%------------------------------------------------------------------------------
% 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 : n004.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 23:09:29 EDT 2024

% Result   : Theorem 1.15s 0.53s
% Output   : Refutation 1.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  979
% Syntax   : Number of formulae    : 2064 ( 566 unt; 332 typ;   0 def)
%            Number of atoms       : 4197 ( 886 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 3996 (1531   ~;1446   |; 417   &)
%                                         ( 459 <=>; 143  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of FOOLs       :    4 (   4 fml;   0 var)
%            Number arithmetic     : 5312 (1753 atm; 464 fun;1453 num;1642 var)
%            Number of types       :   38 (  35 usr;   2 ari)
%            Number of type conns  :  407 ( 275   >; 132   *;   0   +;   0  <<)
%            Number of predicates  :  412 ( 408 usr; 383 prp; 0-3 aty)
%            Number of functors    :  280 ( 271 usr;  28 con; 0-3 aty)
%            Number of variables   : 2512 (2429   !;  83   ?;2512   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(type_def_24,type,
    tlbool: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(func_def_0,type,
    'fun_app$j': ( 'A_a_cols_vec_fun$' * 'A$' ) > 'A_cols_vec$' ).

tff(func_def_1,type,
    'times$b': ( 'A_rows_vec_rows_vec$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_2,type,
    'dbl_inc$': 'Int_int_fun$' ).

tff(func_def_3,type,
    'uminus$': 'A_rows_vec_rows_vec$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_4,type,
    'p_Gauss_Jordan$': 'A_cols_vec_rows_vec$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_5,type,
    'matrix_matrix_mult$c': ( 'A_cols_vec_rows_vec$' * 'A_cols_vec_cols_vec$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_6,type,
    'uu$': 'Int_int_bool_fun_fun$' ).

tff(func_def_7,type,
    'interchange_rows$': ( 'A_rows_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_8,type,
    'interchange_rows$a': ( 'A_cols_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_9,type,
    'vec_nth$': 'A_rows_vec_rows_vec$' > 'Rows_a_rows_vec_fun$' ).

tff(func_def_10,type,
    'matrix_matrix_mult$b': ( 'A_cols_vec_rows_vec$' * 'A_rows_vec_cols_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_11,type,
    'vector_matrix_mult$c': ( 'A_cols_vec$' * 'A_cols_vec_cols_vec$' ) > 'A_cols_vec$' ).

tff(func_def_12,type,
    'map_matrix$c': ( 'A_a_fun$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_13,type,
    'dbl_inc$a': 'Real_real_fun$' ).

tff(func_def_14,type,
    'fun_app$d': ( 'Rows_a_rows_vec_fun$' * 'Rows$' ) > 'A_rows_vec$' ).

tff(func_def_15,type,
    'vec$': 'A_rows_vec$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_16,type,
    'uminus$b': 'A_cols_vec_rows_vec$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_17,type,
    'transpose$a': 'A_rows_vec_cols_vec$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_18,type,
    'interchange_columns$': ( 'A_rows_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_19,type,
    'map_matrix$a': ( 'A_rows_vec_a_fun$' * 'A_rows_vec_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_20,type,
    'fun_app$p': ( 'Real_int_fun$' * $real ) > $int ).

tff(func_def_21,type,
    'transpose_row$d': 'A_rows_vec_cols_vec$' > 'Rows_a_cols_vec_fun$' ).

tff(func_def_22,type,
    'fun_app$a': ( 'Real_real_bool_fun_fun$' * $real ) > 'Real_bool_fun$' ).

tff(func_def_23,type,
    'transpose_row$': 'A_rows_vec_rows_vec$' > 'Rows_a_rows_vec_fun$' ).

tff(func_def_24,type,
    'mat_mult_row$': ( 'A_rows_vec_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'Rows_a_cols_vec_fun$' ).

tff(func_def_25,type,
    'map_matrix$e': ( 'A_a_cols_vec_fun$' * 'A_rows_vec_rows_vec$' ) > 'A_cols_vec_rows_vec_rows_vec$' ).

tff(func_def_26,type,
    'one$e': 'Rows$' ).

tff(func_def_27,type,
    'matrix_matrix_mult$a': ( 'A_rows_vec_rows_vec$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_28,type,
    'of_nat$': 'Nat$' > $int ).

tff(func_def_29,type,
    'fun_app$n': ( 'Rows_a_cols_vec_bool_fun_fun$' * 'Rows$' ) > 'A_cols_vec_bool_fun$' ).

