
    ! [X0: 'A_iarray_iarray_nat_fun$',X1: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'some$'(X1))) = $sum('fun_app$l'('of_nat$','fun_app$q'(X0,X1)),$sum(0,1)) ),
    inference(cnf_transformation,[],[f467]) ).

tff(f467,axiom,
    ! [X0: 'A_iarray_iarray_nat_fun$',X1: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'some$'(X1))) = $sum('fun_app$l'('of_nat$','fun_app$q'(X0,X1)),$sum(0,1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom465) ).

tff(f8397,plain,
    spl230_617,
    inference(avatar_split_clause,[],[f3360,f8395]) ).

tff(f8395,plain,
    ( spl230_617
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','cons$'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_617])]) ).

tff(f3360,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','cons$'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$m'('size$',X1))) ),
    inference(forward_demodulation,[],[f2025,f664]) ).

tff(f2025,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','cons$'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),1) ),
    inference(cnf_transformation,[],[f492]) ).

tff(f492,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$','cons$'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$m'('size$',X1)),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom490) ).

tff(f8393,plain,
    spl230_616,
    inference(avatar_split_clause,[],[f3359,f8391]) ).

tff(f8391,plain,
    ( spl230_616
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','cons$b'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_616])]) ).

tff(f3359,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','cons$b'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$v'('size$b',X1))) ),
    inference(forward_demodulation,[],[f2024,f664]) ).

tff(f2024,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','cons$b'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$v'('size$b',X1)),1) ),
    inference(cnf_transformation,[],[f491]) ).

tff(f491,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b','cons$b'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$v'('size$b',X1)),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom489) ).

tff(f8389,plain,
    spl230_615,
    inference(avatar_split_clause,[],[f3358,f8387]) ).

tff(f8387,plain,
    ( spl230_615
  <=> ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','cons$a'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_615])]) ).

tff(f3358,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','cons$a'(X0,X1))) = $sum(1,'fun_app$l'('of_nat$','fun_app$u'('size$a',X1))) ),
    inference(forward_demodulation,[],[f2023,f664]) ).

tff(f2023,plain,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','cons$a'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$u'('size$a',X1)),1) ),
    inference(cnf_transformation,[],[f490]) ).

tff(f490,axiom,
    ! [X0: 'Nat_a_iarray_prod$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a','cons$a'(X0,X1))) = $sum('fun_app$l'('of_nat$','fun_app$u'('size$a',X1)),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom488) ).

tff(f8385,plain,
    spl230_614,
    inference(avatar_split_clause,[],[f3349,f8383]) ).

tff(f8383,plain,
    ( spl230_614
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = $sum(1,'fun_app$l'('of_nat$',sK46(X0))) )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_614])]) ).

tff(f3349,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(1,'fun_app$l'('of_nat$',sK46(X0))) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(forward_demodulation,[],[f1937,f664]) ).

tff(f1937,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK46(X0)),1) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(cnf_transformation,[],[f1186]) ).

tff(f1186,plain,
    ! [X0: 'Nat$'] :
      ( ( $less(0,'fun_app$l'('of_nat$',X0))
        | ! [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X1),1) ) )
      & ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK46(X0)),1) )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1184,f1185]) ).

tff(f1185,plain,
    ! [X0: 'Nat$'] :
      ( ? [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X2),1) )
     => ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK46(X0)),1) ) ),
    introduced(choice_axiom,[]) ).

tff(f1184,plain,
    ! [X0: 'Nat$'] :
      ( ( $less(0,'fun_app$l'('of_nat$',X0))
        | ! [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X1),1) ) )
      & ( ? [X2: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X2),1) )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    inference(rectify,[],[f1183]) ).

tff(f1183,plain,
    ! [X0: 'Nat$'] :
      ( ( $less(0,'fun_app$l'('of_nat$',X0))
        | ! [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X1),1) ) )
      & ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    inference(nnf_transformation,[],[f634]) ).

tff(f634,axiom,
    ! [X0: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',X0))
    <=> ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom632) ).

tff(f8381,plain,
    ( spl230_613
    | ~ spl230_75
    | ~ spl230_150 ),
    inference(avatar_split_clause,[],[f5012,f4223,f3827,f8379]) ).

tff(f8379,plain,
    ( spl230_613
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( sK43('pair$b'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_613])]) ).

tff(f3827,plain,
    ( spl230_75
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'snd$k'('pair$b'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_75])]) ).

tff(f4223,plain,
    ( spl230_150
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'snd$k'(X0) = sK43(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_150])]) ).

tff(f5012,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( sK43('pair$b'(X0,X1)) = X1 )
    | ~ spl230_75
    | ~ spl230_150 ),
    inference(superposition,[],[f4224,f3828]) ).

tff(f3828,plain,
    ( ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'snd$k'('pair$b'(X0,X1)) = X1 )
    | ~ spl230_75 ),
    inference(avatar_component_clause,[],[f3827]) ).

tff(f4224,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'snd$k'(X0) = sK43(X0) )
    | ~ spl230_150 ),
    inference(avatar_component_clause,[],[f4223]) ).

tff(f8377,plain,
    spl230_612,
    inference(avatar_split_clause,[],[f3345,f8375]) ).

tff(f8375,plain,
    ( spl230_612
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = $sum(1,'fun_app$l'('of_nat$',sK32(X0))) )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_612])]) ).

tff(f3345,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(1,'fun_app$l'('of_nat$',sK32(X0))) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(forward_demodulation,[],[f1877,f664]) ).

tff(f1877,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK32(X0)),1) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(cnf_transformation,[],[f1144]) ).

tff(f1144,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK32(X0)),1) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f798,f1143]) ).

tff(f1143,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
     => ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK32(X0)),1) ) ),
    introduced(choice_axiom,[]) ).

tff(f798,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(ennf_transformation,[],[f632]) ).

tff(f632,axiom,
    ! [X0: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',X0))
     => ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom630) ).

tff(f8373,plain,
    spl230_611,
    inference(avatar_split_clause,[],[f3258,f8371]) ).

tff(f8371,plain,
    ( spl230_611
  <=> ! [X2: 'Nat$',X4: 'Nat_int_fun$',X5: 'Nat_set$',X1: 'Nat_int_fun$'] :
        ( 'member$g'('pair$c'('fun_app$l'(X1,X2),'fun_app$l'(X4,X2)),'image2$'(X5,X1,X4))
        | ~ 'member$c'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_611])]) ).

tff(f3258,plain,
    ! [X2: 'Nat$',X1: 'Nat_int_fun$',X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( 'member$g'('pair$c'('fun_app$l'(X1,X2),'fun_app$l'(X4,X2)),'image2$'(X5,X1,X4))
      | ~ 'member$c'(X2,X5) ),
    inference(equality_resolution,[],[f3257]) ).

tff(f3257,plain,
    ! [X2: 'Nat$',X0: $int,X1: 'Nat_int_fun$',X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( 'member$g'('pair$c'(X0,'fun_app$l'(X4,X2)),'image2$'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$l'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2907]) ).

tff(f2907,plain,
    ! [X2: 'Nat$',X3: $int,X0: $int,X1: 'Nat_int_fun$',X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$l'(X4,X2) != X3 )
      | ( 'fun_app$l'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1067]) ).

tff(f1067,plain,
    ! [X0: $int,X1: 'Nat_int_fun$',X2: 'Nat$',X3: $int,X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$l'(X4,X2) != X3 )
      | ( 'fun_app$l'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1066]) ).

tff(f1066,plain,
    ! [X0: $int,X1: 'Nat_int_fun$',X2: 'Nat$',X3: $int,X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$l'(X4,X2) != X3 )
      | ( 'fun_app$l'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f355]) ).

tff(f355,axiom,
    ! [X0: $int,X1: 'Nat_int_fun$',X2: 'Nat$',X3: $int,X4: 'Nat_int_fun$',X5: 'Nat_set$'] :
      ( ( 'member$c'(X2,X5)
        & ( 'fun_app$l'(X4,X2) = X3 )
        & ( 'fun_app$l'(X1,X2) = X0 ) )
     => 'member$g'('pair$c'(X0,X3),'image2$'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom353) ).

tff(f8369,plain,
    spl230_610,
    inference(avatar_split_clause,[],[f3256,f8367]) ).

tff(f8367,plain,
    ( spl230_610
  <=> ! [X2: 'A_iarray$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$',X1: 'A_iarray_a_iarray_fun$'] :
        ( 'member$f'('pair$a'('fun_app$ad'(X1,X2),'fun_app$ad'(X4,X2)),'image2$f'(X5,X1,X4))
        | ~ 'member$a'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_610])]) ).

tff(f3256,plain,
    ! [X2: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( 'member$f'('pair$a'('fun_app$ad'(X1,X2),'fun_app$ad'(X4,X2)),'image2$f'(X5,X1,X4))
      | ~ 'member$a'(X2,X5) ),
    inference(equality_resolution,[],[f3255]) ).

tff(f3255,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( 'member$f'('pair$a'(X0,'fun_app$ad'(X4,X2)),'image2$f'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$ad'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2906]) ).

tff(f2906,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$f'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$ad'(X4,X2) != X3 )
      | ( 'fun_app$ad'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1065]) ).

tff(f1065,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X2: 'A_iarray$',X3: 'A_iarray$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$f'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$ad'(X4,X2) != X3 )
      | ( 'fun_app$ad'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1064]) ).

tff(f1064,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X2: 'A_iarray$',X3: 'A_iarray$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$f'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$ad'(X4,X2) != X3 )
      | ( 'fun_app$ad'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f361]) ).

tff(f361,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_fun$',X2: 'A_iarray$',X3: 'A_iarray$',X4: 'A_iarray_a_iarray_fun$',X5: 'A_iarray_set$'] :
      ( ( 'member$a'(X2,X5)
        & ( 'fun_app$ad'(X4,X2) = X3 )
        & ( 'fun_app$ad'(X1,X2) = X0 ) )
     => 'member$f'('pair$a'(X0,X3),'image2$f'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom359) ).

tff(f8365,plain,
    spl230_609,
    inference(avatar_split_clause,[],[f3254,f8363]) ).

tff(f8363,plain,
    ( spl230_609
  <=> ! [X2: $int,X4: 'Int_int_fun$',X5: 'Int_set$',X1: 'Int_int_fun$'] :
        ( 'member$g'('pair$c'('fun_app$ak'(X1,X2),'fun_app$ak'(X4,X2)),'image2$a'(X5,X1,X4))
        | ~ 'member$d'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_609])]) ).

tff(f3254,plain,
    ! [X2: $int,X1: 'Int_int_fun$',X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( 'member$g'('pair$c'('fun_app$ak'(X1,X2),'fun_app$ak'(X4,X2)),'image2$a'(X5,X1,X4))
      | ~ 'member$d'(X2,X5) ),
    inference(equality_resolution,[],[f3253]) ).

tff(f3253,plain,
    ! [X2: $int,X0: $int,X1: 'Int_int_fun$',X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( 'member$g'('pair$c'(X0,'fun_app$ak'(X4,X2)),'image2$a'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ak'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2905]) ).

tff(f2905,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$',X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$a'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ak'(X4,X2) != X3 )
      | ( 'fun_app$ak'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1063]) ).

tff(f1063,plain,
    ! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int,X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$a'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ak'(X4,X2) != X3 )
      | ( 'fun_app$ak'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1062]) ).

tff(f1062,plain,
    ! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int,X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$a'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ak'(X4,X2) != X3 )
      | ( 'fun_app$ak'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f356]) ).

tff(f356,axiom,
    ! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int,X4: 'Int_int_fun$',X5: 'Int_set$'] :
      ( ( 'member$d'(X2,X5)
        & ( 'fun_app$ak'(X4,X2) = X3 )
        & ( 'fun_app$ak'(X1,X2) = X0 ) )
     => 'member$g'('pair$c'(X0,X3),'image2$a'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom354) ).

tff(f8361,plain,
    spl230_608,
    inference(avatar_split_clause,[],[f3252,f8359]) ).

tff(f8359,plain,
    ( spl230_608
  <=> ! [X2: 'A_iarray$',X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$',X1: 'A_iarray_int_fun$'] :
        ( 'member$g'('pair$c'('fun_app$al'(X1,X2),'fun_app$al'(X4,X2)),'image2$b'(X5,X1,X4))
        | ~ 'member$a'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_608])]) ).

tff(f3252,plain,
    ! [X2: 'A_iarray$',X1: 'A_iarray_int_fun$',X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( 'member$g'('pair$c'('fun_app$al'(X1,X2),'fun_app$al'(X4,X2)),'image2$b'(X5,X1,X4))
      | ~ 'member$a'(X2,X5) ),
    inference(equality_resolution,[],[f3251]) ).

tff(f3251,plain,
    ! [X2: 'A_iarray$',X0: $int,X1: 'A_iarray_int_fun$',X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( 'member$g'('pair$c'(X0,'fun_app$al'(X4,X2)),'image2$b'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$al'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2904]) ).

tff(f2904,plain,
    ! [X2: 'A_iarray$',X3: $int,X0: $int,X1: 'A_iarray_int_fun$',X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$b'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$al'(X4,X2) != X3 )
      | ( 'fun_app$al'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1061]) ).

tff(f1061,plain,
    ! [X0: $int,X1: 'A_iarray_int_fun$',X2: 'A_iarray$',X3: $int,X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$b'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$al'(X4,X2) != X3 )
      | ( 'fun_app$al'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1060]) ).

tff(f1060,plain,
    ! [X0: $int,X1: 'A_iarray_int_fun$',X2: 'A_iarray$',X3: $int,X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$b'(X5,X1,X4))
      | ~ 'member$a'(X2,X5)
      | ( 'fun_app$al'(X4,X2) != X3 )
      | ( 'fun_app$al'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f357]) ).

tff(f357,axiom,
    ! [X0: $int,X1: 'A_iarray_int_fun$',X2: 'A_iarray$',X3: $int,X4: 'A_iarray_int_fun$',X5: 'A_iarray_set$'] :
      ( ( 'member$a'(X2,X5)
        & ( 'fun_app$al'(X4,X2) = X3 )
        & ( 'fun_app$al'(X1,X2) = X0 ) )
     => 'member$g'('pair$c'(X0,X3),'image2$b'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom355) ).

tff(f8357,plain,
    spl230_607,
    inference(avatar_split_clause,[],[f3250,f8355]) ).

tff(f8355,plain,
    ( spl230_607
  <=> ! [X2: 'Nat$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$',X1: 'Nat_a_iarray_list_fun$'] :
        ( 'member$'('pair$b'('fun_app$ar'(X1,X2),'fun_app$ar'(X4,X2)),'image2$i'(X5,X1,X4))
        | ~ 'member$c'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_607])]) ).

tff(f3250,plain,
    ! [X2: 'Nat$',X1: 'Nat_a_iarray_list_fun$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( 'member$'('pair$b'('fun_app$ar'(X1,X2),'fun_app$ar'(X4,X2)),'image2$i'(X5,X1,X4))
      | ~ 'member$c'(X2,X5) ),
    inference(equality_resolution,[],[f3249]) ).

tff(f3249,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_a_iarray_list_fun$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( 'member$'('pair$b'(X0,'fun_app$ar'(X4,X2)),'image2$i'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ar'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2903]) ).

tff(f2903,plain,
    ! [X2: 'Nat$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'Nat_a_iarray_list_fun$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( 'member$'('pair$b'(X0,X3),'image2$i'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ar'(X4,X2) != X3 )
      | ( 'fun_app$ar'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1059]) ).

tff(f1059,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat_a_iarray_list_fun$',X2: 'Nat$',X3: 'A_iarray_list$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( 'member$'('pair$b'(X0,X3),'image2$i'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ar'(X4,X2) != X3 )
      | ( 'fun_app$ar'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1058]) ).

tff(f1058,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat_a_iarray_list_fun$',X2: 'Nat$',X3: 'A_iarray_list$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( 'member$'('pair$b'(X0,X3),'image2$i'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ar'(X4,X2) != X3 )
      | ( 'fun_app$ar'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f364]) ).

tff(f364,axiom,
    ! [X0: 'A_iarray_list$',X1: 'Nat_a_iarray_list_fun$',X2: 'Nat$',X3: 'A_iarray_list$',X4: 'Nat_a_iarray_list_fun$',X5: 'Nat_set$'] :
      ( ( 'member$c'(X2,X5)
        & ( 'fun_app$ar'(X4,X2) = X3 )
        & ( 'fun_app$ar'(X1,X2) = X0 ) )
     => 'member$'('pair$b'(X0,X3),'image2$i'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom362) ).

tff(f8353,plain,
    spl230_606,
    inference(avatar_split_clause,[],[f3248,f8351]) ).

tff(f8351,plain,
    ( spl230_606
  <=> ! [X2: 'Nat$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$',X1: 'Nat_a_iarray_iarray_fun$'] :
        ( 'member$e'('pair$'('fun_app$ap'(X1,X2),'fun_app$ap'(X4,X2)),'image2$g'(X5,X1,X4))
        | ~ 'member$c'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_606])]) ).

tff(f3248,plain,
    ! [X2: 'Nat$',X1: 'Nat_a_iarray_iarray_fun$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$e'('pair$'('fun_app$ap'(X1,X2),'fun_app$ap'(X4,X2)),'image2$g'(X5,X1,X4))
      | ~ 'member$c'(X2,X5) ),
    inference(equality_resolution,[],[f3247]) ).

tff(f3247,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_iarray$',X1: 'Nat_a_iarray_iarray_fun$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$e'('pair$'(X0,'fun_app$ap'(X4,X2)),'image2$g'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ap'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2902]) ).

tff(f2902,plain,
    ! [X2: 'Nat$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray$',X1: 'Nat_a_iarray_iarray_fun$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$g'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ap'(X4,X2) != X3 )
      | ( 'fun_app$ap'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1057]) ).

tff(f1057,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'Nat_a_iarray_iarray_fun$',X2: 'Nat$',X3: 'A_iarray_iarray$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$g'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ap'(X4,X2) != X3 )
      | ( 'fun_app$ap'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1056]) ).

tff(f1056,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'Nat_a_iarray_iarray_fun$',X2: 'Nat$',X3: 'A_iarray_iarray$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$g'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$ap'(X4,X2) != X3 )
      | ( 'fun_app$ap'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f362]) ).

tff(f362,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'Nat_a_iarray_iarray_fun$',X2: 'Nat$',X3: 'A_iarray_iarray$',X4: 'Nat_a_iarray_iarray_fun$',X5: 'Nat_set$'] :
      ( ( 'member$c'(X2,X5)
        & ( 'fun_app$ap'(X4,X2) = X3 )
        & ( 'fun_app$ap'(X1,X2) = X0 ) )
     => 'member$e'('pair$'(X0,X3),'image2$g'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom360) ).

tff(f8349,plain,
    spl230_605,
    inference(avatar_split_clause,[],[f3246,f8347]) ).

tff(f8347,plain,
    ( spl230_605
  <=> ! [X2: 'Nat$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$',X1: 'Nat_a_iarray_fun$'] :
        ( 'member$f'('pair$a'('fun_app$an'(X1,X2),'fun_app$an'(X4,X2)),'image2$d'(X5,X1,X4))
        | ~ 'member$c'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_605])]) ).

tff(f3246,plain,
    ! [X2: 'Nat$',X1: 'Nat_a_iarray_fun$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$f'('pair$a'('fun_app$an'(X1,X2),'fun_app$an'(X4,X2)),'image2$d'(X5,X1,X4))
      | ~ 'member$c'(X2,X5) ),
    inference(equality_resolution,[],[f3245]) ).

tff(f3245,plain,
    ! [X2: 'Nat$',X0: 'A_iarray$',X1: 'Nat_a_iarray_fun$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$f'('pair$a'(X0,'fun_app$an'(X4,X2)),'image2$d'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$an'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2901]) ).

tff(f2901,plain,
    ! [X2: 'Nat$',X3: 'A_iarray$',X0: 'A_iarray$',X1: 'Nat_a_iarray_fun$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$d'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$an'(X4,X2) != X3 )
      | ( 'fun_app$an'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1055]) ).

tff(f1055,plain,
    ! [X0: 'A_iarray$',X1: 'Nat_a_iarray_fun$',X2: 'Nat$',X3: 'A_iarray$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$d'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$an'(X4,X2) != X3 )
      | ( 'fun_app$an'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1054]) ).

tff(f1054,plain,
    ! [X0: 'A_iarray$',X1: 'Nat_a_iarray_fun$',X2: 'Nat$',X3: 'A_iarray$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$d'(X5,X1,X4))
      | ~ 'member$c'(X2,X5)
      | ( 'fun_app$an'(X4,X2) != X3 )
      | ( 'fun_app$an'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f359]) ).

tff(f359,axiom,
    ! [X0: 'A_iarray$',X1: 'Nat_a_iarray_fun$',X2: 'Nat$',X3: 'A_iarray$',X4: 'Nat_a_iarray_fun$',X5: 'Nat_set$'] :
      ( ( 'member$c'(X2,X5)
        & ( 'fun_app$an'(X4,X2) = X3 )
        & ( 'fun_app$an'(X1,X2) = X0 ) )
     => 'member$f'('pair$a'(X0,X3),'image2$d'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom357) ).

tff(f8345,plain,
    spl230_604,
    inference(avatar_split_clause,[],[f3244,f8343]) ).

tff(f8343,plain,
    ( spl230_604
  <=> ! [X2: $int,X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$',X1: 'Int_a_iarray_iarray_fun$'] :
        ( 'member$e'('pair$'('fun_app$aq'(X1,X2),'fun_app$aq'(X4,X2)),'image2$h'(X5,X1,X4))
        | ~ 'member$d'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_604])]) ).

tff(f3244,plain,
    ! [X2: $int,X1: 'Int_a_iarray_iarray_fun$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$e'('pair$'('fun_app$aq'(X1,X2),'fun_app$aq'(X4,X2)),'image2$h'(X5,X1,X4))
      | ~ 'member$d'(X2,X5) ),
    inference(equality_resolution,[],[f3243]) ).

tff(f3243,plain,
    ! [X2: $int,X0: 'A_iarray_iarray$',X1: 'Int_a_iarray_iarray_fun$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$e'('pair$'(X0,'fun_app$aq'(X4,X2)),'image2$h'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$aq'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2900]) ).

tff(f2900,plain,
    ! [X2: $int,X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray$',X1: 'Int_a_iarray_iarray_fun$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$h'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$aq'(X4,X2) != X3 )
      | ( 'fun_app$aq'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1053]) ).

tff(f1053,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'Int_a_iarray_iarray_fun$',X2: $int,X3: 'A_iarray_iarray$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$h'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$aq'(X4,X2) != X3 )
      | ( 'fun_app$aq'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1052]) ).

tff(f1052,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'Int_a_iarray_iarray_fun$',X2: $int,X3: 'A_iarray_iarray$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$e'('pair$'(X0,X3),'image2$h'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$aq'(X4,X2) != X3 )
      | ( 'fun_app$aq'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f363]) ).

tff(f363,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'Int_a_iarray_iarray_fun$',X2: $int,X3: 'A_iarray_iarray$',X4: 'Int_a_iarray_iarray_fun$',X5: 'Int_set$'] :
      ( ( 'member$d'(X2,X5)
        & ( 'fun_app$aq'(X4,X2) = X3 )
        & ( 'fun_app$aq'(X1,X2) = X0 ) )
     => 'member$e'('pair$'(X0,X3),'image2$h'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom361) ).

tff(f8341,plain,
    spl230_603,
    inference(avatar_split_clause,[],[f3242,f8339]) ).

tff(f8339,plain,
    ( spl230_603
  <=> ! [X2: $int,X4: 'Int_a_iarray_fun$',X5: 'Int_set$',X1: 'Int_a_iarray_fun$'] :
        ( 'member$f'('pair$a'('fun_app$ao'(X1,X2),'fun_app$ao'(X4,X2)),'image2$e'(X5,X1,X4))
        | ~ 'member$d'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_603])]) ).

tff(f3242,plain,
    ! [X2: $int,X1: 'Int_a_iarray_fun$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$f'('pair$a'('fun_app$ao'(X1,X2),'fun_app$ao'(X4,X2)),'image2$e'(X5,X1,X4))
      | ~ 'member$d'(X2,X5) ),
    inference(equality_resolution,[],[f3241]) ).

tff(f3241,plain,
    ! [X2: $int,X0: 'A_iarray$',X1: 'Int_a_iarray_fun$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$f'('pair$a'(X0,'fun_app$ao'(X4,X2)),'image2$e'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ao'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2899]) ).

tff(f2899,plain,
    ! [X2: $int,X3: 'A_iarray$',X0: 'A_iarray$',X1: 'Int_a_iarray_fun$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$e'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ao'(X4,X2) != X3 )
      | ( 'fun_app$ao'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1051]) ).

tff(f1051,plain,
    ! [X0: 'A_iarray$',X1: 'Int_a_iarray_fun$',X2: $int,X3: 'A_iarray$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$e'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ao'(X4,X2) != X3 )
      | ( 'fun_app$ao'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1050]) ).

tff(f1050,plain,
    ! [X0: 'A_iarray$',X1: 'Int_a_iarray_fun$',X2: $int,X3: 'A_iarray$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( 'member$f'('pair$a'(X0,X3),'image2$e'(X5,X1,X4))
      | ~ 'member$d'(X2,X5)
      | ( 'fun_app$ao'(X4,X2) != X3 )
      | ( 'fun_app$ao'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f360]) ).

tff(f360,axiom,
    ! [X0: 'A_iarray$',X1: 'Int_a_iarray_fun$',X2: $int,X3: 'A_iarray$',X4: 'Int_a_iarray_fun$',X5: 'Int_set$'] :
      ( ( 'member$d'(X2,X5)
        & ( 'fun_app$ao'(X4,X2) = X3 )
        & ( 'fun_app$ao'(X1,X2) = X0 ) )
     => 'member$f'('pair$a'(X0,X3),'image2$e'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom358) ).

tff(f8337,plain,
    ( spl230_602
    | ~ spl230_74
    | ~ spl230_149 ),
    inference(avatar_split_clause,[],[f4992,f4210,f3823,f8335]) ).

tff(f8335,plain,
    ( spl230_602
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( sK38('pair$a'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_602])]) ).

tff(f3823,plain,
    ( spl230_74
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'fst$e'('pair$a'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_74])]) ).

tff(f4210,plain,
    ( spl230_149
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'fst$e'(X0) = sK38(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_149])]) ).

tff(f4992,plain,
    ( ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( sK38('pair$a'(X0,X1)) = X0 )
    | ~ spl230_74
    | ~ spl230_149 ),
    inference(superposition,[],[f4211,f3824]) ).

tff(f3824,plain,
    ( ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'fst$e'('pair$a'(X0,X1)) = X0 )
    | ~ spl230_74 ),
    inference(avatar_component_clause,[],[f3823]) ).

tff(f4211,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'fst$e'(X0) = sK38(X0) )
    | ~ spl230_149 ),
    inference(avatar_component_clause,[],[f4210]) ).

tff(f8333,plain,
    spl230_601,
    inference(avatar_split_clause,[],[f3240,f8331]) ).

tff(f8331,plain,
    ( spl230_601
  <=> ! [X2: 'A_iarray_list$',X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$',X1: 'A_iarray_list_int_fun$'] :
        ( 'member$g'('pair$c'('fun_app$am'(X1,X2),'fun_app$am'(X4,X2)),'image2$c'(X5,X1,X4))
        | ~ 'member$b'(X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_601])]) ).

tff(f3240,plain,
    ! [X2: 'A_iarray_list$',X1: 'A_iarray_list_int_fun$',X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( 'member$g'('pair$c'('fun_app$am'(X1,X2),'fun_app$am'(X4,X2)),'image2$c'(X5,X1,X4))
      | ~ 'member$b'(X2,X5) ),
    inference(equality_resolution,[],[f3239]) ).

tff(f3239,plain,
    ! [X2: 'A_iarray_list$',X0: $int,X1: 'A_iarray_list_int_fun$',X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( 'member$g'('pair$c'(X0,'fun_app$am'(X4,X2)),'image2$c'(X5,X1,X4))
      | ~ 'member$b'(X2,X5)
      | ( 'fun_app$am'(X1,X2) != X0 ) ),
    inference(equality_resolution,[],[f2898]) ).

tff(f2898,plain,
    ! [X2: 'A_iarray_list$',X3: $int,X0: $int,X1: 'A_iarray_list_int_fun$',X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$c'(X5,X1,X4))
      | ~ 'member$b'(X2,X5)
      | ( 'fun_app$am'(X4,X2) != X3 )
      | ( 'fun_app$am'(X1,X2) != X0 ) ),
    inference(cnf_transformation,[],[f1049]) ).

tff(f1049,plain,
    ! [X0: $int,X1: 'A_iarray_list_int_fun$',X2: 'A_iarray_list$',X3: $int,X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$c'(X5,X1,X4))
      | ~ 'member$b'(X2,X5)
      | ( 'fun_app$am'(X4,X2) != X3 )
      | ( 'fun_app$am'(X1,X2) != X0 ) ),
    inference(flattening,[],[f1048]) ).

tff(f1048,plain,
    ! [X0: $int,X1: 'A_iarray_list_int_fun$',X2: 'A_iarray_list$',X3: $int,X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( 'member$g'('pair$c'(X0,X3),'image2$c'(X5,X1,X4))
      | ~ 'member$b'(X2,X5)
      | ( 'fun_app$am'(X4,X2) != X3 )
      | ( 'fun_app$am'(X1,X2) != X0 ) ),
    inference(ennf_transformation,[],[f358]) ).

tff(f358,axiom,
    ! [X0: $int,X1: 'A_iarray_list_int_fun$',X2: 'A_iarray_list$',X3: $int,X4: 'A_iarray_list_int_fun$',X5: 'A_iarray_list_set$'] :
      ( ( 'member$b'(X2,X5)
        & ( 'fun_app$am'(X4,X2) = X3 )
        & ( 'fun_app$am'(X1,X2) = X0 ) )
     => 'member$g'('pair$c'(X0,X3),'image2$c'(X5,X1,X4)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom356) ).

tff(f8329,plain,
    spl230_600,
    inference(avatar_split_clause,[],[f2958,f8327]) ).

tff(f8327,plain,
    ( spl230_600
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_inv$'(X0) = X1 )
        | ( 'matrix_matrix_mult$'(X1,X0) != 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_600])]) ).

tff(f2958,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = X1 )
      | ( 'matrix_matrix_mult$'(X1,X0) != 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(definition_unfolding,[],[f2074,f1818]) ).

tff(f2074,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = X1 )
      | ( 'gauss_Jordan$'(X0) != 'matrix_matrix_mult$'(X1,X0) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f837]) ).

tff(f837,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = X1 )
      | ( 'gauss_Jordan$'(X0) != 'matrix_matrix_mult$'(X1,X0) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(flattening,[],[f836]) ).

tff(f836,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = X1 )
      | ( 'gauss_Jordan$'(X0) != 'matrix_matrix_mult$'(X1,X0) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f179]) ).

tff(f179,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
        & 'fun_app$o'('invertible$',X0) )
     => ( 'matrix_inv$'(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom177) ).

tff(f8325,plain,
    spl230_599,
    inference(avatar_split_clause,[],[f2888,f8323]) ).

tff(f8323,plain,
    ( spl230_599
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
        | ( X1 = X2 )
        | ~ sP30(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_599])]) ).

tff(f2888,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
      | ( X1 = X2 )
      | ~ sP30(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f8321,plain,
    spl230_598,
    inference(avatar_split_clause,[],[f2883,f8319]) ).

tff(f8319,plain,
    ( spl230_598
  <=> ! [X4: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
        | ~ 'member$f'('pair$a'(X0,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_598])]) ).

tff(f2883,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$',X4: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('cons$'(X0,X1),'cons$'(X2,X3)),'lexord$c'(X4))
      | ~ 'member$f'('pair$a'(X0,X2),X4) ),
    inference(cnf_transformation,[],[f1729]) ).

tff(f8317,plain,
    spl230_597,
    inference(avatar_split_clause,[],[f2859,f8315]) ).

tff(f8315,plain,
    ( spl230_597
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
        | ( X1 = X2 )
        | ~ sP27(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_597])]) ).

tff(f2859,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
      | ( X1 = X2 )
      | ~ sP27(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f8313,plain,
    spl230_596,
    inference(avatar_split_clause,[],[f2854,f8311]) ).

tff(f8311,plain,
    ( spl230_596
  <=> ! [X4: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
        | ~ 'member$'('pair$b'(X0,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_596])]) ).

tff(f2854,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X1),'cons$b'(X2,X3)),'lexord$b'(X4))
      | ~ 'member$'('pair$b'(X0,X2),X4) ),
    inference(cnf_transformation,[],[f1715]) ).

tff(f8309,plain,
    spl230_595,
    inference(avatar_split_clause,[],[f2839,f8307]) ).

tff(f8307,plain,
    ( spl230_595
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
        | ( X1 = X2 )
        | ~ sP25(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_595])]) ).

tff(f2839,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
      | ( X1 = X2 )
      | ~ sP25(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f8305,plain,
    spl230_594,
    inference(avatar_split_clause,[],[f2831,f8303]) ).

tff(f8303,plain,
    ( spl230_594
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
        | ( X1 = X2 )
        | ~ sP24(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_594])]) ).

tff(f2831,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
      | ( X1 = X2 )
      | ~ sP24(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f8301,plain,
    spl230_593,
    inference(avatar_split_clause,[],[f2826,f8299]) ).

tff(f8299,plain,
    ( spl230_593
  <=> ! [X4: 'Int_int_prod_set$',X0: $int,X3: 'Int_list$',X2: $int,X1: 'Int_list$'] :
        ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
        | ~ 'member$g'('pair$c'(X0,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_593])]) ).

tff(f2826,plain,
    ! [X2: $int,X3: 'Int_list$',X0: $int,X1: 'Int_list$',X4: 'Int_int_prod_set$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X1),'cons$c'(X2,X3)),'lexord$'(X4))
      | ~ 'member$g'('pair$c'(X0,X2),X4) ),
    inference(cnf_transformation,[],[f1701]) ).

tff(f8297,plain,
    spl230_592,
    inference(avatar_split_clause,[],[f2822,f8295]) ).

tff(f8295,plain,
    ( spl230_592
  <=> ! [X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$'] :
        ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
        | ~ 'member$e'('pair$'(X0,X2),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_592])]) ).

tff(f2822,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X1),'cons$d'(X2,X3)),'lexord$a'(X4))
      | ~ 'member$e'('pair$'(X0,X2),X4) ),
    inference(cnf_transformation,[],[f1699]) ).

tff(f8293,plain,
    ( spl230_591
    | ~ spl230_76
    | ~ spl230_148 ),
    inference(avatar_split_clause,[],[f4829,f4194,f3831,f8291]) ).

tff(f8291,plain,
    ( spl230_591
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( sK39('pair$a'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_591])]) ).

tff(f3831,plain,
    ( spl230_76
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'snd$e'('pair$a'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_76])]) ).

tff(f4194,plain,
    ( spl230_148
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'snd$e'(X0) = sK39(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_148])]) ).

tff(f4829,plain,
    ( ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( sK39('pair$a'(X0,X1)) = X1 )
    | ~ spl230_76
    | ~ spl230_148 ),
    inference(superposition,[],[f4195,f3832]) ).

tff(f3832,plain,
    ( ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'snd$e'('pair$a'(X0,X1)) = X1 )
    | ~ spl230_76 ),
    inference(avatar_component_clause,[],[f3831]) ).

tff(f4195,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'snd$e'(X0) = sK39(X0) )
    | ~ spl230_148 ),
    inference(avatar_component_clause,[],[f4194]) ).

tff(f8289,plain,
    spl230_590,
    inference(avatar_split_clause,[],[f2792,f8287]) ).

tff(f8287,plain,
    ( spl230_590
  <=> ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
        ( 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,sK223(X0)),sK225(X0)),sK227(X0)),sK229(X0))
        | ~ sP20(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_590])]) ).

tff(f2792,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,sK223(X0)),sK225(X0)),sK227(X0)),sK229(X0))
      | ~ sP20(X0) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f1685,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,'cons$'(sK222(X0),sK223(X0))),'cons$'(sK224(X0),sK225(X0))),'cons$'(sK226(X0),sK227(X0))),'cons$'(sK228(X0),sK229(X0)))
        & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,sK223(X0)),sK225(X0)),sK227(X0)),sK229(X0))
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK229(X0))) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK223(X0))) ) )
      | ~ sP20(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK222,sK223,sK224,sK225,sK226,sK227,sK228,sK229])],[f1683,f1684]) ).

tff(f1684,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ? [X1: 'A_iarray$',X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$',X7: 'A_iarray$',X8: 'A_iarray_list$'] :
          ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,'cons$'(X1,X2)),'cons$'(X3,X4)),'cons$'(X5,X6)),'cons$'(X7,X8))
          & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,X2),X4),X6),X8)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X4)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X4)) ) )
     => ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,'cons$'(sK222(X0),sK223(X0))),'cons$'(sK224(X0),sK225(X0))),'cons$'(sK226(X0),sK227(X0))),'cons$'(sK228(X0),sK229(X0)))
        & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,sK223(X0)),sK225(X0)),sK227(X0)),sK229(X0))
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK229(X0))) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) )
        & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK223(X0))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1683,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ? [X1: 'A_iarray$',X2: 'A_iarray_list$',X3: 'A_iarray$',X4: 'A_iarray_list$',X5: 'A_iarray$',X6: 'A_iarray_list$',X7: 'A_iarray$',X8: 'A_iarray_list$'] :
          ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,'cons$'(X1,X2)),'cons$'(X3,X4)),'cons$'(X5,X6)),'cons$'(X7,X8))
          & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X0,X2),X4),X6),X8)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X4)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X2)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X4)) ) )
      | ~ sP20(X0) ),
    inference(rectify,[],[f1682]) ).

tff(f1682,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ? [X5: 'A_iarray$',X6: 'A_iarray_list$',X7: 'A_iarray$',X8: 'A_iarray_list$',X9: 'A_iarray$',X10: 'A_iarray_list$',X11: 'A_iarray$',X12: 'A_iarray_list$'] :
          ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X4,'cons$'(X5,X6)),'cons$'(X7,X8)),'cons$'(X9,X10)),'cons$'(X11,X12))
          & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X4,X6),X8),X10),X12)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X10)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X12)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X10)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) ) )
      | ~ sP20(X4) ),
    inference(nnf_transformation,[],[f1117]) ).

tff(f1117,plain,
    ! [X4: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ? [X5: 'A_iarray$',X6: 'A_iarray_list$',X7: 'A_iarray$',X8: 'A_iarray_list$',X9: 'A_iarray$',X10: 'A_iarray_list$',X11: 'A_iarray$',X12: 'A_iarray_list$'] :
          ( ~ 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X4,'cons$'(X5,X6)),'cons$'(X7,X8)),'cons$'(X9,X10)),'cons$'(X11,X12))
          & 'fun_app$b'('fun_app$i'('fun_app$be'('fun_app$bf'(X4,X6),X8),X10),X12)
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X10)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X12)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X10)) )
          & ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X6)) = 'fun_app$l'('of_nat$','fun_app$m'('size$',X8)) ) )
      | ~ sP20(X4) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).

tff(f8285,plain,
    spl230_589,
    inference(avatar_split_clause,[],[f2791,f8283]) ).

tff(f8283,plain,
    ( spl230_589
  <=> ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK229(X0))) )
        | ~ sP20(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_589])]) ).

tff(f2791,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK229(X0))) )
      | ~ sP20(X0) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f8281,plain,
    spl230_588,
    inference(avatar_split_clause,[],[f2790,f8279]) ).

tff(f8279,plain,
    ( spl230_588
  <=> ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) )
        | ~ sP20(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_588])]) ).

tff(f2790,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK227(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) )
      | ~ sP20(X0) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f8277,plain,
    spl230_587,
    inference(avatar_split_clause,[],[f2789,f8275]) ).

tff(f8275,plain,
    ( spl230_587
  <=> ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK223(X0))) )
        | ~ sP20(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_587])]) ).

tff(f2789,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sK225(X0))) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK223(X0))) )
      | ~ sP20(X0) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f8273,plain,
    spl230_586,
    inference(avatar_split_clause,[],[f2761,f8271]) ).

tff(f8271,plain,
    ( spl230_586
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X1),sK221(X0,X1,X2,X3)) = X0 )
        | ~ sP19(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_586])]) ).

tff(f2761,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),sK221(X0,X1,X2,X3)) = X0 )
      | ~ sP19(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1680]) ).

tff(f8269,plain,
    spl230_585,
    inference(avatar_split_clause,[],[f2753,f8267]) ).

tff(f8267,plain,
    ( spl230_585
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X1),sK218(X0,X1,X2,X3)) = X0 )
        | ~ sP18(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_585])]) ).

tff(f2753,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),sK218(X0,X1,X2,X3)) = X0 )
      | ~ sP18(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1674]) ).

tff(f8265,plain,
    spl230_584,
    inference(avatar_split_clause,[],[f2716,f8263]) ).

tff(f8263,plain,
    ( spl230_584
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$n'(X2,def_7(X1,X0))
        | ( 'some$'('the$a'(X0)) != X0 )
        | ~ sP17(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_584])]) ).

tff(f2716,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,def_7(X1,X0))
      | ( 'some$'('the$a'(X0)) != X0 )
      | ~ sP17(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1650]) ).

tff(f1650,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
      ( ( sP17(X0,X1,X2,X3)
        | ( ~ 'fun_app$n'(X2,def_7(X1,X0))
          & ( 'some$'('the$a'(X0)) = X0 ) )
        | ( ~ 'fun_app$n'(X2,X3)
          & ( 'none$' = X0 ) ) )
      & ( ( ( 'fun_app$n'(X2,def_7(X1,X0))
            | ( 'some$'('the$a'(X0)) != X0 ) )
          & ( 'fun_app$n'(X2,X3)
            | ( 'none$' != X0 ) ) )
        | ~ sP17(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f1649]) ).

tff(f1649,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( sP17(X3,X2,X0,X1)
        | ( ~ 'fun_app$n'(X0,def_7(X2,X3))
          & ( 'some$'('the$a'(X3)) = X3 ) )
        | ( ~ 'fun_app$n'(X0,X1)
          & ( 'none$' = X3 ) ) )
      & ( ( ( 'fun_app$n'(X0,def_7(X2,X3))
            | ( 'some$'('the$a'(X3)) != X3 ) )
          & ( 'fun_app$n'(X0,X1)
            | ( 'none$' != X3 ) ) )
        | ~ sP17(X3,X2,X0,X1) ) ),
    inference(flattening,[],[f1648]) ).

tff(f1648,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( sP17(X3,X2,X0,X1)
        | ( ~ 'fun_app$n'(X0,def_7(X2,X3))
          & ( 'some$'('the$a'(X3)) = X3 ) )
        | ( ~ 'fun_app$n'(X0,X1)
          & ( 'none$' = X3 ) ) )
      & ( ( ( 'fun_app$n'(X0,def_7(X2,X3))
            | ( 'some$'('the$a'(X3)) != X3 ) )
          & ( 'fun_app$n'(X0,X1)
            | ( 'none$' != X3 ) ) )
        | ~ sP17(X3,X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f1111]) ).

tff(f1111,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( sP17(X3,X2,X0,X1)
    <=> ( ( 'fun_app$n'(X0,def_7(X2,X3))
          | ( 'some$'('the$a'(X3)) != X3 ) )
        & ( 'fun_app$n'(X0,X1)
          | ( 'none$' != X3 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).

tff(f8261,plain,
    spl230_583,
    inference(avatar_split_clause,[],[f2708,f8259]) ).

tff(f8259,plain,
    ( spl230_583
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$n'(X2,def_5(X1,X0))
        | ( 'some$'('the$a'(X0)) != X0 )
        | ~ sP16(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_583])]) ).

tff(f2708,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,def_5(X1,X0))
      | ( 'some$'('the$a'(X0)) != X0 )
      | ~ sP16(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1646]) ).

tff(f1646,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X2: 'Bool_bool_fun$',X3: tlbool] :
      ( ( sP16(X0,X1,X2,X3)
        | ( ~ 'fun_app$n'(X2,def_5(X1,X0))
          & ( 'some$'('the$a'(X0)) = X0 ) )
        | ( ~ 'fun_app$n'(X2,X3)
          & ( 'none$' = X0 ) ) )
      & ( ( ( 'fun_app$n'(X2,def_5(X1,X0))
            | ( 'some$'('the$a'(X0)) != X0 ) )
          & ( 'fun_app$n'(X2,X3)
            | ( 'none$' != X0 ) ) )
        | ~ sP16(X0,X1,X2,X3) ) ),
    inference(rectify,[],[f1645]) ).

tff(f1645,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( sP16(X3,X2,X0,X1)
        | ( ~ 'fun_app$n'(X0,def_5(X2,X3))
          & ( 'some$'('the$a'(X3)) = X3 ) )
        | ( ~ 'fun_app$n'(X0,X1)
          & ( 'none$' = X3 ) ) )
      & ( ( ( 'fun_app$n'(X0,def_5(X2,X3))
            | ( 'some$'('the$a'(X3)) != X3 ) )
          & ( 'fun_app$n'(X0,X1)
            | ( 'none$' != X3 ) ) )
        | ~ sP16(X3,X2,X0,X1) ) ),
    inference(flattening,[],[f1644]) ).

tff(f1644,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( sP16(X3,X2,X0,X1)
        | ( ~ 'fun_app$n'(X0,def_5(X2,X3))
          & ( 'some$'('the$a'(X3)) = X3 ) )
        | ( ~ 'fun_app$n'(X0,X1)
          & ( 'none$' = X3 ) ) )
      & ( ( ( 'fun_app$n'(X0,def_5(X2,X3))
            | ( 'some$'('the$a'(X3)) != X3 ) )
          & ( 'fun_app$n'(X0,X1)
            | ( 'none$' != X3 ) ) )
        | ~ sP16(X3,X2,X0,X1) ) ),
    inference(nnf_transformation,[],[f1109]) ).

tff(f1109,plain,
    ! [X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( sP16(X3,X2,X0,X1)
    <=> ( ( 'fun_app$n'(X0,def_5(X2,X3))
          | ( 'some$'('the$a'(X3)) != X3 ) )
        & ( 'fun_app$n'(X0,X1)
          | ( 'none$' != X3 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

tff(f8257,plain,
    spl230_582,
    inference(avatar_split_clause,[],[f2706,f8255]) ).

tff(f8255,plain,
    ( spl230_582
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( 'fun_app$n'(X0,def_2(X1,X2,X3))
        | ~ 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_582])]) ).

tff(f2706,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( 'fun_app$n'(X0,def_2(X1,X2,X3))
      | ~ 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3) ),
    inference(cnf_transformation,[],[f1643]) ).

tff(f1643,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( 'fun_app$n'(X0,def_2(X1,X2,X3))
        | ~ 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3) )
      & ( 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3)
        | ~ 'fun_app$n'(X0,def_2(X1,X2,X3)) ) ),
    inference(nnf_transformation,[],[f74]) ).

tff(f74,axiom,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_2(X1,X2,X3))
    <=> 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom72) ).

tff(f8253,plain,
    spl230_581,
    inference(avatar_split_clause,[],[f2705,f8251]) ).

tff(f8251,plain,
    ( spl230_581
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3)
        | ~ 'fun_app$n'(X0,def_2(X1,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_581])]) ).

tff(f2705,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( 'fun_app$t'('case_option$a'(def_3(X0,X1),'uue$'(X0,X2)),X3)
      | ~ 'fun_app$n'(X0,def_2(X1,X2,X3)) ),
    inference(cnf_transformation,[],[f1643]) ).

tff(f8249,plain,
    ( ~ spl230_580
    | ~ spl230_63
    | ~ spl230_147 ),
    inference(avatar_split_clause,[],[f4276,f4157,f3778,f8246]) ).

tff(f8246,plain,
    ( spl230_580
  <=> ( 0 = 'fun_app$l'('of_nat$','size$d'('none$a')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_580])]) ).

tff(f3778,plain,
    ( spl230_63
  <=> ! [X0: 'A_iarray_iarray_option$'] : ( 'fun_app$l'('of_nat$','size$c'(X0)) != 0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_63])]) ).

tff(f4157,plain,
    ( spl230_147
  <=> ( 'size$d'('none$a') = 'size$c'('none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_147])]) ).

tff(f4276,plain,
    ( ( 0 != 'fun_app$l'('of_nat$','size$d'('none$a')) )
    | ~ spl230_63
    | ~ spl230_147 ),
    inference(superposition,[],[f3779,f4159]) ).

tff(f4159,plain,
    ( ( 'size$d'('none$a') = 'size$c'('none$') )
    | ~ spl230_147 ),
    inference(avatar_component_clause,[],[f4157]) ).

tff(f3779,plain,
    ( ! [X0: 'A_iarray_iarray_option$'] : ( 'fun_app$l'('of_nat$','size$c'(X0)) != 0 )
    | ~ spl230_63 ),
    inference(avatar_component_clause,[],[f3778]) ).

tff(f8244,plain,
    spl230_579,
    inference(avatar_split_clause,[],[f2622,f8242]) ).

tff(f8242,plain,
    ( spl230_579
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$s'('pair$z'('cons$b'(X0,X3),'cons$b'(X1,X3)),'listrel1$b'(X2))
        | ~ 'member$'('pair$b'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_579])]) ).

tff(f2622,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X3),'cons$b'(X1,X3)),'listrel1$b'(X2))
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f971]) ).

tff(f971,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'('cons$b'(X0,X3),'cons$b'(X1,X3)),'listrel1$b'(X2))
      | ~ 'member$'('pair$b'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f538]) ).

tff(f538,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list_list$'] :
      ( 'member$'('pair$b'(X0,X1),X2)
     => 'member$s'('pair$z'('cons$b'(X0,X3),'cons$b'(X1,X3)),'listrel1$b'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom536) ).

tff(f8240,plain,
    spl230_578,
    inference(avatar_split_clause,[],[f2621,f8238]) ).

tff(f8238,plain,
    ( spl230_578
  <=> ! [X0: $int,X3: 'Int_list$',X2: 'Int_int_prod_set$',X1: $int] :
        ( 'member$o'('pair$v'('cons$c'(X0,X3),'cons$c'(X1,X3)),'listrel1$'(X2))
        | ~ 'member$g'('pair$c'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_578])]) ).

tff(f2621,plain,
    ! [X2: 'Int_int_prod_set$',X3: 'Int_list$',X0: $int,X1: $int] :
      ( 'member$o'('pair$v'('cons$c'(X0,X3),'cons$c'(X1,X3)),'listrel1$'(X2))
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f970]) ).

tff(f970,plain,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$'] :
      ( 'member$o'('pair$v'('cons$c'(X0,X3),'cons$c'(X1,X3)),'listrel1$'(X2))
      | ~ 'member$g'('pair$c'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f536]) ).

tff(f536,axiom,
    ! [X0: $int,X1: $int,X2: 'Int_int_prod_set$',X3: 'Int_list$'] :
      ( 'member$g'('pair$c'(X0,X1),X2)
     => 'member$o'('pair$v'('cons$c'(X0,X3),'cons$c'(X1,X3)),'listrel1$'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom534) ).

tff(f8236,plain,
    spl230_577,
    inference(avatar_split_clause,[],[f2620,f8234]) ).

tff(f8234,plain,
    ( spl230_577
  <=> ! [X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_list$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
        ( 'member$p'('pair$w'('cons$d'(X0,X3),'cons$d'(X1,X3)),'listrel1$a'(X2))
        | ~ 'member$e'('pair$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_577])]) ).

tff(f2620,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X3),'cons$d'(X1,X3)),'listrel1$a'(X2))
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f969]) ).

tff(f969,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$'] :
      ( 'member$p'('pair$w'('cons$d'(X0,X3),'cons$d'(X1,X3)),'listrel1$a'(X2))
      | ~ 'member$e'('pair$'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f537]) ).

tff(f537,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray_list$'] :
      ( 'member$e'('pair$'(X0,X1),X2)
     => 'member$p'('pair$w'('cons$d'(X0,X3),'cons$d'(X1,X3)),'listrel1$a'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom535) ).

tff(f8232,plain,
    spl230_576,
    inference(avatar_split_clause,[],[f2619,f8230]) ).

tff(f8230,plain,
    ( spl230_576
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
        ( 'member$'('pair$b'('cons$'(X0,X3),'cons$'(X1,X3)),'listrel1$c'(X2))
        | ~ 'member$f'('pair$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_576])]) ).

tff(f2619,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray$'] :
      ( 'member$'('pair$b'('cons$'(X0,X3),'cons$'(X1,X3)),'listrel1$c'(X2))
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f968]) ).

tff(f968,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$'] :
      ( 'member$'('pair$b'('cons$'(X0,X3),'cons$'(X1,X3)),'listrel1$c'(X2))
      | ~ 'member$f'('pair$a'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f539]) ).

tff(f539,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$'] :
      ( 'member$f'('pair$a'(X0,X1),X2)
     => 'member$'('pair$b'('cons$'(X0,X3),'cons$'(X1,X3)),'listrel1$c'(X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom537) ).

tff(f8228,plain,
    spl230_575,
    inference(avatar_split_clause,[],[f2601,f8226]) ).

tff(f8226,plain,
    ( spl230_575
  <=> ! [X0: 'A_iarray_iarray$',X3: 'Int_set$',X2: 'A_iarray_iarray$',X1: 'Int_set$'] : ( 'plus$w'('pair$k'(X0,X1),'pair$k'(X2,X3)) = 'pair$k'('plus$d'(X0,X2),'plus$k'(X1,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_575])]) ).

tff(f2601,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'Int_set$',X0: 'A_iarray_iarray$',X1: 'Int_set$'] : ( 'plus$w'('pair$k'(X0,X1),'pair$k'(X2,X3)) = 'pair$k'('plus$d'(X0,X2),'plus$k'(X1,X3)) ),
    inference(cnf_transformation,[],[f189]) ).

tff(f189,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'Int_set$',X2: 'A_iarray_iarray$',X3: 'Int_set$'] : ( 'plus$w'('pair$k'(X0,X1),'pair$k'(X2,X3)) = 'pair$k'('plus$d'(X0,X2),'plus$k'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom187) ).

tff(f8224,plain,
    spl230_574,
    inference(avatar_split_clause,[],[f2495,f8222]) ).

tff(f8222,plain,
    ( spl230_574
  <=> ! [X2: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
        ( 'fun_app$t'('fun_app$z'(X1,X0),X2)
        | sP13(X2,X0,X1)
        | ( 'none$' = X2 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_574])]) ).

tff(f2495,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( 'fun_app$t'('fun_app$z'(X1,X0),X2)
      | sP13(X2,X0,X1)
      | ( 'none$' = X2 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1104]) ).

tff(f1104,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$z'(X1,X0),X2)
      | sP13(X2,X0,X1)
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(definition_folding,[],[f946,f1103]) ).

tff(f1103,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ~ sP13(X2,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

tff(f946,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$z'(X1,X0),X2)
      | ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(flattening,[],[f945]) ).

tff(f945,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$z'(X1,X0),X2)
      | ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(ennf_transformation,[],[f54]) ).

tff(f54,axiom,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ! [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
            ( ( ( 'some$'(X4) = X2 )
              & ( 'some$'(X3) = X0 ) )
           => 'fun_app$t'('fun_app$z'(X1,X0),X2) )
        & ( ( 'none$' = X2 )
         => 'fun_app$t'('fun_app$z'(X1,X0),X2) )
        & ( ( 'none$' = X0 )
         => 'fun_app$t'('fun_app$z'(X1,X0),X2) ) )
     => 'fun_app$t'('fun_app$z'(X1,X0),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom52) ).

tff(f8220,plain,
    spl230_573,
    inference(avatar_split_clause,[],[f2488,f8218]) ).

tff(f8218,plain,
    ( spl230_573
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
        ( 'fun_app$s'('fun_app$y'(X1,X0),X2)
        | sP12(X2,X0,X1)
        | ( 'none$a' = X2 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_573])]) ).

tff(f2488,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( 'fun_app$s'('fun_app$y'(X1,X0),X2)
      | sP12(X2,X0,X1)
      | ( 'none$a' = X2 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1102]) ).

tff(f1102,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$y'(X1,X0),X2)
      | sP12(X2,X0,X1)
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(definition_folding,[],[f944,f1101]) ).

tff(f1101,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ~ sP12(X2,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

tff(f944,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$y'(X1,X0),X2)
      | ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(flattening,[],[f943]) ).

tff(f943,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$y'(X1,X0),X2)
      | ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
        & ( 'none$' = X0 ) ) ),
    inference(ennf_transformation,[],[f53]) ).

tff(f53,axiom,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
            ( ( ( 'some$a'(X4) = X2 )
              & ( 'some$'(X3) = X0 ) )
           => 'fun_app$s'('fun_app$y'(X1,X0),X2) )
        & ( ( 'none$a' = X2 )
         => 'fun_app$s'('fun_app$y'(X1,X0),X2) )
        & ( ( 'none$' = X0 )
         => 'fun_app$s'('fun_app$y'(X1,X0),X2) ) )
     => 'fun_app$s'('fun_app$y'(X1,X0),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom51) ).

tff(f8216,plain,
    spl230_572,
    inference(avatar_split_clause,[],[f2481,f8214]) ).

tff(f8214,plain,
    ( spl230_572
  <=> ! [X2: 'A_iarray_iarray_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
        ( 'fun_app$t'('fun_app$x'(X1,X0),X2)
        | sP11(X2,X0,X1)
        | ( 'none$' = X2 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_572])]) ).

tff(f2481,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( 'fun_app$t'('fun_app$x'(X1,X0),X2)
      | sP11(X2,X0,X1)
      | ( 'none$' = X2 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1100]) ).

tff(f1100,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$x'(X1,X0),X2)
      | sP11(X2,X0,X1)
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(definition_folding,[],[f942,f1099]) ).

tff(f1099,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ~ sP11(X2,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

tff(f942,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$x'(X1,X0),X2)
      | ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(flattening,[],[f941]) ).

tff(f941,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('fun_app$x'(X1,X0),X2)
      | ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$' = X2 ) )
      | ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(ennf_transformation,[],[f52]) ).

tff(f52,axiom,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ! [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
            ( ( ( 'some$'(X4) = X2 )
              & ( 'some$a'(X3) = X0 ) )
           => 'fun_app$t'('fun_app$x'(X1,X0),X2) )
        & ( ( 'none$' = X2 )
         => 'fun_app$t'('fun_app$x'(X1,X0),X2) )
        & ( ( 'none$a' = X0 )
         => 'fun_app$t'('fun_app$x'(X1,X0),X2) ) )
     => 'fun_app$t'('fun_app$x'(X1,X0),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom50) ).

tff(f8212,plain,
    spl230_571,
    inference(avatar_split_clause,[],[f2474,f8210]) ).

tff(f8210,plain,
    ( spl230_571
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
        ( 'fun_app$s'('fun_app$w'(X1,X0),X2)
        | sP10(X2,X0,X1)
        | ( 'none$a' = X2 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_571])]) ).

tff(f2474,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( 'fun_app$s'('fun_app$w'(X1,X0),X2)
      | sP10(X2,X0,X1)
      | ( 'none$a' = X2 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1098]) ).

tff(f1098,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$w'(X1,X0),X2)
      | sP10(X2,X0,X1)
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(definition_folding,[],[f940,f1097]) ).

tff(f1097,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ~ sP10(X2,X0,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

tff(f940,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$w'(X1,X0),X2)
      | ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(flattening,[],[f939]) ).

tff(f939,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('fun_app$w'(X1,X0),X2)
      | ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X2 ) )
      | ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
        & ( 'none$a' = X0 ) ) ),
    inference(ennf_transformation,[],[f51]) ).

tff(f51,axiom,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
            ( ( ( 'some$a'(X4) = X2 )
              & ( 'some$a'(X3) = X0 ) )
           => 'fun_app$s'('fun_app$w'(X1,X0),X2) )
        & ( ( 'none$a' = X2 )
         => 'fun_app$s'('fun_app$w'(X1,X0),X2) )
        & ( ( 'none$a' = X0 )
         => 'fun_app$s'('fun_app$w'(X1,X0),X2) ) )
     => 'fun_app$s'('fun_app$w'(X1,X0),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom49) ).

tff(f8208,plain,
    spl230_570,
    inference(avatar_split_clause,[],[f2403,f8206]) ).

tff(f8206,plain,
    ( spl230_570
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X1) )
        | ~ 'member$b'(X0,'set$a'('n_lists$'(X1,X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_570])]) ).

tff(f2403,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X1) )
      | ~ 'member$b'(X0,'set$a'('n_lists$'(X1,X2))) ),
    inference(cnf_transformation,[],[f896]) ).

tff(f896,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat$',X2: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X1) )
      | ~ 'member$b'(X0,'set$a'('n_lists$'(X1,X2))) ),
    inference(ennf_transformation,[],[f601]) ).

tff(f601,axiom,
    ! [X0: 'A_iarray_list$',X1: 'Nat$',X2: 'A_iarray_list$'] :
      ( 'member$b'(X0,'set$a'('n_lists$'(X1,X2)))
     => ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 'fun_app$l'('of_nat$',X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom599) ).

tff(f8199,plain,
    spl230_569,
    inference(avatar_split_clause,[],[f2372,f8197]) ).

tff(f8197,plain,
    ( spl230_569
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'('fun_app$p'('append$d'(X0),X1)),X2) = 'fun_app$p'('append$d'(X0),'fun_app$p'('append$d'(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_569])]) ).

tff(f2372,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'('fun_app$p'('append$d'(X0),X1)),X2) = 'fun_app$p'('append$d'(X0),'fun_app$p'('append$d'(X1),X2)) ),
    inference(cnf_transformation,[],[f554]) ).