tff(func_def_30,type,
    'vector_matrix_mult$b': ( 'A_cols_vec$' * 'A_rows_vec_cols_vec$' ) > 'A_rows_vec$' ).

tff(func_def_31,type,
    'map_matrix$d': ( 'A_a_rows_vec_fun$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec_rows_vec$' ).

tff(func_def_32,type,
    'columnvector_row$a': ( 'A_cols_vec_rows_vec$' * 'Rows$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_33,type,
    'fun_app$e': ( 'Rows_a_cols_vec_fun$' * 'Rows$' ) > 'A_cols_vec$' ).

tff(func_def_34,type,
    'transpose$b': 'A_cols_vec_rows_vec$' > 'A_rows_vec_cols_vec$' ).

tff(func_def_35,type,
    'interchange_columns_row$a': ( 'A_cols_vec_rows_vec$' * 'Cols$' * 'Cols$' ) > 'Rows_a_cols_vec_fun$' ).

tff(func_def_36,type,
    'fun_app$t': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).

tff(func_def_37,type,
    'of_nat$d': 'Nat$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_38,type,
    'one$': 'A$' ).

tff(func_def_39,type,
    'rank$a': 'A_rows_vec_cols_vec$' > 'Nat$' ).

tff(func_def_40,type,
    'zero$': 'A_rows_vec$' ).

tff(func_def_41,type,
    'rank$b': 'A_rows_vec_rows_vec$' > 'Nat$' ).

tff(func_def_42,type,
    'of_nat$a': 'Nat_real_fun$' ).

tff(func_def_43,type,
    'uminus$c': 'A_cols_vec$' > 'A_cols_vec$' ).

tff(func_def_44,type,
    'of_nat$e': 'Nat$' > 'A_cols_vec$' ).

tff(func_def_45,type,
    'one$c': 'A_cols_vec_rows_vec$' ).

tff(func_def_46,type,
    tltrue: tlbool ).

tff(func_def_47,type,
    'interchange_columns$a': ( 'A_cols_vec_rows_vec$' * 'Cols$' * 'Cols$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_48,type,
    'transpose$': 'A_rows_vec_rows_vec$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_49,type,
    'a$': 'A_cols_vec_rows_vec$' ).

tff(func_def_50,type,
    'of_nat$c': 'Nat$' > 'A_rows_vec$' ).

tff(func_def_51,type,
    'matrix_matrix_mult$d': ( 'A_rows_vec_cols_vec$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_cols_vec$' ).

tff(func_def_52,type,
    'column$': ( 'Rows$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec$' ).

tff(func_def_53,type,
    'fun_app$q': ( 'Int_real_fun$' * $int ) > $real ).

tff(func_def_54,type,
    'column$a': ( 'Cols$' * 'A_cols_vec_rows_vec$' ) > 'A_rows_vec$' ).

tff(func_def_55,type,
    'matrix_matrix_mult$': ( 'A_rows_vec_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_56,type,
    'one$a': 'A_rows_vec_rows_vec$' ).

tff(func_def_57,type,
    'columnvector_row$': ( 'A_rows_vec_rows_vec$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_58,type,
    'fun_app$h': ( 'A_cols_vec_a_fun$' * 'A_cols_vec$' ) > 'A$' ).

tff(func_def_59,type,
    'fun_app$r': ( 'Real_real_fun$' * $real ) > $real ).

tff(func_def_60,type,
    'fun_app$i': ( 'A_a_rows_vec_fun$' * 'A$' ) > 'A_rows_vec$' ).

tff(func_def_61,type,
    'interchange_rows_row$': ( 'A_rows_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'Rows_a_rows_vec_fun$' ).

tff(func_def_62,type,
    'vec_nth$b': ( 'A_rows_vec$' * 'Rows$' ) > 'A$' ).

tff(func_def_63,type,
    'uua$': 'Real_real_bool_fun_fun$' ).

tff(func_def_64,type,
    'vector_matrix_mult$': ( 'A_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec$' ).

tff(func_def_65,type,
    'zero$d': 'Rows$' ).

tff(func_def_66,type,
    'map_matrix$': ( 'A_a_fun$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_67,type,
    'of_nat$b': 'Nat$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_68,type,
    'fun_app$u': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_69,type,
    'mat$': 'A$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_70,type,
    'times$d': ( 'A_cols_vec_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_71,type,
    'vec_nth$c': ( 'A_rows_vec_rows_vec_rows_vec$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_72,type,
    'fun_app$l': ( 'Rows_a_rows_vec_bool_fun_fun$' * 'Rows$' ) > 'A_rows_vec_bool_fun$' ).

tff(func_def_73,type,
    'interchange_rows_row$a': ( 'A_cols_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'Rows_a_cols_vec_fun$' ).

tff(func_def_74,type,
    'row$': ( 'Rows$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec$' ).

tff(func_def_75,type,
    'transpose_row$c': ( 'A_cols_vec_rows_vec_rows_vec$' * 'Rows$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_76,type,
    'one$d': 'A_cols_vec$' ).

tff(func_def_77,type,
    'zero$e': 'A$' ).

tff(func_def_78,type,
    'vec_nth$d': ( 'A_cols_vec_rows_vec_rows_vec$' * 'Rows$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_79,type,
    'to_nat$': 'Rows$' > 'Nat$' ).

tff(func_def_80,type,
    'zero$a': 'A_cols_vec$' ).

tff(func_def_81,type,
    'one$b': 'A_rows_vec$' ).

tff(func_def_82,type,
    'vec_nth$a': 'A_cols_vec_rows_vec$' > 'Rows_a_cols_vec_fun$' ).

tff(func_def_83,type,
    'gauss_Jordan$a': 'A_cols_vec_rows_vec$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_84,type,
    'gauss_Jordan$': 'A_rows_vec_rows_vec$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_85,type,
    'transpose_row$a': ( 'A_cols_vec_rows_vec$' * 'Cols$' ) > 'A_rows_vec$' ).

tff(func_def_86,type,
    'i$': 'Rows$' ).

tff(func_def_87,type,
    'gauss_Jordan_in_ij$a': ( 'A_cols_vec_rows_vec$' * 'Rows$' * 'Cols$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_88,type,
    'uminus$a': 'A_rows_vec$' > 'A_rows_vec$' ).

tff(func_def_89,type,
    'zero$b': 'A_rows_vec_rows_vec$' ).

tff(func_def_90,type,
    tlfalse: tlbool ).

tff(func_def_91,type,
    'vector_matrix_mult$a': ( 'A_rows_vec$' * 'A_rows_vec_rows_vec$' ) > 'A_rows_vec$' ).

tff(func_def_92,type,
    'nat$': $int > 'Nat$' ).

tff(func_def_93,type,
    'gauss_Jordan_in_ij$': ( 'A_rows_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_94,type,
    'fun_app$f': ( 'A_a_fun$' * 'A$' ) > 'A$' ).

tff(func_def_95,type,
    'row$a': ( 'Rows$' * 'A_cols_vec_rows_vec$' ) > 'A_cols_vec$' ).

tff(func_def_96,type,
    'vec$a': 'A_cols_vec$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_97,type,
    'fun_app$c': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).

tff(func_def_98,type,
    'zero$f': 'Cols$' ).

tff(func_def_99,type,
    'times$c': ( 'A_rows_vec$' * 'A_rows_vec$' ) > 'A_rows_vec$' ).

tff(func_def_100,type,
    'axis$a': ( 'Rows$' * 'A_cols_vec$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_101,type,
    'transpose_row$b': ( 'A_rows_vec_rows_vec_rows_vec$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_102,type,
    'zero$c': 'A_cols_vec_rows_vec$' ).

tff(func_def_103,type,
    'map_matrix$b': ( 'A_cols_vec_a_fun$' * 'A_cols_vec_rows_vec_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_104,type,
    'vec_nth$e': ( 'A_cols_vec$' * 'Cols$' ) > 'A$' ).

tff(func_def_105,type,
    'axis$': ( 'Rows$' * 'A_rows_vec$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_106,type,
    'times$': $real > 'Real_real_fun$' ).

tff(func_def_107,type,
    'fun_app$g': ( 'A_rows_vec_a_fun$' * 'A_rows_vec$' ) > 'A$' ).

tff(func_def_108,type,
    'mat_row$a': ( 'A_cols_vec$' * 'Rows$' ) > 'A_cols_vec_rows_vec$' ).

tff(func_def_109,type,
    'times$a': $int > 'Int_int_fun$' ).

tff(func_def_110,type,
    'rank$': 'A_cols_vec_rows_vec$' > 'Nat$' ).