tff(f554,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'('fun_app$p'('append$d'(X0),X1)),X2) = 'fun_app$p'('append$d'(X0),'fun_app$p'('append$d'(X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom552) ).

tff(f8195,plain,
    spl230_568,
    inference(avatar_split_clause,[],[f2370,f8193]) ).

tff(f8193,plain,
    ( spl230_568
  <=> ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'('fun_app$bd'('append$'(X0),X1)),X2) = 'fun_app$bd'('append$'(X0),'fun_app$bd'('append$'(X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_568])]) ).

tff(f2370,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'('fun_app$bd'('append$'(X0),X1)),X2) = 'fun_app$bd'('append$'(X0),'fun_app$bd'('append$'(X1),X2)) ),
    inference(cnf_transformation,[],[f557]) ).

tff(f557,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'('fun_app$bd'('append$'(X0),X1)),X2) = 'fun_app$bd'('append$'(X0),'fun_app$bd'('append$'(X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom555) ).

tff(f8191,plain,
    spl230_567,
    inference(avatar_split_clause,[],[f2110,f8189]) ).

tff(f8189,plain,
    ( spl230_567
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
        ( ( 'collect$c'(X1) = 'collect$c'(X0) )
        | ~ 'fun_app$c'(X1,sK87(X0,X1))
        | ~ 'fun_app$c'(X0,sK87(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_567])]) ).

tff(f2110,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ( 'collect$c'(X1) = 'collect$c'(X0) )
      | ~ 'fun_app$c'(X1,sK87(X0,X1))
      | ~ 'fun_app$c'(X0,sK87(X0,X1)) ),
    inference(cnf_transformation,[],[f1278]) ).

tff(f1278,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ( 'collect$c'(X1) = 'collect$c'(X0) )
      | ( ( ~ 'fun_app$c'(X1,sK87(X0,X1))
          | ~ 'fun_app$c'(X0,sK87(X0,X1)) )
        & ( 'fun_app$c'(X1,sK87(X0,X1))
          | 'fun_app$c'(X0,sK87(X0,X1)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f1276,f1277]) ).

tff(f1277,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ( ~ 'fun_app$c'(X1,X2)
            | ~ 'fun_app$c'(X0,X2) )
          & ( 'fun_app$c'(X1,X2)
            | 'fun_app$c'(X0,X2) ) )
     => ( ( ~ 'fun_app$c'(X1,sK87(X0,X1))
          | ~ 'fun_app$c'(X0,sK87(X0,X1)) )
        & ( 'fun_app$c'(X1,sK87(X0,X1))
          | 'fun_app$c'(X0,sK87(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1276,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ( 'collect$c'(X1) = 'collect$c'(X0) )
      | ? [X2: 'Nat$'] :
          ( ( ~ 'fun_app$c'(X1,X2)
            | ~ 'fun_app$c'(X0,X2) )
          & ( 'fun_app$c'(X1,X2)
            | 'fun_app$c'(X0,X2) ) ) ),
    inference(nnf_transformation,[],[f872]) ).

tff(f872,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ( 'collect$c'(X1) = 'collect$c'(X0) )
      | ? [X2: 'Nat$'] :
          ( 'fun_app$c'(X0,X2)
        <~> 'fun_app$c'(X1,X2) ) ),
    inference(ennf_transformation,[],[f104]) ).

tff(f104,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ! [X2: 'Nat$'] :
          ( 'fun_app$c'(X0,X2)
        <=> 'fun_app$c'(X1,X2) )
     => ( 'collect$c'(X1) = 'collect$c'(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom102) ).

tff(f8187,plain,
    spl230_566,
    inference(avatar_split_clause,[],[f2109,f8185]) ).

tff(f8185,plain,
    ( spl230_566
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
        ( ( 'collect$c'(X1) = 'collect$c'(X0) )
        | 'fun_app$c'(X1,sK87(X0,X1))
        | 'fun_app$c'(X0,sK87(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_566])]) ).

tff(f2109,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat_bool_fun$'] :
      ( ( 'collect$c'(X1) = 'collect$c'(X0) )
      | 'fun_app$c'(X1,sK87(X0,X1))
      | 'fun_app$c'(X0,sK87(X0,X1)) ),
    inference(cnf_transformation,[],[f1278]) ).

tff(f8183,plain,
    spl230_565,
    inference(avatar_split_clause,[],[f2108,f8181]) ).

tff(f8181,plain,
    ( spl230_565
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'collect$d'(X1) = 'collect$d'(X0) )
        | ~ 'fun_app$'(X1,sK86(X0,X1))
        | ~ 'fun_app$'(X0,sK86(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_565])]) ).

tff(f2108,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'collect$d'(X1) = 'collect$d'(X0) )
      | ~ 'fun_app$'(X1,sK86(X0,X1))
      | ~ 'fun_app$'(X0,sK86(X0,X1)) ),
    inference(cnf_transformation,[],[f1275]) ).

tff(f1275,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'collect$d'(X1) = 'collect$d'(X0) )
      | ( ( ~ 'fun_app$'(X1,sK86(X0,X1))
          | ~ 'fun_app$'(X0,sK86(X0,X1)) )
        & ( 'fun_app$'(X1,sK86(X0,X1))
          | 'fun_app$'(X0,sK86(X0,X1)) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f1273,f1274]) ).

tff(f1274,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ? [X2: 'A_iarray$'] :
          ( ( ~ 'fun_app$'(X1,X2)
            | ~ 'fun_app$'(X0,X2) )
          & ( 'fun_app$'(X1,X2)
            | 'fun_app$'(X0,X2) ) )
     => ( ( ~ 'fun_app$'(X1,sK86(X0,X1))
          | ~ 'fun_app$'(X0,sK86(X0,X1)) )
        & ( 'fun_app$'(X1,sK86(X0,X1))
          | 'fun_app$'(X0,sK86(X0,X1)) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1273,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'collect$d'(X1) = 'collect$d'(X0) )
      | ? [X2: 'A_iarray$'] :
          ( ( ~ 'fun_app$'(X1,X2)
            | ~ 'fun_app$'(X0,X2) )
          & ( 'fun_app$'(X1,X2)
            | 'fun_app$'(X0,X2) ) ) ),
    inference(nnf_transformation,[],[f871]) ).

tff(f871,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'collect$d'(X1) = 'collect$d'(X0) )
      | ? [X2: 'A_iarray$'] :
          ( 'fun_app$'(X0,X2)
        <~> 'fun_app$'(X1,X2) ) ),
    inference(ennf_transformation,[],[f105]) ).

tff(f105,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ! [X2: 'A_iarray$'] :
          ( 'fun_app$'(X0,X2)
        <=> 'fun_app$'(X1,X2) )
     => ( 'collect$d'(X1) = 'collect$d'(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom103) ).

tff(f8179,plain,
    spl230_564,
    inference(avatar_split_clause,[],[f2107,f8177]) ).

tff(f8177,plain,
    ( spl230_564
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'collect$d'(X1) = 'collect$d'(X0) )
        | 'fun_app$'(X1,sK86(X0,X1))
        | 'fun_app$'(X0,sK86(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_564])]) ).

tff(f2107,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'collect$d'(X1) = 'collect$d'(X0) )
      | 'fun_app$'(X1,sK86(X0,X1))
      | 'fun_app$'(X0,sK86(X0,X1)) ),
    inference(cnf_transformation,[],[f1275]) ).

tff(f8175,plain,
    spl230_563,
    inference(avatar_split_clause,[],[f1887,f8173]) ).

tff(f8173,plain,
    ( spl230_563
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK35(X0)),1) )
        | ( 'fun_app$l'('of_nat$',X0) = 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_563])]) ).

tff(f1887,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK35(X0)),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(cnf_transformation,[],[f1150]) ).

tff(f1150,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK35(X0)),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f806,f1149]) ).

tff(f1149,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
     => ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK35(X0)),1) ) ),
    introduced(choice_axiom,[]) ).

tff(f806,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(ennf_transformation,[],[f696]) ).

tff(f696,plain,
    ! [X0: 'Nat$'] :
      ~ ( ! [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X1),1) )
        & ( 'fun_app$l'('of_nat$',X0) != 0 ) ),
    inference(flattening,[],[f695]) ).

tff(f695,plain,
    ! [X0: 'Nat$'] :
      ~ ( ! [X1: 'Nat$'] :
            ( ~ 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
        & ( ~ 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(true_and_false_elimination,[],[f456]) ).

tff(f456,axiom,
    ! [X0: 'Nat$'] :
      ( ( ! [X1: 'Nat$'] :
            ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
           => $false )
        & ( ( 'fun_app$l'('of_nat$',X0) = 0 )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom454) ).

tff(f8171,plain,
    spl230_562,
    inference(avatar_split_clause,[],[f1876,f8169]) ).

tff(f8169,plain,
    ( spl230_562
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK31(X0)),1) )
        | ( 'fun_app$l'('of_nat$',X0) = 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_562])]) ).

tff(f1876,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK31(X0)),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(cnf_transformation,[],[f1142]) ).

tff(f1142,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK31(X0)),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f797,f1141]) ).

tff(f1141,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
     => ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',sK31(X0)),1) ) ),
    introduced(choice_axiom,[]) ).

tff(f797,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(ennf_transformation,[],[f449]) ).

tff(f449,axiom,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) != 0 )
     => ? [X1: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = $sum('fun_app$l'('of_nat$',X1),1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom447) ).

tff(f7808,plain,
    spl230_561,
    inference(avatar_split_clause,[],[f3462,f7806]) ).

tff(f7806,plain,
    ( spl230_561
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK158(X0,X1)))))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_561])]) ).

tff(f3462,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum(1,'fun_app$l'('of_nat$',sK158(X0,X1)))))
      | ~ sP9(X0,X1) ),
    inference(forward_demodulation,[],[f2464,f664]) ).

tff(f2464,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK158(X0,X1)),1)))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f1523]) ).

tff(f1523,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ~ 'fun_app$c'(X0,sK158(X0,X1))
        & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK158(X0,X1)),1)))
        & $less('fun_app$l'('of_nat$',sK158(X0,X1)),'fun_app$l'('of_nat$',X1)) )
      | ~ sP9(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f1521,f1522]) ).

tff(f1522,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X1)) )
     => ( ~ 'fun_app$c'(X0,sK158(X0,X1))
        & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',sK158(X0,X1)),1)))
        & $less('fun_app$l'('of_nat$',sK158(X0,X1)),'fun_app$l'('of_nat$',X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1521,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$c'(X0,X2)
          & 'fun_app$c'(X0,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),1)))
          & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X1)) )
      | ~ sP9(X0,X1) ),
    inference(rectify,[],[f1520]) ).

tff(f1520,plain,
    ! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$c'(X2,X3)
          & 'fun_app$c'(X2,'fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X3),1)))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X1)) )
      | ~ sP9(X2,X1) ),
    inference(nnf_transformation,[],[f1095]) ).

tff(f7804,plain,
    spl230_560,
    inference(avatar_split_clause,[],[f3437,f7802]) ).

tff(f7802,plain,
    ( spl230_560
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( $less('fun_app$l'('of_nat$',sK133(X0,X1)),$sum(1,'fun_app$l'('of_nat$',X1)))
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_560])]) ).

tff(f3437,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',sK133(X0,X1)),$sum(1,'fun_app$l'('of_nat$',X1)))
      | ~ sP7(X0,X1) ),
    inference(forward_demodulation,[],[f2343,f664]) ).

tff(f2343,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',sK133(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1))
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f1485]) ).

tff(f7800,plain,
    spl230_559,
    inference(avatar_split_clause,[],[f3432,f7798]) ).

tff(f7798,plain,
    ( spl230_559
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( $less('fun_app$l'('of_nat$',sK131(X0,X1)),$sum(1,'fun_app$l'('of_nat$',X1)))
        | sP6(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_559])]) ).

tff(f3432,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',sK131(X0,X1)),$sum(1,'fun_app$l'('of_nat$',X1)))
      | sP6(X0,X1) ),
    inference(forward_demodulation,[],[f2337,f664]) ).

tff(f2337,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( sP6(X0,X1)
      | $less('fun_app$l'('of_nat$',sK131(X0,X1)),$sum('fun_app$l'('of_nat$',X1),1)) ),
    inference(cnf_transformation,[],[f1476]) ).

tff(f7796,plain,
    spl230_558,
    inference(avatar_split_clause,[],[f3348,f7794]) ).

tff(f7794,plain,
    ( spl230_558
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) != $sum(1,'fun_app$l'('of_nat$',X1)) )
        | $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_558])]) ).

tff(f3348,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) != $sum(1,'fun_app$l'('of_nat$',X1)) )
      | $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(forward_demodulation,[],[f1938,f664]) ).

tff(f1938,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',X0))
      | ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X1),1) ) ),
    inference(cnf_transformation,[],[f1186]) ).

tff(f7790,plain,
    ( spl230_557
    | ~ spl230_330
    | ~ spl230_403
    | ~ spl230_556 ),
    inference(avatar_split_clause,[],[f7786,f7782,f5925,f5602,f7788]) ).

tff(f7788,plain,
    ( spl230_557
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_matrix_mult_iarray$'(sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))),'matrix_to_iarray$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_557])]) ).

tff(f5602,plain,
    ( spl230_330
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) = sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_330])]) ).

tff(f7782,plain,
    ( spl230_556
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),'matrix_to_iarray$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_556])]) ).

tff(f7786,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_matrix_mult_iarray$'(sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))),'matrix_to_iarray$'(X0)) )
    | ~ spl230_330
    | ~ spl230_403
    | ~ spl230_556 ),
    inference(forward_demodulation,[],[f7785,f5926]) ).

tff(f7785,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'matrix_matrix_mult_iarray$'(sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))),'matrix_to_iarray$'(X0)) )
    | ~ spl230_330
    | ~ spl230_556 ),
    inference(forward_demodulation,[],[f7783,f5603]) ).

tff(f5603,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) = sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
    | ~ spl230_330 ),
    inference(avatar_component_clause,[],[f5602]) ).

tff(f7783,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),'matrix_to_iarray$'(X0)) )
    | ~ spl230_556 ),
    inference(avatar_component_clause,[],[f7782]) ).

tff(f7784,plain,
    spl230_556,
    inference(avatar_split_clause,[],[f3343,f7782]) ).

tff(f3343,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),'matrix_to_iarray$'(X0)) ),
    inference(forward_demodulation,[],[f3342,f2932]) ).

tff(f2932,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
    inference(definition_unfolding,[],[f1820,f1818,f1817]) ).

tff(f1820,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('gauss_Jordan$'(X0)) = 'gauss_Jordan_iarrays$'('matrix_to_iarray$'(X0)) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('gauss_Jordan$'(X0)) = 'gauss_Jordan_iarrays$'('matrix_to_iarray$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom28) ).

tff(f3342,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),'matrix_to_iarray$'(X0)) ),
    inference(forward_demodulation,[],[f1856,f1853]) ).

tff(f1853,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) ),
    inference(cnf_transformation,[],[f175]) ).

tff(f175,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom173) ).

tff(f1856,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_matrix_mult_iarray$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))),'matrix_to_iarray$'(X0)) ),
    inference(cnf_transformation,[],[f216]) ).

tff(f216,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_matrix_mult_iarray$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))),'matrix_to_iarray$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom214) ).

tff(f7780,plain,
    spl230_555,
    inference(avatar_split_clause,[],[f2939,f7778]) ).

tff(f7778,plain,
    ( spl230_555
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_555])]) ).

tff(f2939,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)))) ),
    inference(definition_unfolding,[],[f1855,f1818]) ).

tff(f1855,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','gauss_Jordan$'(X0))) ),
    inference(cnf_transformation,[],[f93]) ).

tff(f93,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','gauss_Jordan$'(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom91) ).

tff(f7776,plain,
    spl230_554,
    inference(avatar_split_clause,[],[f2885,f7774]) ).

tff(f7774,plain,
    ( spl230_554
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X3 = X4 )
        | 'member$f'('pair$a'(X4,X3),X0)
        | ~ sP30(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_554])]) ).

tff(f2885,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( ( X3 = X4 )
      | 'member$f'('pair$a'(X4,X3),X0)
      | ~ sP30(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f7772,plain,
    spl230_553,
    inference(avatar_split_clause,[],[f2873,f7770]) ).

tff(f7770,plain,
    ( spl230_553
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X3 = X4 )
        | 'member$f'('pair$a'(X4,X3),X0)
        | ~ sP29(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_553])]) ).

tff(f2873,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( ( X3 = X4 )
      | 'member$f'('pair$a'(X4,X3),X0)
      | ~ sP29(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1726]) ).

tff(f7768,plain,
    spl230_552,
    inference(avatar_split_clause,[],[f2856,f7766]) ).

tff(f7766,plain,
    ( spl230_552
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( X3 = X4 )
        | 'member$'('pair$b'(X4,X3),X0)
        | ~ sP27(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_552])]) ).

tff(f2856,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( ( X3 = X4 )
      | 'member$'('pair$b'(X4,X3),X0)
      | ~ sP27(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f7764,plain,
    spl230_551,
    inference(avatar_split_clause,[],[f2844,f7762]) ).

tff(f7762,plain,
    ( spl230_551
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( X3 = X4 )
        | 'member$'('pair$b'(X4,X3),X0)
        | ~ sP26(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_551])]) ).

tff(f2844,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( ( X3 = X4 )
      | 'member$'('pair$b'(X4,X3),X0)
      | ~ sP26(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1712]) ).

tff(f7760,plain,
    spl230_550,
    inference(avatar_split_clause,[],[f2836,f7758]) ).

tff(f7758,plain,
    ( spl230_550
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( ( X3 = X4 )
        | 'member$g'('pair$c'(X4,X3),X0)
        | ~ sP25(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_550])]) ).

tff(f2836,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( ( X3 = X4 )
      | 'member$g'('pair$c'(X4,X3),X0)
      | ~ sP25(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f7756,plain,
    spl230_549,
    inference(avatar_split_clause,[],[f2828,f7754]) ).

tff(f7754,plain,
    ( spl230_549
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( ( X3 = X4 )
        | 'member$e'('pair$'(X4,X3),X0)
        | ~ sP24(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_549])]) ).

tff(f2828,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( ( X3 = X4 )
      | 'member$e'('pair$'(X4,X3),X0)
      | ~ sP24(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f7752,plain,
    spl230_548,
    inference(avatar_split_clause,[],[f2812,f7750]) ).

tff(f7750,plain,
    ( spl230_548
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( ( X3 = X4 )
        | 'member$g'('pair$c'(X4,X3),X0)
        | ~ sP23(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_548])]) ).

tff(f2812,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( ( X3 = X4 )
      | 'member$g'('pair$c'(X4,X3),X0)
      | ~ sP23(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f7748,plain,
    spl230_547,
    inference(avatar_split_clause,[],[f2804,f7746]) ).

tff(f7746,plain,
    ( spl230_547
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( ( X3 = X4 )
        | 'member$e'('pair$'(X4,X3),X0)
        | ~ sP22(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_547])]) ).

tff(f2804,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( ( X3 = X4 )
      | 'member$e'('pair$'(X4,X3),X0)
      | ~ sP22(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f7744,plain,
    spl230_546,
    inference(avatar_split_clause,[],[f2796,f7742]) ).

tff(f7742,plain,
    ( spl230_546
  <=> ! [X4: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X3: 'Nat_a_iarray_prod$',X2: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( X3 = X4 )
        | 'member$r'('pair$y'(X4,X3),X0)
        | ~ sP21(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_546])]) ).

tff(f2796,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X3: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod$'] :
      ( ( X3 = X4 )
      | 'member$r'('pair$y'(X4,X3),X0)
      | ~ sP21(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1688]) ).

tff(f7740,plain,
    spl230_545,
    inference(avatar_split_clause,[],[f2648,f7738]) ).

tff(f7738,plain,
    ( spl230_545
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_set$',X2: 'A_iarray$',X1: 'A_iarray_set$'] :
        ( 'member$a'('fun_app$ad'('plus$e'(X0),X2),'plus$f'(X1,X3))
        | ~ 'member$a'(X2,X3)
        | ~ 'member$a'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_545])]) ).

tff(f2648,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
      ( 'member$a'('fun_app$ad'('plus$e'(X0),X2),'plus$f'(X1,X3))
      | ~ 'member$a'(X2,X3)
      | ~ 'member$a'(X0,X1) ),
    inference(cnf_transformation,[],[f995]) ).

tff(f995,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray$',X3: 'A_iarray_set$'] :
      ( 'member$a'('fun_app$ad'('plus$e'(X0),X2),'plus$f'(X1,X3))
      | ~ 'member$a'(X2,X3)
      | ~ 'member$a'(X0,X1) ),
    inference(flattening,[],[f994]) ).

tff(f994,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray$',X3: 'A_iarray_set$'] :
      ( 'member$a'('fun_app$ad'('plus$e'(X0),X2),'plus$f'(X1,X3))
      | ~ 'member$a'(X2,X3)
      | ~ 'member$a'(X0,X1) ),
    inference(ennf_transformation,[],[f106]) ).

tff(f106,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_set$',X2: 'A_iarray$',X3: 'A_iarray_set$'] :
      ( ( 'member$a'(X2,X3)
        & 'member$a'(X0,X1) )
     => 'member$a'('fun_app$ad'('plus$e'(X0),X2),'plus$f'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom104) ).

tff(f7736,plain,
    spl230_544,
    inference(avatar_split_clause,[],[f2429,f7734]) ).

tff(f7734,plain,
    ( spl230_544
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( 'some$'(sK137(X1,X2)) = X2 )
        | ( tltrue = X0 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_544])]) ).

tff(f2429,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( 'some$'(sK137(X1,X2)) = X2 )
      | ( tltrue = X0 )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f1496,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( 'fun_app$f'(X1,sK137(X1,X2))
        & ( 'some$'(sK137(X1,X2)) = X2 ) )
      | ( ( tltrue = X0 )
        & ( 'none$' = X2 ) )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f922,f1495]) ).

tff(f1495,plain,
    ! [X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ? [X3: 'A_iarray_iarray$'] :
          ( 'fun_app$f'(X1,X3)
          & ( 'some$'(X3) = X2 ) )
     => ( 'fun_app$f'(X1,sK137(X1,X2))
        & ( 'some$'(sK137(X1,X2)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f922,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ? [X3: 'A_iarray_iarray$'] :
          ( 'fun_app$f'(X1,X3)
          & ( 'some$'(X3) = X2 ) )
      | ( ( tltrue = X0 )
        & ( 'none$' = X2 ) )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f741]) ).

tff(f741,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ~ ( ! [X3: 'A_iarray_iarray$'] :
            ~ ( 'fun_app$f'(X1,X3)
              & ( 'some$'(X3) = X2 ) )
        & ~ ( ( tltrue = X0 )
            & ( 'none$' = X2 ) )
        & 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(true_and_false_elimination,[],[f65]) ).

tff(f65,axiom,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ! [X3: 'A_iarray_iarray$'] :
            ( ( 'fun_app$f'(X1,X3)
              & ( 'some$'(X3) = X2 ) )
           => $false )
        & ( ( ( tltrue = X0 )
            & ( 'none$' = X2 ) )
         => $false )
        & 'fun_app$t'('case_option$a'(X0,X1),X2) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom63) ).

tff(f7732,plain,
    spl230_543,
    inference(avatar_split_clause,[],[f2428,f7730]) ).

tff(f7730,plain,
    ( spl230_543
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( 'some$'(sK137(X1,X2)) = X2 )
        | ( 'none$' = X2 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_543])]) ).

tff(f2428,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( 'some$'(sK137(X1,X2)) = X2 )
      | ( 'none$' = X2 )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f7728,plain,
    spl230_542,
    inference(avatar_split_clause,[],[f2425,f7726]) ).

tff(f7726,plain,
    ( spl230_542
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
        ( ( 'some$a'(sK136(X1,X2)) = X2 )
        | ( tltrue = X0 )
        | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_542])]) ).

tff(f2425,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
      ( ( 'some$a'(sK136(X1,X2)) = X2 )
      | ( tltrue = X0 )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f1494,plain,
    ! [X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ( 'fun_app$o'(X1,sK136(X1,X2))
        & ( 'some$a'(sK136(X1,X2)) = X2 ) )
      | ( ( tltrue = X0 )
        & ( 'none$a' = X2 ) )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f921,f1493]) ).

tff(f1493,plain,
    ! [X1: 'A_n_vec_n_vec_bool_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] :
          ( 'fun_app$o'(X1,X3)
          & ( 'some$a'(X3) = X2 ) )
     => ( 'fun_app$o'(X1,sK136(X1,X2))
        & ( 'some$a'(sK136(X1,X2)) = X2 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f921,plain,
    ! [X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] :
          ( 'fun_app$o'(X1,X3)
          & ( 'some$a'(X3) = X2 ) )
      | ( ( tltrue = X0 )
        & ( 'none$a' = X2 ) )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(ennf_transformation,[],[f740]) ).

tff(f740,plain,
    ! [X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ~ ( ! [X3: 'A_n_vec_n_vec$'] :
            ~ ( 'fun_app$o'(X1,X3)
              & ( 'some$a'(X3) = X2 ) )
        & ~ ( ( tltrue = X0 )
            & ( 'none$a' = X2 ) )
        & 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(true_and_false_elimination,[],[f64]) ).

tff(f64,axiom,
    ! [X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$',X2: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X3: 'A_n_vec_n_vec$'] :
            ( ( 'fun_app$o'(X1,X3)
              & ( 'some$a'(X3) = X2 ) )
           => $false )
        & ( ( ( tltrue = X0 )
            & ( 'none$a' = X2 ) )
         => $false )
        & 'fun_app$s'('case_option$'(X0,X1),X2) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom62) ).

tff(f7724,plain,
    spl230_541,
    inference(avatar_split_clause,[],[f2424,f7722]) ).

tff(f7722,plain,
    ( spl230_541
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
        ( ( 'some$a'(sK136(X1,X2)) = X2 )
        | ( 'none$a' = X2 )
        | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_541])]) ).

tff(f2424,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
      ( ( 'some$a'(sK136(X1,X2)) = X2 )
      | ( 'none$a' = X2 )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f7720,plain,
    spl230_540,
    inference(avatar_split_clause,[],[f2388,f7718]) ).

tff(f7718,plain,
    ( spl230_540
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
        ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'fun_app$p'('filter$'(X0),X2) )
        | 'fun_app$'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_540])]) ).

tff(f2388,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( ( 'fun_app$p'('filter$'(X0),'cons$'(X1,X2)) = 'fun_app$p'('filter$'(X0),X2) )
      | 'fun_app$'(X0,X1) ),
    inference(cnf_transformation,[],[f881]) ).

tff(f7716,plain,
    spl230_539,
    inference(avatar_split_clause,[],[f2369,f7714]) ).

tff(f7714,plain,
    ( spl230_539
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('filter$'(X1),X2)) = 'fun_app$p'('filter$'('uua$'(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_539])]) ).

tff(f2369,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('filter$'(X1),X2)) = 'fun_app$p'('filter$'('uua$'(X0,X1)),X2) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray_list$'] : ( 'fun_app$p'('filter$'(X0),'fun_app$p'('filter$'(X1),X2)) = 'fun_app$p'('filter$'('uua$'(X0,X1)),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom29) ).

tff(f7710,plain,
    spl230_538,
    inference(avatar_split_clause,[],[f2285,f7708]) ).

tff(f7708,plain,
    ( spl230_538
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
        | ~ $less(0,'fun_app$l'('of_nat$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_538])]) ).

tff(f2285,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
      | ~ $less(0,'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1424]) ).

tff(f7706,plain,
    spl230_537,
    inference(avatar_split_clause,[],[f2284,f7704]) ).

tff(f7704,plain,
    ( spl230_537
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_537])]) ).

tff(f2284,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))
      | ~ $less(0,'fun_app$l'('of_nat$',X0)) ),
    inference(cnf_transformation,[],[f1424]) ).

tff(f7702,plain,
    spl230_536,
    inference(avatar_split_clause,[],[f2281,f7700]) ).

tff(f7700,plain,
    ( spl230_536
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_536])]) ).

tff(f2281,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    inference(cnf_transformation,[],[f1422]) ).

tff(f1422,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 0 = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) )
        | ( 0 != 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
      & ( ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ) ),
    inference(flattening,[],[f1421]) ).

tff(f1421,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 0 = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) )
        | ( 0 != 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
      & ( ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ) ),
    inference(nnf_transformation,[],[f391]) ).

tff(f391,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) )
    <=> ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        & ( 'fun_app$l'('of_nat$',X0) = 0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom389) ).

tff(f7698,plain,
    spl230_535,
    inference(avatar_split_clause,[],[f2280,f7696]) ).

tff(f7696,plain,
    ( spl230_535
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_535])]) ).

tff(f2280,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ( 0 != $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    inference(cnf_transformation,[],[f1422]) ).

tff(f7694,plain,
    spl230_534,
    inference(avatar_split_clause,[],[f2057,f7692]) ).

tff(f7692,plain,
    ( spl230_534
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( $less(0,'fun_app$l'('of_nat$',sK71(X0,X1)))
        | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_534])]) ).

tff(f2057,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',sK71(X0,X1)))
      | ~ $less('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) ),
    inference(cnf_transformation,[],[f1246]) ).

tff(f7690,plain,
    spl230_533,
    inference(avatar_split_clause,[],[f1922,f7688]) ).

tff(f7688,plain,
    ( spl230_533
  <=> ! [X0: 'A_iarray_iarray$'] :
        ( 'fun_app$f'('invertible_iarray$',X0)
        | ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_533])]) ).

tff(f1922,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('invertible_iarray$',X0)
      | ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) ) ),
    inference(cnf_transformation,[],[f1176]) ).

tff(f1176,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( 'fun_app$f'('invertible_iarray$',X0)
        | ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) ) )
      & ( ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) ) ),
    inference(nnf_transformation,[],[f42]) ).

tff(f42,axiom,
    ! [X0: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('invertible_iarray$',X0)
    <=> ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom40) ).

tff(f7686,plain,
    spl230_532,
    inference(avatar_split_clause,[],[f1921,f7684]) ).

tff(f7684,plain,
    ( spl230_532
  <=> ! [X0: 'A_iarray_iarray$'] :
        ( ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_532])]) ).

tff(f1921,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',X0)) )
      | ~ 'fun_app$f'('invertible_iarray$',X0) ),
    inference(cnf_transformation,[],[f1176]) ).

tff(f7442,plain,
    ( spl230_531
    | ~ spl230_345
    | ~ spl230_515 ),
    inference(avatar_split_clause,[],[f7182,f7179,f5678,f7440]) ).

tff(f7440,plain,
    ( spl230_531
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),'matrix_matrix_mult$'('matrix_inv$'(X2),'matrix_matrix_mult$'(X0,X2)))
        | ~ 'fun_app$o'('invertible$',X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_531])]) ).

tff(f7179,plain,
    ( spl230_515
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2))
        | ~ 'fun_app$o'('invertible$',X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_515])]) ).

tff(f7182,plain,
    ( ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),'matrix_matrix_mult$'('matrix_inv$'(X2),'matrix_matrix_mult$'(X0,X2)))
        | ~ 'fun_app$o'('invertible$',X2) )
    | ~ spl230_345
    | ~ spl230_515 ),
    inference(forward_demodulation,[],[f7180,f5679]) ).

tff(f7180,plain,
    ( ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2))
        | ~ 'fun_app$o'('invertible$',X2) )
    | ~ spl230_515 ),
    inference(avatar_component_clause,[],[f7179]) ).

tff(f7425,plain,
    ( spl230_530
    | ~ spl230_56
    | ~ spl230_388 ),
    inference(avatar_split_clause,[],[f6498,f5860,f3742,f7423]) ).

tff(f7423,plain,
    ( spl230_530
  <=> ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_6(tltrue,X0,'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_530])]) ).

tff(f3742,plain,
    ( spl230_56
  <=> ! [X1: 'A_iarray_iarray_bool_fun$'] : 'fun_app$t'('case_option$a'(tltrue,X1),'none$') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_56])]) ).

tff(f5860,plain,
    ( spl230_388
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( tltrue = def_6(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_388])]) ).

tff(f6498,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_6(tltrue,X0,'none$') )
    | ~ spl230_56
    | ~ spl230_388 ),
    inference(resolution,[],[f5861,f3743]) ).

tff(f3743,plain,
    ( ! [X1: 'A_iarray_iarray_bool_fun$'] : 'fun_app$t'('case_option$a'(tltrue,X1),'none$')
    | ~ spl230_56 ),
    inference(avatar_component_clause,[],[f3742]) ).

tff(f5861,plain,
    ( ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ~ 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue = def_6(X0,X1,X2) ) )
    | ~ spl230_388 ),
    inference(avatar_component_clause,[],[f5860]) ).

tff(f7310,plain,
    ( spl230_529
    | ~ spl230_56
    | ~ spl230_386 ),
    inference(avatar_split_clause,[],[f6487,f5852,f3742,f7308]) ).

tff(f7308,plain,
    ( spl230_529
  <=> ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_2(tltrue,X0,'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_529])]) ).

tff(f5852,plain,
    ( spl230_386
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( tltrue = def_2(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_386])]) ).

tff(f6487,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_2(tltrue,X0,'none$') )
    | ~ spl230_56
    | ~ spl230_386 ),
    inference(resolution,[],[f5853,f3743]) ).

tff(f5853,plain,
    ( ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ~ 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue = def_2(X0,X1,X2) ) )
    | ~ spl230_386 ),
    inference(avatar_component_clause,[],[f5852]) ).

tff(f7234,plain,
    spl230_528,
    inference(avatar_split_clause,[],[f3357,f7232]) ).

tff(f7232,plain,
    ( spl230_528
  <=> ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,$sum('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X0)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_528])]) ).

tff(f3357,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,$sum('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X0)))),
    inference(forward_demodulation,[],[f2015,f664]) ).

tff(f2015,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum($sum('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X0)),1)),
    inference(cnf_transformation,[],[f639]) ).

tff(f639,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum($sum('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X0)),1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom637) ).

tff(f7230,plain,
    spl230_527,
    inference(avatar_split_clause,[],[f3356,f7228]) ).

tff(f7228,plain,
    ( spl230_527
  <=> ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_527])]) ).

tff(f3356,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,$sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)))),
    inference(forward_demodulation,[],[f2014,f664]) ).

tff(f2014,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)),1)),
    inference(cnf_transformation,[],[f640]) ).

tff(f640,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum($sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)),1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom638) ).

tff(f7226,plain,
    spl230_526,
    inference(avatar_split_clause,[],[f3300,f7224]) ).

tff(f7224,plain,
    ( spl230_526
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP4(X0,X1)
        | ( 'fun_app$l'('of_nat$',X0) != 1 )
        | ( 0 != 'fun_app$l'('of_nat$',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_526])]) ).

tff(f3300,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 1 )
      | ( 0 != 'fun_app$l'('of_nat$',X1) ) ),
    inference(evaluation,[],[f2323]) ).

tff(f2323,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) )
      | ( 0 != 'fun_app$l'('of_nat$',X1) ) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f1466,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( sP4(X0,X1)
        | ( ( ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) )
            | ( 0 != 'fun_app$l'('of_nat$',X1) ) )
          & ( ( 'fun_app$l'('of_nat$',X0) != 0 )
            | ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
          & ( 0 = 'fun_app$l'('of_nat$',X1) ) )
        | ( ( 'fun_app$l'('of_nat$',X0) = 0 )
          & ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) ) )
        | ~ sP4(X0,X1) ) ),
    inference(rectify,[],[f1465]) ).

tff(f1465,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( ( sP4(X1,X0)
        | ( ( ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) )
            | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
          & ( ( 0 != 'fun_app$l'('of_nat$',X1) )
            | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) )
        | ~ sP4(X1,X0) ) ),
    inference(flattening,[],[f1464]) ).

tff(f1464,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( ( sP4(X1,X0)
        | ( ( ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) )
            | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
          & ( ( 0 != 'fun_app$l'('of_nat$',X1) )
            | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) )
        | ~ sP4(X1,X0) ) ),
    inference(nnf_transformation,[],[f1085]) ).

tff(f1085,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( sP4(X1,X0)
    <=> ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f7222,plain,
    spl230_525,
    inference(avatar_split_clause,[],[f3299,f7220]) ).

tff(f7220,plain,
    ( spl230_525
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP4(X0,X1)
        | ( 'fun_app$l'('of_nat$',X0) != 0 )
        | ( 'fun_app$l'('of_nat$',X1) != 1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_525])]) ).

tff(f3299,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 0 )
      | ( 'fun_app$l'('of_nat$',X1) != 1 ) ),
    inference(evaluation,[],[f2322]) ).

tff(f2322,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 0 )
      | ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) ) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f7218,plain,
    spl230_524,
    inference(avatar_split_clause,[],[f3298,f7216]) ).

tff(f7216,plain,
    ( spl230_524
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 1 )
        | ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_524])]) ).

tff(f3298,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 1 )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP4(X0,X1) ),
    inference(evaluation,[],[f2321]) ).

tff(f2321,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f7214,plain,
    ( spl230_523
    | ~ spl230_56
    | ~ spl230_384 ),
    inference(avatar_split_clause,[],[f6480,f5844,f3742,f7212]) ).

tff(f7212,plain,
    ( spl230_523
  <=> ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_4(tltrue,X0,'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_523])]) ).

tff(f5844,plain,
    ( spl230_384
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( tltrue = def_4(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_384])]) ).

tff(f6480,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$'] : ( tltrue = def_4(tltrue,X0,'none$') )
    | ~ spl230_56
    | ~ spl230_384 ),
    inference(resolution,[],[f5845,f3743]) ).

tff(f5845,plain,
    ( ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ~ 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue = def_4(X0,X1,X2) ) )
    | ~ spl230_384 ),
    inference(avatar_component_clause,[],[f5844]) ).

tff(f7210,plain,
    spl230_522,
    inference(avatar_split_clause,[],[f3297,f7208]) ).

tff(f7208,plain,
    ( spl230_522
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 1 )
        | ( 'fun_app$l'('of_nat$',X1) = 1 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_522])]) ).

tff(f3297,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 1 )
      | ( 'fun_app$l'('of_nat$',X1) = 1 )
      | ~ sP4(X0,X1) ),
    inference(evaluation,[],[f2320]) ).

tff(f2320,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
      | ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f7206,plain,
    spl230_521,
    inference(avatar_split_clause,[],[f3296,f7204]) ).

tff(f7204,plain,
    ( spl230_521
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X1) = 1 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_521])]) ).

tff(f3296,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X1) = 1 )
      | ~ sP4(X0,X1) ),
    inference(evaluation,[],[f2318]) ).

tff(f2318,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f7202,plain,
    spl230_520,
    inference(avatar_split_clause,[],[f3293,f7200]) ).

tff(f7200,plain,
    ( spl230_520
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP5(X0,X1)
        | ( 'fun_app$l'('of_nat$',X0) != 1 )
        | ( 0 != 'fun_app$l'('of_nat$',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_520])]) ).

tff(f3293,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 1 )
      | ( 0 != 'fun_app$l'('of_nat$',X1) ) ),
    inference(evaluation,[],[f2331]) ).

tff(f2331,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) )
      | ( 0 != 'fun_app$l'('of_nat$',X1) ) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f1470,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( sP5(X0,X1)
        | ( ( ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) )
            | ( 0 != 'fun_app$l'('of_nat$',X1) ) )
          & ( ( 'fun_app$l'('of_nat$',X0) != 0 )
            | ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
          & ( 0 = 'fun_app$l'('of_nat$',X1) ) )
        | ( ( 'fun_app$l'('of_nat$',X0) = 0 )
          & ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) ) )
        | ~ sP5(X0,X1) ) ),
    inference(rectify,[],[f1469]) ).

tff(f1469,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( ( sP5(X1,X0)
        | ( ( ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) )
            | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
          & ( ( 0 != 'fun_app$l'('of_nat$',X1) )
            | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) )
        | ~ sP5(X1,X0) ) ),
    inference(flattening,[],[f1468]) ).

tff(f1468,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( ( sP5(X1,X0)
        | ( ( ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) )
            | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
          & ( ( 0 != 'fun_app$l'('of_nat$',X1) )
            | ( 'fun_app$l'('of_nat$',X0) != $sum(0,1) ) ) ) )
      & ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) )
        | ~ sP5(X1,X0) ) ),
    inference(nnf_transformation,[],[f1087]) ).

tff(f1087,plain,
    ! [X1: 'Nat$',X0: 'Nat$'] :
      ( sP5(X1,X0)
    <=> ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

tff(f7198,plain,
    spl230_519,
    inference(avatar_split_clause,[],[f3292,f7196]) ).

tff(f7196,plain,
    ( spl230_519
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP5(X0,X1)
        | ( 'fun_app$l'('of_nat$',X0) != 0 )
        | ( 'fun_app$l'('of_nat$',X1) != 1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_519])]) ).

tff(f3292,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 0 )
      | ( 'fun_app$l'('of_nat$',X1) != 1 ) ),
    inference(evaluation,[],[f2330]) ).

tff(f2330,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X0,X1)
      | ( 'fun_app$l'('of_nat$',X0) != 0 )
      | ( 'fun_app$l'('of_nat$',X1) != $sum(0,1) ) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f7194,plain,
    spl230_518,
    inference(avatar_split_clause,[],[f3291,f7192]) ).

tff(f7192,plain,
    ( spl230_518
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 1 )
        | ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_518])]) ).

tff(f3291,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 1 )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP5(X0,X1) ),
    inference(evaluation,[],[f2329]) ).

tff(f2329,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f7190,plain,
    spl230_517,
    inference(avatar_split_clause,[],[f3290,f7188]) ).

tff(f7188,plain,
    ( spl230_517
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 1 )
        | ( 'fun_app$l'('of_nat$',X1) = 1 )
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_517])]) ).

tff(f3290,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 1 )
      | ( 'fun_app$l'('of_nat$',X1) = 1 )
      | ~ sP5(X0,X1) ),
    inference(evaluation,[],[f2328]) ).

tff(f2328,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) )
      | ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f7186,plain,
    spl230_516,
    inference(avatar_split_clause,[],[f3289,f7184]) ).

tff(f7184,plain,
    ( spl230_516
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X1) = 1 )
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_516])]) ).

tff(f3289,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X1) = 1 )
      | ~ sP5(X0,X1) ),
    inference(evaluation,[],[f2326]) ).

tff(f2326,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f7181,plain,
    spl230_515,
    inference(avatar_split_clause,[],[f3087,f7179]) ).

tff(f3087,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2))
      | ~ 'fun_app$o'('invertible$',X2) ),
    inference(equality_resolution,[],[f2226]) ).

tff(f2226,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1)
      | ( 'matrix_matrix_mult$'('matrix_matrix_mult$'('matrix_inv$'(X2),X0),X2) != X1 )
      | ~ 'fun_app$o'('invertible$',X2) ),
    inference(cnf_transformation,[],[f1376]) ).

tff(f7177,plain,
    spl230_514,
    inference(avatar_split_clause,[],[f2765,f7175]) ).

tff(f7175,plain,
    ( spl230_514
  <=> ! [X0: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
        | ~ sP19(X3,X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_514])]) ).

tff(f2765,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
      | ~ sP19(X3,X0,X2,X1) ),
    inference(cnf_transformation,[],[f1681]) ).

tff(f1681,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
        | ~ sP19(X3,X0,X2,X1) )
      & ( sP19(X3,X0,X2,X1)
        | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ) ),
    inference(nnf_transformation,[],[f1116]) ).

tff(f1116,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
    <=> sP19(X3,X0,X2,X1) ),
    inference(definition_folding,[],[f1028,f1115]) ).

tff(f1028,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X0,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) ) ),
    inference(ennf_transformation,[],[f605]) ).

tff(f605,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'cons$'(X2,X3) )
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X0),X5) = X3 )
          & 'fun_app$'(X0,X2)
          & ! [X6: 'A_iarray$'] :
              ( 'member$a'(X6,'set$'(X4))
             => ~ 'fun_app$'(X0,X6) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X2,X5)) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom603) ).

tff(f7173,plain,
    spl230_513,
    inference(avatar_split_clause,[],[f2764,f7171]) ).

tff(f7171,plain,
    ( spl230_513
  <=> ! [X0: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( sP19(X3,X0,X2,X1)
        | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_513])]) ).

tff(f2764,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( sP19(X3,X0,X2,X1)
      | ( 'fun_app$p'('filter$'(X0),X1) != 'cons$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1681]) ).

tff(f7167,plain,
    spl230_512,
    inference(avatar_split_clause,[],[f2757,f7165]) ).

tff(f7165,plain,
    ( spl230_512
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
        | ~ sP18(X1,X2,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_512])]) ).

tff(f2757,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
      | ~ sP18(X1,X2,X0,X3) ),
    inference(cnf_transformation,[],[f1675]) ).

tff(f1675,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
        | ~ sP18(X1,X2,X0,X3) )
      & ( sP18(X1,X2,X0,X3)
        | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ) ),
    inference(nnf_transformation,[],[f1114]) ).

tff(f1114,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
    <=> sP18(X1,X2,X0,X3) ),
    inference(definition_folding,[],[f1027,f1113]) ).

tff(f1027,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( ~ 'fun_app$'(X2,X6)
              | ~ 'member$a'(X6,'set$'(X4)) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) ) ),
    inference(ennf_transformation,[],[f604]) ).

tff(f604,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'fun_app$p'('filter$'(X2),X3) )
    <=> ? [X4: 'A_iarray_list$',X5: 'A_iarray_list$'] :
          ( ( 'fun_app$p'('filter$'(X2),X5) = X1 )
          & 'fun_app$'(X2,X0)
          & ! [X6: 'A_iarray$'] :
              ( 'member$a'(X6,'set$'(X4))
             => ~ 'fun_app$'(X2,X6) )
          & ( 'fun_app$p'('append$d'(X4),'cons$'(X0,X5)) = X3 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom602) ).

tff(f7163,plain,
    spl230_511,
    inference(avatar_split_clause,[],[f2756,f7161]) ).

tff(f7161,plain,
    ( spl230_511
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( sP18(X1,X2,X0,X3)
        | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_511])]) ).

tff(f2756,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( sP18(X1,X2,X0,X3)
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(cnf_transformation,[],[f1675]) ).

tff(f7159,plain,
    spl230_510,
    inference(avatar_split_clause,[],[f2720,f7157]) ).

tff(f7157,plain,
    ( spl230_510
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP17(X0,X1,X2,X3)
        | ~ 'fun_app$n'(X2,def_7(X1,X0))
        | ~ 'fun_app$n'(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_510])]) ).

tff(f2720,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP17(X0,X1,X2,X3)
      | ~ 'fun_app$n'(X2,def_7(X1,X0))
      | ~ 'fun_app$n'(X2,X3) ),
    inference(cnf_transformation,[],[f1650]) ).

tff(f7155,plain,
    spl230_509,
    inference(avatar_split_clause,[],[f2719,f7153]) ).

tff(f7153,plain,
    ( spl230_509
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP17(X0,X1,X2,X3)
        | ~ 'fun_app$n'(X2,def_7(X1,X0))
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_509])]) ).

tff(f2719,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP17(X0,X1,X2,X3)
      | ~ 'fun_app$n'(X2,def_7(X1,X0))
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1650]) ).

tff(f7151,plain,
    spl230_508,
    inference(avatar_split_clause,[],[f2718,f7149]) ).

tff(f7149,plain,
    ( spl230_508
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP17(X0,X1,X2,X3)
        | ( 'some$'('the$a'(X0)) = X0 )
        | ~ 'fun_app$n'(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_508])]) ).

tff(f2718,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP17(X0,X1,X2,X3)
      | ( 'some$'('the$a'(X0)) = X0 )
      | ~ 'fun_app$n'(X2,X3) ),
    inference(cnf_transformation,[],[f1650]) ).

tff(f7147,plain,
    spl230_507,
    inference(avatar_split_clause,[],[f2712,f7145]) ).

tff(f7145,plain,
    ( spl230_507
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP16(X0,X1,X2,X3)
        | ~ 'fun_app$n'(X2,def_5(X1,X0))
        | ~ 'fun_app$n'(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_507])]) ).

tff(f2712,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP16(X0,X1,X2,X3)
      | ~ 'fun_app$n'(X2,def_5(X1,X0))
      | ~ 'fun_app$n'(X2,X3) ),
    inference(cnf_transformation,[],[f1646]) ).

tff(f7143,plain,
    spl230_506,
    inference(avatar_split_clause,[],[f2711,f7141]) ).

tff(f7141,plain,
    ( spl230_506
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP16(X0,X1,X2,X3)
        | ~ 'fun_app$n'(X2,def_5(X1,X0))
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_506])]) ).

tff(f2711,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP16(X0,X1,X2,X3)
      | ~ 'fun_app$n'(X2,def_5(X1,X0))
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1646]) ).

tff(f7139,plain,
    spl230_505,
    inference(avatar_split_clause,[],[f2710,f7137]) ).

tff(f7137,plain,
    ( spl230_505
  <=> ! [X0: 'A_iarray_iarray_option$',X3: tlbool,X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP16(X0,X1,X2,X3)
        | ( 'some$'('the$a'(X0)) = X0 )
        | ~ 'fun_app$n'(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_505])]) ).

tff(f2710,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP16(X0,X1,X2,X3)
      | ( 'some$'('the$a'(X0)) = X0 )
      | ~ 'fun_app$n'(X2,X3) ),
    inference(cnf_transformation,[],[f1646]) ).

tff(f7135,plain,
    spl230_504,
    inference(avatar_split_clause,[],[f2647,f7133]) ).

tff(f7133,plain,
    ( spl230_504
  <=> ! [X0: 'Nat$',X3: 'Nat_set$',X2: 'Nat$',X1: 'Nat_set$'] :
        ( 'member$c'('plus$g'(X0,X2),'plus$h'(X1,X3))
        | ~ 'member$c'(X2,X3)
        | ~ 'member$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_504])]) ).

tff(f2647,plain,
    ! [X2: 'Nat$',X3: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
      ( 'member$c'('plus$g'(X0,X2),'plus$h'(X1,X3))
      | ~ 'member$c'(X2,X3)
      | ~ 'member$c'(X0,X1) ),
    inference(cnf_transformation,[],[f993]) ).

tff(f993,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat$',X3: 'Nat_set$'] :
      ( 'member$c'('plus$g'(X0,X2),'plus$h'(X1,X3))
      | ~ 'member$c'(X2,X3)
      | ~ 'member$c'(X0,X1) ),
    inference(flattening,[],[f992]) ).

tff(f992,plain,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat$',X3: 'Nat_set$'] :
      ( 'member$c'('plus$g'(X0,X2),'plus$h'(X1,X3))
      | ~ 'member$c'(X2,X3)
      | ~ 'member$c'(X0,X1) ),
    inference(ennf_transformation,[],[f107]) ).

tff(f107,axiom,
    ! [X0: 'Nat$',X1: 'Nat_set$',X2: 'Nat$',X3: 'Nat_set$'] :
      ( ( 'member$c'(X2,X3)
        & 'member$c'(X0,X1) )
     => 'member$c'('plus$g'(X0,X2),'plus$h'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom105) ).

tff(f7131,plain,
    spl230_503,
    inference(avatar_split_clause,[],[f2646,f7129]) ).

tff(f7129,plain,
    ( spl230_503
  <=> ! [X0: $int,X3: 'Int_set$',X2: $int,X1: 'Int_set$'] :
        ( 'member$d'($sum(X0,X2),'plus$k'(X1,X3))
        | ~ 'member$d'(X2,X3)
        | ~ 'member$d'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_503])]) ).

tff(f2646,plain,
    ! [X2: $int,X3: 'Int_set$',X0: $int,X1: 'Int_set$'] :
      ( 'member$d'($sum(X0,X2),'plus$k'(X1,X3))
      | ~ 'member$d'(X2,X3)
      | ~ 'member$d'(X0,X1) ),
    inference(cnf_transformation,[],[f991]) ).

tff(f991,plain,
    ! [X0: $int,X1: 'Int_set$',X2: $int,X3: 'Int_set$'] :
      ( 'member$d'($sum(X0,X2),'plus$k'(X1,X3))
      | ~ 'member$d'(X2,X3)
      | ~ 'member$d'(X0,X1) ),
    inference(flattening,[],[f990]) ).

tff(f990,plain,
    ! [X0: $int,X1: 'Int_set$',X2: $int,X3: 'Int_set$'] :
      ( 'member$d'($sum(X0,X2),'plus$k'(X1,X3))
      | ~ 'member$d'(X2,X3)
      | ~ 'member$d'(X0,X1) ),
    inference(ennf_transformation,[],[f113]) ).

tff(f113,axiom,
    ! [X0: $int,X1: 'Int_set$',X2: $int,X3: 'Int_set$'] :
      ( ( 'member$d'(X2,X3)
        & 'member$d'(X0,X1) )
     => 'member$d'($sum(X0,X2),'plus$k'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom111) ).

tff(f7125,plain,
    spl230_502,
    inference(avatar_split_clause,[],[f2645,f7123]) ).

tff(f7123,plain,
    ( spl230_502
  <=> ! [X0: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
        ( 'member$j'('plus$a'(X0,X2),'plus$m'(X1,X3))
        | ~ 'member$j'(X2,X3)
        | ~ 'member$j'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_502])]) ).

tff(f2645,plain,
    ! [X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
      ( 'member$j'('plus$a'(X0,X2),'plus$m'(X1,X3))
      | ~ 'member$j'(X2,X3)
      | ~ 'member$j'(X0,X1) ),
    inference(cnf_transformation,[],[f989]) ).

tff(f989,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec_set$'] :
      ( 'member$j'('plus$a'(X0,X2),'plus$m'(X1,X3))
      | ~ 'member$j'(X2,X3)
      | ~ 'member$j'(X0,X1) ),
    inference(flattening,[],[f988]) ).

tff(f988,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec_set$'] :
      ( 'member$j'('plus$a'(X0,X2),'plus$m'(X1,X3))
      | ~ 'member$j'(X2,X3)
      | ~ 'member$j'(X0,X1) ),
    inference(ennf_transformation,[],[f111]) ).

tff(f111,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$',X2: 'A_n_vec_n_vec$',X3: 'A_n_vec_n_vec_set$'] :
      ( ( 'member$j'(X2,X3)
        & 'member$j'(X0,X1) )
     => 'member$j'('plus$a'(X0,X2),'plus$m'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom109) ).

tff(f7121,plain,
    spl230_501,
    inference(avatar_split_clause,[],[f2644,f7119]) ).

tff(f7119,plain,
    ( spl230_501
  <=> ! [X0: 'Int_set$',X3: 'Int_set_set$',X2: 'Int_set$',X1: 'Int_set_set$'] :
        ( 'member$i'('plus$k'(X0,X2),'plus$l'(X1,X3))
        | ~ 'member$i'(X2,X3)
        | ~ 'member$i'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_501])]) ).

tff(f2644,plain,
    ! [X2: 'Int_set$',X3: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
      ( 'member$i'('plus$k'(X0,X2),'plus$l'(X1,X3))
      | ~ 'member$i'(X2,X3)
      | ~ 'member$i'(X0,X1) ),
    inference(cnf_transformation,[],[f987]) ).

tff(f987,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set$',X3: 'Int_set_set$'] :
      ( 'member$i'('plus$k'(X0,X2),'plus$l'(X1,X3))
      | ~ 'member$i'(X2,X3)
      | ~ 'member$i'(X0,X1) ),
    inference(flattening,[],[f986]) ).

tff(f986,plain,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set$',X3: 'Int_set_set$'] :
      ( 'member$i'('plus$k'(X0,X2),'plus$l'(X1,X3))
      | ~ 'member$i'(X2,X3)
      | ~ 'member$i'(X0,X1) ),
    inference(ennf_transformation,[],[f110]) ).

tff(f110,axiom,
    ! [X0: 'Int_set$',X1: 'Int_set_set$',X2: 'Int_set$',X3: 'Int_set_set$'] :
      ( ( 'member$i'(X2,X3)
        & 'member$i'(X0,X1) )
     => 'member$i'('plus$k'(X0,X2),'plus$l'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom108) ).

tff(f7117,plain,
    spl230_500,
    inference(avatar_split_clause,[],[f2643,f7115]) ).

tff(f7115,plain,
    ( spl230_500
  <=> ! [X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
        ( 'member$h'('plus$d'(X0,X2),'plus$j'(X1,X3))
        | ~ 'member$h'(X2,X3)
        | ~ 'member$h'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_500])]) ).

tff(f2643,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
      ( 'member$h'('plus$d'(X0,X2),'plus$j'(X1,X3))
      | ~ 'member$h'(X2,X3)
      | ~ 'member$h'(X0,X1) ),
    inference(cnf_transformation,[],[f985]) ).

tff(f985,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_set$'] :
      ( 'member$h'('plus$d'(X0,X2),'plus$j'(X1,X3))
      | ~ 'member$h'(X2,X3)
      | ~ 'member$h'(X0,X1) ),
    inference(flattening,[],[f984]) ).

tff(f984,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_set$'] :
      ( 'member$h'('plus$d'(X0,X2),'plus$j'(X1,X3))
      | ~ 'member$h'(X2,X3)
      | ~ 'member$h'(X0,X1) ),
    inference(ennf_transformation,[],[f109]) ).

tff(f109,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray_set$'] :
      ( ( 'member$h'(X2,X3)
        & 'member$h'(X0,X1) )
     => 'member$h'('plus$d'(X0,X2),'plus$j'(X1,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom107) ).

tff(f7113,plain,
    spl230_499,
    inference(avatar_split_clause,[],[f2600,f7111]) ).

tff(f7111,plain,
    ( spl230_499
  <=> ! [X2: 'N$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X3: 'N$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_in_ij_PA$'('pair$l'(X0,X1),X2,X3)) = 'gauss_Jordan_in_ij$'(X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_499])]) ).

tff(f7109,plain,
    spl230_498,
    inference(avatar_split_clause,[],[f2431,f7107]) ).

tff(f7107,plain,
    ( spl230_498
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$f'(X1,sK137(X1,X2))
        | ( tltrue = X0 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_498])]) ).

tff(f2431,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$f'(X1,sK137(X1,X2))
      | ( tltrue = X0 )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f7105,plain,
    spl230_497,
    inference(avatar_split_clause,[],[f2430,f7103]) ).

tff(f7103,plain,
    ( spl230_497
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$f'(X1,sK137(X1,X2))
        | ( 'none$' = X2 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_497])]) ).

tff(f2430,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$f'(X1,sK137(X1,X2))
      | ( 'none$' = X2 )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f7101,plain,
    spl230_496,
    inference(avatar_split_clause,[],[f2427,f7099]) ).

tff(f7099,plain,
    ( spl230_496
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
        ( 'fun_app$o'(X1,sK136(X1,X2))
        | ( tltrue = X0 )
        | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_496])]) ).

tff(f2427,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
      ( 'fun_app$o'(X1,sK136(X1,X2))
      | ( tltrue = X0 )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f7097,plain,
    spl230_495,
    inference(avatar_split_clause,[],[f2426,f7095]) ).

tff(f7095,plain,
    ( spl230_495
  <=> ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
        ( 'fun_app$o'(X1,sK136(X1,X2))
        | ( 'none$a' = X2 )
        | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_495])]) ).

tff(f2426,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: tlbool,X1: 'A_n_vec_n_vec_bool_fun$'] :
      ( 'fun_app$o'(X1,sK136(X1,X2))
      | ( 'none$a' = X2 )
      | ~ 'fun_app$s'('case_option$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f7093,plain,
    spl230_494,
    inference(avatar_split_clause,[],[f2368,f7091]) ).

tff(f7091,plain,
    ( spl230_494
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'plus$a'(X1,X2)) = 'plus$a'('matrix_matrix_mult$'(X0,X1),'matrix_matrix_mult$'(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_494])]) ).

tff(f2368,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'plus$a'(X1,X2)) = 'plus$a'('matrix_matrix_mult$'(X0,X1),'matrix_matrix_mult$'(X0,X2)) ),
    inference(cnf_transformation,[],[f295]) ).

tff(f295,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'plus$a'(X1,X2)) = 'plus$a'('matrix_matrix_mult$'(X0,X1),'matrix_matrix_mult$'(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom293) ).

tff(f7089,plain,
    spl230_493,
    inference(avatar_split_clause,[],[f2327,f7087]) ).

tff(f7087,plain,
    ( spl230_493
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ sP5(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_493])]) ).

tff(f2327,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP5(X0,X1) ),
    inference(cnf_transformation,[],[f1470]) ).

tff(f7081,plain,
    spl230_492,
    inference(avatar_split_clause,[],[f2319,f7079]) ).

tff(f7079,plain,
    ( spl230_492
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'fun_app$l'('of_nat$',X1) )
        | ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ sP4(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_492])]) ).

tff(f2319,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'fun_app$l'('of_nat$',X1) )
      | ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ sP4(X0,X1) ),
    inference(cnf_transformation,[],[f1466]) ).

tff(f7077,plain,
    spl230_491,
    inference(avatar_split_clause,[],[f2276,f7075]) ).

tff(f7075,plain,
    ( spl230_491
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
        ( ( 'cons$'(sK112(X0),sK113(X0)) = X0 )
        | ~ 'member$'('pair$b'('nil$',X0),'lexord$c'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_491])]) ).

tff(f2276,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'cons$'(sK112(X0),sK113(X0)) = X0 )
      | ~ 'member$'('pair$b'('nil$',X0),'lexord$c'(X1)) ),
    inference(cnf_transformation,[],[f1416]) ).

tff(f1416,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('nil$',X0),'lexord$c'(X1))
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] : ( 'cons$'(X2,X3) != X0 ) )
      & ( ( 'cons$'(sK112(X0),sK113(X0)) = X0 )
        | ~ 'member$'('pair$b'('nil$',X0),'lexord$c'(X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f1414,f1415]) ).