tff(func_def_111,type,
    'interchange_columns_row$': ( 'A_rows_vec_rows_vec$' * 'Rows$' * 'Rows$' ) > 'Rows_a_rows_vec_fun$' ).

tff(func_def_112,type,
    'fun_app$o': ( 'Int_int_fun$' * $int ) > $int ).

tff(func_def_113,type,
    'mat_row$': ( 'A_rows_vec$' * 'Rows$' ) > 'A_rows_vec_rows_vec$' ).

tff(func_def_114,type,
    'times$e': ( 'A_cols_vec$' * 'A_cols_vec$' ) > 'A_cols_vec$' ).

tff(func_def_125,type,
    sK17: $int > 'Nat$' ).

tff(func_def_126,type,
    sK18: $int > 'Nat$' ).

tff(func_def_127,type,
    sK19: $int > 'Nat$' ).

tff(func_def_128,type,
    sK20: $int > 'Nat$' ).

tff(func_def_129,type,
    sK21: $int > 'Nat$' ).

tff(func_def_130,type,
    sK22: $int > 'Nat$' ).

tff(func_def_131,type,
    sK23: $int > 'Nat$' ).

tff(func_def_132,type,
    sK24: ( 'Rows_a_cols_vec_bool_fun_fun$' * 'Rows$' ) > 'A_cols_vec$' ).

tff(func_def_133,type,
    sK25: ( 'Rows_a_cols_vec_bool_fun_fun$' * 'A_cols_vec_rows_vec$' ) > 'Rows$' ).

tff(func_def_134,type,
    sK26: 'Rows_a_cols_vec_bool_fun_fun$' > 'A_cols_vec_rows_vec$' ).

tff(func_def_135,type,
    sK27: 'Rows_a_cols_vec_bool_fun_fun$' > 'Rows$' ).

tff(func_def_136,type,
    sK28: ( 'Rows_a_rows_vec_bool_fun_fun$' * 'Rows$' ) > 'A_rows_vec$' ).

tff(func_def_137,type,
    sK29: ( 'Rows_a_rows_vec_bool_fun_fun$' * 'A_rows_vec_rows_vec$' ) > 'Rows$' ).

tff(func_def_138,type,
    sK30: 'Rows_a_rows_vec_bool_fun_fun$' > 'A_rows_vec_rows_vec$' ).

tff(func_def_139,type,
    sK31: 'Rows_a_rows_vec_bool_fun_fun$' > 'Rows$' ).

tff(func_def_140,type,
    sK32: $real > $real ).

tff(func_def_141,type,
    sK33: $real > $real ).

tff(func_def_142,type,
    sK34: $int > $int ).

tff(func_def_143,type,
    sK35: $int > $int ).

tff(func_def_144,type,
    sK36: $real > 'Nat$' ).

tff(func_def_145,type,
    sK37: $real > 'Nat$' ).

tff(func_def_146,type,
    sK38: ( $real * $real ) > $real ).

tff(func_def_147,type,
    sK39: ( $real * $real ) > $real ).

tff(func_def_148,type,
    sK40: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_149,type,
    sK41: ( $real * $real ) > 'Nat$' ).

tff(func_def_150,type,
    sK42: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_151,type,
    sK43: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_152,type,
    sK44: ( $real * $real ) > $real ).

tff(func_def_153,type,
    sK45: ( $real * $real ) > $real ).

tff(func_def_154,type,
    sK46: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_155,type,
    sK47: ( 'A_cols_vec_rows_vec$' * 'A_cols_vec_rows_vec$' ) > 'Rows$' ).

tff(func_def_156,type,
    sK48: ( 'A_rows_vec_rows_vec$' * 'A_rows_vec_rows_vec$' ) > 'Rows$' ).

tff(func_def_157,type,
    sK49: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_158,type,
    sK50: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_159,type,
    sK51: ( $real * $real * $real ) > $real ).

tff(func_def_160,type,
    sK52: ( $real * $real * $real ) > $real ).

tff(func_def_161,type,
    sK53: ( 'Nat$' * 'Nat_real_fun$' ) > 'Nat$' ).

tff(func_def_162,type,
    sK54: ( 'Nat$' * 'Nat_real_fun$' * 'Nat_real_fun$' ) > 'Nat$' ).