tff(f1415,plain,
    ! [X0: 'A_iarray_list$'] :
      ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] : ( 'cons$'(X4,X5) = X0 )
     => ( 'cons$'(sK112(X0),sK113(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1414,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('nil$',X0),'lexord$c'(X1))
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] : ( 'cons$'(X2,X3) != X0 ) )
      & ( ? [X4: 'A_iarray$',X5: 'A_iarray_list$'] : ( 'cons$'(X4,X5) = X0 )
        | ~ 'member$'('pair$b'('nil$',X0),'lexord$c'(X1)) ) ),
    inference(rectify,[],[f1413]) ).

tff(f1413,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'member$'('pair$b'('nil$',X0),'lexord$c'(X1))
        | ! [X2: 'A_iarray$',X3: 'A_iarray_list$'] : ( 'cons$'(X2,X3) != X0 ) )
      & ( ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] : ( 'cons$'(X2,X3) = X0 )
        | ~ 'member$'('pair$b'('nil$',X0),'lexord$c'(X1)) ) ),
    inference(nnf_transformation,[],[f543]) ).

tff(f543,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('nil$',X0),'lexord$c'(X1))
    <=> ? [X2: 'A_iarray$',X3: 'A_iarray_list$'] : ( 'cons$'(X2,X3) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom541) ).

tff(f7073,plain,
    spl230_490,
    inference(avatar_split_clause,[],[f2262,f7071]) ).

tff(f7071,plain,
    ( spl230_490
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X3: 'A_iarray$'] :
        ( ~ 'fun_app$'(X0,X3)
        | ~ 'member$a'(X3,'set$'(X1))
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_490])]) ).

tff(f2262,plain,
    ! [X3: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ~ 'fun_app$'(X0,X3)
      | ~ 'member$a'(X3,'set$'(X1))
      | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ),
    inference(cnf_transformation,[],[f1404]) ).

tff(f1404,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ( 'fun_app$'(X0,sK110(X0,X1))
          & 'member$a'(sK110(X0,X1),'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK110])],[f1402,f1403]) ).

tff(f1403,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray$'] :
          ( 'fun_app$'(X0,X2)
          & 'member$a'(X2,'set$'(X1)) )
     => ( 'fun_app$'(X0,sK110(X0,X1))
        & 'member$a'(sK110(X0,X1),'set$'(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1402,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ? [X2: 'A_iarray$'] :
            ( 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(rectify,[],[f1401]) ).

tff(f1401,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ? [X2: 'A_iarray$'] :
            ( 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X2: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X2)
            | ~ 'member$a'(X2,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(nnf_transformation,[],[f878]) ).

tff(f878,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
    <=> ! [X2: 'A_iarray$'] :
          ( ~ 'fun_app$'(X0,X2)
          | ~ 'member$a'(X2,'set$'(X1)) ) ),
    inference(ennf_transformation,[],[f597]) ).

tff(f597,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
    <=> ! [X2: 'A_iarray$'] :
          ( 'member$a'(X2,'set$'(X1))
         => ~ 'fun_app$'(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom595) ).

tff(f7069,plain,
    spl230_489,
    inference(avatar_split_clause,[],[f2259,f7067]) ).

tff(f7067,plain,
    ( spl230_489
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X3: 'A_iarray$'] :
        ( 'fun_app$'(X0,X3)
        | ~ 'member$a'(X3,'set$'(X1))
        | ( 'fun_app$p'('filter$'(X0),X1) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_489])]) ).

tff(f2259,plain,
    ! [X3: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'fun_app$'(X0,X3)
      | ~ 'member$a'(X3,'set$'(X1))
      | ( 'fun_app$p'('filter$'(X0),X1) != X1 ) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f1400,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
        | ( ~ 'fun_app$'(X0,sK109(X0,X1))
          & 'member$a'(sK109(X0,X1),'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != X1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f1398,f1399]) ).

tff(f1399,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray$'] :
          ( ~ 'fun_app$'(X0,X2)
          & 'member$a'(X2,'set$'(X1)) )
     => ( ~ 'fun_app$'(X0,sK109(X0,X1))
        & 'member$a'(sK109(X0,X1),'set$'(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1398,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
        | ? [X2: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != X1 ) ) ),
    inference(rectify,[],[f1397]) ).

tff(f1397,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
        | ? [X2: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X2: 'A_iarray$'] :
            ( 'fun_app$'(X0,X2)
            | ~ 'member$a'(X2,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != X1 ) ) ),
    inference(nnf_transformation,[],[f877]) ).

tff(f877,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
    <=> ! [X2: 'A_iarray$'] :
          ( 'fun_app$'(X0,X2)
          | ~ 'member$a'(X2,'set$'(X1)) ) ),
    inference(ennf_transformation,[],[f599]) ).

tff(f599,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
    <=> ! [X2: 'A_iarray$'] :
          ( 'member$a'(X2,'set$'(X1))
         => 'fun_app$'(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom597) ).

tff(f7065,plain,
    spl230_488,
    inference(avatar_split_clause,[],[f2102,f7063]) ).

tff(f7063,plain,
    ( spl230_488
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
        ( ~ 'member$s'('pair$z'(X1,X1),'lexord$b'(X0))
        | 'member$'('pair$b'(sK83(X0),sK83(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_488])]) ).

tff(f2102,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
      ( ~ 'member$s'('pair$z'(X1,X1),'lexord$b'(X0))
      | 'member$'('pair$b'(sK83(X0),sK83(X0)),X0) ),
    inference(cnf_transformation,[],[f1268]) ).

tff(f1268,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
      ( ~ 'member$s'('pair$z'(X1,X1),'lexord$b'(X0))
      | 'member$'('pair$b'(sK83(X0),sK83(X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f868,f1267]) ).

tff(f1267,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ? [X2: 'A_iarray_list$'] : 'member$'('pair$b'(X2,X2),X0)
     => 'member$'('pair$b'(sK83(X0),sK83(X0)),X0) ),
    introduced(choice_axiom,[]) ).

tff(f868,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
      ( ~ 'member$s'('pair$z'(X1,X1),'lexord$b'(X0))
      | ? [X2: 'A_iarray_list$'] : 'member$'('pair$b'(X2,X2),X0) ),
    inference(ennf_transformation,[],[f522]) ).

tff(f522,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$'] :
      ( ! [X2: 'A_iarray_list$'] : ~ 'member$'('pair$b'(X2,X2),X0)
     => ~ 'member$s'('pair$z'(X1,X1),'lexord$b'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom520) ).

tff(f7061,plain,
    spl230_487,
    inference(avatar_split_clause,[],[f2101,f7059]) ).

tff(f7059,plain,
    ( spl230_487
  <=> ! [X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
        ( ~ 'member$o'('pair$v'(X1,X1),'lexord$'(X0))
        | 'member$g'('pair$c'(sK82(X0),sK82(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_487])]) ).

tff(f2101,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
      ( ~ 'member$o'('pair$v'(X1,X1),'lexord$'(X0))
      | 'member$g'('pair$c'(sK82(X0),sK82(X0)),X0) ),
    inference(cnf_transformation,[],[f1266]) ).

tff(f1266,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
      ( ~ 'member$o'('pair$v'(X1,X1),'lexord$'(X0))
      | 'member$g'('pair$c'(sK82(X0),sK82(X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f867,f1265]) ).

tff(f1265,plain,
    ! [X0: 'Int_int_prod_set$'] :
      ( ? [X2: $int] : 'member$g'('pair$c'(X2,X2),X0)
     => 'member$g'('pair$c'(sK82(X0),sK82(X0)),X0) ),
    introduced(choice_axiom,[]) ).

tff(f867,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
      ( ~ 'member$o'('pair$v'(X1,X1),'lexord$'(X0))
      | ? [X2: $int] : 'member$g'('pair$c'(X2,X2),X0) ),
    inference(ennf_transformation,[],[f520]) ).

tff(f520,axiom,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_list$'] :
      ( ! [X2: $int] : ~ 'member$g'('pair$c'(X2,X2),X0)
     => ~ 'member$o'('pair$v'(X1,X1),'lexord$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom518) ).

tff(f7057,plain,
    spl230_486,
    inference(avatar_split_clause,[],[f2100,f7055]) ).

tff(f7055,plain,
    ( spl230_486
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
        ( ~ 'member$p'('pair$w'(X1,X1),'lexord$a'(X0))
        | 'member$e'('pair$'(sK81(X0),sK81(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_486])]) ).

tff(f2100,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
      ( ~ 'member$p'('pair$w'(X1,X1),'lexord$a'(X0))
      | 'member$e'('pair$'(sK81(X0),sK81(X0)),X0) ),
    inference(cnf_transformation,[],[f1264]) ).

tff(f1264,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
      ( ~ 'member$p'('pair$w'(X1,X1),'lexord$a'(X0))
      | 'member$e'('pair$'(sK81(X0),sK81(X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f866,f1263]) ).

tff(f1263,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ? [X2: 'A_iarray_iarray$'] : 'member$e'('pair$'(X2,X2),X0)
     => 'member$e'('pair$'(sK81(X0),sK81(X0)),X0) ),
    introduced(choice_axiom,[]) ).

tff(f866,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
      ( ~ 'member$p'('pair$w'(X1,X1),'lexord$a'(X0))
      | ? [X2: 'A_iarray_iarray$'] : 'member$e'('pair$'(X2,X2),X0) ),
    inference(ennf_transformation,[],[f521]) ).

tff(f521,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$'] :
      ( ! [X2: 'A_iarray_iarray$'] : ~ 'member$e'('pair$'(X2,X2),X0)
     => ~ 'member$p'('pair$w'(X1,X1),'lexord$a'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom519) ).

tff(f7053,plain,
    spl230_485,
    inference(avatar_split_clause,[],[f2099,f7051]) ).

tff(f7051,plain,
    ( spl230_485
  <=> ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
        ( ~ 'member$'('pair$b'(X1,X1),'lexord$c'(X0))
        | 'member$f'('pair$a'(sK80(X0),sK80(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_485])]) ).

tff(f2099,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
      ( ~ 'member$'('pair$b'(X1,X1),'lexord$c'(X0))
      | 'member$f'('pair$a'(sK80(X0),sK80(X0)),X0) ),
    inference(cnf_transformation,[],[f1262]) ).

tff(f1262,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
      ( ~ 'member$'('pair$b'(X1,X1),'lexord$c'(X0))
      | 'member$f'('pair$a'(sK80(X0),sK80(X0)),X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f865,f1261]) ).

tff(f1261,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$'] :
      ( ? [X2: 'A_iarray$'] : 'member$f'('pair$a'(X2,X2),X0)
     => 'member$f'('pair$a'(sK80(X0),sK80(X0)),X0) ),
    introduced(choice_axiom,[]) ).

tff(f865,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
      ( ~ 'member$'('pair$b'(X1,X1),'lexord$c'(X0))
      | ? [X2: 'A_iarray$'] : 'member$f'('pair$a'(X2,X2),X0) ),
    inference(ennf_transformation,[],[f523]) ).

tff(f523,axiom,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$'] :
      ( ! [X2: 'A_iarray$'] : ~ 'member$f'('pair$a'(X2,X2),X0)
     => ~ 'member$'('pair$b'(X1,X1),'lexord$c'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom521) ).

tff(f7049,plain,
    spl230_484,
    inference(avatar_split_clause,[],[f2013,f7047]) ).

tff(f7047,plain,
    ( spl230_484
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1)),X0) = 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_484])]) ).

tff(f2013,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1)),X0) = 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) ),
    inference(cnf_transformation,[],[f297]) ).

tff(f297,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1)),X0) = 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom295) ).

tff(f7045,plain,
    spl230_483,
    inference(avatar_split_clause,[],[f2010,f7043]) ).

tff(f7043,plain,
    ( spl230_483
  <=> ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('snd$','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('snd$',X0),'fun_app$ab'('snd$',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_483])]) ).

tff(f2010,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('snd$','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('snd$',X0),'fun_app$ab'('snd$',X1)) ),
    inference(cnf_transformation,[],[f192]) ).

tff(f192,axiom,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('snd$','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('snd$',X0),'fun_app$ab'('snd$',X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom190) ).

tff(f7038,plain,
    spl230_482,
    inference(avatar_split_clause,[],[f2009,f7036]) ).

tff(f7036,plain,
    ( spl230_482
  <=> ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('fst$a','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('fst$a',X0),'fun_app$ab'('fst$a',X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_482])]) ).

tff(f2009,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('fst$a','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('fst$a',X0),'fun_app$ab'('fst$a',X1)) ),
    inference(cnf_transformation,[],[f89]) ).

tff(f89,axiom,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'fun_app$ab'('fst$a','plus$'(X0,X1)) = 'plus$a'('fun_app$ab'('fst$a',X0),'fun_app$ab'('fst$a',X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom87) ).

tff(f7034,plain,
    spl230_481,
    inference(avatar_split_clause,[],[f2006,f7032]) ).

tff(f7032,plain,
    ( spl230_481
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a','enumerate$'(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_481])]) ).

tff(f2006,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a','enumerate$'(X0,X1))) ),
    inference(cnf_transformation,[],[f504]) ).

tff(f504,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$','fun_app$u'('size$a','enumerate$'(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom502) ).

tff(f6882,plain,
    ( spl230_480
    | ~ spl230_33
    | ~ spl230_425 ),
    inference(avatar_split_clause,[],[f6861,f6201,f3645,f6879]) ).

tff(f6879,plain,
    ( spl230_480
  <=> ( 0 = sK40('zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_480])]) ).

tff(f3645,plain,
    ( spl230_33
  <=> ( 0 = 'fun_app$ac'('fst$b','zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_33])]) ).

tff(f6861,plain,
    ( ( 0 = sK40('zero$a') )
    | ~ spl230_33
    | ~ spl230_425 ),
    inference(superposition,[],[f6202,f3647]) ).

tff(f3647,plain,
    ( ( 0 = 'fun_app$ac'('fst$b','zero$a') )
    | ~ spl230_33 ),
    inference(avatar_component_clause,[],[f3645]) ).

tff(f6807,plain,
    ( spl230_479
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_436 ),
    inference(avatar_split_clause,[],[f6599,f6596,f3895,f3877,f6805]) ).

tff(f6805,plain,
    ( spl230_479
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X0,X1)
        | 'fun_app$c'(X0,sK78(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_479])]) ).

tff(f6596,plain,
    ( spl230_436
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,X1)
        | 'fun_app$c'(X0,sK78(X0))
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_436])]) ).

tff(f6599,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | 'fun_app$c'(X0,X1)
        | 'fun_app$c'(X0,sK78(X0)) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_436 ),
    inference(forward_demodulation,[],[f6597,f4136]) ).

tff(f6597,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,X1)
        | 'fun_app$c'(X0,sK78(X0))
        | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) )
    | ~ spl230_436 ),
    inference(avatar_component_clause,[],[f6596]) ).

tff(f6803,plain,
    ( spl230_478
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_435 ),
    inference(avatar_split_clause,[],[f6594,f6591,f3895,f3877,f6801]) ).

tff(f6801,plain,
    ( spl230_478
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X0,sK77(X0))
        | ~ 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_478])]) ).

tff(f6591,plain,
    ( spl230_435
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
        | ~ 'fun_app$c'(X0,sK77(X0))
        | ~ 'fun_app$c'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_435])]) ).

tff(f6594,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$aa'('rank$','zero$b'))
        | ~ 'fun_app$c'(X0,sK77(X0))
        | ~ 'fun_app$c'(X0,X1) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_435 ),
    inference(forward_demodulation,[],[f6592,f4136]) ).

tff(f6592,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
        | ~ 'fun_app$c'(X0,sK77(X0))
        | ~ 'fun_app$c'(X0,X1) )
    | ~ spl230_435 ),
    inference(avatar_component_clause,[],[f6591]) ).

tff(f6799,plain,
    ( spl230_477
    | ~ spl230_88
    | ~ spl230_290 ),
    inference(avatar_split_clause,[],[f5403,f5150,f3895,f6797]) ).

tff(f6797,plain,
    ( spl230_477
  <=> ! [X0: 'Nat$'] : ( 'fun_app$m'('size$',sK59(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_477])]) ).

tff(f5150,plain,
    ( spl230_290
  <=> ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK59(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_290])]) ).

tff(f5403,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$m'('size$',sK59(X0)) = X0 )
    | ~ spl230_88
    | ~ spl230_290 ),
    inference(forward_demodulation,[],[f5398,f3896]) ).

tff(f5398,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = 'fun_app$m'('size$',sK59(X0)) )
    | ~ spl230_88
    | ~ spl230_290 ),
    inference(superposition,[],[f3896,f5151]) ).

tff(f5151,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK59(X0))) )
    | ~ spl230_290 ),
    inference(avatar_component_clause,[],[f5150]) ).

tff(f6760,plain,
    ( spl230_476
    | ~ spl230_330
    | ~ spl230_475 ),
    inference(avatar_split_clause,[],[f6756,f6753,f5602,f6758]) ).

tff(f6758,plain,
    ( spl230_476
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_476])]) ).

tff(f6753,plain,
    ( spl230_475
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_475])]) ).

tff(f6756,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
        | ~ 'fun_app$o'('invertible$',X0) )
    | ~ spl230_330
    | ~ spl230_475 ),
    inference(forward_demodulation,[],[f6754,f5603]) ).

tff(f6754,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
        | ~ 'fun_app$o'('invertible$',X0) )
    | ~ spl230_475 ),
    inference(avatar_component_clause,[],[f6753]) ).

tff(f6755,plain,
    spl230_475,
    inference(avatar_split_clause,[],[f3344,f6753]) ).

tff(f3344,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(forward_demodulation,[],[f1875,f1853]) ).

tff(f1875,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f796]) ).

tff(f796,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f92]) ).

tff(f92,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
     => ( 'matrix_to_iarray$'('matrix_inv$'(X0)) = 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom90) ).

tff(f6751,plain,
    spl230_474,
    inference(avatar_split_clause,[],[f3295,f6749]) ).

tff(f6749,plain,
    ( spl230_474
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = 1 )
        | ~ sP4(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_474])]) ).

tff(f3295,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = 1 )
      | ~ sP4(X1,X0) ),
    inference(evaluation,[],[f2325]) ).

tff(f2325,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
      | ~ sP4(X1,X0) ),
    inference(cnf_transformation,[],[f1467]) ).

tff(f1467,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
        | ~ sP4(X1,X0) )
      & ( sP4(X1,X0)
        | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != $sum(0,1) ) ) ),
    inference(nnf_transformation,[],[f1086]) ).

tff(f1086,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
    <=> sP4(X1,X0) ),
    inference(definition_folding,[],[f465,f1085]) ).

tff(f465,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
    <=> ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom463) ).

tff(f6747,plain,
    spl230_473,
    inference(avatar_split_clause,[],[f3294,f6745]) ).

tff(f6745,plain,
    ( spl230_473
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP4(X1,X0)
        | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != 1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_473])]) ).

tff(f3294,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X1,X0)
      | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != 1 ) ),
    inference(evaluation,[],[f2324]) ).

tff(f2324,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP4(X1,X0)
      | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != $sum(0,1) ) ),
    inference(cnf_transformation,[],[f1467]) ).

tff(f6743,plain,
    spl230_472,
    inference(avatar_split_clause,[],[f3288,f6741]) ).

tff(f6741,plain,
    ( spl230_472
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = 1 )
        | ~ sP5(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_472])]) ).

tff(f3288,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = 1 )
      | ~ sP5(X1,X0) ),
    inference(evaluation,[],[f2333]) ).

tff(f2333,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
      | ~ sP5(X1,X0) ),
    inference(cnf_transformation,[],[f1471]) ).

tff(f1471,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
        | ~ sP5(X1,X0) )
      & ( sP5(X1,X0)
        | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != $sum(0,1) ) ) ),
    inference(nnf_transformation,[],[f1088]) ).

tff(f1088,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
    <=> sP5(X1,X0) ),
    inference(definition_folding,[],[f464,f1087]) ).

tff(f464,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) = $sum(0,1) )
    <=> ( ( ( 'fun_app$l'('of_nat$',X1) = $sum(0,1) )
          & ( 'fun_app$l'('of_nat$',X0) = 0 ) )
        | ( ( 0 = 'fun_app$l'('of_nat$',X1) )
          & ( 'fun_app$l'('of_nat$',X0) = $sum(0,1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom462) ).

tff(f6739,plain,
    spl230_471,
    inference(avatar_split_clause,[],[f3287,f6737]) ).

tff(f6737,plain,
    ( spl230_471
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( sP5(X1,X0)
        | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != 1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_471])]) ).

tff(f3287,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X1,X0)
      | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != 1 ) ),
    inference(evaluation,[],[f2332]) ).

tff(f2332,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( sP5(X1,X0)
      | ( $sum('fun_app$l'('of_nat$',X0),'fun_app$l'('of_nat$',X1)) != $sum(0,1) ) ),
    inference(cnf_transformation,[],[f1471]) ).

tff(f6735,plain,
    ( spl230_470
    | ~ spl230_88
    | ~ spl230_289 ),
    inference(avatar_split_clause,[],[f5393,f5146,f3895,f6733]) ).

tff(f6733,plain,
    ( spl230_470
  <=> ! [X0: 'Nat$'] : ( 'fun_app$u'('size$a',sK58(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_470])]) ).

tff(f5146,plain,
    ( spl230_289
  <=> ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK58(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_289])]) ).

tff(f5393,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$u'('size$a',sK58(X0)) = X0 )
    | ~ spl230_88
    | ~ spl230_289 ),
    inference(forward_demodulation,[],[f5388,f3896]) ).

tff(f5388,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = 'fun_app$u'('size$a',sK58(X0)) )
    | ~ spl230_88
    | ~ spl230_289 ),
    inference(superposition,[],[f3896,f5147]) ).

tff(f5147,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK58(X0))) )
    | ~ spl230_289 ),
    inference(avatar_component_clause,[],[f5146]) ).

tff(f6731,plain,
    spl230_469,
    inference(avatar_split_clause,[],[f3237,f6729]) ).

tff(f6729,plain,
    ( spl230_469
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP30(X0,X1,X2,X4,X4)
        | ~ 'member$'('pair$b'(X2,X1),'listrel1$c'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_469])]) ).

tff(f3237,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP30(X0,X1,X2,X4,X4)
      | ~ 'member$'('pair$b'(X2,X1),'listrel1$c'(X0)) ),
    inference(equality_resolution,[],[f2890]) ).

tff(f2890,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP30(X0,X1,X2,X3,X4)
      | ~ 'member$'('pair$b'(X2,X1),'listrel1$c'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f6727,plain,
    spl230_468,
    inference(avatar_split_clause,[],[f3235,f6725]) ).

tff(f6725,plain,
    ( spl230_468
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP29(X0,X1,X2,X4,X4)
        | ~ 'member$'('pair$b'(X2,X1),'lex$d'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_468])]) ).

tff(f3235,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP29(X0,X1,X2,X4,X4)
      | ~ 'member$'('pair$b'(X2,X1),'lex$d'(X0)) ),
    inference(equality_resolution,[],[f2878]) ).

tff(f2878,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP29(X0,X1,X2,X3,X4)
      | ~ 'member$'('pair$b'(X2,X1),'lex$d'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1726]) ).

tff(f6723,plain,
    spl230_467,
    inference(avatar_split_clause,[],[f3234,f6721]) ).

tff(f6721,plain,
    ( spl230_467
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( sP28(X0,X1,X2,X4,X4)
        | ~ 'member$'('pair$b'(X2,X1),'lenlex$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_467])]) ).

tff(f3234,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP28(X0,X1,X2,X4,X4)
      | ~ 'member$'('pair$b'(X2,X1),'lenlex$'(X0)) ),
    inference(equality_resolution,[],[f2870]) ).

tff(f2870,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP28(X0,X1,X2,X3,X4)
      | ~ 'member$'('pair$b'(X2,X1),'lenlex$'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1722]) ).

tff(f6719,plain,
    spl230_466,
    inference(avatar_split_clause,[],[f3232,f6717]) ).

tff(f6717,plain,
    ( spl230_466
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( sP27(X0,X1,X2,X4,X4)
        | ~ 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_466])]) ).

tff(f3232,plain,
    ! [X2: 'A_iarray_list_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( sP27(X0,X1,X2,X4,X4)
      | ~ 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0)) ),
    inference(equality_resolution,[],[f2861]) ).

tff(f2861,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( sP27(X0,X1,X2,X3,X4)
      | ~ 'member$s'('pair$z'(X2,X1),'listrel1$b'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f6715,plain,
    spl230_465,
    inference(avatar_split_clause,[],[f3230,f6713]) ).

tff(f6713,plain,
    ( spl230_465
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( sP26(X0,X1,X2,X4,X4)
        | ~ 'member$s'('pair$z'(X2,X1),'lex$c'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_465])]) ).

tff(f3230,plain,
    ! [X2: 'A_iarray_list_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( sP26(X0,X1,X2,X4,X4)
      | ~ 'member$s'('pair$z'(X2,X1),'lex$c'(X0)) ),
    inference(equality_resolution,[],[f2849]) ).

tff(f2849,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( sP26(X0,X1,X2,X3,X4)
      | ~ 'member$s'('pair$z'(X2,X1),'lex$c'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1712]) ).

tff(f6711,plain,
    spl230_464,
    inference(avatar_split_clause,[],[f3228,f6709]) ).

tff(f6709,plain,
    ( spl230_464
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X2: 'Int_list$',X1: 'Int_list$'] :
        ( sP25(X0,X1,X2,X4,X4)
        | ~ 'member$o'('pair$v'(X2,X1),'listrel1$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_464])]) ).

tff(f3228,plain,
    ! [X2: 'Int_list$',X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP25(X0,X1,X2,X4,X4)
      | ~ 'member$o'('pair$v'(X2,X1),'listrel1$'(X0)) ),
    inference(equality_resolution,[],[f2841]) ).

tff(f2841,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP25(X0,X1,X2,X3,X4)
      | ~ 'member$o'('pair$v'(X2,X1),'listrel1$'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f6707,plain,
    spl230_463,
    inference(avatar_split_clause,[],[f3226,f6705]) ).

tff(f6705,plain,
    ( spl230_463
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( sP24(X0,X1,X2,X4,X4)
        | ~ 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_463])]) ).

tff(f3226,plain,
    ! [X2: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP24(X0,X1,X2,X4,X4)
      | ~ 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0)) ),
    inference(equality_resolution,[],[f2833]) ).

tff(f2833,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP24(X0,X1,X2,X3,X4)
      | ~ 'member$p'('pair$w'(X2,X1),'listrel1$a'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f6703,plain,
    spl230_462,
    inference(avatar_split_clause,[],[f3223,f6701]) ).

tff(f6701,plain,
    ( spl230_462
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X2: 'Int_list$',X1: 'Int_list$'] :
        ( sP23(X0,X1,X2,X4,X4)
        | ~ 'member$o'('pair$v'(X2,X1),'lex$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_462])]) ).

tff(f3223,plain,
    ! [X2: 'Int_list$',X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP23(X0,X1,X2,X4,X4)
      | ~ 'member$o'('pair$v'(X2,X1),'lex$'(X0)) ),
    inference(equality_resolution,[],[f2817]) ).

tff(f2817,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP23(X0,X1,X2,X3,X4)
      | ~ 'member$o'('pair$v'(X2,X1),'lex$'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1696]) ).

tff(f6699,plain,
    spl230_461,
    inference(avatar_split_clause,[],[f3222,f6697]) ).

tff(f6697,plain,
    ( spl230_461
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( sP22(X0,X1,X2,X4,X4)
        | ~ 'member$p'('pair$w'(X2,X1),'lex$a'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_461])]) ).

tff(f3222,plain,
    ! [X2: 'A_iarray_iarray_list$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP22(X0,X1,X2,X4,X4)
      | ~ 'member$p'('pair$w'(X2,X1),'lex$a'(X0)) ),
    inference(equality_resolution,[],[f2809]) ).

tff(f2809,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP22(X0,X1,X2,X3,X4)
      | ~ 'member$p'('pair$w'(X2,X1),'lex$a'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1692]) ).

tff(f6695,plain,
    spl230_460,
    inference(avatar_split_clause,[],[f3221,f6693]) ).

tff(f6693,plain,
    ( spl230_460
  <=> ! [X4: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X2: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( sP21(X0,X1,X2,X4,X4)
        | ~ 'member$q'('pair$x'(X2,X1),'lex$b'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_460])]) ).

tff(f3221,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod$'] :
      ( sP21(X0,X1,X2,X4,X4)
      | ~ 'member$q'('pair$x'(X2,X1),'lex$b'(X0)) ),
    inference(equality_resolution,[],[f2801]) ).

tff(f2801,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X3: 'Nat_a_iarray_prod$',X0: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X1: 'Nat_a_iarray_prod_list$',X4: 'Nat_a_iarray_prod$'] :
      ( sP21(X0,X1,X2,X3,X4)
      | ~ 'member$q'('pair$x'(X2,X1),'lex$b'(X0))
      | ( X3 != X4 ) ),
    inference(cnf_transformation,[],[f1688]) ).

tff(f6691,plain,
    ( spl230_459
    | ~ spl230_88
    | ~ spl230_288 ),
    inference(avatar_split_clause,[],[f5385,f5142,f3895,f6689]) ).

tff(f6689,plain,
    ( spl230_459
  <=> ! [X0: 'Nat$'] : ( 'fun_app$v'('size$b',sK57(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_459])]) ).

tff(f5142,plain,
    ( spl230_288
  <=> ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK57(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_288])]) ).

tff(f5385,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$v'('size$b',sK57(X0)) = X0 )
    | ~ spl230_88
    | ~ spl230_288 ),
    inference(forward_demodulation,[],[f5380,f3896]) ).

tff(f5380,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$k'('nat$','fun_app$l'('of_nat$',X0)) = 'fun_app$v'('size$b',sK57(X0)) )
    | ~ spl230_88
    | ~ spl230_288 ),
    inference(superposition,[],[f3896,f5143]) ).

tff(f5143,plain,
    ( ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK57(X0))) )
    | ~ spl230_288 ),
    inference(avatar_component_clause,[],[f5142]) ).

tff(f6687,plain,
    spl230_458,
    inference(avatar_split_clause,[],[f2886,f6685]) ).

tff(f6685,plain,
    ( spl230_458
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X3 = X4 )
        | ( X1 = X2 )
        | ~ sP30(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_458])]) ).

tff(f2886,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( ( X3 = X4 )
      | ( X1 = X2 )
      | ~ sP30(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f6683,plain,
    spl230_457,
    inference(avatar_split_clause,[],[f2857,f6681]) ).

tff(f6681,plain,
    ( spl230_457
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( ( X3 = X4 )
        | ( X1 = X2 )
        | ~ sP27(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_457])]) ).

tff(f2857,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( ( X3 = X4 )
      | ( X1 = X2 )
      | ~ sP27(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f6679,plain,
    spl230_456,
    inference(avatar_split_clause,[],[f2837,f6677]) ).

tff(f6677,plain,
    ( spl230_456
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$',X1: 'Int_list$'] :
        ( ( X3 = X4 )
        | ( X1 = X2 )
        | ~ sP25(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_456])]) ).

tff(f2837,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( ( X3 = X4 )
      | ( X1 = X2 )
      | ~ sP25(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f6675,plain,
    spl230_455,
    inference(avatar_split_clause,[],[f2829,f6673]) ).

tff(f6673,plain,
    ( spl230_455
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$',X1: 'A_iarray_iarray_list$'] :
        ( ( X3 = X4 )
        | ( X1 = X2 )
        | ~ sP24(X0,X1,X2,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_455])]) ).

tff(f2829,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( ( X3 = X4 )
      | ( X1 = X2 )
      | ~ sP24(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f6671,plain,
    spl230_454,
    inference(avatar_split_clause,[],[f2596,f6669]) ).

tff(f6669,plain,
    ( spl230_454
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X1 = X2 )
        | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_454])]) ).

tff(f2596,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X1 = X2 )
      | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X0),X2) ) ),
    inference(cnf_transformation,[],[f1604]) ).

tff(f1604,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X0),X1) = 'fun_app$p'('append$d'(X0),X2) )
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X0),X2) ) ) ),
    inference(nnf_transformation,[],[f560]) ).

tff(f560,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('append$d'(X0),X1) = 'fun_app$p'('append$d'(X0),X2) )
    <=> ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom558) ).

tff(f6667,plain,
    spl230_453,
    inference(avatar_split_clause,[],[f2594,f6665]) ).

tff(f6665,plain,
    ( spl230_453
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X0 = X2 )
        | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X2),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_453])]) ).

tff(f2594,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X0 = X2 )
      | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X2),X1) ) ),
    inference(cnf_transformation,[],[f1603]) ).

tff(f1603,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X0),X1) = 'fun_app$p'('append$d'(X2),X1) )
        | ( X0 != X2 ) )
      & ( ( X0 = X2 )
        | ( 'fun_app$p'('append$d'(X0),X1) != 'fun_app$p'('append$d'(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f558]) ).

tff(f558,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('append$d'(X0),X1) = 'fun_app$p'('append$d'(X2),X1) )
    <=> ( X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom556) ).

tff(f6663,plain,
    spl230_452,
    inference(avatar_split_clause,[],[f2592,f6661]) ).

tff(f6661,plain,
    ( spl230_452
  <=> ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( X0 = X2 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X2),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_452])]) ).

tff(f2592,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( X0 = X2 )
      | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X2),X1) ) ),
    inference(cnf_transformation,[],[f1602]) ).

tff(f1602,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = 'fun_app$bd'('append$'(X2),X1) )
        | ( X0 != X2 ) )
      & ( ( X0 = X2 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X2),X1) ) ) ),
    inference(nnf_transformation,[],[f559]) ).

tff(f559,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = 'fun_app$bd'('append$'(X2),X1) )
    <=> ( X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom557) ).

tff(f6659,plain,
    spl230_451,
    inference(avatar_split_clause,[],[f2590,f6657]) ).

tff(f6657,plain,
    ( spl230_451
  <=> ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( X1 = X2 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X0),X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_451])]) ).

tff(f2590,plain,
    ! [X2: 'Nat_a_iarray_prod_list$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( X1 = X2 )
      | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X0),X2) ) ),
    inference(cnf_transformation,[],[f1601]) ).

tff(f1601,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = 'fun_app$bd'('append$'(X0),X2) )
        | ( X1 != X2 ) )
      & ( ( X1 = X2 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'fun_app$bd'('append$'(X0),X2) ) ) ),
    inference(nnf_transformation,[],[f561]) ).

tff(f561,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$',X2: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = 'fun_app$bd'('append$'(X0),X2) )
    <=> ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom559) ).

tff(f6655,plain,
    spl230_450,
    inference(avatar_split_clause,[],[f2559,f6653]) ).

tff(f6653,plain,
    ( spl230_450
  <=> ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X0,X1),'lexord$c'(X2))
        | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_450])]) ).

tff(f2559,plain,
    ! [X2: 'A_iarray_a_iarray_prod_set$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X0,X1),'lexord$c'(X2))
      | ~ 'member$'('pair$b'(X0,X1),'lex$d'(X2)) ),
    inference(cnf_transformation,[],[f1586]) ).

tff(f6651,plain,
    spl230_449,
    inference(avatar_split_clause,[],[f2554,f6649]) ).

tff(f6649,plain,
    ( spl230_449
  <=> ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
        ( 'member$s'('pair$z'(X0,X1),'lexord$b'(X2))
        | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_449])]) ).

tff(f2554,plain,
    ! [X2: 'A_iarray_list_a_iarray_list_prod_set$',X0: 'A_iarray_list_list$',X1: 'A_iarray_list_list$'] :
      ( 'member$s'('pair$z'(X0,X1),'lexord$b'(X2))
      | ~ 'member$s'('pair$z'(X0,X1),'lex$c'(X2)) ),
    inference(cnf_transformation,[],[f1583]) ).

tff(f6647,plain,
    ( spl230_448
    | ~ spl230_77
    | ~ spl230_265 ),
    inference(avatar_split_clause,[],[f5052,f4890,f3835,f6645]) ).

tff(f6645,plain,
    ( spl230_448
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','matrix_matrix_mult$'(sK60(X0),X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_448])]) ).

tff(f3835,plain,
    ( spl230_77
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_77])]) ).

tff(f4890,plain,
    ( spl230_265
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK60(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_265])]) ).

tff(f5052,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','matrix_matrix_mult$'(sK60(X0),X0))
    | ~ spl230_77
    | ~ spl230_265 ),
    inference(superposition,[],[f3836,f4891]) ).

tff(f4891,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK60(X0),X0) )
    | ~ spl230_265 ),
    inference(avatar_component_clause,[],[f4890]) ).

tff(f3836,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)))
    | ~ spl230_77 ),
    inference(avatar_component_clause,[],[f3835]) ).

tff(f6643,plain,
    spl230_447,
    inference(avatar_split_clause,[],[f2545,f6641]) ).

tff(f6641,plain,
    ( spl230_447
  <=> ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( 'member$q'('pair$x'(X0,X1),'lexord$d'(X2))
        | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_447])]) ).

tff(f2545,plain,
    ! [X2: 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$',X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( 'member$q'('pair$x'(X0,X1),'lexord$d'(X2))
      | ~ 'member$q'('pair$x'(X0,X1),'lex$b'(X2)) ),
    inference(cnf_transformation,[],[f1578]) ).

tff(f6639,plain,
    spl230_446,
    inference(avatar_split_clause,[],[f2532,f6637]) ).

tff(f6637,plain,
    ( spl230_446
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( 'fun_app$'('uuu$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'member$a'(X2,'set$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_446])]) ).

tff(f2532,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'fun_app$'('uuu$'(X0,X1),X2)
      | ~ 'fun_app$'(X0,X2)
      | ~ 'member$a'(X2,'set$'(X1)) ),
    inference(cnf_transformation,[],[f1570]) ).

tff(f1570,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$'] :
      ( ( 'fun_app$'('uuu$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'member$a'(X2,'set$'(X1)) )
      & ( ( 'fun_app$'(X0,X2)
          & 'member$a'(X2,'set$'(X1)) )
        | ~ 'fun_app$'('uuu$'(X0,X1),X2) ) ),
    inference(flattening,[],[f1569]) ).

tff(f1569,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$'] :
      ( ( 'fun_app$'('uuu$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'member$a'(X2,'set$'(X1)) )
      & ( ( 'fun_app$'(X0,X2)
          & 'member$a'(X2,'set$'(X1)) )
        | ~ 'fun_app$'('uuu$'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f10]) ).

tff(f10,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$',X2: 'A_iarray$'] :
      ( 'fun_app$'('uuu$'(X0,X1),X2)
    <=> ( 'fun_app$'(X0,X2)
        & 'member$a'(X2,'set$'(X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).

tff(f6635,plain,
    spl230_445,
    inference(avatar_split_clause,[],[f2463,f6633]) ).

tff(f6633,plain,
    ( spl230_445
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( $less('fun_app$l'('of_nat$',sK158(X0,X1)),'fun_app$l'('of_nat$',X1))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_445])]) ).

tff(f2463,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',sK158(X0,X1)),'fun_app$l'('of_nat$',X1))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f1523]) ).

tff(f6631,plain,
    spl230_444,
    inference(avatar_split_clause,[],[f2266,f6629]) ).

tff(f6629,plain,
    ( spl230_444
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | 'member$a'(sK111(X0,X1),'set$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_444])]) ).

tff(f2266,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
      | 'member$a'(sK111(X0,X1),'set$'(X1)) ),
    inference(cnf_transformation,[],[f1408]) ).

tff(f1408,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ( 'fun_app$'(X0,sK111(X0,X1))
          & 'member$a'(sK111(X0,X1),'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK111])],[f1406,f1407]) ).

tff(f1407,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ? [X2: 'A_iarray$'] :
          ( 'fun_app$'(X0,X2)
          & 'member$a'(X2,'set$'(X1)) )
     => ( 'fun_app$'(X0,sK111(X0,X1))
        & 'member$a'(sK111(X0,X1),'set$'(X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1406,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ? [X2: 'A_iarray$'] :
            ( 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X3: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X3)
            | ~ 'member$a'(X3,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(rectify,[],[f1405]) ).

tff(f1405,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | ? [X2: 'A_iarray$'] :
            ( 'fun_app$'(X0,X2)
            & 'member$a'(X2,'set$'(X1)) ) )
      & ( ! [X2: 'A_iarray$'] :
            ( ~ 'fun_app$'(X0,X2)
            | ~ 'member$a'(X2,'set$'(X1)) )
        | ( 'fun_app$p'('filter$'(X0),X1) != 'nil$' ) ) ),
    inference(nnf_transformation,[],[f879]) ).

tff(f879,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
    <=> ! [X2: 'A_iarray$'] :
          ( ~ 'fun_app$'(X0,X2)
          | ~ 'member$a'(X2,'set$'(X1)) ) ),
    inference(ennf_transformation,[],[f598]) ).

tff(f598,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
    <=> ! [X2: 'A_iarray$'] :
          ( 'member$a'(X2,'set$'(X1))
         => ~ 'fun_app$'(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom596) ).

tff(f6627,plain,
    spl230_443,
    inference(avatar_split_clause,[],[f2263,f6625]) ).

tff(f6625,plain,
    ( spl230_443
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | 'member$a'(sK110(X0,X1),'set$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_443])]) ).

tff(f2263,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
      | 'member$a'(sK110(X0,X1),'set$'(X1)) ),
    inference(cnf_transformation,[],[f1404]) ).

tff(f6623,plain,
    spl230_442,
    inference(avatar_split_clause,[],[f2260,f6621]) ).

tff(f6621,plain,
    ( spl230_442
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
        | 'member$a'(sK109(X0,X1),'set$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_442])]) ).

tff(f2260,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
      | 'member$a'(sK109(X0,X1),'set$'(X1)) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f6619,plain,
    spl230_441,
    inference(avatar_split_clause,[],[f2105,f6617]) ).

tff(f6617,plain,
    ( spl230_441
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
        | 'member$a'(sK85(X0,X1),'set$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_441])]) ).

tff(f2105,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
      | 'member$a'(sK85(X0,X1),'set$'(X0)) ),
    inference(cnf_transformation,[],[f1272]) ).

tff(f1272,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
      | ( ~ 'fun_app$'(X1,sK85(X0,X1))
        & 'member$a'(sK85(X0,X1),'set$'(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f870,f1271]) ).

tff(f1271,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ? [X2: 'A_iarray$'] :
          ( ~ 'fun_app$'(X1,X2)
          & 'member$a'(X2,'set$'(X0)) )
     => ( ~ 'fun_app$'(X1,sK85(X0,X1))
        & 'member$a'(sK85(X0,X1),'set$'(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f870,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
      | ? [X2: 'A_iarray$'] :
          ( ~ 'fun_app$'(X1,X2)
          & 'member$a'(X2,'set$'(X0)) ) ),
    inference(ennf_transformation,[],[f594]) ).

tff(f594,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ! [X2: 'A_iarray$'] :
          ( 'member$a'(X2,'set$'(X0))
         => 'fun_app$'(X1,X2) )
     => ( 'fun_app$p'('filter$'(X1),X0) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom592) ).

tff(f6615,plain,
    spl230_440,
    inference(avatar_split_clause,[],[f2103,f6613]) ).

tff(f6613,plain,
    ( spl230_440
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
        | 'member$a'(sK84(X0,X1),'set$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_440])]) ).

tff(f2103,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
      | 'member$a'(sK84(X0,X1),'set$'(X0)) ),
    inference(cnf_transformation,[],[f1270]) ).

tff(f1270,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
      | ( 'fun_app$'(X1,sK84(X0,X1))
        & 'member$a'(sK84(X0,X1),'set$'(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f869,f1269]) ).

tff(f1269,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ? [X2: 'A_iarray$'] :
          ( 'fun_app$'(X1,X2)
          & 'member$a'(X2,'set$'(X0)) )
     => ( 'fun_app$'(X1,sK84(X0,X1))
        & 'member$a'(sK84(X0,X1),'set$'(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f869,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
      | ? [X2: 'A_iarray$'] :
          ( 'fun_app$'(X1,X2)
          & 'member$a'(X2,'set$'(X0)) ) ),
    inference(ennf_transformation,[],[f596]) ).

tff(f596,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ! [X2: 'A_iarray$'] :
          ( 'member$a'(X2,'set$'(X0))
         => ~ 'fun_app$'(X1,X2) )
     => ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom594) ).

tff(f6611,plain,
    spl230_439,
    inference(avatar_split_clause,[],[f2097,f6609]) ).

tff(f6609,plain,
    ( spl230_439
  <=> ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( X0 = X1 )
        | sP3(X1,X0)
        | ( 'none$' = X1 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_439])]) ).

tff(f2097,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( X0 = X1 )
      | sP3(X1,X0)
      | ( 'none$' = X1 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1260]) ).

tff(f1260,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( X0 = X1 )
      | sP3(X1,X0)
      | ( ( ( 'none$' != X1 )
          | ( 'none$' != X0 ) )
        & ( ( 'none$' = X1 )
          | ( 'none$' = X0 ) ) ) ),
    inference(nnf_transformation,[],[f1084]) ).

tff(f1084,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( X0 = X1 )
      | sP3(X1,X0)
      | ( ( 'none$' = X0 )
      <~> ( 'none$' = X1 ) ) ),
    inference(definition_folding,[],[f864,f1083]) ).

tff(f1083,plain,
    ! [X1: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'the$a'(X0) != 'the$a'(X1) )
        & ( 'none$' != X1 )
        & ( 'none$' != X0 ) )
      | ~ sP3(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f864,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( X0 = X1 )
      | ( ( 'the$a'(X0) != 'the$a'(X1) )
        & ( 'none$' != X1 )
        & ( 'none$' != X0 ) )
      | ( ( 'none$' = X0 )
      <~> ( 'none$' = X1 ) ) ),
    inference(flattening,[],[f863]) ).

tff(f863,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( X0 = X1 )
      | ( ( 'the$a'(X0) != 'the$a'(X1) )
        & ( 'none$' != X1 )
        & ( 'none$' != X0 ) )
      | ( ( 'none$' = X0 )
      <~> ( 'none$' = X1 ) ) ),
    inference(ennf_transformation,[],[f78]) ).

tff(f78,axiom,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( ( ( ( 'none$' != X1 )
            & ( 'none$' != X0 ) )
         => ( 'the$a'(X0) = 'the$a'(X1) ) )
        & ( ( 'none$' = X0 )
        <=> ( 'none$' = X1 ) ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom76) ).

tff(f6607,plain,
    spl230_438,
    inference(avatar_split_clause,[],[f2092,f6605]) ).

tff(f6605,plain,
    ( spl230_438
  <=> ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( X0 = X1 )
        | sP2(X1,X0)
        | ( 'none$a' = X1 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_438])]) ).

tff(f2092,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( X0 = X1 )
      | sP2(X1,X0)
      | ( 'none$a' = X1 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1257]) ).

tff(f1257,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( X0 = X1 )
      | sP2(X1,X0)
      | ( ( ( 'none$a' != X1 )
          | ( 'none$a' != X0 ) )
        & ( ( 'none$a' = X1 )
          | ( 'none$a' = X0 ) ) ) ),
    inference(nnf_transformation,[],[f1082]) ).

tff(f1082,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( X0 = X1 )
      | sP2(X1,X0)
      | ( ( 'none$a' = X0 )
      <~> ( 'none$a' = X1 ) ) ),
    inference(definition_folding,[],[f862,f1081]) ).

tff(f1081,plain,
    ! [X1: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'the$'(X0) != 'the$'(X1) )
        & ( 'none$a' != X1 )
        & ( 'none$a' != X0 ) )
      | ~ sP2(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f862,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( X0 = X1 )
      | ( ( 'the$'(X0) != 'the$'(X1) )
        & ( 'none$a' != X1 )
        & ( 'none$a' != X0 ) )
      | ( ( 'none$a' = X0 )
      <~> ( 'none$a' = X1 ) ) ),
    inference(flattening,[],[f861]) ).

tff(f861,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( X0 = X1 )
      | ( ( 'the$'(X0) != 'the$'(X1) )
        & ( 'none$a' != X1 )
        & ( 'none$a' != X0 ) )
      | ( ( 'none$a' = X0 )
      <~> ( 'none$a' = X1 ) ) ),
    inference(ennf_transformation,[],[f77]) ).

tff(f77,axiom,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( ( ( ( 'none$a' != X1 )
            & ( 'none$a' != X0 ) )
         => ( 'the$'(X0) = 'the$'(X1) ) )
        & ( ( 'none$a' = X0 )
        <=> ( 'none$a' = X1 ) ) )
     => ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom75) ).

tff(f6603,plain,
    ( spl230_437
    | ~ spl230_153
    | ~ spl230_201 ),
    inference(avatar_split_clause,[],[f4678,f4458,f4256,f6601]) ).

tff(f6601,plain,
    ( spl230_437
  <=> ! [X0: $int] :
        ( ~ $less(0,X0)
        | ~ $less(X0,1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_437])]) ).

tff(f4256,plain,
    ( spl230_153
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_153])]) ).

tff(f4678,plain,
    ( ! [X0: $int] :
        ( ~ $less(0,X0)
        | ~ $less(X0,1) )
    | ~ spl230_153
    | ~ spl230_201 ),
    inference(resolution,[],[f4459,f4257]) ).

tff(f4257,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(X0,1))
        | ~ $less(X0,X1) )
    | ~ spl230_153 ),
    inference(avatar_component_clause,[],[f4256]) ).

tff(f6598,plain,
    spl230_436,
    inference(avatar_split_clause,[],[f2079,f6596]) ).

tff(f2079,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,X1)
      | 'fun_app$c'(X0,sK78(X0))
      | ~ 'fun_app$c'(X0,'fun_app$k'('nat$',0)) ),
    inference(cnf_transformation,[],[f1252]) ).

tff(f6593,plain,
    spl230_435,
    inference(avatar_split_clause,[],[f2078,f6591]) ).

tff(f2078,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,'fun_app$k'('nat$',0))
      | ~ 'fun_app$c'(X0,sK77(X0))
      | ~ 'fun_app$c'(X0,X1) ),
    inference(cnf_transformation,[],[f1250]) ).

tff(f6589,plain,
    spl230_434,
    inference(avatar_split_clause,[],[f2005,f6587]) ).

tff(f6587,plain,
    ( spl230_434
  <=> ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','size$g'('enumerate$a'(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_434])]) ).

tff(f2005,plain,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','size$g'('enumerate$a'(X0,X1))) ),
    inference(cnf_transformation,[],[f502]) ).

tff(f502,axiom,
    ! [X0: 'Nat$',X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$','size$g'('enumerate$a'(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom500) ).

tff(f6585,plain,
    spl230_433,
    inference(avatar_split_clause,[],[f2004,f6583]) ).

tff(f6583,plain,
    ( spl230_433
  <=> ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','size$h'('enumerate$b'(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_433])]) ).

tff(f2004,plain,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','size$h'('enumerate$b'(X0,X1))) ),
    inference(cnf_transformation,[],[f503]) ).

tff(f503,axiom,
    ! [X0: 'Nat$',X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$','size$h'('enumerate$b'(X0,X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom501) ).

tff(f6581,plain,
    spl230_432,
    inference(avatar_split_clause,[],[f1854,f6579]) ).

tff(f1854,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) ),
    inference(cnf_transformation,[],[f66]) ).

tff(f66,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$l'('of_nat$','fun_app$aa'('rank$',X0)) = 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'(X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom64) ).

tff(f6570,plain,
    ( spl230_431
    | ~ spl230_152
    | ~ spl230_200 ),
    inference(avatar_split_clause,[],[f4674,f4454,f4252,f6568]) ).

tff(f6568,plain,
    ( spl230_431
  <=> ! [X0: $int] :
        ( $less(0,X0)
        | $less(X0,1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_431])]) ).

tff(f4252,plain,
    ( spl230_152
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_152])]) ).

tff(f4674,plain,
    ( ! [X0: $int] :
        ( $less(0,X0)
        | $less(X0,1) )
    | ~ spl230_152
    | ~ spl230_200 ),
    inference(resolution,[],[f4455,f4253]) ).

tff(f4253,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl230_152 ),
    inference(avatar_component_clause,[],[f4252]) ).

tff(f6520,plain,
    ( spl230_430
    | ~ spl230_55
    | ~ spl230_165 ),
    inference(avatar_split_clause,[],[f4310,f4307,f3738,f6518]) ).

tff(f6518,plain,
    ( spl230_430
  <=> ! [X0: $int] : ( 0 = sK41('pair$c'(X0,0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_430])]) ).

tff(f3738,plain,
    ( spl230_55
  <=> ! [X0: $int] : 'fun_app$ae'('divides_aux$','pair$c'(X0,0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_55])]) ).

tff(f4307,plain,
    ( spl230_165
  <=> ! [X0: 'Int_int_prod$'] :
        ( ( 0 = sK41(X0) )
        | ~ 'fun_app$ae'('divides_aux$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_165])]) ).

tff(f4310,plain,
    ( ! [X0: $int] : ( 0 = sK41('pair$c'(X0,0)) )
    | ~ spl230_55
    | ~ spl230_165 ),
    inference(resolution,[],[f4308,f3739]) ).

tff(f3739,plain,
    ( ! [X0: $int] : 'fun_app$ae'('divides_aux$','pair$c'(X0,0))
    | ~ spl230_55 ),
    inference(avatar_component_clause,[],[f3738]) ).

tff(f4308,plain,
    ( ! [X0: 'Int_int_prod$'] :
        ( ~ 'fun_app$ae'('divides_aux$',X0)
        | ( 0 = sK41(X0) ) )
    | ~ spl230_165 ),
    inference(avatar_component_clause,[],[f4307]) ).

tff(f6495,plain,
    ( spl230_429
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_144 ),
    inference(avatar_split_clause,[],[f4245,f4120,f3895,f3857,f6493]) ).

tff(f6493,plain,
    ( spl230_429
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'size$c'('some$'(X0)) = 'size$d'('none$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_429])]) ).

tff(f4120,plain,
    ( spl230_144
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','size$c'('some$'(X0))) = 1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_144])]) ).

tff(f4245,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'size$c'('some$'(X0)) = 'size$d'('none$a') )
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_144 ),
    inference(forward_demodulation,[],[f4242,f4138]) ).

tff(f4242,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'size$c'('some$'(X0)) = 'fun_app$k'('nat$',1) )
    | ~ spl230_88
    | ~ spl230_144 ),
    inference(superposition,[],[f3896,f4121]) ).

tff(f4121,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','size$c'('some$'(X0))) = 1 )
    | ~ spl230_144 ),
    inference(avatar_component_clause,[],[f4120]) ).

tff(f6466,plain,
    ( spl230_428
    | ~ spl230_94
    | ~ spl230_115 ),
    inference(avatar_split_clause,[],[f4202,f4004,f3920,f6464]) ).

tff(f3920,plain,
    ( spl230_94
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X0),sK37(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_94])]) ).

tff(f4202,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('fst$',X0) = sK36(X0) )
    | ~ spl230_94
    | ~ spl230_115 ),
    inference(superposition,[],[f4005,f3921]) ).

tff(f3921,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X0),sK37(X0)) = X0 )
    | ~ spl230_94 ),
    inference(avatar_component_clause,[],[f3920]) ).

tff(f6462,plain,
    ( spl230_427
    | ~ spl230_94
    | ~ spl230_114 ),
    inference(avatar_split_clause,[],[f4199,f4000,f3920,f6460]) ).

tff(f4199,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('snd$a',X0) = sK37(X0) )
    | ~ spl230_94
    | ~ spl230_114 ),
    inference(superposition,[],[f4001,f3921]) ).

tff(f6452,plain,
    ( spl230_426
    | ~ spl230_96
    | ~ spl230_111 ),
    inference(avatar_split_clause,[],[f4190,f3988,f3928,f6450]) ).

tff(f4190,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('snd$b',X0) = sK41(X0) )
    | ~ spl230_96
    | ~ spl230_111 ),
    inference(superposition,[],[f3989,f3929]) ).

tff(f6203,plain,
    ( spl230_425
    | ~ spl230_96
    | ~ spl230_110 ),
    inference(avatar_split_clause,[],[f4186,f3984,f3928,f6201]) ).

tff(f4186,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('fst$b',X0) = sK40(X0) )
    | ~ spl230_96
    | ~ spl230_110 ),
    inference(superposition,[],[f3985,f3929]) ).

tff(f6126,plain,
    ( spl230_424
    | ~ spl230_82
    | ~ spl230_88 ),
    inference(avatar_split_clause,[],[f4138,f3895,f3857,f6123]) ).

tff(f6123,plain,
    ( spl230_424
  <=> ( 'size$d'('none$a') = 'fun_app$k'('nat$',1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_424])]) ).

tff(f6064,plain,
    spl230_423,
    inference(avatar_split_clause,[],[f3473,f6062]) ).

tff(f6062,plain,
    ( spl230_423
  <=> ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
        ( 'member$c'('fun_app$m'('gen_length$b'(X2),X0),X1)
        | ~ 'fun_app$c'('uut$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_423])]) ).

tff(f3473,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( 'member$c'('fun_app$m'('gen_length$b'(X2),X0),X1)
      | ~ 'fun_app$c'('uut$'(X0,X1),X2) ),
    inference(forward_demodulation,[],[f3472,f1821]) ).

tff(f3472,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( 'member$c'('fun_app$k'('nat$','fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X2),X0))),X1)
      | ~ 'fun_app$c'('uut$'(X0,X1),X2) ),
    inference(forward_demodulation,[],[f2535,f2028]) ).

tff(f2535,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( 'member$c'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))),X1)
      | ~ 'fun_app$c'('uut$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1572]) ).

tff(f1572,plain,
    ! [X0: 'A_iarray_list$',X1: 'Nat_set$',X2: 'Nat$'] :
      ( ( 'fun_app$c'('uut$'(X0,X1),X2)
        | ~ 'member$c'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))),X1) )
      & ( 'member$c'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))),X1)
        | ~ 'fun_app$c'('uut$'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f17]) ).

tff(f17,axiom,
    ! [X0: 'A_iarray_list$',X1: 'Nat_set$',X2: 'Nat$'] :
      ( 'fun_app$c'('uut$'(X0,X1),X2)
    <=> 'member$c'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom16) ).

tff(f6060,plain,
    spl230_422,
    inference(avatar_split_clause,[],[f3471,f6058]) ).

tff(f6058,plain,
    ( spl230_422
  <=> ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
        ( ~ 'member$c'('fun_app$m'('gen_length$b'(X2),X0),X1)
        | 'fun_app$c'('uut$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_422])]) ).

tff(f3471,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( ~ 'member$c'('fun_app$m'('gen_length$b'(X2),X0),X1)
      | 'fun_app$c'('uut$'(X0,X1),X2) ),
    inference(forward_demodulation,[],[f3470,f1821]) ).

tff(f3470,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( ~ 'member$c'('fun_app$k'('nat$','fun_app$l'('of_nat$','fun_app$m'('gen_length$b'(X2),X0))),X1)
      | 'fun_app$c'('uut$'(X0,X1),X2) ),
    inference(forward_demodulation,[],[f2536,f2028]) ).

tff(f2536,plain,
    ! [X2: 'Nat$',X0: 'A_iarray_list$',X1: 'Nat_set$'] :
      ( 'fun_app$c'('uut$'(X0,X1),X2)
      | ~ 'member$c'('fun_app$k'('nat$',$sum('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))),X1) ),
    inference(cnf_transformation,[],[f1572]) ).

tff(f6056,plain,
    spl230_421,
    inference(avatar_split_clause,[],[f3238,f6054]) ).

tff(f6054,plain,
    ( spl230_421
  <=> ! [X4: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray$',X2: 'A_iarray_list$'] :
        ( sP30(X0,X2,X2,X3,X4)
        | ~ 'member$f'('pair$a'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_421])]) ).

tff(f3238,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X4: 'A_iarray$'] :
      ( sP30(X0,X2,X2,X3,X4)
      | ~ 'member$f'('pair$a'(X4,X3),X0) ),
    inference(equality_resolution,[],[f2889]) ).

tff(f2889,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_list$',X4: 'A_iarray$'] :
      ( sP30(X0,X1,X2,X3,X4)
      | ( X1 != X2 )
      | ~ 'member$f'('pair$a'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1732]) ).

tff(f6052,plain,
    spl230_420,
    inference(avatar_split_clause,[],[f3233,f6050]) ).

tff(f6050,plain,
    ( spl230_420
  <=> ! [X4: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X3: 'A_iarray_list$',X2: 'A_iarray_list_list$'] :
        ( sP27(X0,X2,X2,X3,X4)
        | ~ 'member$'('pair$b'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_420])]) ).

tff(f3233,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X4: 'A_iarray_list$'] :
      ( sP27(X0,X2,X2,X3,X4)
      | ~ 'member$'('pair$b'(X4,X3),X0) ),
    inference(equality_resolution,[],[f2860]) ).

tff(f2860,plain,
    ! [X2: 'A_iarray_list_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_list$',X4: 'A_iarray_list$'] :
      ( sP27(X0,X1,X2,X3,X4)
      | ( X1 != X2 )
      | ~ 'member$'('pair$b'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1718]) ).

tff(f6048,plain,
    spl230_419,
    inference(avatar_split_clause,[],[f3229,f6046]) ).

tff(f6046,plain,
    ( spl230_419
  <=> ! [X4: $int,X0: 'Int_int_prod_set$',X3: $int,X2: 'Int_list$'] :
        ( sP25(X0,X2,X2,X3,X4)
        | ~ 'member$g'('pair$c'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_419])]) ).

tff(f3229,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X4: $int] :
      ( sP25(X0,X2,X2,X3,X4)
      | ~ 'member$g'('pair$c'(X4,X3),X0) ),
    inference(equality_resolution,[],[f2840]) ).

tff(f2840,plain,
    ! [X2: 'Int_list$',X3: $int,X0: 'Int_int_prod_set$',X1: 'Int_list$',X4: $int] :
      ( sP25(X0,X1,X2,X3,X4)
      | ( X1 != X2 )
      | ~ 'member$g'('pair$c'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f6036,plain,
    spl230_418,
    inference(avatar_split_clause,[],[f3227,f6034]) ).

tff(f6034,plain,
    ( spl230_418
  <=> ! [X4: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray_list$'] :
        ( sP24(X0,X2,X2,X3,X4)
        | ~ 'member$e'('pair$'(X4,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_418])]) ).

tff(f3227,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X4: 'A_iarray_iarray$'] :
      ( sP24(X0,X2,X2,X3,X4)
      | ~ 'member$e'('pair$'(X4,X3),X0) ),
    inference(equality_resolution,[],[f2832]) ).

tff(f2832,plain,
    ! [X2: 'A_iarray_iarray_list$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_list$',X4: 'A_iarray_iarray$'] :
      ( sP24(X0,X1,X2,X3,X4)
      | ( X1 != X2 )
      | ~ 'member$e'('pair$'(X4,X3),X0) ),
    inference(cnf_transformation,[],[f1704]) ).

tff(f6025,plain,
    ( spl230_417
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_416 ),
    inference(avatar_split_clause,[],[f6021,f6018,f4004,f3920,f6023]) ).

tff(f6023,plain,
    ( spl230_417
  <=> ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X1),sK105(sK36(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_417])]) ).

tff(f6018,plain,
    ( spl230_416
  <=> ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X1),sK105('fun_app$r'('fst$',X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_416])]) ).

tff(f6021,plain,
    ( ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X1),sK105(sK36(X1),X1)) = X1 )
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_416 ),
    inference(forward_demodulation,[],[f6019,f4202]) ).

tff(f6019,plain,
    ( ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X1),sK105('fun_app$r'('fst$',X1),X1)) = X1 )
    | ~ spl230_416 ),
    inference(avatar_component_clause,[],[f6018]) ).

tff(f6020,plain,
    spl230_416,
    inference(avatar_split_clause,[],[f3069,f6018]) ).

tff(f3069,plain,
    ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X1),sK105('fun_app$r'('fst$',X1),X1)) = X1 ),
    inference(equality_resolution,[],[f2186]) ).

tff(f2186,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( 'pair$'(X0,sK105(X0,X1)) = X1 )
      | ( 'fun_app$r'('fst$',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1354]) ).

tff(f1354,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('fst$',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X0,X2) != X1 ) )
      & ( ( 'pair$'(X0,sK105(X0,X1)) = X1 )
        | ( 'fun_app$r'('fst$',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK105])],[f1352,f1353]) ).

tff(f1353,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ? [X3: 'A_iarray_iarray$'] : ( 'pair$'(X0,X3) = X1 )
     => ( 'pair$'(X0,sK105(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1352,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('fst$',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X0,X2) != X1 ) )
      & ( ? [X3: 'A_iarray_iarray$'] : ( 'pair$'(X0,X3) = X1 )
        | ( 'fun_app$r'('fst$',X1) != X0 ) ) ),
    inference(rectify,[],[f1351]) ).

tff(f1351,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('fst$',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X0,X2) != X1 ) )
      & ( ? [X2: 'A_iarray_iarray$'] : ( 'pair$'(X0,X2) = X1 )
        | ( 'fun_app$r'('fst$',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f302]) ).

tff(f302,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( 'fun_app$r'('fst$',X1) = X0 )
    <=> ? [X2: 'A_iarray_iarray$'] : ( 'pair$'(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom300) ).

tff(f6009,plain,
    ( spl230_415
    | ~ spl230_94
    | ~ spl230_114
    | ~ spl230_414 ),
    inference(avatar_split_clause,[],[f6005,f6002,f4000,f3920,f6007]) ).

tff(f6007,plain,
    ( spl230_415
  <=> ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK104(sK37(X1),X1),sK37(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_415])]) ).

tff(f6002,plain,
    ( spl230_414
  <=> ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK104('fun_app$r'('snd$a',X1),X1),'fun_app$r'('snd$a',X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_414])]) ).

tff(f6005,plain,
    ( ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK104(sK37(X1),X1),sK37(X1)) = X1 )
    | ~ spl230_94
    | ~ spl230_114
    | ~ spl230_414 ),
    inference(forward_demodulation,[],[f6003,f4199]) ).

tff(f6003,plain,
    ( ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK104('fun_app$r'('snd$a',X1),X1),'fun_app$r'('snd$a',X1)) = X1 )
    | ~ spl230_414 ),
    inference(avatar_component_clause,[],[f6002]) ).

tff(f6004,plain,
    spl230_414,
    inference(avatar_split_clause,[],[f3067,f6002]) ).

tff(f3067,plain,
    ! [X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK104('fun_app$r'('snd$a',X1),X1),'fun_app$r'('snd$a',X1)) = X1 ),
    inference(equality_resolution,[],[f2184]) ).

tff(f2184,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( 'pair$'(sK104(X0,X1),X0) = X1 )
      | ( 'fun_app$r'('snd$a',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1350]) ).

tff(f1350,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('snd$a',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X2,X0) != X1 ) )
      & ( ( 'pair$'(sK104(X0,X1),X0) = X1 )
        | ( 'fun_app$r'('snd$a',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK104])],[f1348,f1349]) ).

tff(f1349,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ? [X3: 'A_iarray_iarray$'] : ( 'pair$'(X3,X0) = X1 )
     => ( 'pair$'(sK104(X0,X1),X0) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1348,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('snd$a',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X2,X0) != X1 ) )
      & ( ? [X3: 'A_iarray_iarray$'] : ( 'pair$'(X3,X0) = X1 )
        | ( 'fun_app$r'('snd$a',X1) != X0 ) ) ),
    inference(rectify,[],[f1347]) ).

tff(f1347,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( ( 'fun_app$r'('snd$a',X1) = X0 )
        | ! [X2: 'A_iarray_iarray$'] : ( 'pair$'(X2,X0) != X1 ) )
      & ( ? [X2: 'A_iarray_iarray$'] : ( 'pair$'(X2,X0) = X1 )
        | ( 'fun_app$r'('snd$a',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f308]) ).

tff(f308,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ( 'fun_app$r'('snd$a',X1) = X0 )
    <=> ? [X2: 'A_iarray_iarray$'] : ( 'pair$'(X2,X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom306) ).

tff(f6000,plain,
    spl230_413,
    inference(avatar_split_clause,[],[f3065,f5998]) ).

tff(f5998,plain,
    ( spl230_413
  <=> ! [X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'(sK103('fun_app$ab'('snd$',X1),X1),'fun_app$ab'('snd$',X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_413])]) ).

tff(f3065,plain,
    ! [X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'(sK103('fun_app$ab'('snd$',X1),X1),'fun_app$ab'('snd$',X1)) = X1 ),
    inference(equality_resolution,[],[f2182]) ).

tff(f2182,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( 'pair$l'(sK103(X0,X1),X0) = X1 )
      | ( 'fun_app$ab'('snd$',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1346]) ).

tff(f1346,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('snd$',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X2,X0) != X1 ) )
      & ( ( 'pair$l'(sK103(X0,X1),X0) = X1 )
        | ( 'fun_app$ab'('snd$',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK103])],[f1344,f1345]) ).

tff(f1345,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] : ( 'pair$l'(X3,X0) = X1 )
     => ( 'pair$l'(sK103(X0,X1),X0) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1344,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('snd$',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X2,X0) != X1 ) )
      & ( ? [X3: 'A_n_vec_n_vec$'] : ( 'pair$l'(X3,X0) = X1 )
        | ( 'fun_app$ab'('snd$',X1) != X0 ) ) ),
    inference(rectify,[],[f1343]) ).

tff(f1343,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('snd$',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X2,X0) != X1 ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X2,X0) = X1 )
        | ( 'fun_app$ab'('snd$',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f307]) ).

tff(f307,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( 'fun_app$ab'('snd$',X1) = X0 )
    <=> ? [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X2,X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom305) ).

tff(f5996,plain,
    spl230_412,
    inference(avatar_split_clause,[],[f3063,f5994]) ).

tff(f5994,plain,
    ( spl230_412
  <=> ! [X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'('fun_app$ab'('fst$a',X1),sK102('fun_app$ab'('fst$a',X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_412])]) ).

tff(f3063,plain,
    ! [X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'('fun_app$ab'('fst$a',X1),sK102('fun_app$ab'('fst$a',X1),X1)) = X1 ),
    inference(equality_resolution,[],[f2180]) ).

tff(f2180,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( 'pair$l'(X0,sK102(X0,X1)) = X1 )
      | ( 'fun_app$ab'('fst$a',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1342]) ).

tff(f1342,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('fst$a',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X2) != X1 ) )
      & ( ( 'pair$l'(X0,sK102(X0,X1)) = X1 )
        | ( 'fun_app$ab'('fst$a',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK102])],[f1340,f1341]) ).

tff(f1341,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X3) = X1 )
     => ( 'pair$l'(X0,sK102(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1340,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('fst$a',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X2) != X1 ) )
      & ( ? [X3: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X3) = X1 )
        | ( 'fun_app$ab'('fst$a',X1) != X0 ) ) ),
    inference(rectify,[],[f1339]) ).

tff(f1339,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( ( 'fun_app$ab'('fst$a',X1) = X0 )
        | ! [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X2) != X1 ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X2) = X1 )
        | ( 'fun_app$ab'('fst$a',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f300]) ).

tff(f300,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] :
      ( ( 'fun_app$ab'('fst$a',X1) = X0 )
    <=> ? [X2: 'A_n_vec_n_vec$'] : ( 'pair$l'(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom298) ).

tff(f5983,plain,
    ( spl230_411
    | ~ spl230_83
    | ~ spl230_325 ),
    inference(avatar_split_clause,[],[f5794,f5405,f3873,f5981]) ).

tff(f5405,plain,
    ( spl230_325
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_325])]) ).

tff(f5794,plain,
    ( ! [X0: $int] : $less(X0,$sum(1,X0))
    | ~ spl230_83
    | ~ spl230_325 ),
    inference(superposition,[],[f5406,f3874]) ).

tff(f5406,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl230_325 ),
    inference(avatar_component_clause,[],[f5405]) ).

tff(f5979,plain,
    ( spl230_410
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_409 ),
    inference(avatar_split_clause,[],[f5975,f5972,f3988,f3928,f5977]) ).

tff(f5977,plain,
    ( spl230_410
  <=> ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK101(sK41(X1),X1),sK41(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_410])]) ).

tff(f5972,plain,
    ( spl230_409
  <=> ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK101('fun_app$ac'('snd$b',X1),X1),'fun_app$ac'('snd$b',X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_409])]) ).

tff(f5975,plain,
    ( ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK101(sK41(X1),X1),sK41(X1)) = X1 )
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_409 ),
    inference(forward_demodulation,[],[f5973,f4190]) ).

tff(f5973,plain,
    ( ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK101('fun_app$ac'('snd$b',X1),X1),'fun_app$ac'('snd$b',X1)) = X1 )
    | ~ spl230_409 ),
    inference(avatar_component_clause,[],[f5972]) ).

tff(f5974,plain,
    spl230_409,
    inference(avatar_split_clause,[],[f3061,f5972]) ).

tff(f3061,plain,
    ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK101('fun_app$ac'('snd$b',X1),X1),'fun_app$ac'('snd$b',X1)) = X1 ),
    inference(equality_resolution,[],[f2178]) ).

tff(f2178,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( 'pair$c'(sK101(X0,X1),X0) = X1 )
      | ( 'fun_app$ac'('snd$b',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1338]) ).

tff(f1338,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('snd$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X2,X0) != X1 ) )
      & ( ( 'pair$c'(sK101(X0,X1),X0) = X1 )
        | ( 'fun_app$ac'('snd$b',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK101])],[f1336,f1337]) ).

tff(f1337,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ? [X3: $int] : ( 'pair$c'(X3,X0) = X1 )
     => ( 'pair$c'(sK101(X0,X1),X0) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1336,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('snd$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X2,X0) != X1 ) )
      & ( ? [X3: $int] : ( 'pair$c'(X3,X0) = X1 )
        | ( 'fun_app$ac'('snd$b',X1) != X0 ) ) ),
    inference(rectify,[],[f1335]) ).

tff(f1335,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('snd$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X2,X0) != X1 ) )
      & ( ? [X2: $int] : ( 'pair$c'(X2,X0) = X1 )
        | ( 'fun_app$ac'('snd$b',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f309]) ).

tff(f309,axiom,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( 'fun_app$ac'('snd$b',X1) = X0 )
    <=> ? [X2: $int] : ( 'pair$c'(X2,X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom307) ).

tff(f5961,plain,
    ( spl230_408
    | ~ spl230_96
    | ~ spl230_110
    | ~ spl230_407 ),
    inference(avatar_split_clause,[],[f5957,f5954,f3984,f3928,f5959]) ).

tff(f5959,plain,
    ( spl230_408
  <=> ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK40(X1),sK100(sK40(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_408])]) ).

tff(f5954,plain,
    ( spl230_407
  <=> ! [X1: 'Int_int_prod$'] : ( 'pair$c'('fun_app$ac'('fst$b',X1),sK100('fun_app$ac'('fst$b',X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_407])]) ).

tff(f5957,plain,
    ( ! [X1: 'Int_int_prod$'] : ( 'pair$c'(sK40(X1),sK100(sK40(X1),X1)) = X1 )
    | ~ spl230_96
    | ~ spl230_110
    | ~ spl230_407 ),
    inference(forward_demodulation,[],[f5955,f4186]) ).

tff(f5955,plain,
    ( ! [X1: 'Int_int_prod$'] : ( 'pair$c'('fun_app$ac'('fst$b',X1),sK100('fun_app$ac'('fst$b',X1),X1)) = X1 )
    | ~ spl230_407 ),
    inference(avatar_component_clause,[],[f5954]) ).

tff(f5956,plain,
    spl230_407,
    inference(avatar_split_clause,[],[f3059,f5954]) ).

tff(f3059,plain,
    ! [X1: 'Int_int_prod$'] : ( 'pair$c'('fun_app$ac'('fst$b',X1),sK100('fun_app$ac'('fst$b',X1),X1)) = X1 ),
    inference(equality_resolution,[],[f2176]) ).

tff(f2176,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( 'pair$c'(X0,sK100(X0,X1)) = X1 )
      | ( 'fun_app$ac'('fst$b',X1) != X0 ) ),
    inference(cnf_transformation,[],[f1334]) ).

tff(f1334,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('fst$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X0,X2) != X1 ) )
      & ( ( 'pair$c'(X0,sK100(X0,X1)) = X1 )
        | ( 'fun_app$ac'('fst$b',X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK100])],[f1332,f1333]) ).

tff(f1333,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ? [X3: $int] : ( 'pair$c'(X0,X3) = X1 )
     => ( 'pair$c'(X0,sK100(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1332,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('fst$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X0,X2) != X1 ) )
      & ( ? [X3: $int] : ( 'pair$c'(X0,X3) = X1 )
        | ( 'fun_app$ac'('fst$b',X1) != X0 ) ) ),
    inference(rectify,[],[f1331]) ).

tff(f1331,plain,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( ( 'fun_app$ac'('fst$b',X1) = X0 )
        | ! [X2: $int] : ( 'pair$c'(X0,X2) != X1 ) )
      & ( ? [X2: $int] : ( 'pair$c'(X0,X2) = X1 )
        | ( 'fun_app$ac'('fst$b',X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f301]) ).

tff(f301,axiom,
    ! [X0: $int,X1: 'Int_int_prod$'] :
      ( ( 'fun_app$ac'('fst$b',X1) = X0 )
    <=> ? [X2: $int] : ( 'pair$c'(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom299) ).

tff(f5952,plain,
    spl230_406,
    inference(avatar_split_clause,[],[f2969,f5950]) ).

tff(f5950,plain,
    ( spl230_406
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) = 'matrix_matrix_mult$'(sK135(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_406])]) ).

tff(f2969,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) = 'matrix_matrix_mult$'(sK135(X0,X1),X0) ),
    inference(definition_unfolding,[],[f2351,f1999]) ).

tff(f1999,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) = 'gauss_Jordan_upt_k$'(X0,X1) ),
    inference(cnf_transformation,[],[f326]) ).

tff(f326,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_upt_k_PA$'(X0,X1)) = 'gauss_Jordan_upt_k$'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom324) ).

tff(f2351,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : ( 'gauss_Jordan_upt_k$'(X0,X1) = 'matrix_matrix_mult$'(sK135(X0,X1),X0) ),
    inference(cnf_transformation,[],[f1492]) ).

tff(f1492,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( ( 'gauss_Jordan_upt_k$'(X0,X1) = 'matrix_matrix_mult$'(sK135(X0,X1),X0) )
      & 'fun_app$o'('invertible$',sK135(X0,X1)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f327,f1491]) ).

tff(f1491,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( ? [X2: 'A_n_vec_n_vec$'] :
          ( ( 'matrix_matrix_mult$'(X2,X0) = 'gauss_Jordan_upt_k$'(X0,X1) )
          & 'fun_app$o'('invertible$',X2) )
     => ( ( 'gauss_Jordan_upt_k$'(X0,X1) = 'matrix_matrix_mult$'(sK135(X0,X1),X0) )
        & 'fun_app$o'('invertible$',sK135(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f327,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
    ? [X2: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_matrix_mult$'(X2,X0) = 'gauss_Jordan_upt_k$'(X0,X1) )
      & 'fun_app$o'('invertible$',X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom325) ).

tff(f5948,plain,
    spl230_405,
    inference(avatar_split_clause,[],[f2944,f5946]) ).

tff(f5946,plain,
    ( spl230_405
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'the$'('inverse_matrix$'(X0)) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_405])]) ).

tff(f2944,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'the$'('inverse_matrix$'(X0)) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(definition_unfolding,[],[f1873,f1816]) ).

tff(f1816,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'p_Gauss_Jordan$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) ),
    inference(cnf_transformation,[],[f213]) ).

tff(f213,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'p_Gauss_Jordan$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom211) ).

tff(f1873,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'the$'('inverse_matrix$'(X0)) = 'p_Gauss_Jordan$'(X0) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f794]) ).

tff(f794,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'the$'('inverse_matrix$'(X0)) = 'p_Gauss_Jordan$'(X0) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f120]) ).

tff(f120,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
     => ( 'the$'('inverse_matrix$'(X0)) = 'p_Gauss_Jordan$'(X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom118) ).

tff(f5944,plain,
    spl230_404,
    inference(avatar_split_clause,[],[f2941,f5942]) ).

tff(f5942,plain,
    ( spl230_404
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'inverse_matrix$'(X0) = 'some$a'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_404])]) ).

tff(f2941,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'inverse_matrix$'(X0) = 'some$a'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(definition_unfolding,[],[f1864,f1816]) ).

tff(f1864,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'inverse_matrix$'(X0) = 'some$a'('p_Gauss_Jordan$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f788]) ).

tff(f788,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( ( 'none$a' = 'inverse_matrix$'(X0) )
        | 'fun_app$o'('invertible$',X0) )
      & ( ( 'inverse_matrix$'(X0) = 'some$a'('p_Gauss_Jordan$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    inference(ennf_transformation,[],[f121]) ).

tff(f121,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( ~ 'fun_app$o'('invertible$',X0)
       => ( 'none$a' = 'inverse_matrix$'(X0) ) )
      & ( 'fun_app$o'('invertible$',X0)
       => ( 'inverse_matrix$'(X0) = 'some$a'('p_Gauss_Jordan$'(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom119) ).

tff(f5927,plain,
    ( spl230_403
    | ~ spl230_94
    | ~ spl230_114
    | ~ spl230_402 ),
    inference(avatar_split_clause,[],[f5921,f5918,f4000,f3920,f5925]) ).

tff(f5918,plain,
    ( spl230_402
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_402])]) ).

tff(f5921,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = sK37('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
    | ~ spl230_94
    | ~ spl230_114
    | ~ spl230_402 ),
    inference(forward_demodulation,[],[f5919,f4199]) ).

tff(f5919,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
    | ~ spl230_402 ),
    inference(avatar_component_clause,[],[f5918]) ).

tff(f5920,plain,
    spl230_402,
    inference(avatar_split_clause,[],[f2932,f5918]) ).

tff(f5916,plain,
    spl230_401,
    inference(avatar_split_clause,[],[f2722,f5914]) ).

tff(f5914,plain,
    ( spl230_401
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( 'fun_app$n'(X0,def_6(X1,X2,X3))
        | ~ sP17(X3,X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_401])]) ).

tff(f2722,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( 'fun_app$n'(X0,def_6(X1,X2,X3))
      | ~ sP17(X3,X2,X0,X1) ),
    inference(cnf_transformation,[],[f1651]) ).

tff(f1651,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( 'fun_app$n'(X0,def_6(X1,X2,X3))
        | ~ sP17(X3,X2,X0,X1) )
      & ( sP17(X3,X2,X0,X1)
        | ~ 'fun_app$n'(X0,def_6(X1,X2,X3)) ) ),
    inference(nnf_transformation,[],[f1112]) ).

tff(f1112,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_6(X1,X2,X3))
    <=> sP17(X3,X2,X0,X1) ),
    inference(definition_folding,[],[f1026,f1111]) ).

tff(f1026,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_6(X1,X2,X3))
    <=> ( ( 'fun_app$n'(X0,def_7(X2,X3))
          | ( 'some$'('the$a'(X3)) != X3 ) )
        & ( 'fun_app$n'(X0,X1)
          | ( 'none$' != X3 ) ) ) ),
    inference(ennf_transformation,[],[f76]) ).

tff(f76,axiom,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_6(X1,X2,X3))
    <=> ~ ( ( ~ 'fun_app$n'(X0,def_7(X2,X3))
            & ( 'some$'('the$a'(X3)) = X3 ) )
          | ( ~ 'fun_app$n'(X0,X1)
            & ( 'none$' = X3 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom74) ).

tff(f5912,plain,
    spl230_400,
    inference(avatar_split_clause,[],[f2721,f5910]) ).

tff(f5910,plain,
    ( spl230_400
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( sP17(X3,X2,X0,X1)
        | ~ 'fun_app$n'(X0,def_6(X1,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_400])]) ).

tff(f2721,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( sP17(X3,X2,X0,X1)
      | ~ 'fun_app$n'(X0,def_6(X1,X2,X3)) ),
    inference(cnf_transformation,[],[f1651]) ).

tff(f5908,plain,
    spl230_399,
    inference(avatar_split_clause,[],[f2714,f5906]) ).

tff(f5906,plain,
    ( spl230_399
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( 'fun_app$n'(X0,def_4(X1,X2,X3))
        | ~ sP16(X3,X2,X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_399])]) ).

tff(f2714,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( 'fun_app$n'(X0,def_4(X1,X2,X3))
      | ~ sP16(X3,X2,X0,X1) ),
    inference(cnf_transformation,[],[f1647]) ).

tff(f1647,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( 'fun_app$n'(X0,def_4(X1,X2,X3))
        | ~ sP16(X3,X2,X0,X1) )
      & ( sP16(X3,X2,X0,X1)
        | ~ 'fun_app$n'(X0,def_4(X1,X2,X3)) ) ),
    inference(nnf_transformation,[],[f1110]) ).

tff(f1110,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_4(X1,X2,X3))
    <=> sP16(X3,X2,X0,X1) ),
    inference(definition_folding,[],[f1025,f1109]) ).

tff(f1025,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_4(X1,X2,X3))
    <=> ( ( 'fun_app$n'(X0,def_5(X2,X3))
          | ( 'some$'('the$a'(X3)) != X3 ) )
        & ( 'fun_app$n'(X0,X1)
          | ( 'none$' != X3 ) ) ) ),
    inference(ennf_transformation,[],[f75]) ).

tff(f75,axiom,
    ! [X0: 'Bool_bool_fun$',X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( 'fun_app$n'(X0,def_4(X1,X2,X3))
    <=> ( ( ( 'some$'('the$a'(X3)) = X3 )
         => 'fun_app$n'(X0,def_5(X2,X3)) )
        & ( ( 'none$' = X3 )
         => 'fun_app$n'(X0,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom73) ).

tff(f5904,plain,
    spl230_398,
    inference(avatar_split_clause,[],[f2713,f5902]) ).

tff(f5902,plain,
    ( spl230_398
  <=> ! [X0: 'Bool_bool_fun$',X3: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_bool_fun$',X1: tlbool] :
        ( sP16(X3,X2,X0,X1)
        | ~ 'fun_app$n'(X0,def_4(X1,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_398])]) ).

tff(f2713,plain,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$',X0: 'Bool_bool_fun$',X1: tlbool] :
      ( sP16(X3,X2,X0,X1)
      | ~ 'fun_app$n'(X0,def_4(X1,X2,X3)) ),
    inference(cnf_transformation,[],[f1647]) ).

tff(f5900,plain,
    spl230_397,
    inference(avatar_split_clause,[],[f2632,f5898]) ).

tff(f5898,plain,
    ( spl230_397
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( 'fun_app$'(X2,X0)
        | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_397])]) ).

tff(f2632,plain,
    ! [X2: 'A_iarray_bool_fun$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( 'fun_app$'(X2,X0)
      | ( 'cons$'(X0,X1) != 'fun_app$p'('filter$'(X2),X3) ) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f5896,plain,
    spl230_396,
    inference(avatar_split_clause,[],[f2558,f5894]) ).

tff(f5894,plain,
    ( spl230_396
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
        ( 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2)
        | ~ 'member$'('pair$b'(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_396])]) ).

tff(f2558,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
      ( 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2)
      | ~ 'member$'('pair$b'(X1,X2),X0) ),
    inference(cnf_transformation,[],[f1584]) ).

tff(f1584,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( ( 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2)
        | ~ 'member$'('pair$b'(X1,X2),X0) )
      & ( 'member$'('pair$b'(X1,X2),X0)
        | ~ 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f13]) ).

tff(f13,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
      ( 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2)
    <=> 'member$'('pair$b'(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom12) ).

tff(f5892,plain,
    spl230_395,
    inference(avatar_split_clause,[],[f2557,f5890]) ).

tff(f5890,plain,
    ( spl230_395
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
        ( 'member$'('pair$b'(X1,X2),X0)
        | ~ 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_395])]) ).

tff(f2557,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list$'] :
      ( 'member$'('pair$b'(X1,X2),X0)
      | ~ 'fun_app$b'('fun_app$i'('uuq$'(X0),X1),X2) ),
    inference(cnf_transformation,[],[f1584]) ).

tff(f5888,plain,
    spl230_394,
    inference(avatar_split_clause,[],[f2553,f5886]) ).

tff(f5886,plain,
    ( spl230_394
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
        ( 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2)
        | ~ 'member$f'('pair$a'(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_394])]) ).

tff(f2553,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
      ( 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2)
      | ~ 'member$f'('pair$a'(X1,X2),X0) ),
    inference(cnf_transformation,[],[f1581]) ).

tff(f1581,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$',X2: 'A_iarray$'] :
      ( ( 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2)
        | ~ 'member$f'('pair$a'(X1,X2),X0) )
      & ( 'member$f'('pair$a'(X1,X2),X0)
        | ~ 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f12]) ).

tff(f12,axiom,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$',X2: 'A_iarray$'] :
      ( 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2)
    <=> 'member$f'('pair$a'(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom11) ).

tff(f5884,plain,
    spl230_393,
    inference(avatar_split_clause,[],[f2552,f5882]) ).

tff(f5882,plain,
    ( spl230_393
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
        ( 'member$f'('pair$a'(X1,X2),X0)
        | ~ 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_393])]) ).

tff(f2552,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray$'] :
      ( 'member$f'('pair$a'(X1,X2),X0)
      | ~ 'fun_app$'('fun_app$h'('uur$'(X0),X1),X2) ),
    inference(cnf_transformation,[],[f1581]) ).

tff(f5878,plain,
    spl230_392,
    inference(avatar_split_clause,[],[f2551,f5876]) ).

tff(f5876,plain,
    ( spl230_392
  <=> ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
        ( 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2)
        | ~ 'member$e'('pair$'(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_392])]) ).

tff(f2551,plain,
    ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2)
      | ~ 'member$e'('pair$'(X1,X2),X0) ),
    inference(cnf_transformation,[],[f1580]) ).

tff(f1580,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] :
      ( ( 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2)
        | ~ 'member$e'('pair$'(X1,X2),X0) )
      & ( 'member$e'('pair$'(X1,X2),X0)
        | ~ 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f11]) ).

tff(f11,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2)
    <=> 'member$e'('pair$'(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).

tff(f5874,plain,
    spl230_391,
    inference(avatar_split_clause,[],[f2550,f5872]) ).

tff(f5872,plain,
    ( spl230_391
  <=> ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
        ( 'member$e'('pair$'(X1,X2),X0)
        | ~ 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_391])]) ).

tff(f2550,plain,
    ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray$'] :
      ( 'member$e'('pair$'(X1,X2),X0)
      | ~ 'fun_app$f'('fun_app$g'('uup$'(X0),X1),X2) ),
    inference(cnf_transformation,[],[f1580]) ).

tff(f5870,plain,
    spl230_390,
    inference(avatar_split_clause,[],[f2544,f5868]) ).

tff(f5868,plain,
    ( spl230_390
  <=> ! [X2: $int,X0: 'Int_int_prod_set$',X1: $int] :
        ( 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2)
        | ~ 'member$g'('pair$c'(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_390])]) ).

tff(f2544,plain,
    ! [X2: $int,X0: 'Int_int_prod_set$',X1: $int] :
      ( 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2)
      | ~ 'member$g'('pair$c'(X1,X2),X0) ),
    inference(cnf_transformation,[],[f1576]) ).

tff(f1576,plain,
    ! [X0: 'Int_int_prod_set$',X1: $int,X2: $int] :
      ( ( 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2)
        | ~ 'member$g'('pair$c'(X1,X2),X0) )
      & ( 'member$g'('pair$c'(X1,X2),X0)
        | ~ 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2) ) ),
    inference(nnf_transformation,[],[f14]) ).

tff(f14,axiom,
    ! [X0: 'Int_int_prod_set$',X1: $int,X2: $int] :
      ( 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2)
    <=> 'member$g'('pair$c'(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom13) ).

tff(f5866,plain,
    spl230_389,
    inference(avatar_split_clause,[],[f2543,f5864]) ).

tff(f5864,plain,
    ( spl230_389
  <=> ! [X2: $int,X0: 'Int_int_prod_set$',X1: $int] :
        ( 'member$g'('pair$c'(X1,X2),X0)
        | ~ 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_389])]) ).

tff(f2543,plain,
    ! [X2: $int,X0: 'Int_int_prod_set$',X1: $int] :
      ( 'member$g'('pair$c'(X1,X2),X0)
      | ~ 'fun_app$d'('fun_app$j'('uuo$'(X0),X1),X2) ),
    inference(cnf_transformation,[],[f1576]) ).

tff(f5862,plain,
    spl230_388,
    inference(avatar_split_clause,[],[f2542,f5860]) ).

tff(f2542,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = def_6(X0,X1,X2) )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1575]) ).

tff(f1575,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ( tltrue = def_6(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) )
      & ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_6(X0,X1,X2) ) ) ),
    inference(nnf_transformation,[],[f756]) ).

tff(f756,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_6(X0,X1,X2) )
    <=> 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(rectify,[],[f658]) ).

tff(f658,axiom,
    ! [X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_6(X1,X2,X3) )
    <=> 'fun_app$t'('case_option$a'(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_657) ).

tff(f5858,plain,
    spl230_387,
    inference(avatar_split_clause,[],[f2541,f5856]) ).

tff(f5856,plain,
    ( spl230_387
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_6(X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_387])]) ).

tff(f2541,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
      | ( tltrue != def_6(X0,X1,X2) ) ),
    inference(cnf_transformation,[],[f1575]) ).

tff(f5854,plain,
    spl230_386,
    inference(avatar_split_clause,[],[f2540,f5852]) ).

tff(f2540,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = def_2(X0,X1,X2) )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1574]) ).

tff(f1574,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ( tltrue = def_2(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) )
      & ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_2(X0,X1,X2) ) ) ),
    inference(nnf_transformation,[],[f755]) ).

tff(f755,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_2(X0,X1,X2) )
    <=> 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(rectify,[],[f654]) ).

tff(f654,axiom,
    ! [X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_2(X1,X2,X3) )
    <=> 'fun_app$t'('case_option$a'(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_653) ).

tff(f5850,plain,
    spl230_385,
    inference(avatar_split_clause,[],[f2539,f5848]) ).

tff(f5848,plain,
    ( spl230_385
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_2(X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_385])]) ).

tff(f2539,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
      | ( tltrue != def_2(X0,X1,X2) ) ),
    inference(cnf_transformation,[],[f1574]) ).

tff(f5846,plain,
    spl230_384,
    inference(avatar_split_clause,[],[f2538,f5844]) ).

tff(f2538,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = def_4(X0,X1,X2) )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1573]) ).

tff(f1573,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( ( tltrue = def_4(X0,X1,X2) )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) )
      & ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_4(X0,X1,X2) ) ) ),
    inference(nnf_transformation,[],[f754]) ).

tff(f754,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_4(X0,X1,X2) )
    <=> 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(rectify,[],[f656]) ).

tff(f656,axiom,
    ! [X1: tlbool,X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_4(X1,X2,X3) )
    <=> 'fun_app$t'('case_option$a'(X1,X2),X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_655) ).

tff(f5842,plain,
    spl230_383,
    inference(avatar_split_clause,[],[f2537,f5840]) ).

tff(f5840,plain,
    ( spl230_383
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ( tltrue != def_4(X0,X1,X2) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_383])]) ).

tff(f2537,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
      | ( tltrue != def_4(X0,X1,X2) ) ),
    inference(cnf_transformation,[],[f1573]) ).

tff(f5835,plain,
    spl230_382,
    inference(avatar_split_clause,[],[f2529,f5833]) ).

tff(f5833,plain,
    ( spl230_382
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
        ( 'fun_app$'('uua$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'fun_app$'(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_382])]) ).

tff(f2529,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'('uua$'(X0,X1),X2)
      | ~ 'fun_app$'(X0,X2)
      | ~ 'fun_app$'(X1,X2) ),
    inference(cnf_transformation,[],[f1568]) ).

tff(f1568,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$'] :
      ( ( 'fun_app$'('uua$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'fun_app$'(X1,X2) )
      & ( ( 'fun_app$'(X0,X2)
          & 'fun_app$'(X1,X2) )
        | ~ 'fun_app$'('uua$'(X0,X1),X2) ) ),
    inference(flattening,[],[f1567]) ).

tff(f1567,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$'] :
      ( ( 'fun_app$'('uua$'(X0,X1),X2)
        | ~ 'fun_app$'(X0,X2)
        | ~ 'fun_app$'(X1,X2) )
      & ( ( 'fun_app$'(X0,X2)
          & 'fun_app$'(X1,X2) )
        | ~ 'fun_app$'('uua$'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f16]) ).

tff(f16,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$',X2: 'A_iarray$'] :
      ( 'fun_app$'('uua$'(X0,X1),X2)
    <=> ( 'fun_app$'(X0,X2)
        & 'fun_app$'(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom15) ).

tff(f5831,plain,
    spl230_381,
    inference(avatar_split_clause,[],[f2521,f5829]) ).

tff(f5829,plain,
    ( spl230_381
  <=> ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP14(X0,X1,X2)
        | ~ 'fun_app$f'(X1,'the$a'(X0))
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_381])]) ).

tff(f2521,plain,
    ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14(X0,X1,X2)
      | ~ 'fun_app$f'(X1,'the$a'(X0))
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f1564,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X2: tlbool] :
      ( ( sP14(X0,X1,X2)
        | ( ~ 'fun_app$f'(X1,'the$a'(X0))
          & ( 'none$' != X0 ) )
        | ( ( tltrue != X2 )
          & ( 'none$' = X0 ) ) )
      & ( ( ( 'fun_app$f'(X1,'the$a'(X0))
            | ( 'none$' = X0 ) )
          & ( ( tltrue = X2 )
            | ( 'none$' != X0 ) ) )
        | ~ sP14(X0,X1,X2) ) ),
    inference(rectify,[],[f1563]) ).

tff(f1563,plain,
    ! [X2: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X0: tlbool] :
      ( ( sP14(X2,X1,X0)
        | ( ~ 'fun_app$f'(X1,'the$a'(X2))
          & ( 'none$' != X2 ) )
        | ( ( tltrue != X0 )
          & ( 'none$' = X2 ) ) )
      & ( ( ( 'fun_app$f'(X1,'the$a'(X2))
            | ( 'none$' = X2 ) )
          & ( ( tltrue = X0 )
            | ( 'none$' != X2 ) ) )
        | ~ sP14(X2,X1,X0) ) ),
    inference(flattening,[],[f1562]) ).

tff(f1562,plain,
    ! [X2: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X0: tlbool] :
      ( ( sP14(X2,X1,X0)
        | ( ~ 'fun_app$f'(X1,'the$a'(X2))
          & ( 'none$' != X2 ) )
        | ( ( tltrue != X0 )
          & ( 'none$' = X2 ) ) )
      & ( ( ( 'fun_app$f'(X1,'the$a'(X2))
            | ( 'none$' = X2 ) )
          & ( ( tltrue = X0 )
            | ( 'none$' != X2 ) ) )
        | ~ sP14(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f1105]) ).

tff(f1105,plain,
    ! [X2: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$',X0: tlbool] :
      ( sP14(X2,X1,X0)
    <=> ( ( 'fun_app$f'(X1,'the$a'(X2))
          | ( 'none$' = X2 ) )
        & ( ( tltrue = X0 )
          | ( 'none$' != X2 ) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

tff(f5827,plain,
    spl230_380,
    inference(avatar_split_clause,[],[f2518,f5825]) ).

tff(f5825,plain,
    ( spl230_380
  <=> ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$f'(X1,'the$a'(X0))
        | ( 'none$' = X0 )
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_380])]) ).

tff(f2518,plain,
    ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$f'(X1,'the$a'(X0))
      | ( 'none$' = X0 )
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f5823,plain,
    spl230_379,
    inference(avatar_split_clause,[],[f2493,f5821]) ).

tff(f5821,plain,
    ( spl230_379
  <=> ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'some$'(sK171(X0,X1,X2)) = X0 )
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_379])]) ).

tff(f2493,plain,
    ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK171(X0,X1,X2)) = X0 )
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1544]) ).

tff(f1544,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
        & ( 'some$'(sK171(X0,X1,X2)) = X0 )
        & ( 'some$'(sK170(X0,X1,X2)) = X1 ) )
      | ~ sP13(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f1542,f1543]) ).

tff(f1543,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
          & ( 'some$'(X4) = X0 )
          & ( 'some$'(X3) = X1 ) )
     => ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
        & ( 'some$'(sK171(X0,X1,X2)) = X0 )
        & ( 'some$'(sK170(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1542,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
          & ( 'some$'(X4) = X0 )
          & ( 'some$'(X3) = X1 ) )
      | ~ sP13(X0,X1,X2) ),
    inference(rectify,[],[f1541]) ).

tff(f1541,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$z'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ~ sP13(X2,X0,X1) ),
    inference(nnf_transformation,[],[f1103]) ).

tff(f5819,plain,
    spl230_378,
    inference(avatar_split_clause,[],[f2492,f5817]) ).

tff(f5817,plain,
    ( spl230_378
  <=> ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'some$'(sK170(X0,X1,X2)) = X1 )
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_378])]) ).

tff(f2492,plain,
    ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK170(X0,X1,X2)) = X1 )
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1544]) ).

tff(f5815,plain,
    spl230_377,
    inference(avatar_split_clause,[],[f2486,f5813]) ).

tff(f5813,plain,
    ( spl230_377
  <=> ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'some$a'(sK169(X0,X1,X2)) = X0 )
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_377])]) ).

tff(f2486,plain,
    ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'some$a'(sK169(X0,X1,X2)) = X0 )
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1540]) ).

tff(f1540,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
        & ( 'some$a'(sK169(X0,X1,X2)) = X0 )
        & ( 'some$'(sK168(X0,X1,X2)) = X1 ) )
      | ~ sP12(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK168,sK169])],[f1538,f1539]) ).

tff(f1539,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
          & ( 'some$a'(X4) = X0 )
          & ( 'some$'(X3) = X1 ) )
     => ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
        & ( 'some$a'(sK169(X0,X1,X2)) = X0 )
        & ( 'some$'(sK168(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1538,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$',X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
          & ( 'some$a'(X4) = X0 )
          & ( 'some$'(X3) = X1 ) )
      | ~ sP12(X0,X1,X2) ),
    inference(rectify,[],[f1537]) ).

tff(f1537,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_iarray_iarray$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$y'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$'(X3) = X0 ) )
      | ~ sP12(X2,X0,X1) ),
    inference(nnf_transformation,[],[f1101]) ).

tff(f5811,plain,
    spl230_376,
    inference(avatar_split_clause,[],[f2485,f5809]) ).

tff(f5809,plain,
    ( spl230_376
  <=> ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'some$'(sK168(X0,X1,X2)) = X1 )
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_376])]) ).

tff(f2485,plain,
    ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK168(X0,X1,X2)) = X1 )
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1540]) ).

tff(f5807,plain,
    spl230_375,
    inference(avatar_split_clause,[],[f2479,f5805]) ).

tff(f5805,plain,
    ( spl230_375
  <=> ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$'(sK167(X0,X1,X2)) = X0 )
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_375])]) ).

tff(f2479,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$'(sK167(X0,X1,X2)) = X0 )
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1536]) ).

tff(f1536,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
        & ( 'some$'(sK167(X0,X1,X2)) = X0 )
        & ( 'some$a'(sK166(X0,X1,X2)) = X1 ) )
      | ~ sP11(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK166,sK167])],[f1534,f1535]) ).

tff(f1535,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
          & ( 'some$'(X4) = X0 )
          & ( 'some$a'(X3) = X1 ) )
     => ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
        & ( 'some$'(sK167(X0,X1,X2)) = X0 )
        & ( 'some$a'(sK166(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1534,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
          & ( 'some$'(X4) = X0 )
          & ( 'some$a'(X3) = X1 ) )
      | ~ sP11(X0,X1,X2) ),
    inference(rectify,[],[f1533]) ).

tff(f1533,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_iarray_iarray$'] :
          ( ~ 'fun_app$t'('fun_app$x'(X1,X0),X2)
          & ( 'some$'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ~ sP11(X2,X0,X1) ),
    inference(nnf_transformation,[],[f1099]) ).

tff(f5803,plain,
    spl230_374,
    inference(avatar_split_clause,[],[f2478,f5801]) ).

tff(f5801,plain,
    ( spl230_374
  <=> ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'(sK166(X0,X1,X2)) = X1 )
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_374])]) ).

tff(f2478,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK166(X0,X1,X2)) = X1 )
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1536]) ).

tff(f5799,plain,
    spl230_373,
    inference(avatar_split_clause,[],[f2472,f5797]) ).

tff(f5797,plain,
    ( spl230_373
  <=> ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'(sK165(X0,X1,X2)) = X0 )
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_373])]) ).

tff(f2472,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK165(X0,X1,X2)) = X0 )
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1532]) ).

tff(f1532,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
        & ( 'some$a'(sK165(X0,X1,X2)) = X0 )
        & ( 'some$a'(sK164(X0,X1,X2)) = X1 ) )
      | ~ sP10(X0,X1,X2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f1530,f1531]) ).

tff(f1531,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
          & ( 'some$a'(X4) = X0 )
          & ( 'some$a'(X3) = X1 ) )
     => ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
        & ( 'some$a'(sK165(X0,X1,X2)) = X0 )
        & ( 'some$a'(sK164(X0,X1,X2)) = X1 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1530,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$',X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
          & ( 'some$a'(X4) = X0 )
          & ( 'some$a'(X3) = X1 ) )
      | ~ sP10(X0,X1,X2) ),
    inference(rectify,[],[f1529]) ).

tff(f1529,plain,
    ! [X2: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$',X4: 'A_n_vec_n_vec$'] :
          ( ~ 'fun_app$s'('fun_app$w'(X1,X0),X2)
          & ( 'some$a'(X4) = X2 )
          & ( 'some$a'(X3) = X0 ) )
      | ~ sP10(X2,X0,X1) ),
    inference(nnf_transformation,[],[f1097]) ).

tff(f5788,plain,
    spl230_372,
    inference(avatar_split_clause,[],[f2471,f5786]) ).

tff(f5786,plain,
    ( spl230_372
  <=> ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'(sK164(X0,X1,X2)) = X1 )
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_372])]) ).

tff(f2471,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK164(X0,X1,X2)) = X1 )
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1532]) ).

tff(f5784,plain,
    spl230_371,
    inference(avatar_split_clause,[],[f2458,f5782]) ).

tff(f5782,plain,
    ( spl230_371
  <=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
        ( $less('fun_app$l'('of_nat$',sK155(X0)),'fun_app$l'('of_nat$',sK156(X0)))
        | ~ sP8(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_371])]) ).

tff(f2458,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( $less('fun_app$l'('of_nat$',sK155(X0)),'fun_app$l'('of_nat$',sK156(X0)))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f1516]) ).

tff(f1516,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( ( ~ 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK156(X0))
        & 'fun_app$c'('fun_app$as'(X0,sK155(X0)),sK156(X0))
        & 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK155(X0))
        & $less('fun_app$l'('of_nat$',sK155(X0)),'fun_app$l'('of_nat$',sK156(X0)))
        & $less('fun_app$l'('of_nat$',sK154(X0)),'fun_app$l'('of_nat$',sK155(X0))) )
      | ~ sP8(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155,sK156])],[f1514,f1515]) ).

tff(f1515,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
          ( ~ 'fun_app$c'('fun_app$as'(X0,X1),X3)
          & 'fun_app$c'('fun_app$as'(X0,X2),X3)
          & 'fun_app$c'('fun_app$as'(X0,X1),X2)
          & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X3))
          & $less('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X2)) )
     => ( ~ 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK156(X0))
        & 'fun_app$c'('fun_app$as'(X0,sK155(X0)),sK156(X0))
        & 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK155(X0))
        & $less('fun_app$l'('of_nat$',sK155(X0)),'fun_app$l'('of_nat$',sK156(X0)))
        & $less('fun_app$l'('of_nat$',sK154(X0)),'fun_app$l'('of_nat$',sK155(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f1514,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
          ( ~ 'fun_app$c'('fun_app$as'(X0,X1),X3)
          & 'fun_app$c'('fun_app$as'(X0,X2),X3)
          & 'fun_app$c'('fun_app$as'(X0,X1),X2)
          & $less('fun_app$l'('of_nat$',X2),'fun_app$l'('of_nat$',X3))
          & $less('fun_app$l'('of_nat$',X1),'fun_app$l'('of_nat$',X2)) )
      | ~ sP8(X0) ),
    inference(rectify,[],[f1513]) ).

tff(f1513,plain,
    ! [X2: 'Nat_nat_bool_fun_fun$'] :
      ( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
          ( ~ 'fun_app$c'('fun_app$as'(X2,X3),X5)
          & 'fun_app$c'('fun_app$as'(X2,X4),X5)
          & 'fun_app$c'('fun_app$as'(X2,X3),X4)
          & $less('fun_app$l'('of_nat$',X4),'fun_app$l'('of_nat$',X5))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X4)) )
      | ~ sP8(X2) ),
    inference(nnf_transformation,[],[f1093]) ).

tff(f1093,plain,
    ! [X2: 'Nat_nat_bool_fun_fun$'] :
      ( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
          ( ~ 'fun_app$c'('fun_app$as'(X2,X3),X5)
          & 'fun_app$c'('fun_app$as'(X2,X4),X5)
          & 'fun_app$c'('fun_app$as'(X2,X3),X4)
          & $less('fun_app$l'('of_nat$',X4),'fun_app$l'('of_nat$',X5))
          & $less('fun_app$l'('of_nat$',X3),'fun_app$l'('of_nat$',X4)) )
      | ~ sP8(X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

tff(f5780,plain,
    spl230_370,
    inference(avatar_split_clause,[],[f2457,f5778]) ).

tff(f5778,plain,
    ( spl230_370
  <=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
        ( $less('fun_app$l'('of_nat$',sK154(X0)),'fun_app$l'('of_nat$',sK155(X0)))
        | ~ sP8(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_370])]) ).

tff(f2457,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( $less('fun_app$l'('of_nat$',sK154(X0)),'fun_app$l'('of_nat$',sK155(X0)))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f1516]) ).

tff(f5776,plain,
    spl230_369,
    inference(avatar_split_clause,[],[f2455,f5774]) ).

tff(f5774,plain,
    ( spl230_369
  <=> ! [X2: 'Int_int_prod_set$',X0: 'Int_int_prod$',X1: 'Int_int_prod_set$'] :
        ( 'member$g'(sK153(X0,X1,X2),X2)
        | ~ 'member$g'(X0,'plus$n'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_369])]) ).

tff(f2455,plain,
    ! [X2: 'Int_int_prod_set$',X0: 'Int_int_prod$',X1: 'Int_int_prod_set$'] :
      ( 'member$g'(sK153(X0,X1,X2),X2)
      | ~ 'member$g'(X0,'plus$n'(X1,X2)) ),
    inference(cnf_transformation,[],[f1512]) ).

tff(f1512,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod_set$',X2: 'Int_int_prod_set$'] :
      ( ( 'member$g'(sK153(X0,X1,X2),X2)
        & 'member$g'(sK152(X0,X1,X2),X1)
        & ( 'plus$b'(sK152(X0,X1,X2),sK153(X0,X1,X2)) = X0 ) )
      | ~ 'member$g'(X0,'plus$n'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153])],[f930,f1511]) ).

tff(f1511,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod_set$',X2: 'Int_int_prod_set$'] :
      ( ? [X3: 'Int_int_prod$',X4: 'Int_int_prod$'] :
          ( 'member$g'(X4,X2)
          & 'member$g'(X3,X1)
          & ( 'plus$b'(X3,X4) = X0 ) )
     => ( 'member$g'(sK153(X0,X1,X2),X2)
        & 'member$g'(sK152(X0,X1,X2),X1)
        & ( 'plus$b'(sK152(X0,X1,X2),sK153(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f930,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod_set$',X2: 'Int_int_prod_set$'] :
      ( ? [X3: 'Int_int_prod$',X4: 'Int_int_prod$'] :
          ( 'member$g'(X4,X2)
          & 'member$g'(X3,X1)
          & ( 'plus$b'(X3,X4) = X0 ) )
      | ~ 'member$g'(X0,'plus$n'(X1,X2)) ),
    inference(ennf_transformation,[],[f749]) ).

tff(f749,plain,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod_set$',X2: 'Int_int_prod_set$'] :
      ~ ( ! [X3: 'Int_int_prod$',X4: 'Int_int_prod$'] :
            ~ ( 'member$g'(X4,X2)
              & 'member$g'(X3,X1)
              & ( 'plus$b'(X3,X4) = X0 ) )
        & 'member$g'(X0,'plus$n'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f167]) ).

tff(f167,axiom,
    ! [X0: 'Int_int_prod$',X1: 'Int_int_prod_set$',X2: 'Int_int_prod_set$'] :
      ( ( ! [X3: 'Int_int_prod$',X4: 'Int_int_prod$'] :
            ( ( 'member$g'(X4,X2)
              & 'member$g'(X3,X1)
              & ( 'plus$b'(X3,X4) = X0 ) )
           => $false )
        & 'member$g'(X0,'plus$n'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom165) ).

tff(f5772,plain,
    spl230_368,
    inference(avatar_split_clause,[],[f2454,f5770]) ).

tff(f5770,plain,
    ( spl230_368
  <=> ! [X2: 'Int_int_prod_set$',X0: 'Int_int_prod$',X1: 'Int_int_prod_set$'] :
        ( 'member$g'(sK152(X0,X1,X2),X1)
        | ~ 'member$g'(X0,'plus$n'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_368])]) ).

tff(f2454,plain,
    ! [X2: 'Int_int_prod_set$',X0: 'Int_int_prod$',X1: 'Int_int_prod_set$'] :
      ( 'member$g'(sK152(X0,X1,X2),X1)
      | ~ 'member$g'(X0,'plus$n'(X1,X2)) ),
    inference(cnf_transformation,[],[f1512]) ).

tff(f5768,plain,
    spl230_367,
    inference(avatar_split_clause,[],[f2452,f5766]) ).

tff(f5766,plain,
    ( spl230_367
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
        ( 'member$e'(sK151(X0,X1,X2),X2)
        | ~ 'member$e'(X0,'plus$i'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_367])]) ).

tff(f2452,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$e'(sK151(X0,X1,X2),X2)
      | ~ 'member$e'(X0,'plus$i'(X1,X2)) ),
    inference(cnf_transformation,[],[f1510]) ).

tff(f1510,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'member$e'(sK151(X0,X1,X2),X2)
        & 'member$e'(sK150(X0,X1,X2),X1)
        & ( 'plus$c'(sK150(X0,X1,X2),sK151(X0,X1,X2)) = X0 ) )
      | ~ 'member$e'(X0,'plus$i'(X1,X2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151])],[f929,f1509]) ).

tff(f1509,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ? [X3: 'A_iarray_iarray_a_iarray_iarray_prod$',X4: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
          ( 'member$e'(X4,X2)
          & 'member$e'(X3,X1)
          & ( 'plus$c'(X3,X4) = X0 ) )
     => ( 'member$e'(sK151(X0,X1,X2),X2)
        & 'member$e'(sK150(X0,X1,X2),X1)
        & ( 'plus$c'(sK150(X0,X1,X2),sK151(X0,X1,X2)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f929,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ? [X3: 'A_iarray_iarray_a_iarray_iarray_prod$',X4: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
          ( 'member$e'(X4,X2)
          & 'member$e'(X3,X1)
          & ( 'plus$c'(X3,X4) = X0 ) )
      | ~ 'member$e'(X0,'plus$i'(X1,X2)) ),
    inference(ennf_transformation,[],[f748]) ).

tff(f748,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ~ ( ! [X3: 'A_iarray_iarray_a_iarray_iarray_prod$',X4: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
            ~ ( 'member$e'(X4,X2)
              & 'member$e'(X3,X1)
              & ( 'plus$c'(X3,X4) = X0 ) )
        & 'member$e'(X0,'plus$i'(X1,X2)) ),
    inference(true_and_false_elimination,[],[f163]) ).

tff(f163,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( ! [X3: 'A_iarray_iarray_a_iarray_iarray_prod$',X4: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
            ( ( 'member$e'(X4,X2)
              & 'member$e'(X3,X1)
              & ( 'plus$c'(X3,X4) = X0 ) )
           => $false )
        & 'member$e'(X0,'plus$i'(X1,X2)) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom161) ).

tff(f5764,plain,
    spl230_366,
    inference(avatar_split_clause,[],[f2451,f5762]) ).

tff(f5762,plain,
    ( spl230_366
  <=> ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
        ( 'member$e'(sK150(X0,X1,X2),X1)
        | ~ 'member$e'(X0,'plus$i'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_366])]) ).

tff(f2451,plain,
    ! [X2: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X0: 'A_iarray_iarray_a_iarray_iarray_prod$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( 'member$e'(sK150(X0,X1,X2),X1)
      | ~ 'member$e'(X0,'plus$i'(X1,X2)) ),
    inference(cnf_transformation,[],[f1510]) ).

tff(f5760,plain,
    spl230_365,
    inference(avatar_split_clause,[],[f2449,f5758]) ).

tff(f5758,plain,
    ( spl230_365
  <=> ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
        ( 'member$a'(sK149(X0,X1,X2),X2)
        | ~ 'member$a'(X0,'plus$f'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_365])]) ).

tff(f2449,plain,
    ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
      ( 'member$a'(sK149(X0,X1,X2),X2)
      | ~ 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(cnf_transformation,[],[f1508]) ).

tff(f5756,plain,
    spl230_364,
    inference(avatar_split_clause,[],[f2448,f5754]) ).

tff(f5754,plain,
    ( spl230_364
  <=> ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
        ( 'member$a'(sK148(X0,X1,X2),X1)
        | ~ 'member$a'(X0,'plus$f'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_364])]) ).

tff(f2448,plain,
    ! [X2: 'A_iarray_set$',X0: 'A_iarray$',X1: 'A_iarray_set$'] :
      ( 'member$a'(sK148(X0,X1,X2),X1)
      | ~ 'member$a'(X0,'plus$f'(X1,X2)) ),
    inference(cnf_transformation,[],[f1508]) ).

tff(f5752,plain,
    spl230_363,
    inference(avatar_split_clause,[],[f2446,f5750]) ).

tff(f5750,plain,
    ( spl230_363
  <=> ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
        ( 'member$c'(sK147(X0,X1,X2),X2)
        | ~ 'member$c'(X0,'plus$h'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_363])]) ).

tff(f2446,plain,
    ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
      ( 'member$c'(sK147(X0,X1,X2),X2)
      | ~ 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(cnf_transformation,[],[f1506]) ).

tff(f5748,plain,
    ( spl230_362
    | ~ spl230_6
    | ~ spl230_242 ),
    inference(avatar_split_clause,[],[f4989,f4794,f3524,f5746]) ).

tff(f5746,plain,
    ( spl230_362
  <=> ! [X0: 'A_iarray_iarray_option$'] : ( tltrue = def_7('uug$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_362])]) ).

tff(f3524,plain,
    ( spl230_6
  <=> ! [X0: 'A_iarray_iarray$'] : 'fun_app$f'('uug$',X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_6])]) ).

tff(f4794,plain,
    ( spl230_242
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( ( tltrue = def_7(X0,X1) )
        | ~ 'fun_app$f'(X0,'the$a'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_242])]) ).

tff(f4989,plain,
    ( ! [X0: 'A_iarray_iarray_option$'] : ( tltrue = def_7('uug$',X0) )
    | ~ spl230_6
    | ~ spl230_242 ),
    inference(resolution,[],[f4795,f3525]) ).

tff(f3525,plain,
    ( ! [X0: 'A_iarray_iarray$'] : 'fun_app$f'('uug$',X0)
    | ~ spl230_6 ),
    inference(avatar_component_clause,[],[f3524]) ).

tff(f4795,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( ~ 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue = def_7(X0,X1) ) )
    | ~ spl230_242 ),
    inference(avatar_component_clause,[],[f4794]) ).

tff(f5744,plain,
    spl230_361,
    inference(avatar_split_clause,[],[f2445,f5742]) ).

tff(f5742,plain,
    ( spl230_361
  <=> ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
        ( 'member$c'(sK146(X0,X1,X2),X1)
        | ~ 'member$c'(X0,'plus$h'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_361])]) ).

tff(f2445,plain,
    ! [X2: 'Nat_set$',X0: 'Nat$',X1: 'Nat_set$'] :
      ( 'member$c'(sK146(X0,X1,X2),X1)
      | ~ 'member$c'(X0,'plus$h'(X1,X2)) ),
    inference(cnf_transformation,[],[f1506]) ).

tff(f5740,plain,
    spl230_360,
    inference(avatar_split_clause,[],[f2443,f5738]) ).

tff(f5738,plain,
    ( spl230_360
  <=> ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
        ( 'member$d'(sK145(X0,X1,X2),X2)
        | ~ 'member$d'(X0,'plus$k'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_360])]) ).

tff(f2443,plain,
    ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
      ( 'member$d'(sK145(X0,X1,X2),X2)
      | ~ 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(cnf_transformation,[],[f1504]) ).

tff(f5736,plain,
    spl230_359,
    inference(avatar_split_clause,[],[f2442,f5734]) ).

tff(f5734,plain,
    ( spl230_359
  <=> ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
        ( 'member$d'(sK144(X0,X1,X2),X1)
        | ~ 'member$d'(X0,'plus$k'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_359])]) ).

tff(f2442,plain,
    ! [X2: 'Int_set$',X0: $int,X1: 'Int_set$'] :
      ( 'member$d'(sK144(X0,X1,X2),X1)
      | ~ 'member$d'(X0,'plus$k'(X1,X2)) ),
    inference(cnf_transformation,[],[f1504]) ).

tff(f5732,plain,
    spl230_358,
    inference(avatar_split_clause,[],[f2440,f5730]) ).

tff(f5730,plain,
    ( spl230_358
  <=> ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
        ( 'member$j'(sK143(X0,X1,X2),X2)
        | ~ 'member$j'(X0,'plus$m'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_358])]) ).

tff(f2440,plain,
    ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
      ( 'member$j'(sK143(X0,X1,X2),X2)
      | ~ 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(cnf_transformation,[],[f1502]) ).

tff(f5728,plain,
    spl230_357,
    inference(avatar_split_clause,[],[f2439,f5726]) ).

tff(f5726,plain,
    ( spl230_357
  <=> ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
        ( 'member$j'(sK142(X0,X1,X2),X1)
        | ~ 'member$j'(X0,'plus$m'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_357])]) ).

tff(f2439,plain,
    ! [X2: 'A_n_vec_n_vec_set$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec_set$'] :
      ( 'member$j'(sK142(X0,X1,X2),X1)
      | ~ 'member$j'(X0,'plus$m'(X1,X2)) ),
    inference(cnf_transformation,[],[f1502]) ).

tff(f5724,plain,
    spl230_356,
    inference(avatar_split_clause,[],[f2437,f5722]) ).

tff(f5722,plain,
    ( spl230_356
  <=> ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
        ( 'member$i'(sK141(X0,X1,X2),X2)
        | ~ 'member$i'(X0,'plus$l'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_356])]) ).