tff(func_def_163,type,
    sK55: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_164,type,
    sK56: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_165,type,
    sK57: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_166,type,
    sK58: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_167,type,
    sK59: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_168,type,
    sK60: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_169,type,
    sK61: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_170,type,
    sK62: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_171,type,
    sK63: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_172,type,
    sK64: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_173,type,
    sK65: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_174,type,
    sK66: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_175,type,
    sK67: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_176,type,
    sK68: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_177,type,
    sK69: 'Real_real_bool_fun_fun$' > $real ).

tff(func_def_178,type,
    sK70: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_179,type,
    sK71: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_180,type,
    sK72: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_181,type,
    sK73: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_182,type,
    sK74: 'Int_int_bool_fun_fun$' > $int ).

tff(func_def_183,type,
    sK75: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_184,type,
    sK76: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_185,type,
    sK77: 'Real_int_fun$' > $real ).

tff(func_def_186,type,
    sK78: 'Real_int_fun$' > $real ).

tff(func_def_187,type,
    sK79: 'Real_real_fun$' > $real ).

tff(func_def_188,type,
    sK80: 'Real_real_fun$' > $real ).

tff(func_def_189,type,
    sK81: 'Real_real_fun$' > $real ).

tff(func_def_190,type,
    sK82: 'Real_real_fun$' > $real ).

tff(func_def_191,type,
    sK83: 'Real_int_fun$' > $real ).

tff(func_def_192,type,
    sK84: 'Real_int_fun$' > $real ).

tff(func_def_193,type,
    sK85: 'Real_real_fun$' > $real ).

tff(func_def_194,type,
    sK86: 'Real_real_fun$' > $real ).

tff(func_def_195,type,
    sK87: 'Real_int_fun$' > $real ).

tff(func_def_196,type,
    sK88: 'Real_int_fun$' > $real ).

tff(func_def_197,type,
    sK89: 'Int_real_fun$' > $int ).

tff(func_def_198,type,
    sK90: 'Int_real_fun$' > $int ).

tff(func_def_199,type,
    sK91: 'Int_int_fun$' > $int ).

tff(func_def_200,type,
    sK92: 'Int_int_fun$' > $int ).

tff(func_def_201,type,
    sK93: 'Int_real_fun$' > $int ).

tff(func_def_202,type,
    sK94: 'Int_real_fun$' > $int ).

tff(func_def_203,type,
    sK95: 'Int_int_fun$' > $int ).

tff(func_def_204,type,
    sK96: 'Int_int_fun$' > $int ).

tff(func_def_205,type,
    sK97: 'Int_real_fun$' > $int ).

tff(func_def_206,type,
    sK98: 'Int_real_fun$' > $int ).

tff(func_def_207,type,
    sK99: 'Int_int_fun$' > $int ).

tff(func_def_208,type,
    sK100: 'Int_int_fun$' > $int ).

tff(func_def_209,type,
    sK101: 'Real_int_fun$' > $real ).

tff(func_def_210,type,
    sK102: 'Real_int_fun$' > $real ).

tff(func_def_211,type,
    sK103: 'Real_real_fun$' > $real ).

tff(func_def_212,type,
    sK104: 'Real_real_fun$' > $real ).

tff(func_def_213,type,
    sK105: 'Real_real_fun$' > $real ).

tff(func_def_214,type,
    sK106: 'Real_real_fun$' > $real ).

tff(func_def_215,type,
    sK107: 'Real_int_fun$' > $real ).

tff(func_def_216,type,
    sK108: 'Real_int_fun$' > $real ).

tff(func_def_217,type,
    sK109: 'Real_real_fun$' > $real ).

tff(func_def_218,type,
    sK110: 'Real_real_fun$' > $real ).

tff(func_def_219,type,
    sK111: 'Real_int_fun$' > $real ).

tff(func_def_220,type,
    sK112: 'Real_int_fun$' > $real ).

tff(func_def_221,type,
    sK113: 'Int_real_fun$' > $int ).

tff(func_def_222,type,
    sK114: 'Int_real_fun$' > $int ).

tff(func_def_223,type,
    sK115: 'Int_int_fun$' > $int ).

tff(func_def_224,type,
    sK116: 'Int_int_fun$' > $int ).

tff(func_def_225,type,
    sK117: 'Int_real_fun$' > $int ).

tff(func_def_226,type,
    sK118: 'Int_real_fun$' > $int ).

tff(func_def_227,type,
    sK119: 'Int_int_fun$' > $int ).

tff(func_def_228,type,
    sK120: 'Int_int_fun$' > $int ).