tff(f2437,plain,
    ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
      ( 'member$i'(sK141(X0,X1,X2),X2)
      | ~ 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(cnf_transformation,[],[f1500]) ).

tff(f5720,plain,
    spl230_355,
    inference(avatar_split_clause,[],[f2436,f5718]) ).

tff(f5718,plain,
    ( spl230_355
  <=> ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
        ( 'member$i'(sK140(X0,X1,X2),X1)
        | ~ 'member$i'(X0,'plus$l'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_355])]) ).

tff(f2436,plain,
    ! [X2: 'Int_set_set$',X0: 'Int_set$',X1: 'Int_set_set$'] :
      ( 'member$i'(sK140(X0,X1,X2),X1)
      | ~ 'member$i'(X0,'plus$l'(X1,X2)) ),
    inference(cnf_transformation,[],[f1500]) ).

tff(f5716,plain,
    spl230_354,
    inference(avatar_split_clause,[],[f2434,f5714]) ).

tff(f5714,plain,
    ( spl230_354
  <=> ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
        ( 'member$h'(sK139(X0,X1,X2),X2)
        | ~ 'member$h'(X0,'plus$j'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_354])]) ).

tff(f2434,plain,
    ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
      ( 'member$h'(sK139(X0,X1,X2),X2)
      | ~ 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(cnf_transformation,[],[f1498]) ).

tff(f5712,plain,
    spl230_353,
    inference(avatar_split_clause,[],[f2433,f5710]) ).

tff(f5710,plain,
    ( spl230_353
  <=> ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
        ( 'member$h'(sK138(X0,X1,X2),X1)
        | ~ 'member$h'(X0,'plus$j'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_353])]) ).

tff(f2433,plain,
    ! [X2: 'A_iarray_iarray_set$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray_set$'] :
      ( 'member$h'(sK138(X0,X1,X2),X1)
      | ~ 'member$h'(X0,'plus$j'(X1,X2)) ),
    inference(cnf_transformation,[],[f1498]) ).

tff(f5708,plain,
    spl230_352,
    inference(avatar_split_clause,[],[f2423,f5706]) ).

tff(f5706,plain,
    ( spl230_352
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,X2))
        | ~ $less(X1,X2)
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_352])]) ).

tff(f2423,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,$sum(X0,X2))
      | ~ $less(X1,X2)
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f920]) ).

tff(f920,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less(X1,$sum(X0,X2))
      | ~ $less(X1,X2)
      | ~ $less(0,X0) ),
    inference(flattening,[],[f919]) ).

tff(f919,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less(X1,$sum(X0,X2))
      | ~ $less(X1,X2)
      | ~ $less(0,X0) ),
    inference(ennf_transformation,[],[f628]) ).

tff(f628,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $less(X1,X2)
        & $less(0,X0) )
     => $less(X1,$sum(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom626) ).

tff(f5704,plain,
    ( spl230_351
    | ~ spl230_6
    | ~ spl230_240 ),
    inference(avatar_split_clause,[],[f4984,f4784,f3524,f5702]) ).

tff(f5702,plain,
    ( spl230_351
  <=> ! [X0: 'A_iarray_iarray_option$'] : ( tltrue = def_5('uug$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_351])]) ).

tff(f4784,plain,
    ( spl230_240
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( ( tltrue = def_5(X0,X1) )
        | ~ 'fun_app$f'(X0,'the$a'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_240])]) ).

tff(f4984,plain,
    ( ! [X0: 'A_iarray_iarray_option$'] : ( tltrue = def_5('uug$',X0) )
    | ~ spl230_6
    | ~ spl230_240 ),
    inference(resolution,[],[f4785,f3525]) ).

tff(f4785,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( ~ 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue = def_5(X0,X1) ) )
    | ~ spl230_240 ),
    inference(avatar_component_clause,[],[f4784]) ).

tff(f5700,plain,
    spl230_350,
    inference(avatar_split_clause,[],[f2364,f5698]) ).

tff(f5698,plain,
    ( spl230_350
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_350])]) ).

tff(f2364,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ),
    inference(cnf_transformation,[],[f154]) ).

tff(f154,axiom,
    ! [X0: $int,X1: $int,X2: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X1,$sum(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom152) ).

tff(f5696,plain,
    spl230_349,
    inference(avatar_split_clause,[],[f2361,f5694]) ).

tff(f5694,plain,
    ( spl230_349
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'('plus$a'(X0,X1),X2) = 'plus$a'(X0,'plus$a'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_349])]) ).

tff(f2361,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'('plus$a'(X0,X1),X2) = 'plus$a'(X0,'plus$a'(X1,X2)) ),
    inference(cnf_transformation,[],[f190]) ).

tff(f190,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] : ( 'plus$a'('plus$a'(X0,X1),X2) = 'plus$a'(X0,'plus$a'(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom188) ).

tff(f5692,plain,
    spl230_348,
    inference(avatar_split_clause,[],[f2360,f5690]) ).

tff(f5690,plain,
    ( spl230_348
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'plus$a'(X1,X2)) = 'plus$a'(X1,'plus$a'(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_348])]) ).

tff(f2360,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'plus$a'(X1,X2)) = 'plus$a'(X1,'plus$a'(X0,X2)) ),
    inference(cnf_transformation,[],[f152]) ).

tff(f152,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'plus$a'(X1,X2)) = 'plus$a'(X1,'plus$a'(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom150) ).

tff(f5688,plain,
    spl230_347,
    inference(avatar_split_clause,[],[f2355,f5686]) ).

tff(f5686,plain,
    ( spl230_347
  <=> ! [X2: 'Int_set$',X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'('plus$k'(X0,X1),X2) = 'plus$k'(X0,'plus$k'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_347])]) ).

tff(f2355,plain,
    ! [X2: 'Int_set$',X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'('plus$k'(X0,X1),X2) = 'plus$k'(X0,'plus$k'(X1,X2)) ),
    inference(cnf_transformation,[],[f124]) ).

tff(f124,axiom,
    ! [X0: 'Int_set$',X1: 'Int_set$',X2: 'Int_set$'] : ( 'plus$k'('plus$k'(X0,X1),X2) = 'plus$k'(X0,'plus$k'(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom122) ).

tff(f5684,plain,
    spl230_346,
    inference(avatar_split_clause,[],[f2354,f5682]) ).

tff(f5682,plain,
    ( spl230_346
  <=> ! [X2: 'Int_set$',X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'(X0,'plus$k'(X1,X2)) = 'plus$k'(X1,'plus$k'(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_346])]) ).

tff(f2354,plain,
    ! [X2: 'Int_set$',X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'(X0,'plus$k'(X1,X2)) = 'plus$k'(X1,'plus$k'(X0,X2)) ),
    inference(cnf_transformation,[],[f151]) ).

tff(f151,axiom,
    ! [X0: 'Int_set$',X1: 'Int_set$',X2: 'Int_set$'] : ( 'plus$k'(X0,'plus$k'(X1,X2)) = 'plus$k'(X1,'plus$k'(X0,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom149) ).

tff(f5680,plain,
    spl230_345,
    inference(avatar_split_clause,[],[f2353,f5678]) ).

tff(f2353,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f303]) ).

tff(f303,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$'(X0,X1),X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom301) ).

tff(f5676,plain,
    spl230_344,
    inference(avatar_split_clause,[],[f2352,f5674]) ).

tff(f5674,plain,
    ( spl230_344
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'splice$b'('cons$'(X0,X1),X2) = 'cons$'(X0,'splice$b'(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_344])]) ).

tff(f2352,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'splice$b'('cons$'(X0,X1),X2) = 'cons$'(X0,'splice$b'(X2,X1)) ),
    inference(cnf_transformation,[],[f483]) ).

tff(f483,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'splice$b'('cons$'(X0,X1),X2) = 'cons$'(X0,'splice$b'(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom481) ).

tff(f5672,plain,
    spl230_343,
    inference(avatar_split_clause,[],[f2267,f5670]) ).

tff(f5670,plain,
    ( spl230_343
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | 'fun_app$'(X0,sK111(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_343])]) ).

tff(f2267,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
      | 'fun_app$'(X0,sK111(X0,X1)) ),
    inference(cnf_transformation,[],[f1408]) ).

tff(f5668,plain,
    spl230_342,
    inference(avatar_split_clause,[],[f2264,f5666]) ).

tff(f5666,plain,
    ( spl230_342
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
        | 'fun_app$'(X0,sK110(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_342])]) ).

tff(f2264,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = 'nil$' )
      | 'fun_app$'(X0,sK110(X0,X1)) ),
    inference(cnf_transformation,[],[f1404]) ).

tff(f5664,plain,
    spl230_341,
    inference(avatar_split_clause,[],[f2261,f5662]) ).

tff(f5662,plain,
    ( spl230_341
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
        | ~ 'fun_app$'(X0,sK109(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_341])]) ).

tff(f2261,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('filter$'(X0),X1) = X1 )
      | ~ 'fun_app$'(X0,sK109(X0,X1)) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f5658,plain,
    spl230_340,
    inference(avatar_split_clause,[],[f2106,f5656]) ).

tff(f5656,plain,
    ( spl230_340
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
        | ~ 'fun_app$'(X1,sK85(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_340])]) ).

tff(f2106,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'fun_app$p'('filter$'(X1),X0) = X0 )
      | ~ 'fun_app$'(X1,sK85(X0,X1)) ),
    inference(cnf_transformation,[],[f1272]) ).

tff(f5654,plain,
    spl230_339,
    inference(avatar_split_clause,[],[f2104,f5652]) ).

tff(f5652,plain,
    ( spl230_339
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
        ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
        | 'fun_app$'(X1,sK84(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_339])]) ).

tff(f2104,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'nil$' = 'fun_app$p'('filter$'(X1),X0) )
      | 'fun_app$'(X1,sK84(X0,X1)) ),
    inference(cnf_transformation,[],[f1270]) ).

tff(f5650,plain,
    spl230_338,
    inference(avatar_split_clause,[],[f2075,f5648]) ).

tff(f5648,plain,
    ( spl230_338
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X0,X1),0)
        | ~ $less(X1,0)
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_338])]) ).

tff(f2075,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),0)
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f839]) ).

tff(f839,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),0)
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(flattening,[],[f838]) ).

tff(f838,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),0)
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f630]) ).

tff(f630,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(X1,0)
        & $less(X0,0) )
     => $less($sum(X0,X1),0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom628) ).

tff(f5646,plain,
    spl230_337,
    inference(avatar_split_clause,[],[f2073,f5644]) ).

tff(f5644,plain,
    ( spl230_337
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('invertible$','matrix_matrix_mult$'(X0,X1))
        | ~ 'fun_app$o'('invertible$',X1)
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_337])]) ).

tff(f2073,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$','matrix_matrix_mult$'(X0,X1))
      | ~ 'fun_app$o'('invertible$',X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f835]) ).

tff(f835,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$','matrix_matrix_mult$'(X0,X1))
      | ~ 'fun_app$o'('invertible$',X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(flattening,[],[f834]) ).

tff(f834,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$','matrix_matrix_mult$'(X0,X1))
      | ~ 'fun_app$o'('invertible$',X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f296]) ).

tff(f296,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('invertible$',X1)
        & 'fun_app$o'('invertible$',X0) )
     => 'fun_app$o'('invertible$','matrix_matrix_mult$'(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom294) ).

tff(f5642,plain,
    spl230_336,
    inference(avatar_split_clause,[],[f1963,f5640]) ).

tff(f5640,plain,
    ( spl230_336
  <=> ! [X4: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option_bool_fun$'] :
        ( 'fun_app$t'(X0,'some$'(sK56(X0)))
        | 'fun_app$t'(X0,'none$')
        | ~ 'fun_app$t'(X0,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_336])]) ).

tff(f1963,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$',X4: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'(X0,'some$'(sK56(X0)))
      | 'fun_app$t'(X0,'none$')
      | ~ 'fun_app$t'(X0,X4) ),
    inference(cnf_transformation,[],[f1223]) ).

tff(f1223,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( 'fun_app$t'(X0,sK55(X0))
        | ( ! [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
          & ~ 'fun_app$t'(X0,'none$') ) )
      & ( 'fun_app$t'(X0,'some$'(sK56(X0)))
        | 'fun_app$t'(X0,'none$')
        | ! [X4: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f1220,f1222,f1221]) ).

tff(f1221,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
     => 'fun_app$t'(X0,sK55(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f1222,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X3: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X3))
     => 'fun_app$t'(X0,'some$'(sK56(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f1220,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ( ! [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
          & ~ 'fun_app$t'(X0,'none$') ) )
      & ( ? [X3: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X3))
        | 'fun_app$t'(X0,'none$')
        | ! [X4: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X4) ) ),
    inference(rectify,[],[f1219]) ).

tff(f1219,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ( ! [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
          & ~ 'fun_app$t'(X0,'none$') ) )
      & ( ? [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
        | 'fun_app$t'(X0,'none$')
        | ! [X1: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X1) ) ),
    inference(flattening,[],[f1218]) ).

tff(f1218,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ( ! [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
          & ~ 'fun_app$t'(X0,'none$') ) )
      & ( ? [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
        | 'fun_app$t'(X0,'none$')
        | ! [X1: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X1) ) ),
    inference(nnf_transformation,[],[f726]) ).

tff(f726,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
    <=> ( ? [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
        | 'fun_app$t'(X0,'none$') ) ),
    inference(rectify,[],[f41]) ).

tff(f41,axiom,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
    <=> ( ? [X1: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X1))
        | 'fun_app$t'(X0,'none$') ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom39) ).

tff(f5638,plain,
    spl230_335,
    inference(avatar_split_clause,[],[f1960,f5636]) ).

tff(f5636,plain,
    ( spl230_335
  <=> ! [X4: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option_bool_fun$'] :
        ( 'fun_app$s'(X0,'some$a'(sK54(X0)))
        | 'fun_app$s'(X0,'none$a')
        | ~ 'fun_app$s'(X0,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_335])]) ).

tff(f1960,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$',X4: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'(X0,'some$a'(sK54(X0)))
      | 'fun_app$s'(X0,'none$a')
      | ~ 'fun_app$s'(X0,X4) ),
    inference(cnf_transformation,[],[f1217]) ).

tff(f1217,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( 'fun_app$s'(X0,sK53(X0))
        | ( ! [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
          & ~ 'fun_app$s'(X0,'none$a') ) )
      & ( 'fun_app$s'(X0,'some$a'(sK54(X0)))
        | 'fun_app$s'(X0,'none$a')
        | ! [X4: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54])],[f1214,f1216,f1215]) ).

tff(f1215,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
     => 'fun_app$s'(X0,sK53(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f1216,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X3: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X3))
     => 'fun_app$s'(X0,'some$a'(sK54(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f1214,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ( ! [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
          & ~ 'fun_app$s'(X0,'none$a') ) )
      & ( ? [X3: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X3))
        | 'fun_app$s'(X0,'none$a')
        | ! [X4: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X4) ) ),
    inference(rectify,[],[f1213]) ).

tff(f1213,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ( ! [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
          & ~ 'fun_app$s'(X0,'none$a') ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
        | 'fun_app$s'(X0,'none$a')
        | ! [X1: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X1) ) ),
    inference(flattening,[],[f1212]) ).

tff(f1212,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ( ! [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
          & ~ 'fun_app$s'(X0,'none$a') ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
        | 'fun_app$s'(X0,'none$a')
        | ! [X1: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X1) ) ),
    inference(nnf_transformation,[],[f725]) ).

tff(f725,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
    <=> ( ? [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
        | 'fun_app$s'(X0,'none$a') ) ),
    inference(rectify,[],[f40]) ).

tff(f40,axiom,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
    <=> ( ? [X1: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X1))
        | 'fun_app$s'(X0,'none$a') ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom38) ).

tff(f5634,plain,
    spl230_334,
    inference(avatar_split_clause,[],[f1955,f5632]) ).

tff(f5632,plain,
    ( spl230_334
  <=> ! [X0: 'A_iarray_iarray_option_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( 'fun_app$t'(X0,X1)
        | ~ 'fun_app$t'(X0,'some$'(sK49(X0)))
        | ~ 'fun_app$t'(X0,'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_334])]) ).

tff(f1955,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'(X0,X1)
      | ~ 'fun_app$t'(X0,'some$'(sK49(X0)))
      | ~ 'fun_app$t'(X0,'none$') ),
    inference(cnf_transformation,[],[f1203]) ).

tff(f1203,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ~ 'fun_app$t'(X0,'some$'(sK49(X0)))
        | ~ 'fun_app$t'(X0,'none$') )
      & ( ( ! [X3: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X3))
          & 'fun_app$t'(X0,'none$') )
        | ~ 'fun_app$t'(X0,sK50(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50])],[f1200,f1202,f1201]) ).

tff(f1201,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
     => ~ 'fun_app$t'(X0,'some$'(sK49(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f1202,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ? [X4: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X4)
     => ~ 'fun_app$t'(X0,sK50(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f1200,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ? [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
        | ~ 'fun_app$t'(X0,'none$') )
      & ( ( ! [X3: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X3))
          & 'fun_app$t'(X0,'none$') )
        | ? [X4: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X4) ) ),
    inference(rectify,[],[f1199]) ).

tff(f1199,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ? [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
        | ~ 'fun_app$t'(X0,'none$') )
      & ( ( ! [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
          & 'fun_app$t'(X0,'none$') )
        | ? [X1: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X1) ) ),
    inference(flattening,[],[f1198]) ).

tff(f1198,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
        | ? [X2: 'A_iarray_iarray$'] : ~ 'fun_app$t'(X0,'some$'(X2))
        | ~ 'fun_app$t'(X0,'none$') )
      & ( ( ! [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
          & 'fun_app$t'(X0,'none$') )
        | ? [X1: 'A_iarray_iarray_option$'] : ~ 'fun_app$t'(X0,X1) ) ),
    inference(nnf_transformation,[],[f724]) ).

tff(f724,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
    <=> ( ! [X2: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X2))
        & 'fun_app$t'(X0,'none$') ) ),
    inference(rectify,[],[f56]) ).

tff(f56,axiom,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( ! [X1: 'A_iarray_iarray_option$'] : 'fun_app$t'(X0,X1)
    <=> ( ! [X1: 'A_iarray_iarray$'] : 'fun_app$t'(X0,'some$'(X1))
        & 'fun_app$t'(X0,'none$') ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).

tff(f5630,plain,
    spl230_333,
    inference(avatar_split_clause,[],[f1952,f5628]) ).

tff(f5628,plain,
    ( spl230_333
  <=> ! [X0: 'A_n_vec_n_vec_option_bool_fun$',X1: 'A_n_vec_n_vec_option$'] :
        ( 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,'some$a'(sK47(X0)))
        | ~ 'fun_app$s'(X0,'none$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_333])]) ).

tff(f1952,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$',X1: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'(X0,X1)
      | ~ 'fun_app$s'(X0,'some$a'(sK47(X0)))
      | ~ 'fun_app$s'(X0,'none$a') ),
    inference(cnf_transformation,[],[f1197]) ).

tff(f1197,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,'some$a'(sK47(X0)))
        | ~ 'fun_app$s'(X0,'none$a') )
      & ( ( ! [X3: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X3))
          & 'fun_app$s'(X0,'none$a') )
        | ~ 'fun_app$s'(X0,sK48(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48])],[f1194,f1196,f1195]) ).

tff(f1195,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
     => ~ 'fun_app$s'(X0,'some$a'(sK47(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f1196,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ? [X4: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X4)
     => ~ 'fun_app$s'(X0,sK48(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f1194,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ? [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
        | ~ 'fun_app$s'(X0,'none$a') )
      & ( ( ! [X3: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X3))
          & 'fun_app$s'(X0,'none$a') )
        | ? [X4: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X4) ) ),
    inference(rectify,[],[f1193]) ).

tff(f1193,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ? [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
        | ~ 'fun_app$s'(X0,'none$a') )
      & ( ( ! [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
          & 'fun_app$s'(X0,'none$a') )
        | ? [X1: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X1) ) ),
    inference(flattening,[],[f1192]) ).

tff(f1192,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
        | ? [X2: 'A_n_vec_n_vec$'] : ~ 'fun_app$s'(X0,'some$a'(X2))
        | ~ 'fun_app$s'(X0,'none$a') )
      & ( ( ! [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
          & 'fun_app$s'(X0,'none$a') )
        | ? [X1: 'A_n_vec_n_vec_option$'] : ~ 'fun_app$s'(X0,X1) ) ),
    inference(nnf_transformation,[],[f723]) ).

tff(f723,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
    <=> ( ! [X2: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X2))
        & 'fun_app$s'(X0,'none$a') ) ),
    inference(rectify,[],[f55]) ).

tff(f55,axiom,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( ! [X1: 'A_n_vec_n_vec_option$'] : 'fun_app$s'(X0,X1)
    <=> ( ! [X1: 'A_n_vec_n_vec$'] : 'fun_app$s'(X0,'some$a'(X1))
        & 'fun_app$s'(X0,'none$a') ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).

tff(f5624,plain,
    ( spl230_332
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_331 ),
    inference(avatar_split_clause,[],[f5618,f5615,f4004,f3920,f5622]) ).

tff(f5622,plain,
    ( spl230_332
  <=> ! [X0: 'A_iarray_iarray$'] :
        ( ( 'inverse_matrix_iarray$'(X0) = 'some$'(sK36('gauss_Jordan_iarrays_PA$'(X0))) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_332])]) ).

tff(f5615,plain,
    ( spl230_331
  <=> ! [X0: 'A_iarray_iarray$'] :
        ( ( 'inverse_matrix_iarray$'(X0) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'(X0))) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_331])]) ).

tff(f5618,plain,
    ( ! [X0: 'A_iarray_iarray$'] :
        ( ( 'inverse_matrix_iarray$'(X0) = 'some$'(sK36('gauss_Jordan_iarrays_PA$'(X0))) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) )
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_331 ),
    inference(forward_demodulation,[],[f5616,f4202]) ).

tff(f5616,plain,
    ( ! [X0: 'A_iarray_iarray$'] :
        ( ( 'inverse_matrix_iarray$'(X0) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'(X0))) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) )
    | ~ spl230_331 ),
    inference(avatar_component_clause,[],[f5615]) ).

tff(f5617,plain,
    spl230_331,
    inference(avatar_split_clause,[],[f1862,f5615]) ).

tff(f1862,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( 'inverse_matrix_iarray$'(X0) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'(X0))) )
      | ~ 'fun_app$f'('invertible_iarray$',X0) ),
    inference(cnf_transformation,[],[f787]) ).

tff(f787,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( ( 'none$' = 'inverse_matrix_iarray$'(X0) )
        | 'fun_app$f'('invertible_iarray$',X0) )
      & ( ( 'inverse_matrix_iarray$'(X0) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'(X0))) )
        | ~ 'fun_app$f'('invertible_iarray$',X0) ) ),
    inference(ennf_transformation,[],[f32]) ).

tff(f32,axiom,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( ~ 'fun_app$f'('invertible_iarray$',X0)
       => ( 'none$' = 'inverse_matrix_iarray$'(X0) ) )
      & ( 'fun_app$f'('invertible_iarray$',X0)
       => ( 'inverse_matrix_iarray$'(X0) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom30) ).

tff(f5604,plain,
    ( spl230_330
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_329 ),
    inference(avatar_split_clause,[],[f5600,f5597,f4004,f3920,f5602]) ).

tff(f5597,plain,
    ( spl230_329
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_329])]) ).

tff(f5600,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) = sK36('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) )
    | ~ spl230_94
    | ~ spl230_115
    | ~ spl230_329 ),
    inference(forward_demodulation,[],[f5598,f4202]) ).

tff(f5598,plain,
    ( ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) = 'matrix_to_iarray$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) )
    | ~ spl230_329 ),
    inference(avatar_component_clause,[],[f5597]) ).

tff(f5599,plain,
    spl230_329,
    inference(avatar_split_clause,[],[f1853,f5597]) ).

tff(f5595,plain,
    spl230_328,
    inference(avatar_split_clause,[],[f1851,f5593]) ).

tff(f5593,plain,
    ( spl230_328
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_328])]) ).

tff(f1851,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)),X0) ),
    inference(cnf_transformation,[],[f215]) ).

tff(f215,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'('fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom213) ).

tff(f5591,plain,
    spl230_327,
    inference(avatar_split_clause,[],[f665,f5589]) ).

tff(f5589,plain,
    ( spl230_327
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_327])]) ).

tff(f665,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum($sum(X0,X1),X2) = $sum(X0,$sum(X1,X2)) ),
    introduced(theory_axiom_136,[]) ).

tff(f5566,plain,
    ( spl230_326
    | ~ spl230_6
    | ~ spl230_192 ),
    inference(avatar_split_clause,[],[f4645,f4422,f3524,f5564]) ).

tff(f5564,plain,
    ( spl230_326
  <=> ! [X0: 'A_iarray_iarray$'] : ( tltrue = def_1('uug$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_326])]) ).

tff(f4422,plain,
    ( spl230_192
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
        ( ( tltrue = def_1(X0,X1) )
        | ~ 'fun_app$f'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_192])]) ).

tff(f4645,plain,
    ( ! [X0: 'A_iarray_iarray$'] : ( tltrue = def_1('uug$',X0) )
    | ~ spl230_6
    | ~ spl230_192 ),
    inference(resolution,[],[f4423,f3525]) ).

tff(f4423,plain,
    ( ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
        ( ~ 'fun_app$f'(X0,X1)
        | ( tltrue = def_1(X0,X1) ) )
    | ~ spl230_192 ),
    inference(avatar_component_clause,[],[f4422]) ).

tff(f5407,plain,
    ( spl230_325
    | ~ spl230_3
    | ~ spl230_152 ),
    inference(avatar_split_clause,[],[f4559,f4252,f3511,f5405]) ).

tff(f3511,plain,
    ( spl230_3
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_3])]) ).

tff(f4559,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl230_3
    | ~ spl230_152 ),
    inference(resolution,[],[f4253,f3512]) ).

tff(f3512,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl230_3 ),
    inference(avatar_component_clause,[],[f3511]) ).

tff(f5294,plain,
    spl230_324,
    inference(avatar_split_clause,[],[f3305,f5292]) ).

tff(f5292,plain,
    ( spl230_324
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ $less('fun_app$l'('of_nat$',X0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_324])]) ).

tff(f3305,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ $less('fun_app$l'('of_nat$',X0),1) ),
    inference(evaluation,[],[f1948]) ).

tff(f1948,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) = 0 )
      | ~ $less('fun_app$l'('of_nat$',X0),$sum(0,1)) ),
    inference(cnf_transformation,[],[f1191]) ).

tff(f1191,plain,
    ! [X0: 'Nat$'] :
      ( ( $less('fun_app$l'('of_nat$',X0),$sum(0,1))
        | ( 'fun_app$l'('of_nat$',X0) != 0 ) )
      & ( ( 'fun_app$l'('of_nat$',X0) = 0 )
        | ~ $less('fun_app$l'('of_nat$',X0),$sum(0,1)) ) ),
    inference(nnf_transformation,[],[f625]) ).

tff(f625,axiom,
    ! [X0: 'Nat$'] :
      ( $less('fun_app$l'('of_nat$',X0),$sum(0,1))
    <=> ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom623) ).

tff(f5290,plain,
    spl230_323,
    inference(avatar_split_clause,[],[f2957,f5288]) ).

tff(f5288,plain,
    ( spl230_323
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
        ( 'fun_app$c'('id_upt_k$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))),X1)
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_323])]) ).

tff(f2957,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( 'fun_app$c'('id_upt_k$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))),X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(definition_unfolding,[],[f2047,f1818]) ).

tff(f2047,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( 'fun_app$c'('id_upt_k$'('gauss_Jordan$'(X0)),X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f811]) ).

tff(f811,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( 'fun_app$c'('id_upt_k$'('gauss_Jordan$'(X0)),X1)
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f170]) ).

tff(f170,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] :
      ( 'fun_app$o'('invertible$',X0)
     => 'fun_app$c'('id_upt_k$'('gauss_Jordan$'(X0)),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom168) ).

tff(f5286,plain,
    spl230_322,
    inference(avatar_split_clause,[],[f2742,f5284]) ).

tff(f5284,plain,
    ( spl230_322
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray_list$',X3: 'A_iarray_list$'] :
        ( ( X1 = X3 )
        | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_322])]) ).

tff(f2742,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( ( X1 = X3 )
      | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1665]) ).

tff(f1665,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( ( 'cons$'(X0,X1) = 'cons$'(X2,X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) )
      & ( ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ) ),
    inference(flattening,[],[f1664]) ).

tff(f1664,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( ( 'cons$'(X0,X1) = 'cons$'(X2,X3) )
        | ( X1 != X3 )
        | ( X0 != X2 ) )
      & ( ( ( X1 = X3 )
          & ( X0 = X2 ) )
        | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ) ),
    inference(nnf_transformation,[],[f480]) ).

tff(f480,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$',X2: 'A_iarray$',X3: 'A_iarray_list$'] :
      ( ( 'cons$'(X0,X1) = 'cons$'(X2,X3) )
    <=> ( ( X1 = X3 )
        & ( X0 = X2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom478) ).

tff(f5282,plain,
    spl230_321,
    inference(avatar_split_clause,[],[f2741,f5280]) ).

tff(f5280,plain,
    ( spl230_321
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray_list$',X2: 'A_iarray$',X1: 'A_iarray_list$'] :
        ( ( X0 = X2 )
        | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_321])]) ).

tff(f2741,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray$',X1: 'A_iarray_list$'] :
      ( ( X0 = X2 )
      | ( 'cons$'(X0,X1) != 'cons$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1665]) ).

tff(f5278,plain,
    spl230_320,
    inference(avatar_split_clause,[],[f2663,f5276]) ).

tff(f5276,plain,
    ( spl230_320
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$',X3: 'A_iarray_list$'] :
        ( ( X1 = X3 )
        | ( 'pair$b'(X0,X1) != 'pair$b'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_320])]) ).

tff(f2663,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X1 = X3 )
      | ( 'pair$b'(X0,X1) != 'pair$b'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1013]) ).

tff(f1013,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( ( ( X1 = X3 )
        & ( X0 = X2 ) )
      | ( 'pair$b'(X0,X1) != 'pair$b'(X2,X3) ) ),
    inference(ennf_transformation,[],[f760]) ).

tff(f760,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ~ ( ~ ( ( X1 = X3 )
            & ( X0 = X2 ) )
        & ( 'pair$b'(X0,X1) = 'pair$b'(X2,X3) ) ),
    inference(true_and_false_elimination,[],[f243]) ).

tff(f243,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$',X2: 'A_iarray_list$',X3: 'A_iarray_list$'] :
      ( ( ( ( ( X1 = X3 )
            & ( X0 = X2 ) )
         => $false )
        & ( 'pair$b'(X0,X1) = 'pair$b'(X2,X3) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom241) ).

tff(f5274,plain,
    spl230_319,
    inference(avatar_split_clause,[],[f2662,f5272]) ).

tff(f5272,plain,
    ( spl230_319
  <=> ! [X0: 'A_iarray_list$',X3: 'A_iarray_list$',X2: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( X0 = X2 )
        | ( 'pair$b'(X0,X1) != 'pair$b'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_319])]) ).

tff(f2662,plain,
    ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( X0 = X2 )
      | ( 'pair$b'(X0,X1) != 'pair$b'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1013]) ).

tff(f5270,plain,
    spl230_318,
    inference(avatar_split_clause,[],[f2661,f5268]) ).

tff(f5268,plain,
    ( spl230_318
  <=> ! [X2: $int,X0: $int,X1: $int,X3: $int] :
        ( ( X1 = X3 )
        | ( 'pair$c'(X0,X1) != 'pair$c'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_318])]) ).

tff(f2661,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: $int] :
      ( ( X1 = X3 )
      | ( 'pair$c'(X0,X1) != 'pair$c'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1012]) ).

tff(f1012,plain,
    ! [X0: $int,X1: $int,X2: $int,X3: $int] :
      ( ( ( X1 = X3 )
        & ( X0 = X2 ) )
      | ( 'pair$c'(X0,X1) != 'pair$c'(X2,X3) ) ),
    inference(ennf_transformation,[],[f759]) ).

tff(f759,plain,
    ! [X0: $int,X1: $int,X2: $int,X3: $int] :
      ~ ( ~ ( ( X1 = X3 )
            & ( X0 = X2 ) )
        & ( 'pair$c'(X0,X1) = 'pair$c'(X2,X3) ) ),
    inference(true_and_false_elimination,[],[f241]) ).

tff(f241,axiom,
    ! [X0: $int,X1: $int,X2: $int,X3: $int] :
      ( ( ( ( ( X1 = X3 )
            & ( X0 = X2 ) )
         => $false )
        & ( 'pair$c'(X0,X1) = 'pair$c'(X2,X3) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom239) ).

tff(f5266,plain,
    spl230_317,
    inference(avatar_split_clause,[],[f2660,f5264]) ).

tff(f5264,plain,
    ( spl230_317
  <=> ! [X0: $int,X3: $int,X2: $int,X1: $int] :
        ( ( X0 = X2 )
        | ( 'pair$c'(X0,X1) != 'pair$c'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_317])]) ).

tff(f2660,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: $int] :
      ( ( X0 = X2 )
      | ( 'pair$c'(X0,X1) != 'pair$c'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1012]) ).

tff(f5260,plain,
    spl230_316,
    inference(avatar_split_clause,[],[f2659,f5258]) ).

tff(f5258,plain,
    ( spl230_316
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray$',X3: 'A_iarray$'] :
        ( ( X1 = X3 )
        | ( 'pair$a'(X0,X1) != 'pair$a'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_316])]) ).

tff(f2659,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray$'] :
      ( ( X1 = X3 )
      | ( 'pair$a'(X0,X1) != 'pair$a'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1011]) ).

tff(f1011,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray$',X3: 'A_iarray$'] :
      ( ( ( X1 = X3 )
        & ( X0 = X2 ) )
      | ( 'pair$a'(X0,X1) != 'pair$a'(X2,X3) ) ),
    inference(ennf_transformation,[],[f758]) ).

tff(f758,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray$',X3: 'A_iarray$'] :
      ~ ( ~ ( ( X1 = X3 )
            & ( X0 = X2 ) )
        & ( 'pair$a'(X0,X1) = 'pair$a'(X2,X3) ) ),
    inference(true_and_false_elimination,[],[f244]) ).

tff(f244,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$',X2: 'A_iarray$',X3: 'A_iarray$'] :
      ( ( ( ( ( X1 = X3 )
            & ( X0 = X2 ) )
         => $false )
        & ( 'pair$a'(X0,X1) = 'pair$a'(X2,X3) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom242) ).

tff(f5256,plain,
    spl230_315,
    inference(avatar_split_clause,[],[f2658,f5254]) ).

tff(f5254,plain,
    ( spl230_315
  <=> ! [X0: 'A_iarray$',X3: 'A_iarray$',X2: 'A_iarray$',X1: 'A_iarray$'] :
        ( ( X0 = X2 )
        | ( 'pair$a'(X0,X1) != 'pair$a'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_315])]) ).

tff(f2658,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray$',X0: 'A_iarray$',X1: 'A_iarray$'] :
      ( ( X0 = X2 )
      | ( 'pair$a'(X0,X1) != 'pair$a'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1011]) ).

tff(f5252,plain,
    spl230_314,
    inference(avatar_split_clause,[],[f2657,f5250]) ).

tff(f5250,plain,
    ( spl230_314
  <=> ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] :
        ( ( X1 = X3 )
        | ( 'pair$'(X0,X1) != 'pair$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_314])]) ).

tff(f2657,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( ( X1 = X3 )
      | ( 'pair$'(X0,X1) != 'pair$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1010]) ).

tff(f1010,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] :
      ( ( ( X1 = X3 )
        & ( X0 = X2 ) )
      | ( 'pair$'(X0,X1) != 'pair$'(X2,X3) ) ),
    inference(ennf_transformation,[],[f757]) ).

tff(f757,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] :
      ~ ( ~ ( ( X1 = X3 )
            & ( X0 = X2 ) )
        & ( 'pair$'(X0,X1) = 'pair$'(X2,X3) ) ),
    inference(true_and_false_elimination,[],[f242]) ).

tff(f242,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] :
      ( ( ( ( ( X1 = X3 )
            & ( X0 = X2 ) )
         => $false )
        & ( 'pair$'(X0,X1) = 'pair$'(X2,X3) ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom240) ).

tff(f5248,plain,
    spl230_313,
    inference(avatar_split_clause,[],[f2656,f5246]) ).

tff(f5246,plain,
    ( spl230_313
  <=> ! [X0: 'A_iarray_iarray$',X3: 'A_iarray_iarray$',X2: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
        ( ( X0 = X2 )
        | ( 'pair$'(X0,X1) != 'pair$'(X2,X3) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_313])]) ).

tff(f2656,plain,
    ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( ( X0 = X2 )
      | ( 'pair$'(X0,X1) != 'pair$'(X2,X3) ) ),
    inference(cnf_transformation,[],[f1010]) ).

tff(f5244,plain,
    spl230_312,
    inference(avatar_split_clause,[],[f2589,f5242]) ).

tff(f5242,plain,
    ( spl230_312
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X0,X1),$sum(X0,X2))
        | ~ $less(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_312])]) ).

tff(f2589,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less($sum(X0,X1),$sum(X0,X2))
      | ~ $less(X1,X2) ),
    inference(cnf_transformation,[],[f1600]) ).

tff(f1600,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $less($sum(X0,X1),$sum(X0,X2))
        | ~ $less(X1,X2) )
      & ( $less(X1,X2)
        | ~ $less($sum(X0,X1),$sum(X0,X2)) ) ),
    inference(nnf_transformation,[],[f609]) ).

tff(f609,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less($sum(X0,X1),$sum(X0,X2))
    <=> $less(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom607) ).

tff(f5240,plain,
    spl230_311,
    inference(avatar_split_clause,[],[f2588,f5238]) ).

tff(f5238,plain,
    ( spl230_311
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X2)
        | ~ $less($sum(X0,X1),$sum(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_311])]) ).

tff(f2588,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,X2)
      | ~ $less($sum(X0,X1),$sum(X0,X2)) ),
    inference(cnf_transformation,[],[f1600]) ).

tff(f5236,plain,
    spl230_310,
    inference(avatar_split_clause,[],[f2586,f5234]) ).

tff(f5234,plain,
    ( spl230_310
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X0,X2)
        | ~ $less($sum(X0,X1),$sum(X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_310])]) ).

tff(f2586,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X0,X2)
      | ~ $less($sum(X0,X1),$sum(X2,X1)) ),
    inference(cnf_transformation,[],[f1599]) ).

tff(f1599,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $less($sum(X0,X1),$sum(X2,X1))
        | ~ $less(X0,X2) )
      & ( $less(X0,X2)
        | ~ $less($sum(X0,X1),$sum(X2,X1)) ) ),
    inference(nnf_transformation,[],[f610]) ).

tff(f610,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less($sum(X0,X1),$sum(X2,X1))
    <=> $less(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom608) ).

tff(f5232,plain,
    spl230_309,
    inference(avatar_split_clause,[],[f2534,f5230]) ).

tff(f5230,plain,
    ( spl230_309
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_set$',X1: 'A_iarray$'] :
        ( 'fun_app$b'('uus$'(X0,X1),X2)
        | ~ 'member$b'('cons$'(X1,X2),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_309])]) ).

tff(f2534,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_set$',X1: 'A_iarray$'] :
      ( 'fun_app$b'('uus$'(X0,X1),X2)
      | ~ 'member$b'('cons$'(X1,X2),X0) ),
    inference(cnf_transformation,[],[f1571]) ).

tff(f1571,plain,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray$',X2: 'A_iarray_list$'] :
      ( ( 'fun_app$b'('uus$'(X0,X1),X2)
        | ~ 'member$b'('cons$'(X1,X2),X0) )
      & ( 'member$b'('cons$'(X1,X2),X0)
        | ~ 'fun_app$b'('uus$'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f15]) ).

tff(f15,axiom,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray$',X2: 'A_iarray_list$'] :
      ( 'fun_app$b'('uus$'(X0,X1),X2)
    <=> 'member$b'('cons$'(X1,X2),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom14) ).

tff(f5228,plain,
    spl230_308,
    inference(avatar_split_clause,[],[f2533,f5226]) ).

tff(f5226,plain,
    ( spl230_308
  <=> ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_set$',X1: 'A_iarray$'] :
        ( 'member$b'('cons$'(X1,X2),X0)
        | ~ 'fun_app$b'('uus$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_308])]) ).

tff(f2533,plain,
    ! [X2: 'A_iarray_list$',X0: 'A_iarray_list_set$',X1: 'A_iarray$'] :
      ( 'member$b'('cons$'(X1,X2),X0)
      | ~ 'fun_app$b'('uus$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1571]) ).

tff(f5224,plain,
    spl230_307,
    inference(avatar_split_clause,[],[f2526,f5222]) ).

tff(f5222,plain,
    ( spl230_307
  <=> ! [X2: 'A_iarray_iarray$',X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$f'('uue$'(X0,X1),X2)
        | ~ 'fun_app$n'(X0,def_1(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_307])]) ).

tff(f2526,plain,
    ! [X2: 'A_iarray_iarray$',X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$f'('uue$'(X0,X1),X2)
      | ~ 'fun_app$n'(X0,def_1(X1,X2)) ),
    inference(cnf_transformation,[],[f1566]) ).

tff(f1566,plain,
    ! [X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray$'] :
      ( ( 'fun_app$f'('uue$'(X0,X1),X2)
        | ~ 'fun_app$n'(X0,def_1(X1,X2)) )
      & ( 'fun_app$n'(X0,def_1(X1,X2))
        | ~ 'fun_app$f'('uue$'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f18]) ).

tff(f18,axiom,
    ! [X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('uue$'(X0,X1),X2)
    <=> 'fun_app$n'(X0,def_1(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).

tff(f5218,plain,
    spl230_306,
    inference(avatar_split_clause,[],[f2525,f5216]) ).

tff(f5216,plain,
    ( spl230_306
  <=> ! [X2: 'A_iarray_iarray$',X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$n'(X0,def_1(X1,X2))
        | ~ 'fun_app$f'('uue$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_306])]) ).

tff(f2525,plain,
    ! [X2: 'A_iarray_iarray$',X0: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X0,def_1(X1,X2))
      | ~ 'fun_app$f'('uue$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1566]) ).

tff(f5214,plain,
    spl230_305,
    inference(avatar_split_clause,[],[f2412,f5212]) ).

tff(f5212,plain,
    ( spl230_305
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ( X1 = X2 )
        | ( $sum(X0,X2) != $sum(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_305])]) ).

tff(f2412,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ( X1 = X2 )
      | ( $sum(X0,X2) != $sum(X0,X1) ) ),
    inference(cnf_transformation,[],[f905]) ).

tff(f905,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( X1 = X2 )
      | ( $sum(X0,X2) != $sum(X0,X1) ) ),
    inference(ennf_transformation,[],[f157]) ).

tff(f157,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $sum(X0,X2) = $sum(X0,X1) )
     => ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom155) ).

tff(f5210,plain,
    spl230_304,
    inference(avatar_split_clause,[],[f2411,f5208]) ).

tff(f5208,plain,
    ( spl230_304
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ( X0 = X2 )
        | ( $sum(X0,X1) != $sum(X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_304])]) ).

tff(f2411,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ( X0 = X2 )
      | ( $sum(X0,X1) != $sum(X2,X1) ) ),
    inference(cnf_transformation,[],[f904]) ).

tff(f904,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( X0 = X2 )
      | ( $sum(X0,X1) != $sum(X2,X1) ) ),
    inference(ennf_transformation,[],[f160]) ).

tff(f160,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $sum(X0,X1) = $sum(X2,X1) )
     => ( X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom158) ).

tff(f5206,plain,
    spl230_303,
    inference(avatar_split_clause,[],[f2410,f5204]) ).

tff(f5204,plain,
    ( spl230_303
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( X1 = X2 )
        | ( 'plus$a'(X0,X2) != 'plus$a'(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_303])]) ).

tff(f2410,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( X1 = X2 )
      | ( 'plus$a'(X0,X2) != 'plus$a'(X0,X1) ) ),
    inference(cnf_transformation,[],[f903]) ).

tff(f903,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] :
      ( ( X1 = X2 )
      | ( 'plus$a'(X0,X2) != 'plus$a'(X0,X1) ) ),
    inference(ennf_transformation,[],[f155]) ).

tff(f155,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] :
      ( ( 'plus$a'(X0,X2) = 'plus$a'(X0,X1) )
     => ( X1 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom153) ).

tff(f5202,plain,
    spl230_302,
    inference(avatar_split_clause,[],[f2409,f5200]) ).

tff(f5200,plain,
    ( spl230_302
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( X0 = X2 )
        | ( 'plus$a'(X0,X1) != 'plus$a'(X2,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_302])]) ).

tff(f2409,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( X0 = X2 )
      | ( 'plus$a'(X0,X1) != 'plus$a'(X2,X1) ) ),
    inference(cnf_transformation,[],[f902]) ).

tff(f902,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] :
      ( ( X0 = X2 )
      | ( 'plus$a'(X0,X1) != 'plus$a'(X2,X1) ) ),
    inference(ennf_transformation,[],[f158]) ).

tff(f158,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$',X2: 'A_n_vec_n_vec$'] :
      ( ( 'plus$a'(X0,X1) = 'plus$a'(X2,X1) )
     => ( X0 = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom156) ).

tff(f5198,plain,
    spl230_301,
    inference(avatar_split_clause,[],[f2228,f5196]) ).

tff(f5196,plain,
    ( spl230_301
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('invertible$',sK108(X0,X1))
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_301])]) ).

tff(f2228,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',sK108(X0,X1))
      | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ),
    inference(cnf_transformation,[],[f1380]) ).

tff(f5194,plain,
    spl230_300,
    inference(avatar_split_clause,[],[f2227,f5192]) ).

tff(f5192,plain,
    ( spl230_300
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('invertible$',sK107(X0,X1))
        | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_300])]) ).

tff(f2227,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',sK107(X0,X1))
      | ~ 'fun_app$o'('fun_app$ah'('equivalent_matrices$',X0),X1) ),
    inference(cnf_transformation,[],[f1380]) ).

tff(f5190,plain,
    spl230_299,
    inference(avatar_split_clause,[],[f2224,f5188]) ).

tff(f5188,plain,
    ( spl230_299
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('invertible$',sK106(X0,X1))
        | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_299])]) ).

tff(f2224,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',sK106(X0,X1))
      | ~ 'fun_app$o'('fun_app$ah'('similar_matrices$',X0),X1) ),
    inference(cnf_transformation,[],[f1376]) ).

tff(f5186,plain,
    spl230_298,
    inference(avatar_split_clause,[],[f2114,f5184]) ).

tff(f5184,plain,
    ( spl230_298
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
        ( 'fun_app$a'(X0,X1)
        | ~ 'fun_app$a'(X0,'pair$b'(sK94(X0),sK95(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_298])]) ).

tff(f2114,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'fun_app$a'(X0,X1)
      | ~ 'fun_app$a'(X0,'pair$b'(sK94(X0),sK95(X0))) ),
    inference(cnf_transformation,[],[f1286]) ).

tff(f1286,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'fun_app$a'(X0,X1)
      | ~ 'fun_app$a'(X0,'pair$b'(sK94(X0),sK95(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f876,f1285]) ).

tff(f1285,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
      ( ? [X2: 'A_iarray_list$',X3: 'A_iarray_list$'] : ~ 'fun_app$a'(X0,'pair$b'(X2,X3))
     => ~ 'fun_app$a'(X0,'pair$b'(sK94(X0),sK95(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f876,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'fun_app$a'(X0,X1)
      | ? [X2: 'A_iarray_list$',X3: 'A_iarray_list$'] : ~ 'fun_app$a'(X0,'pair$b'(X2,X3)) ),
    inference(ennf_transformation,[],[f239]) ).

tff(f239,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_bool_fun$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ! [X2: 'A_iarray_list$',X3: 'A_iarray_list$'] : 'fun_app$a'(X0,'pair$b'(X2,X3))
     => 'fun_app$a'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom237) ).

tff(f5182,plain,
    spl230_297,
    inference(avatar_split_clause,[],[f2113,f5180]) ).

tff(f5180,plain,
    ( spl230_297
  <=> ! [X0: 'Int_int_prod_bool_fun$',X1: 'Int_int_prod$'] :
        ( 'fun_app$ae'(X0,X1)
        | ~ 'fun_app$ae'(X0,'pair$c'(sK92(X0),sK93(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_297])]) ).

tff(f2113,plain,
    ! [X0: 'Int_int_prod_bool_fun$',X1: 'Int_int_prod$'] :
      ( 'fun_app$ae'(X0,X1)
      | ~ 'fun_app$ae'(X0,'pair$c'(sK92(X0),sK93(X0))) ),
    inference(cnf_transformation,[],[f1284]) ).

tff(f1284,plain,
    ! [X0: 'Int_int_prod_bool_fun$',X1: 'Int_int_prod$'] :
      ( 'fun_app$ae'(X0,X1)
      | ~ 'fun_app$ae'(X0,'pair$c'(sK92(X0),sK93(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93])],[f875,f1283]) ).

tff(f1283,plain,
    ! [X0: 'Int_int_prod_bool_fun$'] :
      ( ? [X2: $int,X3: $int] : ~ 'fun_app$ae'(X0,'pair$c'(X2,X3))
     => ~ 'fun_app$ae'(X0,'pair$c'(sK92(X0),sK93(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f875,plain,
    ! [X0: 'Int_int_prod_bool_fun$',X1: 'Int_int_prod$'] :
      ( 'fun_app$ae'(X0,X1)
      | ? [X2: $int,X3: $int] : ~ 'fun_app$ae'(X0,'pair$c'(X2,X3)) ),
    inference(ennf_transformation,[],[f237]) ).

tff(f237,axiom,
    ! [X0: 'Int_int_prod_bool_fun$',X1: 'Int_int_prod$'] :
      ( ! [X2: $int,X3: $int] : 'fun_app$ae'(X0,'pair$c'(X2,X3))
     => 'fun_app$ae'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom235) ).

tff(f5176,plain,
    spl230_296,
    inference(avatar_split_clause,[],[f2112,f5174]) ).

tff(f5174,plain,
    ( spl230_296
  <=> ! [X0: 'A_iarray_a_iarray_prod_bool_fun$',X1: 'A_iarray_a_iarray_prod$'] :
        ( 'fun_app$ag'(X0,X1)
        | ~ 'fun_app$ag'(X0,'pair$a'(sK90(X0),sK91(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_296])]) ).

tff(f2112,plain,
    ! [X0: 'A_iarray_a_iarray_prod_bool_fun$',X1: 'A_iarray_a_iarray_prod$'] :
      ( 'fun_app$ag'(X0,X1)
      | ~ 'fun_app$ag'(X0,'pair$a'(sK90(X0),sK91(X0))) ),
    inference(cnf_transformation,[],[f1282]) ).

tff(f1282,plain,
    ! [X0: 'A_iarray_a_iarray_prod_bool_fun$',X1: 'A_iarray_a_iarray_prod$'] :
      ( 'fun_app$ag'(X0,X1)
      | ~ 'fun_app$ag'(X0,'pair$a'(sK90(X0),sK91(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK90,sK91])],[f874,f1281]) ).

tff(f1281,plain,
    ! [X0: 'A_iarray_a_iarray_prod_bool_fun$'] :
      ( ? [X2: 'A_iarray$',X3: 'A_iarray$'] : ~ 'fun_app$ag'(X0,'pair$a'(X2,X3))
     => ~ 'fun_app$ag'(X0,'pair$a'(sK90(X0),sK91(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f874,plain,
    ! [X0: 'A_iarray_a_iarray_prod_bool_fun$',X1: 'A_iarray_a_iarray_prod$'] :
      ( 'fun_app$ag'(X0,X1)
      | ? [X2: 'A_iarray$',X3: 'A_iarray$'] : ~ 'fun_app$ag'(X0,'pair$a'(X2,X3)) ),
    inference(ennf_transformation,[],[f240]) ).

tff(f240,axiom,
    ! [X0: 'A_iarray_a_iarray_prod_bool_fun$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ! [X2: 'A_iarray$',X3: 'A_iarray$'] : 'fun_app$ag'(X0,'pair$a'(X2,X3))
     => 'fun_app$ag'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom238) ).

tff(f5172,plain,
    spl230_295,
    inference(avatar_split_clause,[],[f2111,f5170]) ).

tff(f5170,plain,
    ( spl230_295
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
        ( 'fun_app$af'(X0,X1)
        | ~ 'fun_app$af'(X0,'pair$'(sK88(X0),sK89(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_295])]) ).

tff(f2111,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( 'fun_app$af'(X0,X1)
      | ~ 'fun_app$af'(X0,'pair$'(sK88(X0),sK89(X0))) ),
    inference(cnf_transformation,[],[f1280]) ).

tff(f1280,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( 'fun_app$af'(X0,X1)
      | ~ 'fun_app$af'(X0,'pair$'(sK88(X0),sK89(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK88,sK89])],[f873,f1279]) ).

tff(f1279,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$'] :
      ( ? [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] : ~ 'fun_app$af'(X0,'pair$'(X2,X3))
     => ~ 'fun_app$af'(X0,'pair$'(sK88(X0),sK89(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f873,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( 'fun_app$af'(X0,X1)
      | ? [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] : ~ 'fun_app$af'(X0,'pair$'(X2,X3)) ),
    inference(ennf_transformation,[],[f238]) ).

tff(f238,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$',X1: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ! [X2: 'A_iarray_iarray$',X3: 'A_iarray_iarray$'] : 'fun_app$af'(X0,'pair$'(X2,X3))
     => 'fun_app$af'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom236) ).

tff(f5168,plain,
    spl230_294,
    inference(avatar_split_clause,[],[f2003,f5166]) ).

tff(f5166,plain,
    ( spl230_294
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] : ( 'set$'('fun_app$p'('filter$'(X0),X1)) = 'collect$d'('uuu$'(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_294])]) ).

tff(f2003,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] : ( 'set$'('fun_app$p'('filter$'(X0),X1)) = 'collect$d'('uuu$'(X0,X1)) ),
    inference(cnf_transformation,[],[f595]) ).

tff(f595,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] : ( 'set$'('fun_app$p'('filter$'(X0),X1)) = 'collect$d'('uuu$'(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom593) ).

tff(f5164,plain,
    spl230_293,
    inference(avatar_split_clause,[],[f2002,f5162]) ).

tff(f5162,plain,
    ( spl230_293
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('plus$a'(X0,X1)) = 'plus$d'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_293])]) ).

tff(f2002,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('plus$a'(X0,X1)) = 'plus$d'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ),
    inference(cnf_transformation,[],[f123]) ).

tff(f123,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('plus$a'(X0,X1)) = 'plus$d'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom121) ).

tff(f5160,plain,
    spl230_292,
    inference(avatar_split_clause,[],[f2001,f5158]) ).

tff(f5158,plain,
    ( spl230_292
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_292])]) ).

tff(f2001,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ),
    inference(cnf_transformation,[],[f274]) ).

tff(f274,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult_iarray$'('matrix_to_iarray$'(X0),'matrix_to_iarray$'(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom272) ).

tff(f5156,plain,
    spl230_291,
    inference(avatar_split_clause,[],[f2000,f5154]) ).

tff(f5154,plain,
    ( spl230_291
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'vec_to_iarray$'('plus$a'(X0,X1)) = 'plus$x'('vec_to_iarray$'(X0),'vec_to_iarray$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_291])]) ).

tff(f2000,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'vec_to_iarray$'('plus$a'(X0,X1)) = 'plus$x'('vec_to_iarray$'(X0),'vec_to_iarray$'(X1)) ),
    inference(cnf_transformation,[],[f365]) ).

tff(f365,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'vec_to_iarray$'('plus$a'(X0,X1)) = 'plus$x'('vec_to_iarray$'(X0),'vec_to_iarray$'(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom363) ).

tff(f5152,plain,
    spl230_290,
    inference(avatar_split_clause,[],[f1968,f5150]) ).

tff(f1968,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK59(X0))) ),
    inference(cnf_transformation,[],[f1229]) ).

tff(f1229,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK59(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f48,f1228]) ).

tff(f1228,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X0) )
     => ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$m'('size$',sK59(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f48,axiom,
    ! [X0: 'Nat$'] :
    ? [X1: 'A_iarray_list$'] : ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X1)) = 'fun_app$l'('of_nat$',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).

tff(f5148,plain,
    spl230_289,
    inference(avatar_split_clause,[],[f1967,f5146]) ).

tff(f1967,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK58(X0))) ),
    inference(cnf_transformation,[],[f1227]) ).

tff(f1227,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK58(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f46,f1226]) ).

tff(f1226,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X0) )
     => ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$u'('size$a',sK58(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f46,axiom,
    ! [X0: 'Nat$'] :
    ? [X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$l'('of_nat$','fun_app$u'('size$a',X1)) = 'fun_app$l'('of_nat$',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom44) ).

tff(f5144,plain,
    spl230_288,
    inference(avatar_split_clause,[],[f1966,f5142]) ).

tff(f1966,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK57(X0))) ),
    inference(cnf_transformation,[],[f1225]) ).

tff(f1225,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK57(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f47,f1224]) ).

tff(f1224,plain,
    ! [X0: 'Nat$'] :
      ( ? [X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X0) )
     => ( 'fun_app$l'('of_nat$',X0) = 'fun_app$l'('of_nat$','fun_app$v'('size$b',sK57(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f47,axiom,
    ! [X0: 'Nat$'] :
    ? [X1: 'A_iarray_list_list$'] : ( 'fun_app$l'('of_nat$','fun_app$v'('size$b',X1)) = 'fun_app$l'('of_nat$',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom45) ).

tff(f5140,plain,
    spl230_287,
    inference(avatar_split_clause,[],[f1947,f5138]) ).

tff(f5138,plain,
    ( spl230_287
  <=> ! [X0: 'A_iarray_list$'] :
        ( $less(0,'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))
        | ( 'nil$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_287])]) ).

tff(f1947,plain,
    ! [X0: 'A_iarray_list$'] :
      ( $less(0,'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))
      | ( 'nil$' = X0 ) ),
    inference(cnf_transformation,[],[f1190]) ).

tff(f1190,plain,
    ! [X0: 'A_iarray_list$'] :
      ( ( $less(0,'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))
        | ( 'nil$' = X0 ) )
      & ( ( 'nil$' != X0 )
        | ~ $less(0,'fun_app$l'('of_nat$','fun_app$m'('size$',X0))) ) ),
    inference(nnf_transformation,[],[f627]) ).

tff(f627,axiom,
    ! [X0: 'A_iarray_list$'] :
      ( $less(0,'fun_app$l'('of_nat$','fun_app$m'('size$',X0)))
    <=> ( 'nil$' != X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom625) ).

tff(f5132,plain,
    spl230_286,
    inference(avatar_split_clause,[],[f1944,f5130]) ).

tff(f5130,plain,
    ( spl230_286
  <=> ! [X0: 'A_iarray_list$'] :
        ( ( 'nil$' = X0 )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_286])]) ).

tff(f1944,plain,
    ! [X0: 'A_iarray_list$'] :
      ( ( 'nil$' = X0 )
      | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 0 ) ),
    inference(cnf_transformation,[],[f1189]) ).

tff(f1189,plain,
    ! [X0: 'A_iarray_list$'] :
      ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 0 )
        | ( 'nil$' != X0 ) )
      & ( ( 'nil$' = X0 )
        | ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) != 0 ) ) ),
    inference(nnf_transformation,[],[f580]) ).

tff(f580,axiom,
    ! [X0: 'A_iarray_list$'] :
      ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',X0)) = 0 )
    <=> ( 'nil$' = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom578) ).

tff(f5128,plain,
    spl230_285,
    inference(avatar_split_clause,[],[f1929,f5126]) ).

tff(f5126,plain,
    ( spl230_285
  <=> ! [X0: 'Nat$'] :
        ( $less(0,'fun_app$l'('of_nat$',X0))
        | ( 'fun_app$l'('of_nat$',X0) = 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_285])]) ).

tff(f1929,plain,
    ! [X0: 'Nat$'] :
      ( $less(0,'fun_app$l'('of_nat$',X0))
      | ( 'fun_app$l'('of_nat$',X0) = 0 ) ),
    inference(cnf_transformation,[],[f1179]) ).

tff(f1179,plain,
    ! [X0: 'Nat$'] :
      ( ( ( 'fun_app$l'('of_nat$',X0) != 0 )
        | ~ $less(0,'fun_app$l'('of_nat$',X0)) )
      & ( $less(0,'fun_app$l'('of_nat$',X0))
        | ( 'fun_app$l'('of_nat$',X0) = 0 ) ) ),
    inference(nnf_transformation,[],[f613]) ).

tff(f613,axiom,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$l'('of_nat$',X0) != 0 )
    <=> $less(0,'fun_app$l'('of_nat$',X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom611) ).

tff(f5124,plain,
    spl230_284,
    inference(avatar_split_clause,[],[f1874,f5122]) ).

tff(f5122,plain,
    ( spl230_284
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'matrix_inv$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_284])]) ).

tff(f1874,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f795]) ).

tff(f795,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'matrix_inv$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(ennf_transformation,[],[f174]) ).

tff(f174,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
     => ( 'matrix_inv$'(X0) = 'fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom172) ).

tff(f5120,plain,
    spl230_283,
    inference(avatar_split_clause,[],[f1861,f5118]) ).

tff(f5118,plain,
    ( spl230_283
  <=> ! [X0: $int] :
        ( ( 0 = 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) )
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_283])]) ).

tff(f1861,plain,
    ! [X0: $int] :
      ( ( 0 = 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) )
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f786]) ).

tff(f786,plain,
    ! [X0: $int] :
      ( ( ( 0 = 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) )
        | ~ $less(X0,0) )
      & ( ( 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) = X0 )
        | $less(X0,0) ) ),
    inference(ennf_transformation,[],[f663]) ).

tff(f663,plain,
    ! [X0: $int] :
      ( ( $less(X0,0)
       => ( 0 = 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) ) )
      & ( ~ $less(X0,0)
       => ( 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) = X0 ) ) ),
    inference(theory_normalization,[],[f652]) ).

tff(f652,axiom,
    ! [X0: $int] :
      ( ( ~ $lesseq(0,X0)
       => ( 0 = 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) ) )
      & ( $lesseq(0,X0)
       => ( 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom650) ).

tff(f5116,plain,
    spl230_282,
    inference(avatar_split_clause,[],[f1860,f5114]) ).

tff(f5114,plain,
    ( spl230_282
  <=> ! [X0: $int] :
        ( ( 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) = X0 )
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_282])]) ).

tff(f1860,plain,
    ! [X0: $int] :
      ( ( 'fun_app$l'('of_nat$','fun_app$k'('nat$',X0)) = X0 )
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f786]) ).

tff(f5112,plain,
    spl230_281,
    inference(avatar_split_clause,[],[f1858,f5110]) ).

tff(f5110,plain,
    ( spl230_281
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'matrix_to_iarray_option$'(X0) = 'some$'('matrix_to_iarray$'('the$'(X0))) )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_281])]) ).

tff(f1858,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'matrix_to_iarray_option$'(X0) = 'some$'('matrix_to_iarray$'('the$'(X0))) )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f785]) ).

tff(f785,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$' = 'matrix_to_iarray_option$'(X0) )
        | ( 'none$a' != X0 ) )
      & ( ( 'matrix_to_iarray_option$'(X0) = 'some$'('matrix_to_iarray$'('the$'(X0))) )
        | ( 'none$a' = X0 ) ) ),
    inference(ennf_transformation,[],[f58]) ).

tff(f58,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' = X0 )
       => ( 'none$' = 'matrix_to_iarray_option$'(X0) ) )
      & ( ( 'none$a' != X0 )
       => ( 'matrix_to_iarray_option$'(X0) = 'some$'('matrix_to_iarray$'('the$'(X0))) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom56) ).

tff(f5108,plain,
    spl230_280,
    inference(avatar_split_clause,[],[f672,f5106]) ).

tff(f5106,plain,
    ( spl230_280
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_280])]) ).

tff(f672,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f5104,plain,
    spl230_279,
    inference(avatar_split_clause,[],[f667,f5102]) ).

tff(f5102,plain,
    ( spl230_279
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_279])]) ).

tff(f667,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f5079,plain,
    ( spl230_278
    | ~ spl230_148
    | ~ spl230_270 ),
    inference(avatar_split_clause,[],[f4916,f4913,f4194,f5077]) ).

tff(f5077,plain,
    ( spl230_278
  <=> ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK99(sK39(X1),X1),sK39(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_278])]) ).

tff(f4913,plain,
    ( spl230_270
  <=> ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK99('snd$e'(X1),X1),'snd$e'(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_270])]) ).

tff(f4916,plain,
    ( ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK99(sK39(X1),X1),sK39(X1)) = X1 )
    | ~ spl230_148
    | ~ spl230_270 ),
    inference(forward_demodulation,[],[f4914,f4195]) ).

tff(f4914,plain,
    ( ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK99('snd$e'(X1),X1),'snd$e'(X1)) = X1 )
    | ~ spl230_270 ),
    inference(avatar_component_clause,[],[f4913]) ).

tff(f5075,plain,
    ( spl230_277
    | ~ spl230_150
    | ~ spl230_269 ),
    inference(avatar_split_clause,[],[f4911,f4908,f4223,f5073]) ).

tff(f5073,plain,
    ( spl230_277
  <=> ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK98(sK43(X1),X1),sK43(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_277])]) ).

tff(f4908,plain,
    ( spl230_269
  <=> ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK98('snd$k'(X1),X1),'snd$k'(X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_269])]) ).

tff(f4911,plain,
    ( ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK98(sK43(X1),X1),sK43(X1)) = X1 )
    | ~ spl230_150
    | ~ spl230_269 ),
    inference(forward_demodulation,[],[f4909,f4224]) ).

tff(f4909,plain,
    ( ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK98('snd$k'(X1),X1),'snd$k'(X1)) = X1 )
    | ~ spl230_269 ),
    inference(avatar_component_clause,[],[f4908]) ).

tff(f5071,plain,
    ( spl230_276
    | ~ spl230_149
    | ~ spl230_268 ),
    inference(avatar_split_clause,[],[f4906,f4903,f4210,f5069]) ).

tff(f5069,plain,
    ( spl230_276
  <=> ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X1),sK97(sK38(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_276])]) ).

tff(f4903,plain,
    ( spl230_268
  <=> ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X1),sK97('fst$e'(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_268])]) ).

tff(f4906,plain,
    ( ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X1),sK97(sK38(X1),X1)) = X1 )
    | ~ spl230_149
    | ~ spl230_268 ),
    inference(forward_demodulation,[],[f4904,f4211]) ).

tff(f4904,plain,
    ( ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X1),sK97('fst$e'(X1),X1)) = X1 )
    | ~ spl230_268 ),
    inference(avatar_component_clause,[],[f4903]) ).

tff(f5067,plain,
    ( spl230_275
    | ~ spl230_151
    | ~ spl230_267 ),
    inference(avatar_split_clause,[],[f4901,f4898,f4235,f5065]) ).

tff(f5065,plain,
    ( spl230_275
  <=> ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X1),sK96(sK42(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_275])]) ).

tff(f4898,plain,
    ( spl230_267
  <=> ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X1),sK96('fst$k'(X1),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_267])]) ).

tff(f4901,plain,
    ( ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X1),sK96(sK42(X1),X1)) = X1 )
    | ~ spl230_151
    | ~ spl230_267 ),
    inference(forward_demodulation,[],[f4899,f4236]) ).

tff(f4899,plain,
    ( ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X1),sK96('fst$k'(X1),X1)) = X1 )
    | ~ spl230_267 ),
    inference(avatar_component_clause,[],[f4898]) ).

tff(f5048,plain,
    ( ~ spl230_274
    | spl230_53
    | ~ spl230_259 ),
    inference(avatar_split_clause,[],[f5023,f4866,f3728,f5045]) ).

tff(f5045,plain,
    ( spl230_274
  <=> sP14('none$','uug$',tlfalse) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_274])]) ).

tff(f3728,plain,
    ( spl230_53
  <=> 'fun_app$t'('case_option$a'(tlfalse,'uug$'),'none$') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_53])]) ).

tff(f4866,plain,
    ( spl230_259
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ~ sP14(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_259])]) ).

tff(f5023,plain,
    ( ~ sP14('none$','uug$',tlfalse)
    | spl230_53
    | ~ spl230_259 ),
    inference(resolution,[],[f4867,f3730]) ).

tff(f3730,plain,
    ( ~ 'fun_app$t'('case_option$a'(tlfalse,'uug$'),'none$')
    | spl230_53 ),
    inference(avatar_component_clause,[],[f3728]) ).

tff(f4867,plain,
    ( ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ~ sP14(X2,X1,X0) )
    | ~ spl230_259 ),
    inference(avatar_component_clause,[],[f4866]) ).

tff(f4930,plain,
    spl230_273,
    inference(avatar_split_clause,[],[f3341,f4928]) ).

tff(f4928,plain,
    ( spl230_273
  <=> ! [X0: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,'fun_app$l'('of_nat$',X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_273])]) ).

tff(f3341,plain,
    ! [X0: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum(1,'fun_app$l'('of_nat$',X0))),
    inference(forward_demodulation,[],[f1845,f664]) ).

tff(f1845,plain,
    ! [X0: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum('fun_app$l'('of_nat$',X0),1)),
    inference(cnf_transformation,[],[f616]) ).

tff(f616,axiom,
    ! [X0: 'Nat$'] : $less('fun_app$l'('of_nat$',X0),$sum('fun_app$l'('of_nat$',X0),1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom614) ).

tff(f4926,plain,
    ( spl230_272
    | ~ spl230_94
    | ~ spl230_104
    | ~ spl230_115 ),
    inference(avatar_split_clause,[],[f4204,f4004,f3960,f3920,f4924]) ).

tff(f4924,plain,
    ( spl230_272
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( sK36(X0) = sK62(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_272])]) ).

tff(f3960,plain,
    ( spl230_104
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK62(X0),sK63(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_104])]) ).

tff(f4204,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( sK36(X0) = sK62(X0) )
    | ~ spl230_94
    | ~ spl230_104
    | ~ spl230_115 ),
    inference(forward_demodulation,[],[f4203,f4202]) ).

tff(f4203,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('fst$',X0) = sK62(X0) )
    | ~ spl230_104
    | ~ spl230_115 ),
    inference(superposition,[],[f4005,f3961]) ).

tff(f3961,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK62(X0),sK63(X0)) = X0 )
    | ~ spl230_104 ),
    inference(avatar_component_clause,[],[f3960]) ).

tff(f4920,plain,
    spl230_271,
    inference(avatar_split_clause,[],[f3319,f4918]) ).

tff(f4918,plain,
    ( spl230_271
  <=> ! [X0: 'Int_int_prod$'] : ( 'pair$c'('fun_app$ac'('fst$b',X0),'fun_app$ac'('snd$b',X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_271])]) ).

tff(f3319,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'('fun_app$ac'('fst$b',X0),'fun_app$ac'('snd$b',X0)) = X0 ),
    inference(evaluation,[],[f3318]) ).

tff(f3318,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),0),'fun_app$ac'('snd$b',X0)) = X0 ),
    inference(forward_demodulation,[],[f3317,f1759]) ).

tff(f1759,plain,
    0 = 'fun_app$ac'('fst$b','zero$a'),
    inference(cnf_transformation,[],[f390]) ).

tff(f390,axiom,
    0 = 'fun_app$ac'('fst$b','zero$a'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom388) ).

tff(f3317,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b','zero$a')),'fun_app$ac'('snd$b',X0)) = X0 ),
    inference(evaluation,[],[f3316]) ).

tff(f3316,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b','zero$a')),$sum('fun_app$ac'('snd$b',X0),0)) = X0 ),
    inference(forward_demodulation,[],[f2926,f1760]) ).

tff(f1760,plain,
    0 = 'fun_app$ac'('snd$b','zero$a'),
    inference(cnf_transformation,[],[f388]) ).

tff(f388,axiom,
    0 = 'fun_app$ac'('snd$b','zero$a'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom386) ).

tff(f2926,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'($sum('fun_app$ac'('fst$b',X0),'fun_app$ac'('fst$b','zero$a')),$sum('fun_app$ac'('snd$b',X0),'fun_app$ac'('snd$b','zero$a'))) = X0 ),
    inference(definition_unfolding,[],[f1786,f2036]) ).

tff(f1786,plain,
    ! [X0: 'Int_int_prod$'] : ( 'plus$b'(X0,'zero$a') = X0 ),
    inference(cnf_transformation,[],[f412]) ).

tff(f412,axiom,
    ! [X0: 'Int_int_prod$'] : ( 'plus$b'(X0,'zero$a') = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom410) ).

tff(f4915,plain,
    spl230_270,
    inference(avatar_split_clause,[],[f3052,f4913]) ).

tff(f3052,plain,
    ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK99('snd$e'(X1),X1),'snd$e'(X1)) = X1 ),
    inference(equality_resolution,[],[f2132]) ).

tff(f2132,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( 'pair$a'(sK99(X0,X1),X0) = X1 )
      | ( 'snd$e'(X1) != X0 ) ),
    inference(cnf_transformation,[],[f1309]) ).

tff(f1309,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'snd$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X2,X0) != X1 ) )
      & ( ( 'pair$a'(sK99(X0,X1),X0) = X1 )
        | ( 'snd$e'(X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK99])],[f1307,f1308]) ).

tff(f1308,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ? [X3: 'A_iarray$'] : ( 'pair$a'(X3,X0) = X1 )
     => ( 'pair$a'(sK99(X0,X1),X0) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1307,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'snd$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X2,X0) != X1 ) )
      & ( ? [X3: 'A_iarray$'] : ( 'pair$a'(X3,X0) = X1 )
        | ( 'snd$e'(X1) != X0 ) ) ),
    inference(rectify,[],[f1306]) ).

tff(f1306,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'snd$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X2,X0) != X1 ) )
      & ( ? [X2: 'A_iarray$'] : ( 'pair$a'(X2,X0) = X1 )
        | ( 'snd$e'(X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f306]) ).

tff(f306,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( 'snd$e'(X1) = X0 )
    <=> ? [X2: 'A_iarray$'] : ( 'pair$a'(X2,X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom304) ).

tff(f4910,plain,
    spl230_269,
    inference(avatar_split_clause,[],[f3050,f4908]) ).

tff(f3050,plain,
    ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK98('snd$k'(X1),X1),'snd$k'(X1)) = X1 ),
    inference(equality_resolution,[],[f2130]) ).

tff(f2130,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( 'pair$b'(sK98(X0,X1),X0) = X1 )
      | ( 'snd$k'(X1) != X0 ) ),
    inference(cnf_transformation,[],[f1305]) ).

tff(f1305,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'snd$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X2,X0) != X1 ) )
      & ( ( 'pair$b'(sK98(X0,X1),X0) = X1 )
        | ( 'snd$k'(X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK98])],[f1303,f1304]) ).

tff(f1304,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ? [X3: 'A_iarray_list$'] : ( 'pair$b'(X3,X0) = X1 )
     => ( 'pair$b'(sK98(X0,X1),X0) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1303,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'snd$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X2,X0) != X1 ) )
      & ( ? [X3: 'A_iarray_list$'] : ( 'pair$b'(X3,X0) = X1 )
        | ( 'snd$k'(X1) != X0 ) ) ),
    inference(rectify,[],[f1302]) ).

tff(f1302,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'snd$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X2,X0) != X1 ) )
      & ( ? [X2: 'A_iarray_list$'] : ( 'pair$b'(X2,X0) = X1 )
        | ( 'snd$k'(X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f305]) ).

tff(f305,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( 'snd$k'(X1) = X0 )
    <=> ? [X2: 'A_iarray_list$'] : ( 'pair$b'(X2,X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom303) ).

tff(f4905,plain,
    spl230_268,
    inference(avatar_split_clause,[],[f3048,f4903]) ).

tff(f3048,plain,
    ! [X1: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X1),sK97('fst$e'(X1),X1)) = X1 ),
    inference(equality_resolution,[],[f2128]) ).

tff(f2128,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( 'pair$a'(X0,sK97(X0,X1)) = X1 )
      | ( 'fst$e'(X1) != X0 ) ),
    inference(cnf_transformation,[],[f1301]) ).

tff(f1301,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'fst$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X0,X2) != X1 ) )
      & ( ( 'pair$a'(X0,sK97(X0,X1)) = X1 )
        | ( 'fst$e'(X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK97])],[f1299,f1300]) ).

tff(f1300,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ? [X3: 'A_iarray$'] : ( 'pair$a'(X0,X3) = X1 )
     => ( 'pair$a'(X0,sK97(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1299,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'fst$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X0,X2) != X1 ) )
      & ( ? [X3: 'A_iarray$'] : ( 'pair$a'(X0,X3) = X1 )
        | ( 'fst$e'(X1) != X0 ) ) ),
    inference(rectify,[],[f1298]) ).

tff(f1298,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( ( 'fst$e'(X1) = X0 )
        | ! [X2: 'A_iarray$'] : ( 'pair$a'(X0,X2) != X1 ) )
      & ( ? [X2: 'A_iarray$'] : ( 'pair$a'(X0,X2) = X1 )
        | ( 'fst$e'(X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f299]) ).

tff(f299,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_a_iarray_prod$'] :
      ( ( 'fst$e'(X1) = X0 )
    <=> ? [X2: 'A_iarray$'] : ( 'pair$a'(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom297) ).

tff(f4900,plain,
    spl230_267,
    inference(avatar_split_clause,[],[f3046,f4898]) ).

tff(f3046,plain,
    ! [X1: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X1),sK96('fst$k'(X1),X1)) = X1 ),
    inference(equality_resolution,[],[f2126]) ).

tff(f2126,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( 'pair$b'(X0,sK96(X0,X1)) = X1 )
      | ( 'fst$k'(X1) != X0 ) ),
    inference(cnf_transformation,[],[f1297]) ).

tff(f1297,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'fst$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X0,X2) != X1 ) )
      & ( ( 'pair$b'(X0,sK96(X0,X1)) = X1 )
        | ( 'fst$k'(X1) != X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK96])],[f1295,f1296]) ).

tff(f1296,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ? [X3: 'A_iarray_list$'] : ( 'pair$b'(X0,X3) = X1 )
     => ( 'pair$b'(X0,sK96(X0,X1)) = X1 ) ),
    introduced(choice_axiom,[]) ).

tff(f1295,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'fst$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X0,X2) != X1 ) )
      & ( ? [X3: 'A_iarray_list$'] : ( 'pair$b'(X0,X3) = X1 )
        | ( 'fst$k'(X1) != X0 ) ) ),
    inference(rectify,[],[f1294]) ).

tff(f1294,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( ( 'fst$k'(X1) = X0 )
        | ! [X2: 'A_iarray_list$'] : ( 'pair$b'(X0,X2) != X1 ) )
      & ( ? [X2: 'A_iarray_list$'] : ( 'pair$b'(X0,X2) = X1 )
        | ( 'fst$k'(X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f298]) ).

tff(f298,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( 'fst$k'(X1) = X0 )
    <=> ? [X2: 'A_iarray_list$'] : ( 'pair$b'(X0,X2) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom296) ).

tff(f4896,plain,
    spl230_266,
    inference(avatar_split_clause,[],[f2947,f4894]) ).

tff(f4894,plain,
    ( spl230_266
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK61(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_266])]) ).

tff(f2947,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK61(X0),X0) ),
    inference(definition_unfolding,[],[f1972,f1818]) ).

tff(f1972,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK61(X0),X0) ),
    inference(cnf_transformation,[],[f1233]) ).

tff(f1233,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0))
      & ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK61(X0),X0) )
      & 'fun_app$o'('invertible$',sK61(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f329,f1232]) ).

tff(f1232,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ? [X1: 'A_n_vec_n_vec$'] :
          ( 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0))
          & ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
          & 'fun_app$o'('invertible$',X1) )
     => ( 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0))
        & ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK61(X0),X0) )
        & 'fun_app$o'('invertible$',sK61(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f329,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
    ? [X1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0))
      & ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
      & 'fun_app$o'('invertible$',X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom327) ).

tff(f4892,plain,
    spl230_265,
    inference(avatar_split_clause,[],[f2945,f4890]) ).

tff(f2945,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'matrix_matrix_mult$'(sK60(X0),X0) ),
    inference(definition_unfolding,[],[f1970,f1818]) ).

tff(f1970,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK60(X0),X0) ),
    inference(cnf_transformation,[],[f1231]) ).

tff(f1231,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK60(X0),X0) )
      & 'fun_app$o'('invertible$',sK60(X0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f207,f1230]) ).

tff(f1230,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ? [X1: 'A_n_vec_n_vec$'] :
          ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
          & 'fun_app$o'('invertible$',X1) )
     => ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(sK60(X0),X0) )
        & 'fun_app$o'('invertible$',sK60(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f207,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
    ? [X1: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) = 'matrix_matrix_mult$'(X1,X0) )
      & 'fun_app$o'('invertible$',X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom205) ).

tff(f4888,plain,
    spl230_264,
    inference(avatar_split_clause,[],[f2942,f4886]) ).

tff(f4886,plain,
    ( spl230_264
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) != 'zero$b' )
        | ( 'zero$b' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_264])]) ).

tff(f2942,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) != 'zero$b' )
      | ( 'zero$b' = X0 ) ),
    inference(definition_unfolding,[],[f1870,f1818]) ).

tff(f1870,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) != 'zero$b' )
      | ( 'zero$b' = X0 ) ),
    inference(cnf_transformation,[],[f791]) ).

tff(f791,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) != 'zero$b' )
      | ( 'zero$b' = X0 ) ),
    inference(ennf_transformation,[],[f433]) ).

tff(f433,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' != X0 )
     => ( 'gauss_Jordan$'(X0) != 'zero$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom431) ).

tff(f4884,plain,
    spl230_263,
    inference(avatar_split_clause,[],[f2549,f4882]) ).

tff(f4882,plain,
    ( spl230_263
  <=> ! [X2: 'A_iarray_iarray$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2))
        | ~ 'fun_app$f'(X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_263])]) ).

tff(f2549,plain,
    ! [X2: 'A_iarray_iarray$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2))
      | ~ 'fun_app$f'(X1,X2) ),
    inference(cnf_transformation,[],[f1579]) ).

tff(f1579,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray$'] :
      ( ( 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2))
        | ~ 'fun_app$f'(X1,X2) )
      & ( 'fun_app$f'(X1,X2)
        | ~ 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2)) ) ),
    inference(nnf_transformation,[],[f82]) ).

tff(f82,axiom,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2))
    <=> 'fun_app$f'(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom80) ).

tff(f4880,plain,
    spl230_262,
    inference(avatar_split_clause,[],[f2548,f4878]) ).

tff(f4878,plain,
    ( spl230_262
  <=> ! [X2: 'A_iarray_iarray$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( 'fun_app$f'(X1,X2)
        | ~ 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_262])]) ).

tff(f2548,plain,
    ! [X2: 'A_iarray_iarray$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$f'(X1,X2)
      | ~ 'fun_app$t'('case_option$a'(X0,X1),'some$'(X2)) ),
    inference(cnf_transformation,[],[f1579]) ).

tff(f4876,plain,
    ( spl230_261
    | ~ spl230_94
    | ~ spl230_104
    | ~ spl230_114 ),
    inference(avatar_split_clause,[],[f4201,f4000,f3960,f3920,f4874]) ).

tff(f4874,plain,
    ( spl230_261
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( sK37(X0) = sK63(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_261])]) ).

tff(f4201,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( sK37(X0) = sK63(X0) )
    | ~ spl230_94
    | ~ spl230_104
    | ~ spl230_114 ),
    inference(forward_demodulation,[],[f4200,f4199]) ).

tff(f4200,plain,
    ( ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('snd$a',X0) = sK63(X0) )
    | ~ spl230_104
    | ~ spl230_114 ),
    inference(superposition,[],[f4001,f3961]) ).

tff(f4872,plain,
    spl230_260,
    inference(avatar_split_clause,[],[f2530,f4870]) ).

tff(f4870,plain,
    ( spl230_260
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( 'member$a'(X2,'set$'(X1))
        | ~ 'fun_app$'('uuu$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_260])]) ).

tff(f2530,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'member$a'(X2,'set$'(X1))
      | ~ 'fun_app$'('uuu$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1570]) ).

tff(f4868,plain,
    spl230_259,
    inference(avatar_split_clause,[],[f2524,f4866]) ).

tff(f2524,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
      | ~ sP14(X2,X1,X0) ),
    inference(cnf_transformation,[],[f1565]) ).

tff(f1565,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( ( 'fun_app$t'('case_option$a'(X0,X1),X2)
        | ~ sP14(X2,X1,X0) )
      & ( sP14(X2,X1,X0)
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    inference(nnf_transformation,[],[f1106]) ).

tff(f1106,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
    <=> sP14(X2,X1,X0) ),
    inference(definition_folding,[],[f959,f1105]) ).

tff(f959,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
    <=> ( ( 'fun_app$f'(X1,'the$a'(X2))
          | ( 'none$' = X2 ) )
        & ( ( tltrue = X0 )
          | ( 'none$' != X2 ) ) ) ),
    inference(ennf_transformation,[],[f73]) ).

tff(f73,axiom,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),X2)
    <=> ( ( ( 'none$' != X2 )
         => 'fun_app$f'(X1,'the$a'(X2)) )
        & ( ( 'none$' = X2 )
         => ( tltrue = X0 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom71) ).

tff(f4864,plain,
    spl230_258,
    inference(avatar_split_clause,[],[f2523,f4862]) ).

tff(f4862,plain,
    ( spl230_258
  <=> ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP14(X2,X1,X0)
        | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_258])]) ).

tff(f2523,plain,
    ! [X2: 'A_iarray_iarray_option$',X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14(X2,X1,X0)
      | ~ 'fun_app$t'('case_option$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1565]) ).

tff(f4860,plain,
    spl230_257,
    inference(avatar_split_clause,[],[f2494,f4858]) ).

tff(f4858,plain,
    ( spl230_257
  <=> ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_257])]) ).

tff(f2494,plain,
    ! [X2: 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ~ 'fun_app$t'('fun_app$z'(X2,X1),X0)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1544]) ).

tff(f4856,plain,
    spl230_256,
    inference(avatar_split_clause,[],[f2487,f4854]) ).

tff(f4854,plain,
    ( spl230_256
  <=> ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
        ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
        | ~ sP12(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_256])]) ).

tff(f2487,plain,
    ! [X2: 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_iarray_iarray_option$'] :
      ( ~ 'fun_app$s'('fun_app$y'(X2,X1),X0)
      | ~ sP12(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1540]) ).

tff(f4852,plain,
    spl230_255,
    inference(avatar_split_clause,[],[f2480,f4850]) ).

tff(f4850,plain,
    ( spl230_255
  <=> ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_255])]) ).

tff(f2480,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$',X0: 'A_iarray_iarray_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ~ 'fun_app$t'('fun_app$x'(X2,X1),X0)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1536]) ).

tff(f4848,plain,
    spl230_254,
    inference(avatar_split_clause,[],[f2473,f4846]) ).

tff(f4846,plain,
    ( spl230_254
  <=> ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_254])]) ).

tff(f2473,plain,
    ! [X2: 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$',X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ~ 'fun_app$s'('fun_app$w'(X2,X1),X0)
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1532]) ).

tff(f4844,plain,
    spl230_253,
    inference(avatar_split_clause,[],[f2461,f4842]) ).

tff(f4842,plain,
    ( spl230_253
  <=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
        ( ~ 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK156(X0))
        | ~ sP8(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_253])]) ).

tff(f2461,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( ~ 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK156(X0))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f1516]) ).

tff(f4840,plain,
    spl230_252,
    inference(avatar_split_clause,[],[f2460,f4838]) ).

tff(f4838,plain,
    ( spl230_252
  <=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
        ( 'fun_app$c'('fun_app$as'(X0,sK155(X0)),sK156(X0))
        | ~ sP8(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_252])]) ).

tff(f2460,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( 'fun_app$c'('fun_app$as'(X0,sK155(X0)),sK156(X0))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f1516]) ).

tff(f4836,plain,
    spl230_251,
    inference(avatar_split_clause,[],[f2459,f4834]) ).

tff(f4834,plain,
    ( spl230_251
  <=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
        ( 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK155(X0))
        | ~ sP8(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_251])]) ).

tff(f2459,plain,
    ! [X0: 'Nat_nat_bool_fun_fun$'] :
      ( 'fun_app$c'('fun_app$as'(X0,sK154(X0)),sK155(X0))
      | ~ sP8(X0) ),
    inference(cnf_transformation,[],[f1516]) ).

tff(f4828,plain,
    spl230_250,
    inference(avatar_split_clause,[],[f2272,f4826]) ).

tff(f4826,plain,
    ( spl230_250
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'nil$' = X1 )
        | ( 'fun_app$p'('append$d'(X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_250])]) ).

tff(f2272,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'nil$' = X1 )
      | ( 'fun_app$p'('append$d'(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f1411]) ).

tff(f1411,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X0),X1) = X0 )
        | ( 'nil$' != X1 ) )
      & ( ( 'nil$' = X1 )
        | ( 'fun_app$p'('append$d'(X0),X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f569]) ).

tff(f569,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('append$d'(X0),X1) = X0 )
    <=> ( 'nil$' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom567) ).

tff(f4824,plain,
    spl230_249,
    inference(avatar_split_clause,[],[f2268,f4822]) ).

tff(f4822,plain,
    ( spl230_249
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'nil$' = X1 )
        | ( 'fun_app$p'('append$d'(X1),X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_249])]) ).

tff(f2268,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'nil$' = X1 )
      | ( 'fun_app$p'('append$d'(X1),X0) != X0 ) ),
    inference(cnf_transformation,[],[f1409]) ).

tff(f1409,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'fun_app$p'('append$d'(X1),X0) = X0 )
        | ( 'nil$' != X1 ) )
      & ( ( 'nil$' = X1 )
        | ( 'fun_app$p'('append$d'(X1),X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f573]) ).

tff(f573,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('append$d'(X1),X0) = X0 )
    <=> ( 'nil$' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).

tff(f4820,plain,
    spl230_248,
    inference(avatar_split_clause,[],[f2254,f4818]) ).

tff(f4818,plain,
    ( spl230_248
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'nil$a' = X1 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_248])]) ).

tff(f2254,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'nil$a' = X1 )
      | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ),
    inference(cnf_transformation,[],[f1394]) ).

tff(f1394,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = 'nil$a' )
        | ( 'nil$a' != X1 )
        | ( 'nil$a' != X0 ) )
      & ( ( ( 'nil$a' = X1 )
          & ( 'nil$a' = X0 ) )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ) ),
    inference(flattening,[],[f1393]) ).

tff(f1393,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = 'nil$a' )
        | ( 'nil$a' != X1 )
        | ( 'nil$a' != X0 ) )
      & ( ( ( 'nil$a' = X1 )
          & ( 'nil$a' = X0 ) )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ) ),
    inference(nnf_transformation,[],[f576]) ).

tff(f576,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = 'nil$a' )
    <=> ( ( 'nil$a' = X1 )
        & ( 'nil$a' = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom574) ).

tff(f4816,plain,
    spl230_247,
    inference(avatar_split_clause,[],[f2253,f4814]) ).

tff(f4814,plain,
    ( spl230_247
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'nil$a' = X0 )
        | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_247])]) ).

tff(f2253,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'nil$a' = X0 )
      | ( 'fun_app$bd'('append$'(X0),X1) != 'nil$a' ) ),
    inference(cnf_transformation,[],[f1394]) ).

tff(f4812,plain,
    spl230_246,
    inference(avatar_split_clause,[],[f2247,f4810]) ).

tff(f4810,plain,
    ( spl230_246
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'nil$a' = X0 )
        | ( 'fun_app$bd'('append$'(X0),X1) != X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_246])]) ).

tff(f2247,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'nil$a' = X0 )
      | ( 'fun_app$bd'('append$'(X0),X1) != X1 ) ),
    inference(cnf_transformation,[],[f1390]) ).

tff(f1390,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = X1 )
        | ( 'nil$a' != X0 ) )
      & ( ( 'nil$a' = X0 )
        | ( 'fun_app$bd'('append$'(X0),X1) != X1 ) ) ),
    inference(nnf_transformation,[],[f570]) ).

tff(f570,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = X1 )
    <=> ( 'nil$a' = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom568) ).

tff(f4808,plain,
    spl230_245,
    inference(avatar_split_clause,[],[f2245,f4806]) ).

tff(f4806,plain,
    ( spl230_245
  <=> ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
        ( ( 'nil$a' = X1 )
        | ( 'fun_app$bd'('append$'(X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_245])]) ).

tff(f2245,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'nil$a' = X1 )
      | ( 'fun_app$bd'('append$'(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f1389]) ).

tff(f1389,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( ( 'fun_app$bd'('append$'(X0),X1) = X0 )
        | ( 'nil$a' != X1 ) )
      & ( ( 'nil$a' = X1 )
        | ( 'fun_app$bd'('append$'(X0),X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f566]) ).

tff(f566,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = X0 )
    <=> ( 'nil$a' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom564) ).

tff(f4804,plain,
    spl230_244,
    inference(avatar_split_clause,[],[f2240,f4802]) ).

tff(f4802,plain,
    ( spl230_244
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'nil$' = X1 )
        | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_244])]) ).

tff(f2240,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'nil$' = X1 )
      | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1386]) ).

tff(f1386,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'nil$' = 'fun_app$p'('append$d'(X0),X1) )
        | ( 'nil$' != X1 )
        | ( 'nil$' != X0 ) )
      & ( ( ( 'nil$' = X1 )
          & ( 'nil$' = X0 ) )
        | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ) ),
    inference(flattening,[],[f1385]) ).

tff(f1385,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( ( 'nil$' = 'fun_app$p'('append$d'(X0),X1) )
        | ( 'nil$' != X1 )
        | ( 'nil$' != X0 ) )
      & ( ( ( 'nil$' = X1 )
          & ( 'nil$' = X0 ) )
        | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ) ),
    inference(nnf_transformation,[],[f577]) ).

tff(f577,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'nil$' = 'fun_app$p'('append$d'(X0),X1) )
    <=> ( ( 'nil$' = X1 )
        & ( 'nil$' = X0 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom575) ).

tff(f4800,plain,
    spl230_243,
    inference(avatar_split_clause,[],[f2239,f4798]) ).

tff(f4798,plain,
    ( spl230_243
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
        ( ( 'nil$' = X0 )
        | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_243])]) ).

tff(f2239,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'nil$' = X0 )
      | ( 'nil$' != 'fun_app$p'('append$d'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1386]) ).

tff(f4796,plain,
    spl230_242,
    inference(avatar_split_clause,[],[f2165,f4794]) ).

tff(f2165,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_7(X0,X1) )
      | ~ 'fun_app$f'(X0,'the$a'(X1)) ),
    inference(cnf_transformation,[],[f1325]) ).

tff(f1325,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( ( tltrue = def_7(X0,X1) )
        | ~ 'fun_app$f'(X0,'the$a'(X1)) )
      & ( 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue != def_7(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f736]) ).

tff(f736,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_7(X0,X1) )
    <=> 'fun_app$f'(X0,'the$a'(X1)) ),
    inference(rectify,[],[f659]) ).

tff(f659,axiom,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_7(X2,X3) )
    <=> 'fun_app$f'(X2,'the$a'(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_658) ).

tff(f4792,plain,
    spl230_241,
    inference(avatar_split_clause,[],[f2164,f4790]) ).

tff(f4790,plain,
    ( spl230_241
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue != def_7(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_241])]) ).

tff(f2164,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( 'fun_app$f'(X0,'the$a'(X1))
      | ( tltrue != def_7(X0,X1) ) ),
    inference(cnf_transformation,[],[f1325]) ).

tff(f4786,plain,
    spl230_240,
    inference(avatar_split_clause,[],[f2163,f4784]) ).

tff(f2163,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_5(X0,X1) )
      | ~ 'fun_app$f'(X0,'the$a'(X1)) ),
    inference(cnf_transformation,[],[f1324]) ).

tff(f1324,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( ( tltrue = def_5(X0,X1) )
        | ~ 'fun_app$f'(X0,'the$a'(X1)) )
      & ( 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue != def_5(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f735]) ).

tff(f735,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_5(X0,X1) )
    <=> 'fun_app$f'(X0,'the$a'(X1)) ),
    inference(rectify,[],[f657]) ).

tff(f657,axiom,
    ! [X2: 'A_iarray_iarray_bool_fun$',X3: 'A_iarray_iarray_option$'] :
      ( ( tltrue = def_5(X2,X3) )
    <=> 'fun_app$f'(X2,'the$a'(X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_656) ).

tff(f4782,plain,
    spl230_239,
    inference(avatar_split_clause,[],[f2162,f4780]) ).

tff(f4780,plain,
    ( spl230_239
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
        ( 'fun_app$f'(X0,'the$a'(X1))
        | ( tltrue != def_5(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_239])]) ).

tff(f2162,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray_option$'] :
      ( 'fun_app$f'(X0,'the$a'(X1))
      | ( tltrue != def_5(X0,X1) ) ),
    inference(cnf_transformation,[],[f1324]) ).

tff(f4778,plain,
    spl230_238,
    inference(avatar_split_clause,[],[f1866,f4776]) ).

tff(f4776,plain,
    ( spl230_238
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'inverse_matrix$'(X0) = 'some$a'('matrix_inv$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_238])]) ).

tff(f1866,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'inverse_matrix$'(X0) = 'some$a'('matrix_inv$'(X0)) )
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f789]) ).

tff(f789,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( ( 'none$a' = 'inverse_matrix$'(X0) )
        | 'fun_app$o'('invertible$',X0) )
      & ( ( 'inverse_matrix$'(X0) = 'some$a'('matrix_inv$'(X0)) )
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    inference(ennf_transformation,[],[f169]) ).

tff(f169,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( ~ 'fun_app$o'('invertible$',X0)
       => ( 'none$a' = 'inverse_matrix$'(X0) ) )
      & ( 'fun_app$o'('invertible$',X0)
       => ( 'inverse_matrix$'(X0) = 'some$a'('matrix_inv$'(X0)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom167) ).

tff(f4772,plain,
    spl230_237,
    inference(avatar_split_clause,[],[f1841,f4770]) ).

tff(f4770,plain,
    ( spl230_237
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X0),'fun_app$r'('snd$a',X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_237])]) ).

tff(f1841,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X0),'fun_app$r'('snd$a',X0)) = X0 ),
    inference(cnf_transformation,[],[f212]) ).

tff(f212,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'('fun_app$r'('fst$',X0),'fun_app$r'('snd$a',X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom210) ).

tff(f4768,plain,
    spl230_236,
    inference(avatar_split_clause,[],[f1839,f4766]) ).

tff(f4766,plain,
    ( spl230_236
  <=> ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'('fun_app$ab'('fst$a',X0),'fun_app$ab'('snd$',X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_236])]) ).

tff(f1839,plain,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'('fun_app$ab'('fst$a',X0),'fun_app$ab'('snd$',X0)) = X0 ),
    inference(cnf_transformation,[],[f210]) ).

tff(f210,axiom,
    ! [X0: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$'] : ( 'pair$l'('fun_app$ab'('fst$a',X0),'fun_app$ab'('snd$',X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom208) ).

tff(f4764,plain,
    spl230_235,
    inference(avatar_split_clause,[],[f1835,f4762]) ).

tff(f4762,plain,
    ( spl230_235
  <=> ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_235])]) ).

tff(f1835,plain,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X0),1) ),
    inference(cnf_transformation,[],[f447]) ).

tff(f447,axiom,
    ! [X0: 'Nat$'] : ( 'fun_app$l'('of_nat$',X0) != $sum('fun_app$l'('of_nat$',X0),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom445) ).

tff(f4760,plain,
    spl230_234,
    inference(avatar_split_clause,[],[f671,f4758]) ).

tff(f4758,plain,
    ( spl230_234
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_234])]) ).

tff(f671,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f4756,plain,
    spl230_233,
    inference(avatar_split_clause,[],[f670,f4754]) ).

tff(f4754,plain,
    ( spl230_233
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_233])]) ).

tff(f670,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f4751,plain,
    ( spl230_232
    | ~ spl230_6
    | ~ spl230_221 ),
    inference(avatar_split_clause,[],[f4735,f4540,f3524,f4749]) ).

tff(f4749,plain,
    ( spl230_232
  <=> ! [X0: 'A_iarray_iarray_option$'] : sP14(X0,'uug$',tltrue) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_232])]) ).

tff(f4540,plain,
    ( spl230_221
  <=> ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( sP14(X0,X1,tltrue)
        | ~ 'fun_app$f'(X1,'the$a'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_221])]) ).

tff(f4735,plain,
    ( ! [X0: 'A_iarray_iarray_option$'] : sP14(X0,'uug$',tltrue)
    | ~ spl230_6
    | ~ spl230_221 ),
    inference(resolution,[],[f4541,f3525]) ).

tff(f4541,plain,
    ( ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
        ( ~ 'fun_app$f'(X1,'the$a'(X0))
        | sP14(X0,X1,tltrue) )
    | ~ spl230_221 ),
    inference(avatar_component_clause,[],[f4540]) ).

tff(f4733,plain,
    ( spl230_231
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_212 ),
    inference(avatar_split_clause,[],[f4506,f4503,f3895,f3877,f4731]) ).

tff(f4731,plain,
    ( spl230_231
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | sP7(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_231])]) ).

tff(f4503,plain,
    ( spl230_212
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( sP7(X1,X0)
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_212])]) ).

tff(f4506,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( ~ 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | sP7(X1,X0) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_212 ),
    inference(forward_demodulation,[],[f4504,f4136]) ).

tff(f4504,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( sP7(X1,X0)
        | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) )
    | ~ spl230_212 ),
    inference(avatar_component_clause,[],[f4503]) ).

tff(f4728,plain,
    ( spl230_230
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_210 ),
    inference(avatar_split_clause,[],[f4497,f4494,f3895,f3877,f4726]) ).

tff(f4726,plain,
    ( spl230_230
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | ~ sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_230])]) ).

tff(f4494,plain,
    ( spl230_210
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP6(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_210])]) ).

tff(f4497,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$aa'('rank$','zero$b'))
        | ~ sP6(X1,X0) )
    | ~ spl230_84
    | ~ spl230_88
    | ~ spl230_210 ),
    inference(forward_demodulation,[],[f4495,f4136]) ).

tff(f4495,plain,
    ( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,'fun_app$k'('nat$',0))
        | ~ sP6(X1,X0) )
    | ~ spl230_210 ),
    inference(avatar_component_clause,[],[f4494]) ).

tff(f4651,plain,
    ( spl230_229
    | ~ spl230_181 ),
    inference(avatar_split_clause,[],[f4622,f4378,f4649]) ).

tff(f4649,plain,
    ( spl230_229
  <=> ! [X0: 'A_iarray_iarray_option$'] : ~ sP3(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_229])]) ).

tff(f4378,plain,
    ( spl230_181
  <=> ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'the$a'(X0) != 'the$a'(X1) )
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_181])]) ).

tff(f4622,plain,
    ( ! [X0: 'A_iarray_iarray_option$'] : ~ sP3(X0,X0)
    | ~ spl230_181 ),
    inference(equality_resolution,[],[f4379]) ).

tff(f4379,plain,
    ( ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
        ( ( 'the$a'(X0) != 'the$a'(X1) )
        | ~ sP3(X0,X1) )
    | ~ spl230_181 ),
    inference(avatar_component_clause,[],[f4378]) ).

tff(f4626,plain,
    ( spl230_228
    | ~ spl230_180 ),
    inference(avatar_split_clause,[],[f4619,f4374,f4624]) ).

tff(f4624,plain,
    ( spl230_228
  <=> ! [X0: 'A_n_vec_n_vec_option$'] : ~ sP2(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_228])]) ).

tff(f4374,plain,
    ( spl230_180
  <=> ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'the$'(X0) != 'the$'(X1) )
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_180])]) ).

tff(f4619,plain,
    ( ! [X0: 'A_n_vec_n_vec_option$'] : ~ sP2(X0,X0)
    | ~ spl230_180 ),
    inference(equality_resolution,[],[f4375]) ).

tff(f4375,plain,
    ( ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
        ( ( 'the$'(X0) != 'the$'(X1) )
        | ~ sP2(X0,X1) )
    | ~ spl230_180 ),
    inference(avatar_component_clause,[],[f4374]) ).

tff(f4598,plain,
    ( spl230_227
    | ~ spl230_96
    | ~ spl230_106
    | ~ spl230_111 ),
    inference(avatar_split_clause,[],[f4192,f3988,f3968,f3928,f4596]) ).

tff(f4596,plain,
    ( spl230_227
  <=> ! [X0: 'Int_int_prod$'] : ( sK41(X0) = sK67(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_227])]) ).

tff(f3968,plain,
    ( spl230_106
  <=> ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK66(X0),sK67(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_106])]) ).

tff(f4192,plain,
    ( ! [X0: 'Int_int_prod$'] : ( sK41(X0) = sK67(X0) )
    | ~ spl230_96
    | ~ spl230_106
    | ~ spl230_111 ),
    inference(forward_demodulation,[],[f4191,f4190]) ).

tff(f4191,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('snd$b',X0) = sK67(X0) )
    | ~ spl230_106
    | ~ spl230_111 ),
    inference(superposition,[],[f3989,f3969]) ).

tff(f3969,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK66(X0),sK67(X0)) = X0 )
    | ~ spl230_106 ),
    inference(avatar_component_clause,[],[f3968]) ).

tff(f4573,plain,
    ( spl230_226
    | ~ spl230_96
    | ~ spl230_106
    | ~ spl230_110 ),
    inference(avatar_split_clause,[],[f4188,f3984,f3968,f3928,f4571]) ).

tff(f4571,plain,
    ( spl230_226
  <=> ! [X0: 'Int_int_prod$'] : ( sK40(X0) = sK66(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_226])]) ).

tff(f4188,plain,
    ( ! [X0: 'Int_int_prod$'] : ( sK40(X0) = sK66(X0) )
    | ~ spl230_96
    | ~ spl230_106
    | ~ spl230_110 ),
    inference(forward_demodulation,[],[f4187,f4186]) ).

tff(f4187,plain,
    ( ! [X0: 'Int_int_prod$'] : ( 'fun_app$ac'('fst$b',X0) = sK66(X0) )
    | ~ spl230_106
    | ~ spl230_110 ),
    inference(superposition,[],[f3985,f3969]) ).

tff(f4558,plain,
    spl230_225,
    inference(avatar_split_clause,[],[f3308,f4556]) ).

tff(f3308,plain,
    ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$ax'('size_option$a'(X0),'none$a')) ),
    inference(evaluation,[],[f1849]) ).

tff(f1849,plain,
    ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( $sum(0,1) = 'fun_app$l'('of_nat$','fun_app$ax'('size_option$a'(X0),'none$a')) ),
    inference(cnf_transformation,[],[f468]) ).

tff(f468,axiom,
    ! [X0: 'A_n_vec_n_vec_nat_fun$'] : ( $sum(0,1) = 'fun_app$l'('of_nat$','fun_app$ax'('size_option$a'(X0),'none$a')) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom466) ).

tff(f4554,plain,
    spl230_224,
    inference(avatar_split_clause,[],[f3307,f4552]) ).

tff(f3307,plain,
    ! [X0: 'A_iarray_iarray_nat_fun$'] : ( 1 = 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'none$')) ),
    inference(evaluation,[],[f1850]) ).

tff(f1850,plain,
    ! [X0: 'A_iarray_iarray_nat_fun$'] : ( $sum(0,1) = 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'none$')) ),
    inference(cnf_transformation,[],[f469]) ).

tff(f469,axiom,
    ! [X0: 'A_iarray_iarray_nat_fun$'] : ( $sum(0,1) = 'fun_app$l'('of_nat$','fun_app$aw'('size_option$'(X0),'none$')) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom467) ).

tff(f4550,plain,
    spl230_223,
    inference(avatar_split_clause,[],[f3178,f4548]) ).

tff(f4548,plain,
    ( spl230_223
  <=> ! [X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$',X3: tlbool] :
        ( 'fun_app$n'(X2,X3)
        | ~ sP17('none$',X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_223])]) ).

tff(f3178,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,X3)
      | ~ sP17('none$',X1,X2,X3) ),
    inference(equality_resolution,[],[f2715]) ).

tff(f2715,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,X3)
      | ( 'none$' != X0 )
      | ~ sP17(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1650]) ).

tff(f4546,plain,
    spl230_222,
    inference(avatar_split_clause,[],[f3177,f4544]) ).

tff(f4544,plain,
    ( spl230_222
  <=> ! [X2: 'Bool_bool_fun$',X1: 'A_iarray_iarray_bool_fun$',X3: tlbool] :
        ( 'fun_app$n'(X2,X3)
        | ~ sP16('none$',X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_222])]) ).

tff(f3177,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,X3)
      | ~ sP16('none$',X1,X2,X3) ),
    inference(equality_resolution,[],[f2707]) ).

tff(f2707,plain,
    ! [X2: 'Bool_bool_fun$',X3: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$n'(X2,X3)
      | ( 'none$' != X0 )
      | ~ sP16(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1646]) ).

tff(f4542,plain,
    spl230_221,
    inference(avatar_split_clause,[],[f3135,f4540]) ).

tff(f3135,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14(X0,X1,tltrue)
      | ~ 'fun_app$f'(X1,'the$a'(X0)) ),
    inference(equality_resolution,[],[f2522]) ).

tff(f2522,plain,
    ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14(X0,X1,X2)
      | ~ 'fun_app$f'(X1,'the$a'(X0))
      | ( tltrue != X2 ) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f4538,plain,
    ( spl230_220
    | ~ spl230_73
    | ~ spl230_97
    | ~ spl230_107 ),
    inference(avatar_split_clause,[],[f4168,f3972,f3932,f3819,f4536]) ).

tff(f4536,plain,
    ( spl230_220
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( sK42(X0) = sK68(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_220])]) ).

tff(f3932,plain,
    ( spl230_97
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X0),sK43(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_97])]) ).

tff(f3972,plain,
    ( spl230_107
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK68(X0),sK69(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_107])]) ).

tff(f4168,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( sK42(X0) = sK68(X0) )
    | ~ spl230_73
    | ~ spl230_97
    | ~ spl230_107 ),
    inference(forward_demodulation,[],[f4166,f4153]) ).

tff(f4153,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'fst$k'(X0) = sK42(X0) )
    | ~ spl230_73
    | ~ spl230_97 ),
    inference(superposition,[],[f3820,f3933]) ).

tff(f3933,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X0),sK43(X0)) = X0 )
    | ~ spl230_97 ),
    inference(avatar_component_clause,[],[f3932]) ).

tff(f4166,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'fst$k'(X0) = sK68(X0) )
    | ~ spl230_73
    | ~ spl230_107 ),
    inference(superposition,[],[f3820,f3973]) ).

tff(f3973,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK68(X0),sK69(X0)) = X0 )
    | ~ spl230_107 ),
    inference(avatar_component_clause,[],[f3972]) ).

tff(f4534,plain,
    spl230_219,
    inference(avatar_split_clause,[],[f3105,f4532]) ).

tff(f4532,plain,
    ( spl230_219
  <=> ! [X2: 'A_iarray$',X1: 'A_iarray_a_iarray_prod_set$',X3: 'A_iarray_list$'] : 'member$'('pair$b'('nil$','cons$'(X2,X3)),'lexord$c'(X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_219])]) ).

tff(f3105,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] : 'member$'('pair$b'('nil$','cons$'(X2,X3)),'lexord$c'(X1)),
    inference(equality_resolution,[],[f2277]) ).

tff(f2277,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( 'member$'('pair$b'('nil$',X0),'lexord$c'(X1))
      | ( 'cons$'(X2,X3) != X0 ) ),
    inference(cnf_transformation,[],[f1416]) ).

tff(f4530,plain,
    spl230_218,
    inference(avatar_split_clause,[],[f2760,f4528]) ).

tff(f4528,plain,
    ( spl230_218
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
        ( 'fun_app$'(X1,X2)
        | ~ sP19(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_218])]) ).

tff(f2760,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'(X1,X2)
      | ~ sP19(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1680]) ).

tff(f4526,plain,
    spl230_217,
    inference(avatar_split_clause,[],[f2752,f4524]) ).

tff(f4524,plain,
    ( spl230_217
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$',X3: 'A_iarray_list$'] :
        ( 'fun_app$'(X1,X2)
        | ~ sP18(X0,X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_217])]) ).

tff(f2752,plain,
    ! [X2: 'A_iarray$',X3: 'A_iarray_list$',X0: 'A_iarray_list$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'(X1,X2)
      | ~ sP18(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f1674]) ).

tff(f4522,plain,
    spl230_216,
    inference(avatar_split_clause,[],[f2531,f4520]) ).

tff(f4520,plain,
    ( spl230_216
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
        ( 'fun_app$'(X0,X2)
        | ~ 'fun_app$'('uuu$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_216])]) ).

tff(f2531,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'fun_app$'(X0,X2)
      | ~ 'fun_app$'('uuu$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1570]) ).

tff(f4518,plain,
    spl230_215,
    inference(avatar_split_clause,[],[f2528,f4516]) ).

tff(f4516,plain,
    ( spl230_215
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
        ( 'fun_app$'(X0,X2)
        | ~ 'fun_app$'('uua$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_215])]) ).

tff(f2528,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'(X0,X2)
      | ~ 'fun_app$'('uua$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1568]) ).

tff(f4514,plain,
    spl230_214,
    inference(avatar_split_clause,[],[f2527,f4512]) ).

tff(f4512,plain,
    ( spl230_214
  <=> ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
        ( 'fun_app$'(X1,X2)
        | ~ 'fun_app$'('uua$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_214])]) ).

tff(f2527,plain,
    ! [X2: 'A_iarray$',X0: 'A_iarray_bool_fun$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'(X1,X2)
      | ~ 'fun_app$'('uua$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f1568]) ).

tff(f4510,plain,
    spl230_213,
    inference(avatar_split_clause,[],[f2465,f4508]) ).

tff(f4508,plain,
    ( spl230_213
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$c'(X0,sK158(X0,X1))
        | ~ sP9(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_213])]) ).

tff(f2465,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ 'fun_app$c'(X0,sK158(X0,X1))
      | ~ sP9(X0,X1) ),
    inference(cnf_transformation,[],[f1523]) ).

tff(f4505,plain,
    spl230_212,
    inference(avatar_split_clause,[],[f2348,f4503]) ).

tff(f2348,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( sP7(X1,X0)
      | ~ 'fun_app$c'(X1,'fun_app$k'('nat$',0)) ),
    inference(cnf_transformation,[],[f1490]) ).

tff(f4501,plain,
    spl230_211,
    inference(avatar_split_clause,[],[f2344,f4499]) ).

tff(f4499,plain,
    ( spl230_211
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$c'(X0,sK133(X0,X1))
        | ~ sP7(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_211])]) ).

tff(f2344,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$c'(X0,sK133(X0,X1))
      | ~ sP7(X0,X1) ),
    inference(cnf_transformation,[],[f1485]) ).

tff(f4496,plain,
    spl230_210,
    inference(avatar_split_clause,[],[f2339,f4494]) ).

tff(f2339,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,'fun_app$k'('nat$',0))
      | ~ sP6(X1,X0) ),
    inference(cnf_transformation,[],[f1481]) ).

tff(f4492,plain,
    ( spl230_209
    | ~ spl230_75
    | ~ spl230_97
    | ~ spl230_107 ),
    inference(avatar_split_clause,[],[f4167,f3972,f3932,f3827,f4490]) ).

tff(f4490,plain,
    ( spl230_209
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( sK43(X0) = sK69(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_209])]) ).

tff(f4167,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( sK43(X0) = sK69(X0) )
    | ~ spl230_75
    | ~ spl230_97
    | ~ spl230_107 ),
    inference(forward_demodulation,[],[f4165,f4152]) ).

tff(f4152,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'snd$k'(X0) = sK43(X0) )
    | ~ spl230_75
    | ~ spl230_97 ),
    inference(superposition,[],[f3828,f3933]) ).

tff(f4165,plain,
    ( ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'snd$k'(X0) = sK69(X0) )
    | ~ spl230_75
    | ~ spl230_107 ),
    inference(superposition,[],[f3828,f3973]) ).

tff(f4488,plain,
    spl230_208,
    inference(avatar_split_clause,[],[f2338,f4486]) ).

tff(f4486,plain,
    ( spl230_208
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( sP6(X0,X1)
        | ~ 'fun_app$c'(X0,sK131(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_208])]) ).

tff(f2338,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( sP6(X0,X1)
      | ~ 'fun_app$c'(X0,sK131(X0,X1)) ),
    inference(cnf_transformation,[],[f1476]) ).

tff(f4484,plain,
    spl230_207,
    inference(avatar_split_clause,[],[f2238,f4482]) ).

tff(f4482,plain,
    ( spl230_207
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X0,X1),X0)
        | ~ $less(X1,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_207])]) ).

tff(f2238,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),X0)
      | ~ $less(X1,0) ),
    inference(cnf_transformation,[],[f1384]) ).

tff(f1384,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less($sum(X0,X1),X0)
        | ~ $less(X1,0) )
      & ( $less(X1,0)
        | ~ $less($sum(X0,X1),X0) ) ),
    inference(nnf_transformation,[],[f618]) ).

tff(f618,axiom,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),X0)
    <=> $less(X1,0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom616) ).

tff(f4480,plain,
    spl230_206,
    inference(avatar_split_clause,[],[f2237,f4478]) ).

tff(f4478,plain,
    ( spl230_206
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,0)
        | ~ $less($sum(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_206])]) ).

tff(f2237,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,0)
      | ~ $less($sum(X0,X1),X0) ),
    inference(cnf_transformation,[],[f1384]) ).

tff(f4476,plain,
    spl230_205,
    inference(avatar_split_clause,[],[f2236,f4474]) ).

tff(f4474,plain,
    ( spl230_205
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X0,X1),X1)
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_205])]) ).

tff(f2236,plain,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),X1)
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1383]) ).

tff(f1383,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less($sum(X0,X1),X1)
        | ~ $less(X0,0) )
      & ( $less(X0,0)
        | ~ $less($sum(X0,X1),X1) ) ),
    inference(nnf_transformation,[],[f619]) ).

tff(f619,axiom,
    ! [X0: $int,X1: $int] :
      ( $less($sum(X0,X1),X1)
    <=> $less(X0,0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom617) ).

tff(f4472,plain,
    spl230_204,
    inference(avatar_split_clause,[],[f2235,f4470]) ).

tff(f4470,plain,
    ( spl230_204
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,0)
        | ~ $less($sum(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_204])]) ).

tff(f2235,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,0)
      | ~ $less($sum(X0,X1),X1) ),
    inference(cnf_transformation,[],[f1383]) ).

tff(f4468,plain,
    spl230_203,
    inference(avatar_split_clause,[],[f2234,f4466]) ).

tff(f2234,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,$sum(X0,X1))
      | ~ $less(0,X1) ),
    inference(cnf_transformation,[],[f1382]) ).

tff(f1382,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less(X0,$sum(X0,X1))
        | ~ $less(0,X1) )
      & ( $less(0,X1)
        | ~ $less(X0,$sum(X0,X1)) ) ),
    inference(nnf_transformation,[],[f620]) ).

tff(f620,axiom,
    ! [X0: $int,X1: $int] :
      ( $less(X0,$sum(X0,X1))
    <=> $less(0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom618) ).

tff(f4464,plain,
    spl230_202,
    inference(avatar_split_clause,[],[f2233,f4462]) ).

tff(f2233,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X1)
      | ~ $less(X0,$sum(X0,X1)) ),
    inference(cnf_transformation,[],[f1382]) ).

tff(f4460,plain,
    spl230_201,
    inference(avatar_split_clause,[],[f2232,f4458]) ).

tff(f2232,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,$sum(X1,X0))
      | ~ $less(0,X1) ),
    inference(cnf_transformation,[],[f1381]) ).

tff(f1381,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less(X0,$sum(X1,X0))
        | ~ $less(0,X1) )
      & ( $less(0,X1)
        | ~ $less(X0,$sum(X1,X0)) ) ),
    inference(nnf_transformation,[],[f621]) ).

tff(f621,axiom,
    ! [X0: $int,X1: $int] :
      ( $less(X0,$sum(X1,X0))
    <=> $less(0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom619) ).

tff(f4456,plain,
    spl230_200,
    inference(avatar_split_clause,[],[f2231,f4454]) ).

tff(f2231,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X1)
      | ~ $less(X0,$sum(X1,X0)) ),
    inference(cnf_transformation,[],[f1381]) ).

tff(f4452,plain,
    spl230_199,
    inference(avatar_split_clause,[],[f2222,f4450]) ).

tff(f4450,plain,
    ( spl230_199
  <=> ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( tltrue = X0 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_199])]) ).

tff(f2222,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = X0 )
      | ~ 'fun_app$t'('case_option$a'(X0,X1),'none$') ),
    inference(cnf_transformation,[],[f1372]) ).

tff(f1372,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( 'fun_app$t'('case_option$a'(X0,X1),'none$')
        | ( tltrue != X0 ) )
      & ( ( tltrue = X0 )
        | ~ 'fun_app$t'('case_option$a'(X0,X1),'none$') ) ),
    inference(nnf_transformation,[],[f81]) ).

tff(f81,axiom,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),'none$')
    <=> ( tltrue = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom79) ).

tff(f4448,plain,
    ( spl230_198
    | ~ spl230_74
    | ~ spl230_95
    | ~ spl230_105 ),
    inference(avatar_split_clause,[],[f4164,f3964,f3924,f3823,f4446]) ).

tff(f4446,plain,
    ( spl230_198
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( sK38(X0) = sK64(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_198])]) ).

tff(f3924,plain,
    ( spl230_95
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X0),sK39(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_95])]) ).

tff(f3964,plain,
    ( spl230_105
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK64(X0),sK65(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_105])]) ).

tff(f4164,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( sK38(X0) = sK64(X0) )
    | ~ spl230_74
    | ~ spl230_95
    | ~ spl230_105 ),
    inference(forward_demodulation,[],[f4162,f4151]) ).

tff(f4151,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'fst$e'(X0) = sK38(X0) )
    | ~ spl230_74
    | ~ spl230_95 ),
    inference(superposition,[],[f3824,f3925]) ).

tff(f3925,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X0),sK39(X0)) = X0 )
    | ~ spl230_95 ),
    inference(avatar_component_clause,[],[f3924]) ).

tff(f4162,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'fst$e'(X0) = sK64(X0) )
    | ~ spl230_74
    | ~ spl230_105 ),
    inference(superposition,[],[f3824,f3965]) ).

tff(f3965,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK64(X0),sK65(X0)) = X0 )
    | ~ spl230_105 ),
    inference(avatar_component_clause,[],[f3964]) ).

tff(f4444,plain,
    spl230_197,
    inference(avatar_split_clause,[],[f2220,f4442]) ).

tff(f4442,plain,
    ( spl230_197
  <=> ! [X0: $int,X1: $int] :
        ( ( 0 = X1 )
        | ~ 'fun_app$ae'('divides_aux$','pair$c'(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_197])]) ).