tff(func_def_229,type,
    sK121: 'Int_real_fun$' > $int ).

tff(func_def_230,type,
    sK122: 'Int_real_fun$' > $int ).

tff(func_def_231,type,
    sK123: 'Int_int_fun$' > $int ).

tff(func_def_232,type,
    sK124: 'Int_int_fun$' > $int ).

tff(func_def_233,type,
    sK125: 'Real_int_fun$' > $real ).

tff(func_def_234,type,
    sK126: 'Real_int_fun$' > $real ).

tff(func_def_235,type,
    sK127: 'Int_real_fun$' > $int ).

tff(func_def_236,type,
    sK128: 'Int_real_fun$' > $int ).

tff(func_def_237,type,
    sK129: 'Real_int_fun$' > $real ).

tff(func_def_238,type,
    sK130: 'Real_int_fun$' > $real ).

tff(func_def_239,type,
    sK131: 'Int_real_fun$' > $int ).

tff(func_def_240,type,
    sK132: 'Int_real_fun$' > $int ).

tff(func_def_241,type,
    sK133: 'Int_int_fun$' > $int ).

tff(func_def_242,type,
    sK134: 'Int_int_fun$' > $int ).

tff(func_def_243,type,
    sK135: 'Int_int_fun$' > $int ).

tff(func_def_244,type,
    sK136: 'Int_int_fun$' > $int ).

tff(func_def_245,type,
    sK137: 'Real_real_fun$' > $real ).

tff(func_def_246,type,
    sK138: 'Real_real_fun$' > $real ).

tff(func_def_247,type,
    sK139: 'Real_real_fun$' > $real ).

tff(func_def_248,type,
    sK140: 'Real_real_fun$' > $real ).

tff(func_def_249,type,
    sK141: 'Int_real_fun$' > $int ).

tff(func_def_250,type,
    sK142: 'Int_real_fun$' > $int ).

tff(func_def_251,type,
    sK143: 'Int_real_fun$' > $int ).

tff(func_def_252,type,
    sK144: 'Int_real_fun$' > $int ).

tff(func_def_253,type,
    sK145: 'Real_real_fun$' > $real ).

tff(func_def_254,type,
    sK146: 'Real_real_fun$' > $real ).

tff(func_def_255,type,
    sK147: 'Real_real_fun$' > $real ).

tff(func_def_256,type,
    sK148: 'Real_real_fun$' > $real ).

tff(func_def_257,type,
    sK149: 'Real_int_fun$' > $real ).

tff(func_def_258,type,
    sK150: 'Real_int_fun$' > $real ).

tff(func_def_259,type,
    sK151: 'Real_int_fun$' > $real ).

tff(func_def_260,type,
    sK152: 'Real_int_fun$' > $real ).

tff(func_def_261,type,
    sK153: 'Int_int_fun$' > $int ).

tff(func_def_262,type,
    sK154: 'Int_int_fun$' > $int ).

tff(func_def_263,type,
    sK155: 'Int_int_fun$' > $int ).

tff(func_def_264,type,
    sK156: 'Int_int_fun$' > $int ).

tff(func_def_265,type,
    sK157: 'Int_real_fun$' > $int ).

tff(func_def_266,type,
    sK158: 'Int_real_fun$' > $int ).

tff(func_def_267,type,
    sK159: 'Int_real_fun$' > $int ).

tff(func_def_268,type,
    sK160: 'Int_real_fun$' > $int ).

tff(func_def_269,type,
    sK161: 'Real_real_fun$' > $real ).

tff(func_def_270,type,
    sK162: 'Real_real_fun$' > $real ).

tff(func_def_271,type,
    sK163: 'Real_real_fun$' > $real ).

tff(func_def_272,type,
    sK164: 'Real_real_fun$' > $real ).

tff(func_def_273,type,
    sK165: 'Real_int_fun$' > $real ).

tff(func_def_274,type,
    sK166: 'Real_int_fun$' > $real ).

tff(func_def_275,type,
    sK167: 'Real_int_fun$' > $real ).

tff(func_def_276,type,
    sK168: 'Real_int_fun$' > $real ).

tff(func_def_277,type,
    sK169: 'Int_int_fun$' > $int ).

tff(func_def_278,type,
    sK170: 'Int_int_fun$' > $int ).

tff(func_def_279,type,
    sK171: 'Int_int_fun$' > $int ).