tff(f2220,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X1 )
      | ~ 'fun_app$ae'('divides_aux$','pair$c'(X0,X1)) ),
    inference(cnf_transformation,[],[f1371]) ).

tff(f1371,plain,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$ae'('divides_aux$','pair$c'(X0,X1))
        | ( 0 != X1 ) )
      & ( ( 0 = X1 )
        | ~ 'fun_app$ae'('divides_aux$','pair$c'(X0,X1)) ) ),
    inference(nnf_transformation,[],[f440]) ).

tff(f440,axiom,
    ! [X0: $int,X1: $int] :
      ( 'fun_app$ae'('divides_aux$','pair$c'(X0,X1))
    <=> ( 0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom438) ).

tff(f4440,plain,
    spl230_196,
    inference(avatar_split_clause,[],[f2212,f4438]) ).

tff(f2212,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X0 )
      | ( $sum(X0,X1) != X1 ) ),
    inference(cnf_transformation,[],[f1367]) ).

tff(f1367,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( $sum(X0,X1) = X1 )
        | ( 0 != X0 ) )
      & ( ( 0 = X0 )
        | ( $sum(X0,X1) != X1 ) ) ),
    inference(nnf_transformation,[],[f373]) ).

tff(f373,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $sum(X0,X1) = X1 )
    <=> ( 0 = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom371) ).

tff(f4436,plain,
    spl230_195,
    inference(avatar_split_clause,[],[f2210,f4434]) ).

tff(f2210,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X1 )
      | ( $sum(X0,X1) != X0 ) ),
    inference(cnf_transformation,[],[f1366]) ).

tff(f1366,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( $sum(X0,X1) = X0 )
        | ( 0 != X1 ) )
      & ( ( 0 = X1 )
        | ( $sum(X0,X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f376]) ).

tff(f376,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $sum(X0,X1) = X0 )
    <=> ( 0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom374) ).

tff(f4432,plain,
    spl230_194,
    inference(avatar_split_clause,[],[f2202,f4430]) ).

tff(f4430,plain,
    ( spl230_194
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'zero$b' = X1 )
        | ( 'plus$a'(X0,X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_194])]) ).

tff(f2202,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' = X1 )
      | ( 'plus$a'(X0,X1) != X0 ) ),
    inference(cnf_transformation,[],[f1362]) ).

tff(f1362,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( ( 'plus$a'(X0,X1) = X0 )
        | ( 'zero$b' != X1 ) )
      & ( ( 'zero$b' = X1 )
        | ( 'plus$a'(X0,X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f381]) ).

tff(f381,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'plus$a'(X0,X1) = X0 )
    <=> ( 'zero$b' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom379) ).

tff(f4428,plain,
    spl230_193,
    inference(avatar_split_clause,[],[f2200,f4426]) ).

tff(f4426,plain,
    ( spl230_193
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( 'zero$b' = X1 )
        | ( 'plus$a'(X1,X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_193])]) ).

tff(f2200,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' = X1 )
      | ( 'plus$a'(X1,X0) != X0 ) ),
    inference(cnf_transformation,[],[f1361]) ).

tff(f1361,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( ( 'plus$a'(X1,X0) = X0 )
        | ( 'zero$b' != X1 ) )
      & ( ( 'zero$b' = X1 )
        | ( 'plus$a'(X1,X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f378]) ).

tff(f378,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( 'plus$a'(X1,X0) = X0 )
    <=> ( 'zero$b' = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom376) ).

tff(f4424,plain,
    spl230_192,
    inference(avatar_split_clause,[],[f2189,f4422]) ).

tff(f2189,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
      ( ( tltrue = def_1(X0,X1) )
      | ~ 'fun_app$f'(X0,X1) ),
    inference(cnf_transformation,[],[f1355]) ).

tff(f1355,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
      ( ( ( tltrue = def_1(X0,X1) )
        | ~ 'fun_app$f'(X0,X1) )
      & ( 'fun_app$f'(X0,X1)
        | ( tltrue != def_1(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f737]) ).

tff(f737,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
      ( ( tltrue = def_1(X0,X1) )
    <=> 'fun_app$f'(X0,X1) ),
    inference(rectify,[],[f653]) ).

tff(f653,axiom,
    ! [X1: 'A_iarray_iarray_bool_fun$',X2: 'A_iarray_iarray$'] :
      ( ( def_1(X1,X2) = tltrue )
    <=> 'fun_app$f'(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_652) ).

tff(f4420,plain,
    spl230_191,
    inference(avatar_split_clause,[],[f2188,f4418]) ).

tff(f4418,plain,
    ( spl230_191
  <=> ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
        ( 'fun_app$f'(X0,X1)
        | ( tltrue != def_1(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_191])]) ).

tff(f2188,plain,
    ! [X0: 'A_iarray_iarray_bool_fun$',X1: 'A_iarray_iarray$'] :
      ( 'fun_app$f'(X0,X1)
      | ( tltrue != def_1(X0,X1) ) ),
    inference(cnf_transformation,[],[f1355]) ).

tff(f4416,plain,
    spl230_190,
    inference(avatar_split_clause,[],[f2174,f4414]) ).

tff(f4414,plain,
    ( spl230_190
  <=> ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
        ( ( X0 = X1 )
        | ( 'some$'(X1) != 'some$'(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_190])]) ).

tff(f2174,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( ( X0 = X1 )
      | ( 'some$'(X1) != 'some$'(X0) ) ),
    inference(cnf_transformation,[],[f1330]) ).

tff(f1330,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( ( ( 'some$'(X1) = 'some$'(X0) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'some$'(X1) != 'some$'(X0) ) ) ),
    inference(nnf_transformation,[],[f33]) ).

tff(f33,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] :
      ( ( 'some$'(X1) = 'some$'(X0) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom31) ).

tff(f4412,plain,
    spl230_189,
    inference(avatar_split_clause,[],[f2172,f4410]) ).

tff(f4410,plain,
    ( spl230_189
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod_set$'] :
        ( ( X0 = X1 )
        | ( 'uuq$'(X0) != 'uuq$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_189])]) ).

tff(f2172,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( X0 = X1 )
      | ( 'uuq$'(X0) != 'uuq$'(X1) ) ),
    inference(cnf_transformation,[],[f1329]) ).

tff(f1329,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( ( 'uuq$'(X0) = 'uuq$'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'uuq$'(X0) != 'uuq$'(X1) ) ) ),
    inference(nnf_transformation,[],[f332]) ).

tff(f332,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod_set$'] :
      ( ( 'uuq$'(X0) = 'uuq$'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom330) ).

tff(f4408,plain,
    spl230_188,
    inference(avatar_split_clause,[],[f2170,f4406]) ).

tff(f4406,plain,
    ( spl230_188
  <=> ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_a_iarray_prod_set$'] :
        ( ( X0 = X1 )
        | ( 'uur$'(X0) != 'uur$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_188])]) ).

tff(f2170,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( X0 = X1 )
      | ( 'uur$'(X0) != 'uur$'(X1) ) ),
    inference(cnf_transformation,[],[f1328]) ).

tff(f1328,plain,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( ( 'uur$'(X0) = 'uur$'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'uur$'(X0) != 'uur$'(X1) ) ) ),
    inference(nnf_transformation,[],[f333]) ).

tff(f333,axiom,
    ! [X0: 'A_iarray_a_iarray_prod_set$',X1: 'A_iarray_a_iarray_prod_set$'] :
      ( ( 'uur$'(X0) = 'uur$'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom331) ).

tff(f4404,plain,
    ( spl230_187
    | ~ spl230_76
    | ~ spl230_95
    | ~ spl230_105 ),
    inference(avatar_split_clause,[],[f4163,f3964,f3924,f3831,f4402]) ).

tff(f4402,plain,
    ( spl230_187
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( sK39(X0) = sK65(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_187])]) ).

tff(f4163,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( sK39(X0) = sK65(X0) )
    | ~ spl230_76
    | ~ spl230_95
    | ~ spl230_105 ),
    inference(forward_demodulation,[],[f4161,f4150]) ).

tff(f4150,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'snd$e'(X0) = sK39(X0) )
    | ~ spl230_76
    | ~ spl230_95 ),
    inference(superposition,[],[f3832,f3925]) ).

tff(f4161,plain,
    ( ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'snd$e'(X0) = sK65(X0) )
    | ~ spl230_76
    | ~ spl230_105 ),
    inference(superposition,[],[f3832,f3965]) ).

tff(f4400,plain,
    spl230_186,
    inference(avatar_split_clause,[],[f2168,f4398]) ).

tff(f4398,plain,
    ( spl230_186
  <=> ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
        ( ( X0 = X1 )
        | ( 'uup$'(X0) != 'uup$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_186])]) ).

tff(f2168,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( X0 = X1 )
      | ( 'uup$'(X0) != 'uup$'(X1) ) ),
    inference(cnf_transformation,[],[f1327]) ).

tff(f1327,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( ( 'uup$'(X0) = 'uup$'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'uup$'(X0) != 'uup$'(X1) ) ) ),
    inference(nnf_transformation,[],[f331]) ).

tff(f331,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod_set$',X1: 'A_iarray_iarray_a_iarray_iarray_prod_set$'] :
      ( ( 'uup$'(X0) = 'uup$'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom329) ).

tff(f4396,plain,
    spl230_185,
    inference(avatar_split_clause,[],[f2166,f4394]) ).

tff(f4394,plain,
    ( spl230_185
  <=> ! [X0: 'Int_int_prod_set$',X1: 'Int_int_prod_set$'] :
        ( ( X0 = X1 )
        | ( 'uuo$'(X0) != 'uuo$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_185])]) ).

tff(f2166,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_int_prod_set$'] :
      ( ( X0 = X1 )
      | ( 'uuo$'(X0) != 'uuo$'(X1) ) ),
    inference(cnf_transformation,[],[f1326]) ).

tff(f1326,plain,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_int_prod_set$'] :
      ( ( ( 'uuo$'(X0) = 'uuo$'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'uuo$'(X0) != 'uuo$'(X1) ) ) ),
    inference(nnf_transformation,[],[f330]) ).

tff(f330,axiom,
    ! [X0: 'Int_int_prod_set$',X1: 'Int_int_prod_set$'] :
      ( ( 'uuo$'(X0) = 'uuo$'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom328) ).

tff(f4392,plain,
    spl230_184,
    inference(avatar_split_clause,[],[f2161,f4390]) ).

tff(f4390,plain,
    ( spl230_184
  <=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
        ( ( tltrue = def_3(X0,X1) )
        | ~ 'fun_app$n'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_184])]) ).

tff(f2161,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( tltrue = def_3(X0,X1) )
      | ~ 'fun_app$n'(X0,X1) ),
    inference(cnf_transformation,[],[f1323]) ).

tff(f1323,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( ( tltrue = def_3(X0,X1) )
        | ~ 'fun_app$n'(X0,X1) )
      & ( 'fun_app$n'(X0,X1)
        | ( tltrue != def_3(X0,X1) ) ) ),
    inference(nnf_transformation,[],[f655]) ).

tff(f655,axiom,
    ! [X0: 'Bool_bool_fun$',X1: tlbool] :
      ( ( tltrue = def_3(X0,X1) )
    <=> 'fun_app$n'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_654) ).

tff(f4388,plain,
    spl230_183,
    inference(avatar_split_clause,[],[f2160,f4386]) ).

tff(f4386,plain,
    ( spl230_183
  <=> ! [X0: 'Bool_bool_fun$',X1: tlbool] :
        ( 'fun_app$n'(X0,X1)
        | ( tltrue != def_3(X0,X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_183])]) ).

tff(f2160,plain,
    ! [X0: 'Bool_bool_fun$',X1: tlbool] :
      ( 'fun_app$n'(X0,X1)
      | ( tltrue != def_3(X0,X1) ) ),
    inference(cnf_transformation,[],[f1323]) ).

tff(f4384,plain,
    spl230_182,
    inference(avatar_split_clause,[],[f2116,f4382]) ).

tff(f4382,plain,
    ( spl230_182
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
        ( ( X0 = X1 )
        | ( 'matrix_to_iarray$'(X0) != 'matrix_to_iarray$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_182])]) ).

tff(f2116,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( X0 = X1 )
      | ( 'matrix_to_iarray$'(X0) != 'matrix_to_iarray$'(X1) ) ),
    inference(cnf_transformation,[],[f1287]) ).

tff(f1287,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( ( X0 = X1 )
        | ( 'matrix_to_iarray$'(X0) != 'matrix_to_iarray$'(X1) ) )
      & ( ( 'matrix_to_iarray$'(X0) = 'matrix_to_iarray$'(X1) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f59]) ).

tff(f59,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] :
      ( ( X0 = X1 )
    <=> ( 'matrix_to_iarray$'(X0) = 'matrix_to_iarray$'(X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom57) ).

tff(f4380,plain,
    spl230_181,
    inference(avatar_split_clause,[],[f2096,f4378]) ).

tff(f2096,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'the$a'(X0) != 'the$a'(X1) )
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1259]) ).

tff(f1259,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( ( 'the$a'(X0) != 'the$a'(X1) )
        & ( 'none$' != X0 )
        & ( 'none$' != X1 ) )
      | ~ sP3(X0,X1) ),
    inference(rectify,[],[f1258]) ).

tff(f1258,plain,
    ! [X1: 'A_iarray_iarray_option$',X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'the$a'(X0) != 'the$a'(X1) )
        & ( 'none$' != X1 )
        & ( 'none$' != X0 ) )
      | ~ sP3(X1,X0) ),
    inference(nnf_transformation,[],[f1083]) ).

tff(f4376,plain,
    spl230_180,
    inference(avatar_split_clause,[],[f2091,f4374]) ).

tff(f2091,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'the$'(X0) != 'the$'(X1) )
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1256]) ).

tff(f1256,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'the$'(X0) != 'the$'(X1) )
        & ( 'none$a' != X0 )
        & ( 'none$a' != X1 ) )
      | ~ sP2(X0,X1) ),
    inference(rectify,[],[f1255]) ).

tff(f1255,plain,
    ! [X1: 'A_n_vec_n_vec_option$',X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'the$'(X0) != 'the$'(X1) )
        & ( 'none$a' != X1 )
        & ( 'none$a' != X0 ) )
      | ~ sP2(X1,X0) ),
    inference(nnf_transformation,[],[f1081]) ).

tff(f4372,plain,
    spl230_179,
    inference(avatar_split_clause,[],[f1965,f4370]) ).

tff(f4370,plain,
    ( spl230_179
  <=> ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_option_bool_fun$'] :
        ( 'fun_app$t'(X0,sK55(X0))
        | ~ 'fun_app$t'(X0,'some$'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_179])]) ).

tff(f1965,plain,
    ! [X2: 'A_iarray_iarray$',X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( 'fun_app$t'(X0,sK55(X0))
      | ~ 'fun_app$t'(X0,'some$'(X2)) ),
    inference(cnf_transformation,[],[f1223]) ).

tff(f4368,plain,
    spl230_178,
    inference(avatar_split_clause,[],[f1962,f4366]) ).

tff(f4366,plain,
    ( spl230_178
  <=> ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec_option_bool_fun$'] :
        ( 'fun_app$s'(X0,sK53(X0))
        | ~ 'fun_app$s'(X0,'some$a'(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_178])]) ).

tff(f1962,plain,
    ! [X2: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( 'fun_app$s'(X0,sK53(X0))
      | ~ 'fun_app$s'(X0,'some$a'(X2)) ),
    inference(cnf_transformation,[],[f1217]) ).

tff(f4364,plain,
    spl230_177,
    inference(avatar_split_clause,[],[f1958,f4362]) ).

tff(f4362,plain,
    ( spl230_177
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( ( 'none$' = X0 )
        | ( 'some$'(sK52(X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_177])]) ).

tff(f1958,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' = X0 )
      | ( 'some$'(sK52(X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1211]) ).

tff(f1211,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 )
        | ( 'none$' != X0 ) )
      & ( ( 'none$' = X0 )
        | ( 'some$'(sK52(X0)) = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f1209,f1210]) ).

tff(f1210,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ? [X2: 'A_iarray_iarray$'] : ( 'some$'(X2) = X0 )
     => ( 'some$'(sK52(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1209,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 )
        | ( 'none$' != X0 ) )
      & ( ( 'none$' = X0 )
        | ? [X2: 'A_iarray_iarray$'] : ( 'some$'(X2) = X0 ) ) ),
    inference(rectify,[],[f1208]) ).

tff(f1208,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 )
        | ( 'none$' != X0 ) )
      & ( ( 'none$' = X0 )
        | ? [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) = X0 ) ) ),
    inference(nnf_transformation,[],[f28]) ).

tff(f28,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 )
    <=> ( 'none$' = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom26) ).

tff(f4357,plain,
    spl230_176,
    inference(avatar_split_clause,[],[f1956,f4355]) ).

tff(f4355,plain,
    ( spl230_176
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'none$a' = X0 )
        | ( 'some$a'(sK51(X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_176])]) ).

tff(f1956,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' = X0 )
      | ( 'some$a'(sK51(X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1207]) ).

tff(f1207,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 )
        | ( 'none$a' != X0 ) )
      & ( ( 'none$a' = X0 )
        | ( 'some$a'(sK51(X0)) = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1205,f1206]) ).

tff(f1206,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ? [X2: 'A_n_vec_n_vec$'] : ( 'some$a'(X2) = X0 )
     => ( 'some$a'(sK51(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1205,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 )
        | ( 'none$a' != X0 ) )
      & ( ( 'none$a' = X0 )
        | ? [X2: 'A_n_vec_n_vec$'] : ( 'some$a'(X2) = X0 ) ) ),
    inference(rectify,[],[f1204]) ).

tff(f1204,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 )
        | ( 'none$a' != X0 ) )
      & ( ( 'none$a' = X0 )
        | ? [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) = X0 ) ) ),
    inference(nnf_transformation,[],[f27]) ).

tff(f27,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 )
    <=> ( 'none$a' = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom25) ).

tff(f4353,plain,
    spl230_175,
    inference(avatar_split_clause,[],[f1954,f4351]) ).

tff(f4351,plain,
    ( spl230_175
  <=> ! [X0: 'A_iarray_iarray_option_bool_fun$',X3: 'A_iarray_iarray$'] :
        ( 'fun_app$t'(X0,'some$'(X3))
        | ~ 'fun_app$t'(X0,sK50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_175])]) ).

tff(f1954,plain,
    ! [X3: 'A_iarray_iarray$',X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( 'fun_app$t'(X0,'some$'(X3))
      | ~ 'fun_app$t'(X0,sK50(X0)) ),
    inference(cnf_transformation,[],[f1203]) ).

tff(f4349,plain,
    spl230_174,
    inference(avatar_split_clause,[],[f1951,f4347]) ).

tff(f4347,plain,
    ( spl230_174
  <=> ! [X0: 'A_n_vec_n_vec_option_bool_fun$',X3: 'A_n_vec_n_vec$'] :
        ( 'fun_app$s'(X0,'some$a'(X3))
        | ~ 'fun_app$s'(X0,sK48(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_174])]) ).

tff(f1951,plain,
    ! [X3: 'A_n_vec_n_vec$',X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( 'fun_app$s'(X0,'some$a'(X3))
      | ~ 'fun_app$s'(X0,sK48(X0)) ),
    inference(cnf_transformation,[],[f1197]) ).

tff(f4345,plain,
    spl230_173,
    inference(avatar_split_clause,[],[f1943,f4343]) ).

tff(f4343,plain,
    ( spl230_173
  <=> ! [X0: $int] :
        ( $less($sum(X0,X0),0)
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_173])]) ).

tff(f1943,plain,
    ! [X0: $int] :
      ( $less($sum(X0,X0),0)
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1188]) ).

tff(f1188,plain,
    ! [X0: $int] :
      ( ( $less($sum(X0,X0),0)
        | ~ $less(X0,0) )
      & ( $less(X0,0)
        | ~ $less($sum(X0,X0),0) ) ),
    inference(nnf_transformation,[],[f622]) ).

tff(f622,axiom,
    ! [X0: $int] :
      ( $less($sum(X0,X0),0)
    <=> $less(X0,0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom620) ).

tff(f4341,plain,
    spl230_172,
    inference(avatar_split_clause,[],[f1942,f4339]) ).

tff(f4339,plain,
    ( spl230_172
  <=> ! [X0: $int] :
        ( $less(X0,0)
        | ~ $less($sum(X0,X0),0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_172])]) ).

tff(f1942,plain,
    ! [X0: $int] :
      ( $less(X0,0)
      | ~ $less($sum(X0,X0),0) ),
    inference(cnf_transformation,[],[f1188]) ).

tff(f4337,plain,
    spl230_171,
    inference(avatar_split_clause,[],[f1940,f4335]) ).

tff(f4335,plain,
    ( spl230_171
  <=> ! [X0: $int] :
        ( $less(0,$sum(X0,X0))
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_171])]) ).

tff(f1940,plain,
    ! [X0: $int] :
      ( $less(0,$sum(X0,X0))
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1187]) ).

tff(f1187,plain,
    ! [X0: $int] :
      ( ( $less(0,$sum(X0,X0))
        | ~ $less(0,X0) )
      & ( $less(0,X0)
        | ~ $less(0,$sum(X0,X0)) ) ),
    inference(nnf_transformation,[],[f623]) ).

tff(f623,axiom,
    ! [X0: $int] :
      ( $less(0,$sum(X0,X0))
    <=> $less(0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom621) ).

tff(f4333,plain,
    spl230_170,
    inference(avatar_split_clause,[],[f1939,f4331]) ).

tff(f4331,plain,
    ( spl230_170
  <=> ! [X0: $int] :
        ( $less(0,X0)
        | ~ $less(0,$sum(X0,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_170])]) ).

tff(f1939,plain,
    ! [X0: $int] :
      ( $less(0,X0)
      | ~ $less(0,$sum(X0,X0)) ),
    inference(cnf_transformation,[],[f1187]) ).

tff(f4329,plain,
    spl230_169,
    inference(avatar_split_clause,[],[f1933,f4327]) ).

tff(f4327,plain,
    ( spl230_169
  <=> ! [X0: $int] :
        ( ( 0 = X0 )
        | ( 0 != $sum(X0,X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_169])]) ).

tff(f1933,plain,
    ! [X0: $int] :
      ( ( 0 = X0 )
      | ( 0 != $sum(X0,X0) ) ),
    inference(cnf_transformation,[],[f1181]) ).

tff(f1181,plain,
    ! [X0: $int] :
      ( ( ( 0 = $sum(X0,X0) )
        | ( 0 != X0 ) )
      & ( ( 0 = X0 )
        | ( 0 != $sum(X0,X0) ) ) ),
    inference(nnf_transformation,[],[f370]) ).

tff(f370,axiom,
    ! [X0: $int] :
      ( ( 0 = $sum(X0,X0) )
    <=> ( 0 = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom368) ).

tff(f4325,plain,
    ( spl230_168
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_166 ),
    inference(avatar_split_clause,[],[f4316,f4313,f3988,f3928,f4323]) ).

tff(f4323,plain,
    ( spl230_168
  <=> ! [X0: 'Int_int_prod$'] :
        ( ( 0 != sK41(X0) )
        | 'fun_app$ae'('divides_aux$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_168])]) ).

tff(f4313,plain,
    ( spl230_166
  <=> ! [X0: 'Int_int_prod$'] :
        ( 'fun_app$ae'('divides_aux$',X0)
        | ( 'fun_app$ac'('snd$b',X0) != 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_166])]) ).

tff(f4316,plain,
    ( ! [X0: 'Int_int_prod$'] :
        ( ( 0 != sK41(X0) )
        | 'fun_app$ae'('divides_aux$',X0) )
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_166 ),
    inference(forward_demodulation,[],[f4314,f4190]) ).

tff(f4314,plain,
    ( ! [X0: 'Int_int_prod$'] :
        ( 'fun_app$ae'('divides_aux$',X0)
        | ( 'fun_app$ac'('snd$b',X0) != 0 ) )
    | ~ spl230_166 ),
    inference(avatar_component_clause,[],[f4313]) ).

tff(f4321,plain,
    ( spl230_167
    | ~ spl230_69
    | ~ spl230_165 ),
    inference(avatar_split_clause,[],[f4311,f4307,f3802,f4318]) ).

tff(f3802,plain,
    ( spl230_69
  <=> 'fun_app$ae'('divides_aux$','zero$a') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_69])]) ).

tff(f4311,plain,
    ( ( 0 = sK41('zero$a') )
    | ~ spl230_69
    | ~ spl230_165 ),
    inference(resolution,[],[f4308,f3804]) ).

tff(f3804,plain,
    ( 'fun_app$ae'('divides_aux$','zero$a')
    | ~ spl230_69 ),
    inference(avatar_component_clause,[],[f3802]) ).

tff(f4315,plain,
    spl230_166,
    inference(avatar_split_clause,[],[f1918,f4313]) ).

tff(f1918,plain,
    ! [X0: 'Int_int_prod$'] :
      ( 'fun_app$ae'('divides_aux$',X0)
      | ( 'fun_app$ac'('snd$b',X0) != 0 ) ),
    inference(cnf_transformation,[],[f1175]) ).

tff(f1175,plain,
    ! [X0: 'Int_int_prod$'] :
      ( ( 'fun_app$ae'('divides_aux$',X0)
        | ( 'fun_app$ac'('snd$b',X0) != 0 ) )
      & ( ( 'fun_app$ac'('snd$b',X0) = 0 )
        | ~ 'fun_app$ae'('divides_aux$',X0) ) ),
    inference(nnf_transformation,[],[f466]) ).

tff(f466,axiom,
    ! [X0: 'Int_int_prod$'] :
      ( 'fun_app$ae'('divides_aux$',X0)
    <=> ( 'fun_app$ac'('snd$b',X0) = 0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom464) ).

tff(f4309,plain,
    ( spl230_165
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_164 ),
    inference(avatar_split_clause,[],[f4305,f4302,f3988,f3928,f4307]) ).

tff(f4302,plain,
    ( spl230_164
  <=> ! [X0: 'Int_int_prod$'] :
        ( ( 'fun_app$ac'('snd$b',X0) = 0 )
        | ~ 'fun_app$ae'('divides_aux$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_164])]) ).

tff(f4305,plain,
    ( ! [X0: 'Int_int_prod$'] :
        ( ( 0 = sK41(X0) )
        | ~ 'fun_app$ae'('divides_aux$',X0) )
    | ~ spl230_96
    | ~ spl230_111
    | ~ spl230_164 ),
    inference(forward_demodulation,[],[f4303,f4190]) ).

tff(f4303,plain,
    ( ! [X0: 'Int_int_prod$'] :
        ( ( 'fun_app$ac'('snd$b',X0) = 0 )
        | ~ 'fun_app$ae'('divides_aux$',X0) )
    | ~ spl230_164 ),
    inference(avatar_component_clause,[],[f4302]) ).

tff(f4304,plain,
    spl230_164,
    inference(avatar_split_clause,[],[f1917,f4302]) ).

tff(f1917,plain,
    ! [X0: 'Int_int_prod$'] :
      ( ( 'fun_app$ac'('snd$b',X0) = 0 )
      | ~ 'fun_app$ae'('divides_aux$',X0) ),
    inference(cnf_transformation,[],[f1175]) ).

tff(f4300,plain,
    spl230_163,
    inference(avatar_split_clause,[],[f1914,f4298]) ).

tff(f4298,plain,
    ( spl230_163
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( ( 'none$' = X0 )
        | ~ 'fun_app$t'('case_option$a'(tltrue,'uui$'),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_163])]) ).

tff(f1914,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' = X0 )
      | ~ 'fun_app$t'('case_option$a'(tltrue,'uui$'),X0) ),
    inference(cnf_transformation,[],[f1173]) ).

tff(f1173,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'none$' = X0 )
        | ~ 'fun_app$t'('case_option$a'(tltrue,'uui$'),X0) )
      & ( 'fun_app$t'('case_option$a'(tltrue,'uui$'),X0)
        | ( 'none$' != X0 ) ) ),
    inference(nnf_transformation,[],[f86]) ).

tff(f86,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' = X0 )
    <=> 'fun_app$t'('case_option$a'(tltrue,'uui$'),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom84) ).

tff(f4296,plain,
    spl230_162,
    inference(avatar_split_clause,[],[f1908,f4294]) ).

tff(f4294,plain,
    ( spl230_162
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'none$a' = X0 )
        | ~ 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_162])]) ).

tff(f1908,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' = X0 )
      | ~ 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0) ),
    inference(cnf_transformation,[],[f1170]) ).

tff(f1170,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' = X0 )
        | ~ 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0) )
      & ( 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0)
        | ( 'none$a' != X0 ) ) ),
    inference(nnf_transformation,[],[f85]) ).

tff(f85,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' = X0 )
    <=> 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom83) ).

tff(f4292,plain,
    spl230_161,
    inference(avatar_split_clause,[],[f1903,f4290]) ).

tff(f4290,plain,
    ( spl230_161
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( ( 'some$'(sK45(X0)) = X0 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_161])]) ).

tff(f1903,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK45(X0)) = X0 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1168]) ).

tff(f1168,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'none$' != X0 )
        | ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 ) )
      & ( ( 'some$'(sK45(X0)) = X0 )
        | ( 'none$' = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1166,f1167]) ).

tff(f1167,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ? [X2: 'A_iarray_iarray$'] : ( 'some$'(X2) = X0 )
     => ( 'some$'(sK45(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1166,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'none$' != X0 )
        | ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 ) )
      & ( ? [X2: 'A_iarray_iarray$'] : ( 'some$'(X2) = X0 )
        | ( 'none$' = X0 ) ) ),
    inference(rectify,[],[f1165]) ).

tff(f1165,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'none$' != X0 )
        | ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 ) )
      & ( ? [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) = X0 )
        | ( 'none$' = X0 ) ) ),
    inference(nnf_transformation,[],[f26]) ).

tff(f26,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X0 )
    <=> ? [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom24) ).

tff(f4288,plain,
    spl230_160,
    inference(avatar_split_clause,[],[f1901,f4286]) ).

tff(f4286,plain,
    ( spl230_160
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0)
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_160])]) ).

tff(f1901,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0)
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1164]) ).

tff(f1164,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ( 'none$' != X0 )
        | ~ 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0) )
      & ( 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0)
        | ( 'none$' = X0 ) ) ),
    inference(nnf_transformation,[],[f84]) ).

tff(f84,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X0 )
    <=> 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom82) ).

tff(f4284,plain,
    spl230_159,
    inference(avatar_split_clause,[],[f1899,f4282]) ).

tff(f4282,plain,
    ( spl230_159
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'(sK44(X0)) = X0 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_159])]) ).

tff(f1899,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK44(X0)) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1163]) ).

tff(f1163,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' != X0 )
        | ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 ) )
      & ( ( 'some$a'(sK44(X0)) = X0 )
        | ( 'none$a' = X0 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1161,f1162]) ).

tff(f1162,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ? [X2: 'A_n_vec_n_vec$'] : ( 'some$a'(X2) = X0 )
     => ( 'some$a'(sK44(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1161,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' != X0 )
        | ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 ) )
      & ( ? [X2: 'A_n_vec_n_vec$'] : ( 'some$a'(X2) = X0 )
        | ( 'none$a' = X0 ) ) ),
    inference(rectify,[],[f1160]) ).

tff(f1160,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' != X0 )
        | ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 ) )
      & ( ? [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) = X0 )
        | ( 'none$a' = X0 ) ) ),
    inference(nnf_transformation,[],[f25]) ).

tff(f25,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X0 )
    <=> ? [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom23) ).

tff(f4280,plain,
    spl230_158,
    inference(avatar_split_clause,[],[f1897,f4278]) ).

tff(f4278,plain,
    ( spl230_158
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0)
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_158])]) ).

tff(f1897,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0)
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1159]) ).

tff(f1159,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ( 'none$a' != X0 )
        | ~ 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0) )
      & ( 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0)
        | ( 'none$a' = X0 ) ) ),
    inference(nnf_transformation,[],[f83]) ).

tff(f83,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X0 )
    <=> 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom81) ).

tff(f4274,plain,
    spl230_157,
    inference(avatar_split_clause,[],[f1885,f4272]) ).

tff(f4272,plain,
    ( spl230_157
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( ( 'some$'(sK34(X0)) = X0 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_157])]) ).

tff(f1885,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK34(X0)) = X0 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f1148]) ).

tff(f1148,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'some$'(sK34(X0)) = X0 )
      | ( 'none$' = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f804,f1147]) ).

tff(f1147,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ? [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) = X0 )
     => ( 'some$'(sK34(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f804,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ? [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) = X0 )
      | ( 'none$' = X0 ) ),
    inference(ennf_transformation,[],[f692]) ).

tff(f692,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ~ ( ! [X1: 'A_iarray_iarray$'] : ( 'some$'(X1) != X0 )
        & ( 'none$' != X0 ) ),
    inference(flattening,[],[f691]) ).

tff(f691,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ~ ( ! [X1: 'A_iarray_iarray$'] :
            ( ~ 'some$'(X1) = X0 )
        & ( ~ 'none$' = X0 ) ),
    inference(true_and_false_elimination,[],[f39]) ).

tff(f39,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( ! [X1: 'A_iarray_iarray$'] :
            ( ( 'some$'(X1) = X0 )
           => $false )
        & ( ( 'none$' = X0 )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom37) ).

tff(f4270,plain,
    spl230_156,
    inference(avatar_split_clause,[],[f1882,f4268]) ).

tff(f4268,plain,
    ( spl230_156
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'(sK33(X0)) = X0 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_156])]) ).

tff(f1882,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK33(X0)) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f1146]) ).

tff(f1146,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'(sK33(X0)) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f801,f1145]) ).

tff(f1145,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ? [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) = X0 )
     => ( 'some$a'(sK33(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f801,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ? [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(ennf_transformation,[],[f686]) ).

tff(f686,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ~ ( ! [X1: 'A_n_vec_n_vec$'] : ( 'some$a'(X1) != X0 )
        & ( 'none$a' != X0 ) ),
    inference(flattening,[],[f685]) ).

tff(f685,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ~ ( ! [X1: 'A_n_vec_n_vec$'] :
            ( ~ 'some$a'(X1) = X0 )
        & ( ~ 'none$a' = X0 ) ),
    inference(true_and_false_elimination,[],[f38]) ).

tff(f38,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( ! [X1: 'A_n_vec_n_vec$'] :
            ( ( 'some$a'(X1) = X0 )
           => $false )
        & ( ( 'none$a' = X0 )
         => $false ) )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom36) ).

tff(f4266,plain,
    spl230_155,
    inference(avatar_split_clause,[],[f1871,f4264]) ).

tff(f4264,plain,
    ( spl230_155
  <=> ! [X0: 'A_iarray_iarray_option$'] :
        ( ( 'some$'('the$a'(X0)) = X0 )
        | ( 'none$' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_155])]) ).

tff(f1871,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'some$'('the$a'(X0)) = X0 )
      | ( 'none$' = X0 ) ),
    inference(cnf_transformation,[],[f792]) ).

tff(f792,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'some$'('the$a'(X0)) = X0 )
      | ( 'none$' = X0 ) ),
    inference(ennf_transformation,[],[f68]) ).

tff(f68,axiom,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X0 )
     => ( 'some$'('the$a'(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom66) ).

tff(f4262,plain,
    spl230_154,
    inference(avatar_split_clause,[],[f1869,f4260]) ).

tff(f4260,plain,
    ( spl230_154
  <=> ! [X0: 'A_n_vec_n_vec_option$'] :
        ( ( 'some$a'('the$'(X0)) = X0 )
        | ( 'none$a' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_154])]) ).

tff(f1869,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'('the$'(X0)) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(cnf_transformation,[],[f790]) ).

tff(f790,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'some$a'('the$'(X0)) = X0 )
      | ( 'none$a' = X0 ) ),
    inference(ennf_transformation,[],[f67]) ).

tff(f67,axiom,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X0 )
     => ( 'some$a'('the$'(X0)) = X0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom65) ).

tff(f4258,plain,
    spl230_153,
    inference(avatar_split_clause,[],[f675,f4256]) ).

tff(f675,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f4254,plain,
    spl230_152,
    inference(avatar_split_clause,[],[f673,f4252]) ).

tff(f673,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f4237,plain,
    ( spl230_151
    | ~ spl230_73
    | ~ spl230_97 ),
    inference(avatar_split_clause,[],[f4153,f3932,f3819,f4235]) ).

tff(f4225,plain,
    ( spl230_150
    | ~ spl230_75
    | ~ spl230_97 ),
    inference(avatar_split_clause,[],[f4152,f3932,f3827,f4223]) ).

tff(f4212,plain,
    ( spl230_149
    | ~ spl230_74
    | ~ spl230_95 ),
    inference(avatar_split_clause,[],[f4151,f3924,f3823,f4210]) ).

tff(f4196,plain,
    ( spl230_148
    | ~ spl230_76
    | ~ spl230_95 ),
    inference(avatar_split_clause,[],[f4150,f3924,f3831,f4194]) ).

tff(f4160,plain,
    ( spl230_147
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_146 ),
    inference(avatar_split_clause,[],[f4149,f4145,f3895,f3857,f4157]) ).

tff(f4145,plain,
    ( spl230_146
  <=> ( 'size$c'('none$') = 'fun_app$k'('nat$',1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_146])]) ).

tff(f4149,plain,
    ( ( 'size$d'('none$a') = 'size$c'('none$') )
    | ~ spl230_82
    | ~ spl230_88
    | ~ spl230_146 ),
    inference(forward_demodulation,[],[f4147,f4138]) ).

tff(f4147,plain,
    ( ( 'size$c'('none$') = 'fun_app$k'('nat$',1) )
    | ~ spl230_146 ),
    inference(avatar_component_clause,[],[f4145]) ).

tff(f4148,plain,
    ( spl230_146
    | ~ spl230_81
    | ~ spl230_88 ),
    inference(avatar_split_clause,[],[f4135,f3895,f3852,f4145]) ).

tff(f3852,plain,
    ( spl230_81
  <=> ( 1 = 'fun_app$l'('of_nat$','size$c'('none$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_81])]) ).

tff(f4135,plain,
    ( ( 'size$c'('none$') = 'fun_app$k'('nat$',1) )
    | ~ spl230_81
    | ~ spl230_88 ),
    inference(superposition,[],[f3896,f3854]) ).

tff(f3854,plain,
    ( ( 1 = 'fun_app$l'('of_nat$','size$c'('none$')) )
    | ~ spl230_81 ),
    inference(avatar_component_clause,[],[f3852]) ).

tff(f4126,plain,
    spl230_145,
    inference(avatar_split_clause,[],[f3340,f4124]) ).

tff(f4124,plain,
    ( spl230_145
  <=> ! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$l'('of_nat$',X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_145])]) ).

tff(f3340,plain,
    ! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$l'('of_nat$',X0))),
    inference(forward_demodulation,[],[f1826,f664]) ).

tff(f1826,plain,
    ! [X0: 'Nat$'] : $less(0,$sum('fun_app$l'('of_nat$',X0),1)),
    inference(cnf_transformation,[],[f624]) ).

tff(f624,axiom,
    ! [X0: 'Nat$'] : $less(0,$sum('fun_app$l'('of_nat$',X0),1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom622) ).

tff(f4122,plain,
    spl230_144,
    inference(avatar_split_clause,[],[f3309,f4120]) ).

tff(f3309,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','size$c'('some$'(X0))) = 1 ),
    inference(evaluation,[],[f1838]) ).

tff(f1838,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','size$c'('some$'(X0))) = $sum(0,1) ),
    inference(cnf_transformation,[],[f437]) ).

tff(f437,axiom,
    ! [X0: 'A_iarray_iarray$'] : ( 'fun_app$l'('of_nat$','size$c'('some$'(X0))) = $sum(0,1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom435) ).

tff(f4118,plain,
    spl230_143,
    inference(avatar_split_clause,[],[f3139,f4116]) ).

tff(f4116,plain,
    ( spl230_143
  <=> ! [X2: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
        ( ( tltrue = X2 )
        | ~ sP14('none$',X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_143])]) ).

tff(f3139,plain,
    ! [X2: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = X2 )
      | ~ sP14('none$',X1,X2) ),
    inference(equality_resolution,[],[f2517]) ).

tff(f2517,plain,
    ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( ( tltrue = X2 )
      | ( 'none$' != X0 )
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f4114,plain,
    spl230_142,
    inference(avatar_split_clause,[],[f2159,f4112]) ).

tff(f4112,plain,
    ( spl230_142
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
        ( 'member$'(X0,'collect$'(X1))
        | ~ 'fun_app$a'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_142])]) ).

tff(f2159,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
      ( 'member$'(X0,'collect$'(X1))
      | ~ 'fun_app$a'(X1,X0) ),
    inference(cnf_transformation,[],[f1322]) ).

tff(f1322,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
      ( ( 'member$'(X0,'collect$'(X1))
        | ~ 'fun_app$a'(X1,X0) )
      & ( 'fun_app$a'(X1,X0)
        | ~ 'member$'(X0,'collect$'(X1)) ) ),
    inference(nnf_transformation,[],[f94]) ).

tff(f94,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
      ( 'member$'(X0,'collect$'(X1))
    <=> 'fun_app$a'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom92) ).

tff(f4110,plain,
    spl230_141,
    inference(avatar_split_clause,[],[f2158,f4108]) ).

tff(f4108,plain,
    ( spl230_141
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
        ( 'fun_app$a'(X1,X0)
        | ~ 'member$'(X0,'collect$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_141])]) ).

tff(f2158,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$',X1: 'A_iarray_list_a_iarray_list_prod_bool_fun$'] :
      ( 'fun_app$a'(X1,X0)
      | ~ 'member$'(X0,'collect$'(X1)) ),
    inference(cnf_transformation,[],[f1322]) ).

tff(f4106,plain,
    spl230_140,
    inference(avatar_split_clause,[],[f2157,f4104]) ).

tff(f4104,plain,
    ( spl230_140
  <=> ! [X0: 'Nat_set$',X1: 'Nat$'] :
        ( 'fun_app$c'('uum$'(X0),X1)
        | ~ 'member$c'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_140])]) ).

tff(f2157,plain,
    ! [X0: 'Nat_set$',X1: 'Nat$'] :
      ( 'fun_app$c'('uum$'(X0),X1)
      | ~ 'member$c'(X1,X0) ),
    inference(cnf_transformation,[],[f1321]) ).

tff(f1321,plain,
    ! [X0: 'Nat_set$',X1: 'Nat$'] :
      ( ( 'fun_app$c'('uum$'(X0),X1)
        | ~ 'member$c'(X1,X0) )
      & ( 'member$c'(X1,X0)
        | ~ 'fun_app$c'('uum$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f5,axiom,
    ! [X0: 'Nat_set$',X1: 'Nat$'] :
      ( 'fun_app$c'('uum$'(X0),X1)
    <=> 'member$c'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom4) ).

tff(f4102,plain,
    spl230_139,
    inference(avatar_split_clause,[],[f2156,f4100]) ).

tff(f4100,plain,
    ( spl230_139
  <=> ! [X0: 'Nat_set$',X1: 'Nat$'] :
        ( 'member$c'(X1,X0)
        | ~ 'fun_app$c'('uum$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_139])]) ).

tff(f2156,plain,
    ! [X0: 'Nat_set$',X1: 'Nat$'] :
      ( 'member$c'(X1,X0)
      | ~ 'fun_app$c'('uum$'(X0),X1) ),
    inference(cnf_transformation,[],[f1321]) ).

tff(f4098,plain,
    spl230_138,
    inference(avatar_split_clause,[],[f2155,f4096]) ).

tff(f4096,plain,
    ( spl230_138
  <=> ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
        ( 'fun_app$b'('uuk$'(X0),X1)
        | ~ 'member$b'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_138])]) ).

tff(f2155,plain,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
      ( 'fun_app$b'('uuk$'(X0),X1)
      | ~ 'member$b'(X1,X0) ),
    inference(cnf_transformation,[],[f1320]) ).

tff(f1320,plain,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$b'('uuk$'(X0),X1)
        | ~ 'member$b'(X1,X0) )
      & ( 'member$b'(X1,X0)
        | ~ 'fun_app$b'('uuk$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f4]) ).

tff(f4,axiom,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
      ( 'fun_app$b'('uuk$'(X0),X1)
    <=> 'member$b'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).

tff(f4094,plain,
    spl230_137,
    inference(avatar_split_clause,[],[f2154,f4092]) ).

tff(f4092,plain,
    ( spl230_137
  <=> ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
        ( 'member$b'(X1,X0)
        | ~ 'fun_app$b'('uuk$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_137])]) ).

tff(f2154,plain,
    ! [X0: 'A_iarray_list_set$',X1: 'A_iarray_list$'] :
      ( 'member$b'(X1,X0)
      | ~ 'fun_app$b'('uuk$'(X0),X1) ),
    inference(cnf_transformation,[],[f1320]) ).

tff(f4090,plain,
    spl230_136,
    inference(avatar_split_clause,[],[f2153,f4088]) ).

tff(f4088,plain,
    ( spl230_136
  <=> ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
        ( 'fun_app$b'('uuc$'(X0),X1)
        | 'fun_app$b'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_136])]) ).

tff(f2153,plain,
    ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'fun_app$b'('uuc$'(X0),X1)
      | 'fun_app$b'(X0,X1) ),
    inference(cnf_transformation,[],[f1319]) ).

tff(f1319,plain,
    ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$b'('uuc$'(X0),X1)
        | 'fun_app$b'(X0,X1) )
      & ( ~ 'fun_app$b'(X0,X1)
        | ~ 'fun_app$b'('uuc$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
      ( 'fun_app$b'('uuc$'(X0),X1)
    <=> ~ 'fun_app$b'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom8) ).

tff(f4086,plain,
    spl230_135,
    inference(avatar_split_clause,[],[f2152,f4084]) ).

tff(f4084,plain,
    ( spl230_135
  <=> ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
        ( ~ 'fun_app$b'(X0,X1)
        | ~ 'fun_app$b'('uuc$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_135])]) ).

tff(f2152,plain,
    ! [X0: 'A_iarray_list_bool_fun$',X1: 'A_iarray_list$'] :
      ( ~ 'fun_app$b'(X0,X1)
      | ~ 'fun_app$b'('uuc$'(X0),X1) ),
    inference(cnf_transformation,[],[f1319]) ).

tff(f4082,plain,
    spl230_134,
    inference(avatar_split_clause,[],[f2151,f4080]) ).

tff(f4080,plain,
    ( spl230_134
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( 'member$a'(X0,'collect$d'(X1))
        | ~ 'fun_app$'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_134])]) ).

tff(f2151,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
      ( 'member$a'(X0,'collect$d'(X1))
      | ~ 'fun_app$'(X1,X0) ),
    inference(cnf_transformation,[],[f1318]) ).

tff(f1318,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
      ( ( 'member$a'(X0,'collect$d'(X1))
        | ~ 'fun_app$'(X1,X0) )
      & ( 'fun_app$'(X1,X0)
        | ~ 'member$a'(X0,'collect$d'(X1)) ) ),
    inference(nnf_transformation,[],[f98]) ).

tff(f98,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
      ( 'member$a'(X0,'collect$d'(X1))
    <=> 'fun_app$'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom96) ).

tff(f4078,plain,
    spl230_133,
    inference(avatar_split_clause,[],[f2150,f4076]) ).

tff(f4076,plain,
    ( spl230_133
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
        ( 'fun_app$'(X1,X0)
        | ~ 'member$a'(X0,'collect$d'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_133])]) ).

tff(f2150,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_bool_fun$'] :
      ( 'fun_app$'(X1,X0)
      | ~ 'member$a'(X0,'collect$d'(X1)) ),
    inference(cnf_transformation,[],[f1318]) ).

tff(f4074,plain,
    spl230_132,
    inference(avatar_split_clause,[],[f2149,f4072]) ).

tff(f4072,plain,
    ( spl230_132
  <=> ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
        ( 'fun_app$'('uun$'(X0),X1)
        | ~ 'member$a'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_132])]) ).

tff(f2149,plain,
    ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
      ( 'fun_app$'('uun$'(X0),X1)
      | ~ 'member$a'(X1,X0) ),
    inference(cnf_transformation,[],[f1317]) ).

tff(f1317,plain,
    ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
      ( ( 'fun_app$'('uun$'(X0),X1)
        | ~ 'member$a'(X1,X0) )
      & ( 'member$a'(X1,X0)
        | ~ 'fun_app$'('uun$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f3]) ).

tff(f3,axiom,
    ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
      ( 'fun_app$'('uun$'(X0),X1)
    <=> 'member$a'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).

tff(f4070,plain,
    spl230_131,
    inference(avatar_split_clause,[],[f2148,f4068]) ).

tff(f4068,plain,
    ( spl230_131
  <=> ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
        ( 'member$a'(X1,X0)
        | ~ 'fun_app$'('uun$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_131])]) ).

tff(f2148,plain,
    ! [X0: 'A_iarray_set$',X1: 'A_iarray$'] :
      ( 'member$a'(X1,X0)
      | ~ 'fun_app$'('uun$'(X0),X1) ),
    inference(cnf_transformation,[],[f1317]) ).

tff(f4066,plain,
    spl230_130,
    inference(avatar_split_clause,[],[f2147,f4064]) ).

tff(f4064,plain,
    ( spl230_130
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
        ( 'fun_app$'('uud$'(X0),X1)
        | 'fun_app$'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_130])]) ).

tff(f2147,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( 'fun_app$'('uud$'(X0),X1)
      | 'fun_app$'(X0,X1) ),
    inference(cnf_transformation,[],[f1316]) ).

tff(f1316,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( ( 'fun_app$'('uud$'(X0),X1)
        | 'fun_app$'(X0,X1) )
      & ( ~ 'fun_app$'(X0,X1)
        | ~ 'fun_app$'('uud$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( 'fun_app$'('uud$'(X0),X1)
    <=> ~ 'fun_app$'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom7) ).

tff(f4062,plain,
    spl230_129,
    inference(avatar_split_clause,[],[f2146,f4060]) ).

tff(f4060,plain,
    ( spl230_129
  <=> ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
        ( ~ 'fun_app$'(X0,X1)
        | ~ 'fun_app$'('uud$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_129])]) ).

tff(f2146,plain,
    ! [X0: 'A_iarray_bool_fun$',X1: 'A_iarray$'] :
      ( ~ 'fun_app$'(X0,X1)
      | ~ 'fun_app$'('uud$'(X0),X1) ),
    inference(cnf_transformation,[],[f1316]) ).

tff(f4058,plain,
    spl230_128,
    inference(avatar_split_clause,[],[f2145,f4056]) ).

tff(f4056,plain,
    ( spl230_128
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'member$c'(X0,'collect$c'(X1))
        | ~ 'fun_app$c'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_128])]) ).

tff(f2145,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'member$c'(X0,'collect$c'(X1))
      | ~ 'fun_app$c'(X1,X0) ),
    inference(cnf_transformation,[],[f1315]) ).

tff(f1315,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ( 'member$c'(X0,'collect$c'(X1))
        | ~ 'fun_app$c'(X1,X0) )
      & ( 'fun_app$c'(X1,X0)
        | ~ 'member$c'(X0,'collect$c'(X1)) ) ),
    inference(nnf_transformation,[],[f97]) ).

tff(f97,axiom,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'member$c'(X0,'collect$c'(X1))
    <=> 'fun_app$c'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom95) ).

tff(f4054,plain,
    spl230_127,
    inference(avatar_split_clause,[],[f2144,f4052]) ).

tff(f4052,plain,
    ( spl230_127
  <=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$c'(X1,X0)
        | ~ 'member$c'(X0,'collect$c'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_127])]) ).

tff(f2144,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$c'(X1,X0)
      | ~ 'member$c'(X0,'collect$c'(X1)) ),
    inference(cnf_transformation,[],[f1315]) ).

tff(f4050,plain,
    spl230_126,
    inference(avatar_split_clause,[],[f2143,f4048]) ).

tff(f4048,plain,
    ( spl230_126
  <=> ! [X0: $int,X1: 'Int_bool_fun$'] :
        ( 'member$d'(X0,'collect$b'(X1))
        | ~ 'fun_app$d'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_126])]) ).

tff(f2143,plain,
    ! [X0: $int,X1: 'Int_bool_fun$'] :
      ( 'member$d'(X0,'collect$b'(X1))
      | ~ 'fun_app$d'(X1,X0) ),
    inference(cnf_transformation,[],[f1314]) ).

tff(f1314,plain,
    ! [X0: $int,X1: 'Int_bool_fun$'] :
      ( ( 'member$d'(X0,'collect$b'(X1))
        | ~ 'fun_app$d'(X1,X0) )
      & ( 'fun_app$d'(X1,X0)
        | ~ 'member$d'(X0,'collect$b'(X1)) ) ),
    inference(nnf_transformation,[],[f96]) ).

tff(f96,axiom,
    ! [X0: $int,X1: 'Int_bool_fun$'] :
      ( 'member$d'(X0,'collect$b'(X1))
    <=> 'fun_app$d'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom94) ).

tff(f4046,plain,
    spl230_125,
    inference(avatar_split_clause,[],[f2142,f4044]) ).

tff(f4044,plain,
    ( spl230_125
  <=> ! [X0: $int,X1: 'Int_bool_fun$'] :
        ( 'fun_app$d'(X1,X0)
        | ~ 'member$d'(X0,'collect$b'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_125])]) ).

tff(f2142,plain,
    ! [X0: $int,X1: 'Int_bool_fun$'] :
      ( 'fun_app$d'(X1,X0)
      | ~ 'member$d'(X0,'collect$b'(X1)) ),
    inference(cnf_transformation,[],[f1314]) ).

tff(f4042,plain,
    spl230_124,
    inference(avatar_split_clause,[],[f2141,f4040]) ).

tff(f4040,plain,
    ( spl230_124
  <=> ! [X0: 'Int_set$',X1: $int] :
        ( 'fun_app$d'('uul$'(X0),X1)
        | ~ 'member$d'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_124])]) ).

tff(f2141,plain,
    ! [X0: 'Int_set$',X1: $int] :
      ( 'fun_app$d'('uul$'(X0),X1)
      | ~ 'member$d'(X1,X0) ),
    inference(cnf_transformation,[],[f1313]) ).

tff(f1313,plain,
    ! [X0: 'Int_set$',X1: $int] :
      ( ( 'fun_app$d'('uul$'(X0),X1)
        | ~ 'member$d'(X1,X0) )
      & ( 'member$d'(X1,X0)
        | ~ 'fun_app$d'('uul$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f6]) ).

tff(f6,axiom,
    ! [X0: 'Int_set$',X1: $int] :
      ( 'fun_app$d'('uul$'(X0),X1)
    <=> 'member$d'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).

tff(f4038,plain,
    spl230_123,
    inference(avatar_split_clause,[],[f2140,f4036]) ).

tff(f4036,plain,
    ( spl230_123
  <=> ! [X0: 'Int_set$',X1: $int] :
        ( 'member$d'(X1,X0)
        | ~ 'fun_app$d'('uul$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_123])]) ).

tff(f2140,plain,
    ! [X0: 'Int_set$',X1: $int] :
      ( 'member$d'(X1,X0)
      | ~ 'fun_app$d'('uul$'(X0),X1) ),
    inference(cnf_transformation,[],[f1313]) ).

tff(f4034,plain,
    spl230_122,
    inference(avatar_split_clause,[],[f2139,f4032]) ).

tff(f4032,plain,
    ( spl230_122
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
        ( 'fun_app$a'('uuj$'(X0),X1)
        | ~ 'member$'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_122])]) ).

tff(f2139,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'fun_app$a'('uuj$'(X0),X1)
      | ~ 'member$'(X1,X0) ),
    inference(cnf_transformation,[],[f1312]) ).

tff(f1312,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ( 'fun_app$a'('uuj$'(X0),X1)
        | ~ 'member$'(X1,X0) )
      & ( 'member$'(X1,X0)
        | ~ 'fun_app$a'('uuj$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'fun_app$a'('uuj$'(X0),X1)
    <=> 'member$'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).

tff(f4030,plain,
    spl230_121,
    inference(avatar_split_clause,[],[f2138,f4028]) ).

tff(f4028,plain,
    ( spl230_121
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
        ( 'member$'(X1,X0)
        | ~ 'fun_app$a'('uuj$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_121])]) ).

tff(f2138,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$',X1: 'A_iarray_list_a_iarray_list_prod$'] :
      ( 'member$'(X1,X0)
      | ~ 'fun_app$a'('uuj$'(X0),X1) ),
    inference(cnf_transformation,[],[f1312]) ).

tff(f4026,plain,
    spl230_120,
    inference(avatar_split_clause,[],[f2137,f4024]) ).

tff(f4024,plain,
    ( spl230_120
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
        ( 'member$b'(X0,'collect$a'(X1))
        | ~ 'fun_app$b'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_120])]) ).

tff(f2137,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
      ( 'member$b'(X0,'collect$a'(X1))
      | ~ 'fun_app$b'(X1,X0) ),
    inference(cnf_transformation,[],[f1311]) ).

tff(f1311,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
      ( ( 'member$b'(X0,'collect$a'(X1))
        | ~ 'fun_app$b'(X1,X0) )
      & ( 'fun_app$b'(X1,X0)
        | ~ 'member$b'(X0,'collect$a'(X1)) ) ),
    inference(nnf_transformation,[],[f95]) ).

tff(f95,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
      ( 'member$b'(X0,'collect$a'(X1))
    <=> 'fun_app$b'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom93) ).

tff(f4022,plain,
    spl230_119,
    inference(avatar_split_clause,[],[f2136,f4020]) ).

tff(f4020,plain,
    ( spl230_119
  <=> ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
        ( 'fun_app$b'(X1,X0)
        | ~ 'member$b'(X0,'collect$a'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_119])]) ).

tff(f2136,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list_bool_fun$'] :
      ( 'fun_app$b'(X1,X0)
      | ~ 'member$b'(X0,'collect$a'(X1)) ),
    inference(cnf_transformation,[],[f1311]) ).

tff(f4018,plain,
    spl230_118,
    inference(avatar_split_clause,[],[f2135,f4016]) ).

tff(f4016,plain,
    ( spl230_118
  <=> ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
        ( 'fun_app$e'('uub$'(X0),X1)
        | 'fun_app$e'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_118])]) ).

tff(f2135,plain,
    ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
      ( 'fun_app$e'('uub$'(X0),X1)
      | 'fun_app$e'(X0,X1) ),
    inference(cnf_transformation,[],[f1310]) ).

tff(f1310,plain,
    ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
      ( ( 'fun_app$e'('uub$'(X0),X1)
        | 'fun_app$e'(X0,X1) )
      & ( ~ 'fun_app$e'(X0,X1)
        | ~ 'fun_app$e'('uub$'(X0),X1) ) ),
    inference(nnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
      ( 'fun_app$e'('uub$'(X0),X1)
    <=> ~ 'fun_app$e'(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom6) ).

tff(f4014,plain,
    spl230_117,
    inference(avatar_split_clause,[],[f2134,f4012]) ).

tff(f4012,plain,
    ( spl230_117
  <=> ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
        ( ~ 'fun_app$e'(X0,X1)
        | ~ 'fun_app$e'('uub$'(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_117])]) ).

tff(f2134,plain,
    ! [X0: 'Nat_a_iarray_prod_bool_fun$',X1: 'Nat_a_iarray_prod$'] :
      ( ~ 'fun_app$e'(X0,X1)
      | ~ 'fun_app$e'('uub$'(X0),X1) ),
    inference(cnf_transformation,[],[f1310]) ).

tff(f4010,plain,
    spl230_116,
    inference(avatar_split_clause,[],[f1993,f4008]) ).

tff(f4008,plain,
    ( spl230_116
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_116])]) ).

tff(f1993,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1))),
    inference(cnf_transformation,[],[f304]) ).

tff(f304,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_upt_k_PA$'(X0,X1))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom302) ).

tff(f4006,plain,
    spl230_115,
    inference(avatar_split_clause,[],[f1992,f4004]) ).

tff(f1992,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('fst$','pair$'(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f259]) ).

tff(f259,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('fst$','pair$'(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom257) ).

tff(f4002,plain,
    spl230_114,
    inference(avatar_split_clause,[],[f1991,f4000]) ).

tff(f1991,plain,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f253]) ).

tff(f253,axiom,
    ! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom251) ).

tff(f3998,plain,
    spl230_113,
    inference(avatar_split_clause,[],[f1990,f3996]) ).

tff(f3996,plain,
    ( spl230_113
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','pair$l'(X0,X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_113])]) ).

tff(f1990,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','pair$l'(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f252]) ).

tff(f252,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','pair$l'(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom250) ).

tff(f3994,plain,
    spl230_112,
    inference(avatar_split_clause,[],[f1989,f3992]) ).

tff(f3992,plain,
    ( spl230_112
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('fst$a','pair$l'(X0,X1)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_112])]) ).

tff(f1989,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('fst$a','pair$l'(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f257]) ).

tff(f257,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('fst$a','pair$l'(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom255) ).

tff(f3990,plain,
    spl230_111,
    inference(avatar_split_clause,[],[f1988,f3988]) ).

tff(f1988,plain,
    ! [X0: $int,X1: $int] : ( 'fun_app$ac'('snd$b','pair$c'(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f254]) ).

tff(f254,axiom,
    ! [X0: $int,X1: $int] : ( 'fun_app$ac'('snd$b','pair$c'(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom252) ).

tff(f3986,plain,
    spl230_110,
    inference(avatar_split_clause,[],[f1987,f3984]) ).

tff(f1987,plain,
    ! [X0: $int,X1: $int] : ( 'fun_app$ac'('fst$b','pair$c'(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f258]) ).

tff(f258,axiom,
    ! [X0: $int,X1: $int] : ( 'fun_app$ac'('fst$b','pair$c'(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom256) ).

tff(f3982,plain,
    spl230_109,
    inference(avatar_split_clause,[],[f1985,f3980]) ).

tff(f3980,plain,
    ( spl230_109
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,X1) = 'plus$a'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_109])]) ).

tff(f1985,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,X1) = 'plus$a'(X1,X0) ),
    inference(cnf_transformation,[],[f148]) ).

tff(f148,axiom,
    ! [X0: 'A_n_vec_n_vec$',X1: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,X1) = 'plus$a'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom146) ).

tff(f3978,plain,
    spl230_108,
    inference(avatar_split_clause,[],[f1983,f3976]) ).

tff(f3976,plain,
    ( spl230_108
  <=> ! [X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'(X0,X1) = 'plus$k'(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_108])]) ).

tff(f1983,plain,
    ! [X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'(X0,X1) = 'plus$k'(X1,X0) ),
    inference(cnf_transformation,[],[f147]) ).

tff(f147,axiom,
    ! [X0: 'Int_set$',X1: 'Int_set$'] : ( 'plus$k'(X0,X1) = 'plus$k'(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom145) ).

tff(f3974,plain,
    spl230_107,
    inference(avatar_split_clause,[],[f1977,f3972]) ).

tff(f1977,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK68(X0),sK69(X0)) = X0 ),
    inference(cnf_transformation,[],[f1241]) ).

tff(f1241,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK68(X0),sK69(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69])],[f235,f1240]) ).

tff(f1240,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ? [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'pair$b'(X1,X2) = X0 )
     => ( 'pair$b'(sK68(X0),sK69(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f235,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
    ? [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'pair$b'(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom233) ).

tff(f3970,plain,
    spl230_106,
    inference(avatar_split_clause,[],[f1976,f3968]) ).

tff(f1976,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK66(X0),sK67(X0)) = X0 ),
    inference(cnf_transformation,[],[f1239]) ).

tff(f1239,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK66(X0),sK67(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f233,f1238]) ).

tff(f1238,plain,
    ! [X0: 'Int_int_prod$'] :
      ( ? [X1: $int,X2: $int] : ( 'pair$c'(X1,X2) = X0 )
     => ( 'pair$c'(sK66(X0),sK67(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f233,axiom,
    ! [X0: 'Int_int_prod$'] :
    ? [X1: $int,X2: $int] : ( 'pair$c'(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom231) ).

tff(f3966,plain,
    spl230_105,
    inference(avatar_split_clause,[],[f1975,f3964]) ).

tff(f1975,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK64(X0),sK65(X0)) = X0 ),
    inference(cnf_transformation,[],[f1237]) ).

tff(f1237,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK64(X0),sK65(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65])],[f236,f1236]) ).

tff(f1236,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
      ( ? [X1: 'A_iarray$',X2: 'A_iarray$'] : ( 'pair$a'(X1,X2) = X0 )
     => ( 'pair$a'(sK64(X0),sK65(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f236,axiom,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
    ? [X1: 'A_iarray$',X2: 'A_iarray$'] : ( 'pair$a'(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom234) ).

tff(f3962,plain,
    spl230_104,
    inference(avatar_split_clause,[],[f1974,f3960]) ).

tff(f1974,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK62(X0),sK63(X0)) = X0 ),
    inference(cnf_transformation,[],[f1235]) ).

tff(f1235,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK62(X0),sK63(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f234,f1234]) ).

tff(f1234,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ? [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( 'pair$'(X1,X2) = X0 )
     => ( 'pair$'(sK62(X0),sK63(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f234,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
    ? [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( 'pair$'(X1,X2) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom232) ).

tff(f3958,plain,
    spl230_103,
    inference(avatar_split_clause,[],[f1964,f3956]) ).

tff(f3956,plain,
    ( spl230_103
  <=> ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
        ( 'fun_app$t'(X0,sK55(X0))
        | ~ 'fun_app$t'(X0,'none$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_103])]) ).

tff(f1964,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( 'fun_app$t'(X0,sK55(X0))
      | ~ 'fun_app$t'(X0,'none$') ),
    inference(cnf_transformation,[],[f1223]) ).

tff(f3954,plain,
    spl230_102,
    inference(avatar_split_clause,[],[f1961,f3952]) ).

tff(f3952,plain,
    ( spl230_102
  <=> ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
        ( 'fun_app$s'(X0,sK53(X0))
        | ~ 'fun_app$s'(X0,'none$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_102])]) ).

tff(f1961,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( 'fun_app$s'(X0,sK53(X0))
      | ~ 'fun_app$s'(X0,'none$a') ),
    inference(cnf_transformation,[],[f1217]) ).

tff(f3950,plain,
    spl230_101,
    inference(avatar_split_clause,[],[f1953,f3948]) ).

tff(f3948,plain,
    ( spl230_101
  <=> ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
        ( 'fun_app$t'(X0,'none$')
        | ~ 'fun_app$t'(X0,sK50(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_101])]) ).

tff(f1953,plain,
    ! [X0: 'A_iarray_iarray_option_bool_fun$'] :
      ( 'fun_app$t'(X0,'none$')
      | ~ 'fun_app$t'(X0,sK50(X0)) ),
    inference(cnf_transformation,[],[f1203]) ).

tff(f3946,plain,
    spl230_100,
    inference(avatar_split_clause,[],[f1950,f3944]) ).

tff(f3944,plain,
    ( spl230_100
  <=> ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
        ( 'fun_app$s'(X0,'none$a')
        | ~ 'fun_app$s'(X0,sK48(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_100])]) ).

tff(f1950,plain,
    ! [X0: 'A_n_vec_n_vec_option_bool_fun$'] :
      ( 'fun_app$s'(X0,'none$a')
      | ~ 'fun_app$s'(X0,sK48(X0)) ),
    inference(cnf_transformation,[],[f1197]) ).

tff(f3942,plain,
    spl230_99,
    inference(avatar_split_clause,[],[f1928,f3940]) ).

tff(f3940,plain,
    ( spl230_99
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$o'('invertible$',X0)
        | ~ 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_99])]) ).

tff(f1928,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
      | ~ 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0)) ),
    inference(cnf_transformation,[],[f1178]) ).

tff(f1178,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$o'('invertible$',X0)
        | ~ 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0)) )
      & ( 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0))
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    inference(nnf_transformation,[],[f69]) ).

tff(f69,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('invertible$',X0)
    <=> 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom67) ).

tff(f3938,plain,
    spl230_98,
    inference(avatar_split_clause,[],[f1927,f3936]) ).

tff(f3936,plain,
    ( spl230_98
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0))
        | ~ 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_98])]) ).

tff(f1927,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$f'('invertible_iarray$','matrix_to_iarray$'(X0))
      | ~ 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f1178]) ).

tff(f3934,plain,
    spl230_97,
    inference(avatar_split_clause,[],[f1896,f3932]) ).

tff(f1896,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X0),sK43(X0)) = X0 ),
    inference(cnf_transformation,[],[f1158]) ).

tff(f1158,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'(sK42(X0),sK43(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43])],[f810,f1157]) ).

tff(f1157,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ? [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'pair$b'(X1,X2) = X0 )
     => ( 'pair$b'(sK42(X0),sK43(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f810,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
    ? [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'pair$b'(X1,X2) = X0 ),
    inference(ennf_transformation,[],[f714]) ).

tff(f714,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
      ~ ! [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] : ( 'pair$b'(X1,X2) != X0 ),
    inference(flattening,[],[f713]) ).

tff(f713,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
      ~ ! [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
          ( ~ 'pair$b'(X1,X2) = X0 ),
    inference(true_and_false_elimination,[],[f231]) ).

tff(f231,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] :
      ( ! [X1: 'A_iarray_list$',X2: 'A_iarray_list$'] :
          ( ( 'pair$b'(X1,X2) = X0 )
         => $false )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom229) ).

tff(f3930,plain,
    spl230_96,
    inference(avatar_split_clause,[],[f1895,f3928]) ).

tff(f1895,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK40(X0),sK41(X0)) = X0 ),
    inference(cnf_transformation,[],[f1156]) ).

tff(f1156,plain,
    ! [X0: 'Int_int_prod$'] : ( 'pair$c'(sK40(X0),sK41(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f809,f1155]) ).

tff(f1155,plain,
    ! [X0: 'Int_int_prod$'] :
      ( ? [X1: $int,X2: $int] : ( 'pair$c'(X1,X2) = X0 )
     => ( 'pair$c'(sK40(X0),sK41(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f809,plain,
    ! [X0: 'Int_int_prod$'] :
    ? [X1: $int,X2: $int] : ( 'pair$c'(X1,X2) = X0 ),
    inference(ennf_transformation,[],[f712]) ).

tff(f712,plain,
    ! [X0: 'Int_int_prod$'] :
      ~ ! [X1: $int,X2: $int] : ( 'pair$c'(X1,X2) != X0 ),
    inference(flattening,[],[f711]) ).

tff(f711,plain,
    ! [X0: 'Int_int_prod$'] :
      ~ ! [X1: $int,X2: $int] :
          ( ~ 'pair$c'(X1,X2) = X0 ),
    inference(true_and_false_elimination,[],[f229]) ).

tff(f229,axiom,
    ! [X0: 'Int_int_prod$'] :
      ( ! [X1: $int,X2: $int] :
          ( ( 'pair$c'(X1,X2) = X0 )
         => $false )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom227) ).

tff(f3926,plain,
    spl230_95,
    inference(avatar_split_clause,[],[f1894,f3924]) ).

tff(f1894,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X0),sK39(X0)) = X0 ),
    inference(cnf_transformation,[],[f1154]) ).

tff(f1154,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'(sK38(X0),sK39(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f808,f1153]) ).

tff(f1153,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
      ( ? [X1: 'A_iarray$',X2: 'A_iarray$'] : ( 'pair$a'(X1,X2) = X0 )
     => ( 'pair$a'(sK38(X0),sK39(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f808,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
    ? [X1: 'A_iarray$',X2: 'A_iarray$'] : ( 'pair$a'(X1,X2) = X0 ),
    inference(ennf_transformation,[],[f710]) ).

tff(f710,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
      ~ ! [X1: 'A_iarray$',X2: 'A_iarray$'] : ( 'pair$a'(X1,X2) != X0 ),
    inference(flattening,[],[f709]) ).

tff(f709,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
      ~ ! [X1: 'A_iarray$',X2: 'A_iarray$'] :
          ( ~ 'pair$a'(X1,X2) = X0 ),
    inference(true_and_false_elimination,[],[f232]) ).

tff(f232,axiom,
    ! [X0: 'A_iarray_a_iarray_prod$'] :
      ( ! [X1: 'A_iarray$',X2: 'A_iarray$'] :
          ( ( 'pair$a'(X1,X2) = X0 )
         => $false )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom230) ).

tff(f3922,plain,
    spl230_94,
    inference(avatar_split_clause,[],[f1893,f3920]) ).

tff(f1893,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X0),sK37(X0)) = X0 ),
    inference(cnf_transformation,[],[f1152]) ).

tff(f1152,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK36(X0),sK37(X0)) = X0 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f807,f1151]) ).

tff(f1151,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ? [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( 'pair$'(X1,X2) = X0 )
     => ( 'pair$'(sK36(X0),sK37(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f807,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
    ? [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( 'pair$'(X1,X2) = X0 ),
    inference(ennf_transformation,[],[f708]) ).

tff(f708,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ~ ! [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( 'pair$'(X1,X2) != X0 ),
    inference(flattening,[],[f707]) ).

tff(f707,plain,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ~ ! [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] :
          ( ~ 'pair$'(X1,X2) = X0 ),
    inference(true_and_false_elimination,[],[f230]) ).

tff(f230,axiom,
    ! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
      ( ! [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] :
          ( ( 'pair$'(X1,X2) = X0 )
         => $false )
     => $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom228) ).

tff(f3918,plain,
    spl230_93,
    inference(avatar_split_clause,[],[f1865,f3916]) ).

tff(f3916,plain,
    ( spl230_93
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'none$a' = 'inverse_matrix$'(X0) )
        | 'fun_app$o'('invertible$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_93])]) ).

tff(f1865,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'none$a' = 'inverse_matrix$'(X0) )
      | 'fun_app$o'('invertible$',X0) ),
    inference(cnf_transformation,[],[f788]) ).

tff(f3914,plain,
    spl230_92,
    inference(avatar_split_clause,[],[f1863,f3912]) ).

tff(f3912,plain,
    ( spl230_92
  <=> ! [X0: 'A_iarray_iarray$'] :
        ( ( 'none$' = 'inverse_matrix_iarray$'(X0) )
        | 'fun_app$f'('invertible_iarray$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_92])]) ).

tff(f1863,plain,
    ! [X0: 'A_iarray_iarray$'] :
      ( ( 'none$' = 'inverse_matrix_iarray$'(X0) )
      | 'fun_app$f'('invertible_iarray$',X0) ),
    inference(cnf_transformation,[],[f787]) ).

tff(f3910,plain,
    spl230_91,
    inference(avatar_split_clause,[],[f1824,f3908]) ).

tff(f3908,plain,
    ( spl230_91
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X0),'snd$k'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_91])]) ).

tff(f1824,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X0),'snd$k'(X0)) = X0 ),
    inference(cnf_transformation,[],[f281]) ).

tff(f281,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod$'] : ( 'pair$b'('fst$k'(X0),'snd$k'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom279) ).

tff(f3906,plain,
    spl230_90,
    inference(avatar_split_clause,[],[f1822,f3904]) ).

tff(f3904,plain,
    ( spl230_90
  <=> ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X0),'snd$e'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_90])]) ).

tff(f1822,plain,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X0),'snd$e'(X0)) = X0 ),
    inference(cnf_transformation,[],[f282]) ).

tff(f282,axiom,
    ! [X0: 'A_iarray_a_iarray_prod$'] : ( 'pair$a'('fst$e'(X0),'snd$e'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom280) ).

tff(f3902,plain,
    ( spl230_89
    | ~ spl230_77
    | ~ spl230_78 ),
    inference(avatar_split_clause,[],[f3868,f3839,f3835,f3899]) ).

tff(f3899,plain,
    ( spl230_89
  <=> 'fun_app$o'('reduced_row_echelon_form$','zero$b') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_89])]) ).

tff(f3839,plain,
    ( spl230_78
  <=> ( 'zero$b' = 'fun_app$ab'('snd$','gauss_Jordan_PA$'('zero$b')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_78])]) ).

tff(f3868,plain,
    ( 'fun_app$o'('reduced_row_echelon_form$','zero$b')
    | ~ spl230_77
    | ~ spl230_78 ),
    inference(superposition,[],[f3836,f3841]) ).

tff(f3841,plain,
    ( ( 'zero$b' = 'fun_app$ab'('snd$','gauss_Jordan_PA$'('zero$b')) )
    | ~ spl230_78 ),
    inference(avatar_component_clause,[],[f3839]) ).

tff(f3897,plain,
    spl230_88,
    inference(avatar_split_clause,[],[f1821,f3895]) ).

tff(f3893,plain,
    spl230_87,
    inference(avatar_split_clause,[],[f1819,f3891]) ).

tff(f3891,plain,
    ( spl230_87
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray_option$'('inverse_matrix$'(X0)) = 'inverse_matrix_iarray$'('matrix_to_iarray$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_87])]) ).

tff(f1819,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray_option$'('inverse_matrix$'(X0)) = 'inverse_matrix_iarray$'('matrix_to_iarray$'(X0)) ),
    inference(cnf_transformation,[],[f57]) ).

tff(f57,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray_option$'('inverse_matrix$'(X0)) = 'inverse_matrix_iarray$'('matrix_to_iarray$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom55) ).

tff(f3889,plain,
    spl230_86,
    inference(avatar_split_clause,[],[f1812,f3887]) ).

tff(f1812,plain,
    ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$l'('of_nat$',X0),1) ),
    inference(cnf_transformation,[],[f460]) ).

tff(f460,axiom,
    ! [X0: 'Nat$'] : ( 0 != $sum('fun_app$l'('of_nat$',X0),1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom458) ).

tff(f3885,plain,
    spl230_85,
    inference(avatar_split_clause,[],[f1765,f3882]) ).

tff(f1765,plain,
    0 = 'fun_app$l'('of_nat$','fun_app$m'('size$','nil$')),
    inference(cnf_transformation,[],[f587]) ).

tff(f587,axiom,
    0 = 'fun_app$l'('of_nat$','fun_app$m'('size$','nil$')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom585) ).

tff(f3880,plain,
    spl230_84,
    inference(avatar_split_clause,[],[f1764,f3877]) ).

tff(f1764,plain,
    0 = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','zero$b')),
    inference(cnf_transformation,[],[f435]) ).

tff(f435,axiom,
    0 = 'fun_app$l'('of_nat$','fun_app$aa'('rank$','zero$b')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom433) ).

tff(f3875,plain,
    spl230_83,
    inference(avatar_split_clause,[],[f664,f3873]) ).

tff(f3860,plain,
    spl230_82,
    inference(avatar_split_clause,[],[f3311,f3857]) ).

tff(f3311,plain,
    1 = 'fun_app$l'('of_nat$','size$d'('none$a')),
    inference(evaluation,[],[f1766]) ).

tff(f1766,plain,
    $sum(0,1) = 'fun_app$l'('of_nat$','size$d'('none$a')),
    inference(cnf_transformation,[],[f438]) ).

tff(f438,axiom,
    $sum(0,1) = 'fun_app$l'('of_nat$','size$d'('none$a')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom436) ).

tff(f3855,plain,
    spl230_81,
    inference(avatar_split_clause,[],[f3310,f3852]) ).

tff(f3310,plain,
    1 = 'fun_app$l'('of_nat$','size$c'('none$')),
    inference(evaluation,[],[f1767]) ).

tff(f1767,plain,
    $sum(0,1) = 'fun_app$l'('of_nat$','size$c'('none$')),
    inference(cnf_transformation,[],[f439]) ).

tff(f439,axiom,
    $sum(0,1) = 'fun_app$l'('of_nat$','size$c'('none$')),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom437) ).

tff(f3850,plain,
    spl230_80,
    inference(avatar_split_clause,[],[f3101,f3848]) ).

tff(f3848,plain,
    ( spl230_80
  <=> ! [X0: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'('nil$'),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_80])]) ).

tff(f3101,plain,
    ! [X0: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'('nil$'),X0) = X0 ),
    inference(equality_resolution,[],[f2269]) ).

tff(f2269,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] :
      ( ( 'fun_app$p'('append$d'(X1),X0) = X0 )
      | ( 'nil$' != X1 ) ),
    inference(cnf_transformation,[],[f1409]) ).

tff(f3846,plain,
    spl230_79,
    inference(avatar_split_clause,[],[f3094,f3844]) ).

tff(f3844,plain,
    ( spl230_79
  <=> ! [X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'('nil$a'),X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_79])]) ).

tff(f3094,plain,
    ! [X1: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'('nil$a'),X1) = X1 ),
    inference(equality_resolution,[],[f2248]) ).

tff(f2248,plain,
    ! [X0: 'Nat_a_iarray_prod_list$',X1: 'Nat_a_iarray_prod_list$'] :
      ( ( 'fun_app$bd'('append$'(X0),X1) = X1 )
      | ( 'nil$a' != X0 ) ),
    inference(cnf_transformation,[],[f1390]) ).

tff(f3842,plain,
    spl230_78,
    inference(avatar_split_clause,[],[f2999,f3839]) ).

tff(f2999,plain,
    'zero$b' = 'fun_app$ab'('snd$','gauss_Jordan_PA$'('zero$b')),
    inference(equality_resolution,[],[f2943]) ).

tff(f2943,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'zero$b' )
      | ( 'zero$b' != X0 ) ),
    inference(definition_unfolding,[],[f1872,f1818]) ).

tff(f1872,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) = 'zero$b' )
      | ( 'zero$b' != X0 ) ),
    inference(cnf_transformation,[],[f793]) ).

tff(f793,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'gauss_Jordan$'(X0) = 'zero$b' )
      | ( 'zero$b' != X0 ) ),
    inference(ennf_transformation,[],[f434]) ).

tff(f434,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' = X0 )
     => ( 'gauss_Jordan$'(X0) = 'zero$b' ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom432) ).

tff(f3837,plain,
    spl230_77,
    inference(avatar_split_clause,[],[f2924,f3835]) ).

tff(f2924,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))),
    inference(definition_unfolding,[],[f1770,f1818]) ).

tff(f1770,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0)),
    inference(cnf_transformation,[],[f350]) ).

tff(f350,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('reduced_row_echelon_form$','gauss_Jordan$'(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom348) ).

tff(f3833,plain,
    spl230_76,
    inference(avatar_split_clause,[],[f1982,f3831]) ).

tff(f1982,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'snd$e'('pair$a'(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f251]) ).

tff(f251,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'snd$e'('pair$a'(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom249) ).

tff(f3829,plain,
    spl230_75,
    inference(avatar_split_clause,[],[f1981,f3827]) ).

tff(f1981,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'snd$k'('pair$b'(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f250]) ).

tff(f250,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'snd$k'('pair$b'(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom248) ).

tff(f3825,plain,
    spl230_74,
    inference(avatar_split_clause,[],[f1980,f3823]) ).

tff(f1980,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'fst$e'('pair$a'(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f256]) ).

tff(f256,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray$'] : ( 'fst$e'('pair$a'(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom254) ).

tff(f3821,plain,
    spl230_73,
    inference(avatar_split_clause,[],[f1979,f3819]) ).

tff(f1979,plain,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fst$k'('pair$b'(X0,X1)) = X0 ),
    inference(cnf_transformation,[],[f255]) ).

tff(f255,axiom,
    ! [X0: 'A_iarray_list$',X1: 'A_iarray_list$'] : ( 'fst$k'('pair$b'(X0,X1)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom253) ).

tff(f3817,plain,
    spl230_72,
    inference(avatar_split_clause,[],[f1924,f3815]) ).

tff(f3815,plain,
    ( spl230_72
  <=> ! [X0: 'A_iarray$'] :
        ( 'fun_app$'('uu$',X0)
        | 'fun_app$'('is_zero_iarray$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_72])]) ).

tff(f1924,plain,
    ! [X0: 'A_iarray$'] :
      ( 'fun_app$'('uu$',X0)
      | 'fun_app$'('is_zero_iarray$',X0) ),
    inference(cnf_transformation,[],[f1177]) ).

tff(f1177,plain,
    ! [X0: 'A_iarray$'] :
      ( ( 'fun_app$'('uu$',X0)
        | 'fun_app$'('is_zero_iarray$',X0) )
      & ( ~ 'fun_app$'('is_zero_iarray$',X0)
        | ~ 'fun_app$'('uu$',X0) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: 'A_iarray$'] :
      ( 'fun_app$'('uu$',X0)
    <=> ~ 'fun_app$'('is_zero_iarray$',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom0) ).

tff(f3813,plain,
    spl230_71,
    inference(avatar_split_clause,[],[f1923,f3811]) ).

tff(f3811,plain,
    ( spl230_71
  <=> ! [X0: 'A_iarray$'] :
        ( ~ 'fun_app$'('is_zero_iarray$',X0)
        | ~ 'fun_app$'('uu$',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_71])]) ).

tff(f1923,plain,
    ! [X0: 'A_iarray$'] :
      ( ~ 'fun_app$'('is_zero_iarray$',X0)
      | ~ 'fun_app$'('uu$',X0) ),
    inference(cnf_transformation,[],[f1177]) ).

tff(f3809,plain,
    spl230_70,
    inference(avatar_split_clause,[],[f1912,f3807]) ).

tff(f3807,plain,
    ( spl230_70
  <=> ! [X0: 'A_n_vec_n_vec$'] :
        ( ( 'zero$b' = X0 )
        | ~ 'is_zero_iarray$a'('vec_to_iarray$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_70])]) ).

tff(f1912,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' = X0 )
      | ~ 'is_zero_iarray$a'('vec_to_iarray$'(X0)) ),
    inference(cnf_transformation,[],[f1172]) ).

tff(f1172,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( ( 'zero$b' = X0 )
        | ~ 'is_zero_iarray$a'('vec_to_iarray$'(X0)) )
      & ( 'is_zero_iarray$a'('vec_to_iarray$'(X0))
        | ( 'zero$b' != X0 ) ) ),
    inference(nnf_transformation,[],[f436]) ).

tff(f436,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( ( 'zero$b' = X0 )
    <=> 'is_zero_iarray$a'('vec_to_iarray$'(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom434) ).

tff(f3805,plain,
    ( spl230_69
    | ~ spl230_30
    | ~ spl230_55 ),
    inference(avatar_split_clause,[],[f3745,f3738,f3630,f3802]) ).

tff(f3630,plain,
    ( spl230_30
  <=> ( 'zero$a' = 'pair$c'(0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_30])]) ).

tff(f3745,plain,
    ( 'fun_app$ae'('divides_aux$','zero$a')
    | ~ spl230_30
    | ~ spl230_55 ),
    inference(superposition,[],[f3739,f3632]) ).

tff(f3632,plain,
    ( ( 'zero$a' = 'pair$c'(0,0) )
    | ~ spl230_30 ),
    inference(avatar_component_clause,[],[f3630]) ).

tff(f3800,plain,
    spl230_68,
    inference(avatar_split_clause,[],[f1868,f3798]) ).

tff(f1868,plain,
    ! [X0: tlbool] :
      ( ( tlfalse = X0 )
      | ( tltrue = X0 ) ),
    inference(cnf_transformation,[],[f676]) ).

tff(f676,plain,
    ! [X0: tlbool] :
      ( ( tlfalse = X0 )
      | ( tltrue = X0 ) ),
    inference(rectify,[],[f660]) ).

tff(f660,axiom,
    ! [X13: tlbool] :
      ( ( tlfalse = X13 )
      | ( tltrue = X13 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_659) ).

tff(f3796,plain,
    spl230_67,
    inference(avatar_split_clause,[],[f1811,f3794]) ).

tff(f3794,plain,
    ( spl230_67
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_67])]) ).

tff(f1811,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),
    inference(cnf_transformation,[],[f214]) ).

tff(f214,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$','fun_app$ab'('fst$a','gauss_Jordan_PA$'(X0))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom212) ).

tff(f3792,plain,
    spl230_66,
    inference(avatar_split_clause,[],[f1809,f3790]) ).

tff(f3790,plain,
    ( spl230_66
  <=> ! [X0: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'(X0),'nil$') = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_66])]) ).

tff(f1809,plain,
    ! [X0: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'(X0),'nil$') = X0 ),
    inference(cnf_transformation,[],[f563]) ).

tff(f563,axiom,
    ! [X0: 'A_iarray_list$'] : ( 'fun_app$p'('append$d'(X0),'nil$') = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom561) ).

tff(f3788,plain,
    spl230_65,
    inference(avatar_split_clause,[],[f1807,f3786]) ).

tff(f3786,plain,
    ( spl230_65
  <=> ! [X0: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'(X0),'nil$a') = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_65])]) ).

tff(f1807,plain,
    ! [X0: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'(X0),'nil$a') = X0 ),
    inference(cnf_transformation,[],[f562]) ).

tff(f562,axiom,
    ! [X0: 'Nat_a_iarray_prod_list$'] : ( 'fun_app$bd'('append$'(X0),'nil$a') = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom560) ).

tff(f3784,plain,
    spl230_64,
    inference(avatar_split_clause,[],[f1806,f3782]) ).

tff(f3782,plain,
    ( spl230_64
  <=> ! [X0: 'A_iarray_bool_fun$'] : ( 'nil$' = 'fun_app$p'('filter$'(X0),'nil$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_64])]) ).

tff(f1806,plain,
    ! [X0: 'A_iarray_bool_fun$'] : ( 'nil$' = 'fun_app$p'('filter$'(X0),'nil$') ),
    inference(cnf_transformation,[],[f586]) ).

tff(f586,axiom,
    ! [X0: 'A_iarray_bool_fun$'] : ( 'nil$' = 'fun_app$p'('filter$'(X0),'nil$') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom584) ).

tff(f3780,plain,
    spl230_63,
    inference(avatar_split_clause,[],[f1805,f3778]) ).

tff(f1805,plain,
    ! [X0: 'A_iarray_iarray_option$'] : ( 'fun_app$l'('of_nat$','size$c'(X0)) != 0 ),
    inference(cnf_transformation,[],[f393]) ).

tff(f393,axiom,
    ! [X0: 'A_iarray_iarray_option$'] : ( 'fun_app$l'('of_nat$','size$c'(X0)) != 0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom391) ).

tff(f3776,plain,
    spl230_62,
    inference(avatar_split_clause,[],[f1763,f3773]) ).

tff(f3773,plain,
    ( spl230_62
  <=> ( 'size$' = 'gen_length$b'('fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_62])]) ).

tff(f1763,plain,
    'size$' = 'gen_length$b'('fun_app$k'('nat$',0)),
    inference(cnf_transformation,[],[f422]) ).

tff(f422,axiom,
    'size$' = 'gen_length$b'('fun_app$k'('nat$',0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom420) ).

tff(f3771,plain,
    spl230_61,
    inference(avatar_split_clause,[],[f1762,f3768]) ).

tff(f3768,plain,
    ( spl230_61
  <=> ( 'size$b' = 'gen_length$a'('fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_61])]) ).

tff(f1762,plain,
    'size$b' = 'gen_length$a'('fun_app$k'('nat$',0)),
    inference(cnf_transformation,[],[f421]) ).

tff(f421,axiom,
    'size$b' = 'gen_length$a'('fun_app$k'('nat$',0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom419) ).

tff(f3766,plain,
    spl230_60,
    inference(avatar_split_clause,[],[f1761,f3763]) ).

tff(f3763,plain,
    ( spl230_60
  <=> ( 'size$a' = 'gen_length$'('fun_app$k'('nat$',0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_60])]) ).

tff(f1761,plain,
    'size$a' = 'gen_length$'('fun_app$k'('nat$',0)),
    inference(cnf_transformation,[],[f420]) ).

tff(f420,axiom,
    'size$a' = 'gen_length$'('fun_app$k'('nat$',0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom418) ).

tff(f3761,plain,
    spl230_59,
    inference(avatar_split_clause,[],[f668,f3759]) ).

tff(f668,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f3757,plain,
    ( ~ spl230_58
    | spl230_57 ),
    inference(avatar_split_clause,[],[f3752,f3747,f3754]) ).

tff(f3747,plain,
    ( spl230_57
  <=> ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_57])]) ).

tff(f3752,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$aa'('rank$','a$')) )
    | spl230_57 ),
    inference(forward_demodulation,[],[f3751,f1854]) ).

tff(f3751,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$q'('rank_iarray$','matrix_to_iarray$'('a$'))) )
    | spl230_57 ),
    inference(forward_demodulation,[],[f3749,f2940]) ).

tff(f3749,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
    | spl230_57 ),
    inference(avatar_component_clause,[],[f3747]) ).

tff(f3750,plain,
    ( spl230_1
    | ~ spl230_57 ),
    inference(avatar_split_clause,[],[f2922,f3747,f3502]) ).

tff(f2922,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
    | sP0 ),
    inference(definition_unfolding,[],[f1743,f1817]) ).

tff(f1743,plain,
    ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
    | sP0 ),
    inference(cnf_transformation,[],[f1080]) ).

tff(f3744,plain,
    spl230_56,
    inference(avatar_split_clause,[],[f3086,f3742]) ).

tff(f3086,plain,
    ! [X1: 'A_iarray_iarray_bool_fun$'] : 'fun_app$t'('case_option$a'(tltrue,X1),'none$'),
    inference(equality_resolution,[],[f2223]) ).

tff(f2223,plain,
    ! [X0: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( 'fun_app$t'('case_option$a'(X0,X1),'none$')
      | ( tltrue != X0 ) ),
    inference(cnf_transformation,[],[f1372]) ).

tff(f3740,plain,
    spl230_55,
    inference(avatar_split_clause,[],[f3085,f3738]) ).

tff(f3085,plain,
    ! [X0: $int] : 'fun_app$ae'('divides_aux$','pair$c'(X0,0)),
    inference(equality_resolution,[],[f2221]) ).

tff(f2221,plain,
    ! [X0: $int,X1: $int] :
      ( 'fun_app$ae'('divides_aux$','pair$c'(X0,X1))
      | ( 0 != X1 ) ),
    inference(cnf_transformation,[],[f1371]) ).

tff(f3736,plain,
    spl230_54,
    inference(avatar_split_clause,[],[f3008,f3733]) ).

tff(f3733,plain,
    ( spl230_54
  <=> 'fun_app$s'('case_option$'(tltrue,'uuh$'),'none$a') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_54])]) ).

tff(f3008,plain,
    'fun_app$s'('case_option$'(tltrue,'uuh$'),'none$a'),
    inference(equality_resolution,[],[f1907]) ).

tff(f1907,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( 'fun_app$s'('case_option$'(tltrue,'uuh$'),X0)
      | ( 'none$a' != X0 ) ),
    inference(cnf_transformation,[],[f1170]) ).

tff(f3731,plain,
    ~ spl230_53,
    inference(avatar_split_clause,[],[f3004,f3728]) ).

tff(f3004,plain,
    ~ 'fun_app$t'('case_option$a'(tlfalse,'uug$'),'none$'),
    inference(equality_resolution,[],[f1902]) ).

tff(f1902,plain,
    ! [X0: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X0 )
      | ~ 'fun_app$t'('case_option$a'(tlfalse,'uug$'),X0) ),
    inference(cnf_transformation,[],[f1164]) ).

tff(f3726,plain,
    ~ spl230_52,
    inference(avatar_split_clause,[],[f3002,f3723]) ).

tff(f3723,plain,
    ( spl230_52
  <=> 'fun_app$s'('case_option$'(tlfalse,'uuf$'),'none$a') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_52])]) ).

tff(f3002,plain,
    ~ 'fun_app$s'('case_option$'(tlfalse,'uuf$'),'none$a'),
    inference(equality_resolution,[],[f1898]) ).

tff(f1898,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X0 )
      | ~ 'fun_app$s'('case_option$'(tlfalse,'uuf$'),X0) ),
    inference(cnf_transformation,[],[f1159]) ).

tff(f3721,plain,
    spl230_51,
    inference(avatar_split_clause,[],[f2350,f3719]) ).

tff(f3719,plain,
    ( spl230_51
  <=> ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : 'fun_app$o'('invertible$',sK135(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_51])]) ).

tff(f2350,plain,
    ! [X0: 'A_n_vec_n_vec$',X1: 'Nat$'] : 'fun_app$o'('invertible$',sK135(X0,X1)),
    inference(cnf_transformation,[],[f1492]) ).

tff(f3717,plain,
    spl230_50,
    inference(avatar_split_clause,[],[f1978,f3715]) ).

tff(f3715,plain,
    ( spl230_50
  <=> ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'cons$'(X0,X1) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_50])]) ).

tff(f1978,plain,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'cons$'(X0,X1) != X1 ),
    inference(cnf_transformation,[],[f481]) ).

tff(f481,axiom,
    ! [X0: 'A_iarray$',X1: 'A_iarray_list$'] : ( 'cons$'(X0,X1) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom479) ).

tff(f3713,plain,
    spl230_49,
    inference(avatar_split_clause,[],[f1804,f3711]) ).

tff(f3711,plain,
    ( spl230_49
  <=> ! [X0: 'Nat$'] : ~ $less('fun_app$l'('of_nat$',X0),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_49])]) ).

tff(f1804,plain,
    ! [X0: 'Nat$'] : ~ $less('fun_app$l'('of_nat$',X0),0),
    inference(cnf_transformation,[],[f662]) ).

tff(f662,plain,
    ! [X0: 'Nat$'] : ~ $less('fun_app$l'('of_nat$',X0),0),
    inference(theory_normalization,[],[f650]) ).

tff(f650,axiom,
    ! [X0: 'Nat$'] : $lesseq(0,'fun_app$l'('of_nat$',X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom648) ).

tff(f3709,plain,
    spl230_48,
    inference(avatar_split_clause,[],[f1795,f3707]) ).

tff(f3707,plain,
    ( spl230_48
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'('zero$b',X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_48])]) ).

tff(f1795,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'('zero$b',X0) = X0 ),
    inference(cnf_transformation,[],[f385]) ).

tff(f385,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'('zero$b',X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom383) ).

tff(f3705,plain,
    spl230_47,
    inference(avatar_split_clause,[],[f1792,f3703]) ).

tff(f3703,plain,
    ( spl230_47
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'zero$b') = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_47])]) ).

tff(f1792,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'zero$b') = X0 ),
    inference(cnf_transformation,[],[f368]) ).

tff(f368,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'plus$a'(X0,'zero$b') = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom366) ).

tff(f3701,plain,
    spl230_46,
    inference(avatar_split_clause,[],[f1784,f3699]) ).

tff(f3699,plain,
    ( spl230_46
  <=> ! [X0: 'Int_set$'] : ( 'plus$k'('zero$',X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_46])]) ).

tff(f1784,plain,
    ! [X0: 'Int_set$'] : ( 'plus$k'('zero$',X0) = X0 ),
    inference(cnf_transformation,[],[f383]) ).

tff(f383,axiom,
    ! [X0: 'Int_set$'] : ( 'plus$k'('zero$',X0) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom381) ).

tff(f3697,plain,
    spl230_45,
    inference(avatar_split_clause,[],[f1782,f3695]) ).

tff(f3695,plain,
    ( spl230_45
  <=> ! [X0: 'Int_set$'] : ( 'plus$k'(X0,'zero$') = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_45])]) ).

tff(f1782,plain,
    ! [X0: 'Int_set$'] : ( 'plus$k'(X0,'zero$') = X0 ),
    inference(cnf_transformation,[],[f411]) ).

tff(f411,axiom,
    ! [X0: 'Int_set$'] : ( 'plus$k'(X0,'zero$') = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom409) ).

tff(f3693,plain,
    spl230_44,
    inference(avatar_split_clause,[],[f1781,f3691]) ).

tff(f3691,plain,
    ( spl230_44
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'the$a'('some$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_44])]) ).

tff(f1781,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'the$a'('some$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f80]) ).

tff(f80,axiom,
    ! [X0: 'A_iarray_iarray$'] : ( 'the$a'('some$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom78) ).

tff(f3689,plain,
    spl230_43,
    inference(avatar_split_clause,[],[f1780,f3687]) ).

tff(f3687,plain,
    ( spl230_43
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'the$'('some$a'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_43])]) ).

tff(f1780,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'the$'('some$a'(X0)) = X0 ),
    inference(cnf_transformation,[],[f79]) ).

tff(f79,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'the$'('some$a'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom77) ).

tff(f3685,plain,
    spl230_42,
    inference(avatar_split_clause,[],[f1778,f3683]) ).

tff(f3683,plain,
    ( spl230_42
  <=> ! [X0: 'A_iarray_set$'] : ( 'collect$d'('uun$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_42])]) ).

tff(f1778,plain,
    ! [X0: 'A_iarray_set$'] : ( 'collect$d'('uun$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f103]) ).

tff(f103,axiom,
    ! [X0: 'A_iarray_set$'] : ( 'collect$d'('uun$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom101) ).

tff(f3681,plain,
    spl230_41,
    inference(avatar_split_clause,[],[f1777,f3679]) ).

tff(f3679,plain,
    ( spl230_41
  <=> ! [X0: 'Nat_set$'] : ( 'collect$c'('uum$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_41])]) ).

tff(f1777,plain,
    ! [X0: 'Nat_set$'] : ( 'collect$c'('uum$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f102]) ).

tff(f102,axiom,
    ! [X0: 'Nat_set$'] : ( 'collect$c'('uum$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom100) ).

tff(f3677,plain,
    spl230_40,
    inference(avatar_split_clause,[],[f1776,f3675]) ).

tff(f3675,plain,
    ( spl230_40
  <=> ! [X0: 'A_iarray_list_set$'] : ( 'collect$a'('uuk$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_40])]) ).

tff(f1776,plain,
    ! [X0: 'A_iarray_list_set$'] : ( 'collect$a'('uuk$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f100]) ).

tff(f100,axiom,
    ! [X0: 'A_iarray_list_set$'] : ( 'collect$a'('uuk$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom98) ).

tff(f3673,plain,
    spl230_39,
    inference(avatar_split_clause,[],[f1775,f3671]) ).

tff(f3671,plain,
    ( spl230_39
  <=> ! [X0: 'A_iarray_list_a_iarray_list_prod_set$'] : ( 'collect$'('uuj$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_39])]) ).

tff(f1775,plain,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$'] : ( 'collect$'('uuj$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f99]) ).

tff(f99,axiom,
    ! [X0: 'A_iarray_list_a_iarray_list_prod_set$'] : ( 'collect$'('uuj$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom97) ).

tff(f3669,plain,
    spl230_38,
    inference(avatar_split_clause,[],[f1774,f3667]) ).

tff(f3667,plain,
    ( spl230_38
  <=> ! [X0: 'Int_set$'] : ( 'collect$b'('uul$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_38])]) ).

tff(f1774,plain,
    ! [X0: 'Int_set$'] : ( 'collect$b'('uul$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f101]) ).

tff(f101,axiom,
    ! [X0: 'Int_set$'] : ( 'collect$b'('uul$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom99) ).

tff(f3665,plain,
    spl230_37,
    inference(avatar_split_clause,[],[f1773,f3663]) ).

tff(f3663,plain,
    ( spl230_37
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'iarray_to_matrix$'('matrix_to_iarray$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_37])]) ).

tff(f1773,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'iarray_to_matrix$'('matrix_to_iarray$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f122]) ).

tff(f122,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'iarray_to_matrix$'('matrix_to_iarray$'(X0)) = X0 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom120) ).

tff(f3661,plain,
    spl230_36,
    inference(avatar_split_clause,[],[f1772,f3659]) ).

tff(f3659,plain,
    ( spl230_36
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'('zero$b',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_36])]) ).

tff(f1772,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'('zero$b',X0) ),
    inference(cnf_transformation,[],[f432]) ).

tff(f432,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'('zero$b',X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom430) ).

tff(f3657,plain,
    spl230_35,
    inference(avatar_split_clause,[],[f1771,f3655]) ).

tff(f1771,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'(X0,'zero$b') ),
    inference(cnf_transformation,[],[f431]) ).

tff(f431,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'zero$b' = 'matrix_matrix_mult$'(X0,'zero$b') ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom429) ).

tff(f3653,plain,
    spl230_34,
    inference(avatar_split_clause,[],[f1760,f3650]) ).

tff(f3650,plain,
    ( spl230_34
  <=> ( 0 = 'fun_app$ac'('snd$b','zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_34])]) ).

tff(f3648,plain,
    spl230_33,
    inference(avatar_split_clause,[],[f1759,f3645]) ).

tff(f3643,plain,
    spl230_32,
    inference(avatar_split_clause,[],[f1758,f3640]) ).

tff(f3640,plain,
    ( spl230_32
  <=> ( 'zero$b' = 'fun_app$ab'('snd$','zero$c') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_32])]) ).

tff(f1758,plain,
    'zero$b' = 'fun_app$ab'('snd$','zero$c'),
    inference(cnf_transformation,[],[f387]) ).

tff(f387,axiom,
    'zero$b' = 'fun_app$ab'('snd$','zero$c'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom385) ).

tff(f3638,plain,
    spl230_31,
    inference(avatar_split_clause,[],[f1757,f3635]) ).

tff(f3635,plain,
    ( spl230_31
  <=> ( 'zero$b' = 'fun_app$ab'('fst$a','zero$c') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_31])]) ).

tff(f1757,plain,
    'zero$b' = 'fun_app$ab'('fst$a','zero$c'),
    inference(cnf_transformation,[],[f389]) ).

tff(f389,axiom,
    'zero$b' = 'fun_app$ab'('fst$a','zero$c'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom387) ).

tff(f3633,plain,
    spl230_30,
    inference(avatar_split_clause,[],[f1756,f3630]) ).

tff(f1756,plain,
    'zero$a' = 'pair$c'(0,0),
    inference(cnf_transformation,[],[f406]) ).

tff(f406,axiom,
    'zero$a' = 'pair$c'(0,0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom404) ).

tff(f3628,plain,
    spl230_29,
    inference(avatar_split_clause,[],[f1755,f3625]) ).

tff(f3625,plain,
    ( spl230_29
  <=> ( 'zero$c' = 'pair$l'('zero$b','zero$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_29])]) ).

tff(f1755,plain,
    'zero$c' = 'pair$l'('zero$b','zero$b'),
    inference(cnf_transformation,[],[f405]) ).

tff(f405,axiom,
    'zero$c' = 'pair$l'('zero$b','zero$b'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom403) ).

tff(f3623,plain,
    spl230_28,
    inference(avatar_split_clause,[],[f1754,f3620]) ).

tff(f3620,plain,
    ( spl230_28
  <=> ( 'zero$d' = 'pair$g'(0,'zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_28])]) ).

tff(f1754,plain,
    'zero$d' = 'pair$g'(0,'zero$a'),
    inference(cnf_transformation,[],[f398]) ).

tff(f398,axiom,
    'zero$d' = 'pair$g'(0,'zero$a'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom396) ).

tff(f3618,plain,
    spl230_27,
    inference(avatar_split_clause,[],[f1753,f3615]) ).

tff(f3615,plain,
    ( spl230_27
  <=> ( 'zero$f' = 'pair$j'('zero$a',0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_27])]) ).

tff(f1753,plain,
    'zero$f' = 'pair$j'('zero$a',0),
    inference(cnf_transformation,[],[f400]) ).

tff(f400,axiom,
    'zero$f' = 'pair$j'('zero$a',0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom398) ).

tff(f3613,plain,
    spl230_26,
    inference(avatar_split_clause,[],[f1752,f3610]) ).

tff(f3610,plain,
    ( spl230_26
  <=> ( 'zero$g' = 'pair$n'('zero$a','zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_26])]) ).

tff(f1752,plain,
    'zero$g' = 'pair$n'('zero$a','zero$a'),
    inference(cnf_transformation,[],[f401]) ).

tff(f401,axiom,
    'zero$g' = 'pair$n'('zero$a','zero$a'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom399) ).

tff(f3608,plain,
    spl230_25,
    inference(avatar_split_clause,[],[f1751,f3605]) ).

tff(f3605,plain,
    ( spl230_25
  <=> ( 'zero$e' = 'pair$m'(0,'zero$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_25])]) ).

tff(f1751,plain,
    'zero$e' = 'pair$m'(0,'zero$b'),
    inference(cnf_transformation,[],[f399]) ).

tff(f399,axiom,
    'zero$e' = 'pair$m'(0,'zero$b'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom397) ).

tff(f3603,plain,
    spl230_24,
    inference(avatar_split_clause,[],[f1750,f3600]) ).

tff(f3600,plain,
    ( spl230_24
  <=> ( 'zero$i' = 'pair$p'('zero$b',0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_24])]) ).

tff(f1750,plain,
    'zero$i' = 'pair$p'('zero$b',0),
    inference(cnf_transformation,[],[f403]) ).

tff(f403,axiom,
    'zero$i' = 'pair$p'('zero$b',0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom401) ).

tff(f3598,plain,
    spl230_23,
    inference(avatar_split_clause,[],[f1749,f3595]) ).

tff(f3595,plain,
    ( spl230_23
  <=> ( 'zero$j' = 'pair$q'('zero$b','zero$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_23])]) ).

tff(f1749,plain,
    'zero$j' = 'pair$q'('zero$b','zero$a'),
    inference(cnf_transformation,[],[f404]) ).

tff(f404,axiom,
    'zero$j' = 'pair$q'('zero$b','zero$a'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom402) ).

tff(f3593,plain,
    spl230_22,
    inference(avatar_split_clause,[],[f1748,f3590]) ).

tff(f3590,plain,
    ( spl230_22
  <=> ( 'zero$h' = 'pair$o'('zero$a','zero$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_22])]) ).

tff(f1748,plain,
    'zero$h' = 'pair$o'('zero$a','zero$b'),
    inference(cnf_transformation,[],[f402]) ).

tff(f402,axiom,
    'zero$h' = 'pair$o'('zero$a','zero$b'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom400) ).

tff(f3588,plain,
    spl230_21,
    inference(avatar_split_clause,[],[f674,f3586]) ).

tff(f3586,plain,
    ( spl230_21
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_21])]) ).

tff(f674,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f3584,plain,
    spl230_20,
    inference(avatar_split_clause,[],[f666,f3582]) ).

tff(f3582,plain,
    ( spl230_20
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_20])]) ).

tff(f666,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f3580,plain,
    spl230_19,
    inference(avatar_split_clause,[],[f3137,f3578]) ).

tff(f3137,plain,
    ! [X1: 'A_iarray_iarray_bool_fun$'] : sP14('none$',X1,tltrue),
    inference(equality_resolution,[],[f3136]) ).

tff(f3136,plain,
    ! [X2: tlbool,X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14('none$',X1,X2)
      | ( tltrue != X2 ) ),
    inference(equality_resolution,[],[f2520]) ).

tff(f2520,plain,
    ! [X2: tlbool,X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_bool_fun$'] :
      ( sP14(X0,X1,X2)
      | ( 'none$' != X0 )
      | ( tltrue != X2 ) ),
    inference(cnf_transformation,[],[f1564]) ).

tff(f3576,plain,
    spl230_18,
    inference(avatar_split_clause,[],[f2998,f3573]) ).

tff(f3573,plain,
    ( spl230_18
  <=> ( 'none$' = 'matrix_to_iarray_option$'('none$a') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_18])]) ).

tff(f2998,plain,
    'none$' = 'matrix_to_iarray_option$'('none$a'),
    inference(equality_resolution,[],[f1859]) ).

tff(f1859,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$' = 'matrix_to_iarray_option$'(X0) )
      | ( 'none$a' != X0 ) ),
    inference(cnf_transformation,[],[f785]) ).

tff(f3571,plain,
    spl230_17,
    inference(avatar_split_clause,[],[f1971,f3569]) ).

tff(f3569,plain,
    ( spl230_17
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$',sK61(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_17])]) ).

tff(f1971,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$',sK61(X0)),
    inference(cnf_transformation,[],[f1233]) ).

tff(f3567,plain,
    spl230_16,
    inference(avatar_split_clause,[],[f1969,f3565]) ).

tff(f3565,plain,
    ( spl230_16
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$',sK60(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_16])]) ).

tff(f1969,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('invertible$',sK60(X0)),
    inference(cnf_transformation,[],[f1231]) ).

tff(f3563,plain,
    spl230_15,
    inference(avatar_split_clause,[],[f1769,f3561]) ).

tff(f3561,plain,
    ( spl230_15
  <=> ! [X0: 'A_iarray_iarray$'] : ( 'none$' != 'some$'(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_15])]) ).

tff(f1769,plain,
    ! [X0: 'A_iarray_iarray$'] : ( 'none$' != 'some$'(X0) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,axiom,
    ! [X0: 'A_iarray_iarray$'] : ( 'none$' != 'some$'(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom33) ).

tff(f3559,plain,
    spl230_14,
    inference(avatar_split_clause,[],[f1768,f3557]) ).

tff(f3557,plain,
    ( spl230_14
  <=> ! [X0: 'A_n_vec_n_vec$'] : ( 'none$a' != 'some$a'(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_14])]) ).

tff(f1768,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'none$a' != 'some$a'(X0) ),
    inference(cnf_transformation,[],[f34]) ).

tff(f34,axiom,
    ! [X0: 'A_n_vec_n_vec$'] : ( 'none$a' != 'some$a'(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom32) ).

tff(f3555,plain,
    spl230_13,
    inference(avatar_split_clause,[],[f3035,f3553]) ).

tff(f3553,plain,
    ( spl230_13
  <=> ! [X0: 'A_iarray_iarray_option$'] : ~ sP3(X0,'none$') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_13])]) ).

tff(f3035,plain,
    ! [X0: 'A_iarray_iarray_option$'] : ~ sP3(X0,'none$'),
    inference(equality_resolution,[],[f2094]) ).

tff(f2094,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X1 )
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1259]) ).

tff(f3551,plain,
    spl230_12,
    inference(avatar_split_clause,[],[f3034,f3549]) ).

tff(f3549,plain,
    ( spl230_12
  <=> ! [X1: 'A_iarray_iarray_option$'] : ~ sP3('none$',X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_12])]) ).

tff(f3034,plain,
    ! [X1: 'A_iarray_iarray_option$'] : ~ sP3('none$',X1),
    inference(equality_resolution,[],[f2095]) ).

tff(f2095,plain,
    ! [X0: 'A_iarray_iarray_option$',X1: 'A_iarray_iarray_option$'] :
      ( ( 'none$' != X0 )
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1259]) ).

tff(f3547,plain,
    spl230_11,
    inference(avatar_split_clause,[],[f3031,f3545]) ).

tff(f3545,plain,
    ( spl230_11
  <=> ! [X0: 'A_n_vec_n_vec_option$'] : ~ sP2(X0,'none$a') ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_11])]) ).

tff(f3031,plain,
    ! [X0: 'A_n_vec_n_vec_option$'] : ~ sP2(X0,'none$a'),
    inference(equality_resolution,[],[f2089]) ).

tff(f2089,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X1 )
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1256]) ).

tff(f3543,plain,
    spl230_10,
    inference(avatar_split_clause,[],[f3030,f3541]) ).

tff(f3541,plain,
    ( spl230_10
  <=> ! [X1: 'A_n_vec_n_vec_option$'] : ~ sP2('none$a',X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_10])]) ).

tff(f3030,plain,
    ! [X1: 'A_n_vec_n_vec_option$'] : ~ sP2('none$a',X1),
    inference(equality_resolution,[],[f2090]) ).

tff(f2090,plain,
    ! [X0: 'A_n_vec_n_vec_option$',X1: 'A_n_vec_n_vec_option$'] :
      ( ( 'none$a' != X0 )
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1256]) ).

tff(f3539,plain,
    spl230_9,
    inference(avatar_split_clause,[],[f3011,f3536]) ).

tff(f3536,plain,
    ( spl230_9
  <=> 'is_zero_iarray$a'('vec_to_iarray$'('zero$b')) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_9])]) ).

tff(f3011,plain,
    'is_zero_iarray$a'('vec_to_iarray$'('zero$b')),
    inference(equality_resolution,[],[f1911]) ).

tff(f1911,plain,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'is_zero_iarray$a'('vec_to_iarray$'(X0))
      | ( 'zero$b' != X0 ) ),
    inference(cnf_transformation,[],[f1172]) ).

tff(f3534,plain,
    spl230_8,
    inference(avatar_split_clause,[],[f1926,f3532]) ).

tff(f3532,plain,
    ( spl230_8
  <=> ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('uuf$',X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_8])]) ).

tff(f1926,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('uuf$',X0),
    inference(cnf_transformation,[],[f720]) ).

tff(f720,plain,
    ! [X0: 'A_n_vec_n_vec$'] : 'fun_app$o'('uuf$',X0),
    inference(true_and_false_elimination,[],[f21]) ).

tff(f21,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('uuf$',X0)
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom20) ).

tff(f3530,plain,
    spl230_7,
    inference(avatar_split_clause,[],[f1925,f3528]) ).

tff(f3528,plain,
    ( spl230_7
  <=> ! [X0: 'A_n_vec_n_vec$'] : ~ 'fun_app$o'('uuh$',X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_7])]) ).

tff(f1925,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ~ 'fun_app$o'('uuh$',X0),
    inference(cnf_transformation,[],[f719]) ).

tff(f719,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ~ 'fun_app$o'('uuh$',X0),
    inference(flattening,[],[f718]) ).

tff(f718,plain,
    ! [X0: 'A_n_vec_n_vec$'] : ~ 'fun_app$o'('uuh$',X0),
    inference(true_and_false_elimination,[],[f19]) ).

tff(f19,axiom,
    ! [X0: 'A_n_vec_n_vec$'] :
      ( 'fun_app$o'('uuh$',X0)
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom18) ).

tff(f3526,plain,
    spl230_6,
    inference(avatar_split_clause,[],[f1920,f3524]) ).

tff(f1920,plain,
    ! [X0: 'A_iarray_iarray$'] : 'fun_app$f'('uug$',X0),
    inference(cnf_transformation,[],[f717]) ).

tff(f717,plain,
    ! [X0: 'A_iarray_iarray$'] : 'fun_app$f'('uug$',X0),
    inference(true_and_false_elimination,[],[f22]) ).

tff(f22,axiom,
    ! [X0: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('uug$',X0)
    <=> $true ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom21) ).

tff(f3522,plain,
    spl230_5,
    inference(avatar_split_clause,[],[f1919,f3520]) ).

tff(f3520,plain,
    ( spl230_5
  <=> ! [X0: 'A_iarray_iarray$'] : ~ 'fun_app$f'('uui$',X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_5])]) ).

tff(f1919,plain,
    ! [X0: 'A_iarray_iarray$'] : ~ 'fun_app$f'('uui$',X0),
    inference(cnf_transformation,[],[f716]) ).

tff(f716,plain,
    ! [X0: 'A_iarray_iarray$'] : ~ 'fun_app$f'('uui$',X0),
    inference(flattening,[],[f715]) ).

tff(f715,plain,
    ! [X0: 'A_iarray_iarray$'] : ~ 'fun_app$f'('uui$',X0),
    inference(true_and_false_elimination,[],[f20]) ).

tff(f20,axiom,
    ! [X0: 'A_iarray_iarray$'] :
      ( 'fun_app$f'('uui$',X0)
    <=> $false ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom19) ).

tff(f3518,plain,
    ~ spl230_4,
    inference(avatar_split_clause,[],[f1746,f3515]) ).

tff(f3515,plain,
    ( spl230_4
  <=> ( tltrue = tlfalse ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl230_4])]) ).

tff(f1746,plain,
    tltrue != tlfalse,
    inference(cnf_transformation,[],[f661]) ).

tff(f661,axiom,
    tltrue != tlfalse,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',formula_660) ).

tff(f3513,plain,
    spl230_3,
    inference(avatar_split_clause,[],[f669,f3511]) ).

tff(f669,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f3509,plain,
    ( spl230_1
    | spl230_2 ),
    inference(avatar_split_clause,[],[f1745,f3506,f3502]) ).

tff(f1745,plain,
    ( sP1
    | sP0 ),
    inference(cnf_transformation,[],[f1080]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% 0.14/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.34  % Computer : n006.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit   : 300
% 0.15/0.34  % WCLimit    : 300
% 0.15/0.34  % DateTime   : Sat May 18 16:56:08 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.35  % (3411)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.41  % (3414)WARNING: value z3 for option sas not known
% 0.21/0.41  % (3418)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.41  % (3412)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.41  % (3413)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.41  % (3415)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.41  % (3414)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.41  % (3416)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.41  % (3417)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.45  % (3413)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.45  % (3413)Terminated due to inappropriate strategy.
% 0.21/0.45  % (3413)------------------------------
% 0.21/0.45  % (3413)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45  % (3413)Termination reason: Inappropriate
% 0.21/0.45  
% 0.21/0.45  % (3413)Memory used [KB]: 2426
% 0.21/0.45  % (3413)Time elapsed: 0.044 s
% 0.21/0.45  % (3413)Instructions burned: 105 (million)
% 0.21/0.45  % (3413)------------------------------
% 0.21/0.45  % (3413)------------------------------
% 0.21/0.45  % (3412)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.45  % (3412)Terminated due to inappropriate strategy.
% 0.21/0.45  % (3412)------------------------------
% 0.21/0.45  % (3412)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.45  % (3412)Termination reason: Inappropriate
% 0.21/0.45  
% 0.21/0.45  % (3412)Memory used [KB]: 2426
% 0.21/0.45  % (3412)Time elapsed: 0.045 s
% 0.21/0.45  % (3412)Instructions burned: 107 (million)
% 0.21/0.45  % (3412)------------------------------
% 0.21/0.45  % (3412)------------------------------
% 0.21/0.46  % (3415)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.46  % (3415)Terminated due to inappropriate strategy.
% 0.21/0.46  % (3415)------------------------------
% 0.21/0.46  % (3415)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46  % (3415)Termination reason: Inappropriate
% 0.21/0.46  
% 0.21/0.46  % (3415)Memory used [KB]: 2439
% 0.21/0.46  % (3415)Time elapsed: 0.047 s
% 0.21/0.46  % (3415)Instructions burned: 114 (million)
% 0.21/0.46  % (3415)------------------------------
% 0.21/0.46  % (3415)------------------------------
% 0.21/0.47  % (3419)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.47  % (3420)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.47  % (3421)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.50  % (3419)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.50  % (3419)Terminated due to inappropriate strategy.
% 0.21/0.50  % (3419)------------------------------
% 0.21/0.50  % (3419)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.50  % (3419)Termination reason: Inappropriate
% 0.21/0.50  
% 0.21/0.50  % (3419)Memory used [KB]: 2321
% 0.21/0.50  % (3419)Time elapsed: 0.037 s
% 0.21/0.50  % (3419)Instructions burned: 87 (million)
% 0.21/0.50  % (3419)------------------------------
% 0.21/0.50  % (3419)------------------------------
% 0.21/0.52  % (3422)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 1.94/0.66  % (3416)First to succeed.
% 1.94/0.70  % (3416)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3411"
% 1.94/0.70  % (3416)Refutation found. Thanks to Tanya!
% 1.94/0.70  % SZS status Theorem for theBenchmark
% 1.94/0.70  % SZS output start Proof for theBenchmark
% See solution above
% 2.33/0.72  % (3416)------------------------------
% 2.33/0.72  % (3416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.33/0.72  % (3416)Termination reason: Refutation
% 2.33/0.72  
% 2.33/0.72  % (3416)Memory used [KB]: 6991
% 2.33/0.72  % (3416)Time elapsed: 0.289 s
% 2.33/0.72  % (3416)Instructions burned: 737 (million)
% 2.33/0.72  % (3411)Success in time 0.37 s
%------------------------------------------------------------------------------