tff(func_def_280,type,
    sK172: 'Int_int_fun$' > $int ).

tff(pred_def_1,type,
    'reduced_row_echelon_form$': 'A_rows_vec_rows_vec$' > $o ).

tff(pred_def_2,type,
    'fun_app$k': ( 'A_rows_vec_bool_fun$' * 'A_rows_vec$' ) > $o ).

tff(pred_def_3,type,
    'fun_app$m': ( 'A_cols_vec_bool_fun$' * 'A_cols_vec$' ) > $o ).

tff(pred_def_4,type,
    'less_eq$': ( 'Rows$' * 'Rows$' ) > $o ).

tff(pred_def_5,type,
    'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).

tff(pred_def_6,type,
    'reduced_row_echelon_form$a': 'A_cols_vec_rows_vec$' > $o ).

tff(pred_def_7,type,
    'less$': ( 'Rows$' * 'Rows$' ) > $o ).

tff(pred_def_8,type,
    'fun_app$s': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_9,type,
    'fun_app$b': ( 'Int_bool_fun$' * $int ) > $o ).

tff(pred_def_14,type,
    sP0: ( $real * $real ) > $o ).

tff(pred_def_15,type,
    sP1: ( $real * $real ) > $o ).

tff(pred_def_16,type,
    sP2: ( $int * $int ) > $o ).

tff(pred_def_17,type,
    sP3: ( $int * $int ) > $o ).

tff(pred_def_18,type,
    sP4: ( $real * $real * $real ) > $o ).

tff(pred_def_19,type,
    sP5: ( $real * $real * $real ) > $o ).

tff(pred_def_20,type,
    sP6: ( $real * $real * $real ) > $o ).

tff(pred_def_21,type,
    sP7: ( $real * $real * $real ) > $o ).

tff(pred_def_22,type,
    sP8: ( $int * $int * $int ) > $o ).

tff(pred_def_23,type,
    sP9: ( $int * $int * $int ) > $o ).

tff(pred_def_24,type,
    sP10: ( $int * $int * $int ) > $o ).

tff(pred_def_25,type,
    sP11: ( $int * $int * $int ) > $o ).

tff(pred_def_26,type,
    sP12: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_27,type,
    sP13: ( $real * $real * $real ) > $o ).

tff(pred_def_28,type,
    sP14: ( $real * $real * $real ) > $o ).

tff(pred_def_29,type,
    sP15: ( $int * $int * $int ) > $o ).

tff(pred_def_30,type,
    sP16: ( $int * $int * $int ) > $o ).

tff(f6775,plain,
    $false,
    inference(avatar_sat_refutation,[],[f3106,f3110,f3115,f3120,f3127,f3131,f3135,f3139,f3143,f3147,f3151,f3155,f3159,f3163,f3167,f3171,f3175,f3179,f3184,f3189,f3194,f3199,f3204,f3209,f3214,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3251,f3256,f3268,f3272,f3277,f3283,f3289,f3293,f3297,f3301,f3305,f3309,f3313,f3317,f3321,f3325,f3329,f3334,f3339,f3343,f3347,f3351,f3355,f3359,f3363,f3367,f3371,f3375,f3380,f3384,f3388,f3392,f3397,f3402,f3406,f3410,f3414,f3418,f3424,f3429,f3435,f3472,f3488,f3498,f3503,f3507,f3511,f3515,f3520,f3524,f3528,f3532,f3536,f3540,f3544,f3548,f3552,f3556,f3560,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3596,f3600,f3604,f3608,f3612,f3616,f3620,f3624,f3628,f3632,f3636,f3640,f3644,f3648,f3652,f3656,f3660,f3664,f3668,f3672,f3676,f3680,f3684,f3688,f3692,f3696,f3769,f3773,f3777,f3781,f3785,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3831,f3835,f3839,f3843,f3847,f3851,f3855,f3859,f3863,f3867,f3871,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f4125,f4160,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4328,f4332,f4336,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4373,f4377,f4381,f4385,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4418,f4422,f4426,f4430,f4434,f4438,f4730,f4810,f4901,f4905,f4909,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5087,f5091,f5181,f5301,f5305,f5309,f5342,f5346,f5350,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5412,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5454,f5458,f5462,f5579,f5588,f5667,f5676,f5746,f5753,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5796,f5800,f5804,f5808,f5813,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f6052,f6133,f6137,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6459,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6568,f6688,f6751,f6756,f6760,f6764,f6769,f6773,f6774]) ).

tff(f6774,plain,
    ( spl173_376
    | ~ spl173_295
    | ~ spl173_377 ),
    inference(avatar_split_clause,[],[f6752,f6748,f5435,f6685]) ).

tff(f6685,plain,
    ( spl173_376
  <=> ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_376])]) ).

tff(f5435,plain,
    ( spl173_295
  <=> ! [X2: 'A_cols_vec_rows_vec$',X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$'('row$'(X0,X1),X2) = 'row$a'(X0,'matrix_matrix_mult$'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_295])]) ).

tff(f6748,plain,
    ( spl173_377
  <=> ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'vector_matrix_mult$'('row$'('i$','p_Gauss_Jordan$'('a$')),'a$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_377])]) ).

tff(f6752,plain,
    ( ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) )
    | ~ spl173_295
    | ~ spl173_377 ),
    inference(forward_demodulation,[],[f6750,f5436]) ).

tff(f5436,plain,
    ( ! [X2: 'A_cols_vec_rows_vec$',X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$'('row$'(X0,X1),X2) = 'row$a'(X0,'matrix_matrix_mult$'(X1,X2)) )
    | ~ spl173_295 ),
    inference(avatar_component_clause,[],[f5435]) ).

tff(f6750,plain,
    ( ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'vector_matrix_mult$'('row$'('i$','p_Gauss_Jordan$'('a$')),'a$') )
    | ~ spl173_377 ),
    inference(avatar_component_clause,[],[f6748]) ).

tff(f6773,plain,
    spl173_382,
    inference(avatar_split_clause,[],[f2864,f6771]) ).

tff(f6771,plain,
    ( spl173_382
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vec_nth$b'('fun_app$d'('vec_nth$'(X0),X2),X1) = 'vec_nth$b'('fun_app$d'('vec_nth$'('transpose$'(X0)),X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_382])]) ).

tff(f2864,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vec_nth$b'('fun_app$d'('vec_nth$'(X0),X2),X1) = 'vec_nth$b'('fun_app$d'('vec_nth$'('transpose$'(X0)),X1),X2) ),
    inference(definition_unfolding,[],[f2546,f1949]) ).

tff(f1949,plain,
    ! [X0: 'A_rows_vec_rows_vec$'] : ( 'transpose_row$'(X0) = 'vec_nth$'('transpose$'(X0)) ),
    inference(cnf_transformation,[],[f43]) ).

tff(f43,axiom,
    ! [X0: 'A_rows_vec_rows_vec$'] : ( 'transpose_row$'(X0) = 'vec_nth$'('transpose$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).

tff(f2546,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vec_nth$b'('fun_app$d'('transpose_row$'(X0),X1),X2) = 'vec_nth$b'('fun_app$d'('vec_nth$'(X0),X2),X1) ),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'vec_nth$b'('fun_app$d'('transpose_row$'(X0),X1),X2) = 'vec_nth$b'('fun_app$d'('vec_nth$'(X0),X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).

tff(f6769,plain,
    spl173_381,
    inference(avatar_split_clause,[],[f2589,f6767]) ).

tff(f6767,plain,
    ( spl173_381
  <=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,sK49(X0))
        | $less('of_nat$'(X2),'of_nat$'(sK50(X0,X2)))
        | ~ 'fun_app$s'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_381])]) ).

tff(f2589,plain,
    ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,sK49(X0))
      | $less('of_nat$'(X2),'of_nat$'(sK50(X0,X2)))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(cnf_transformation,[],[f1677]) ).

tff(f1677,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ( ! [X4: 'Nat$'] :
            ( ~ $less('of_nat$'(sK49(X0)),'of_nat$'(X4))
            | ~ 'fun_app$s'(X0,X4) )
        & 'fun_app$s'(X0,sK49(X0)) )
      | ( $less('of_nat$'(X2),'of_nat$'(sK50(X0,X2)))
        & 'fun_app$s'(X0,sK50(X0,X2)) )
      | ~ 'fun_app$s'(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50])],[f1674,f1676,f1675]) ).

tff(f1675,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X3: 'Nat$'] :
          ( ! [X4: 'Nat$'] :
              ( ~ $less('of_nat$'(X3),'of_nat$'(X4))
              | ~ 'fun_app$s'(X0,X4) )
          & 'fun_app$s'(X0,X3) )
     => ( ! [X4: 'Nat$'] :
            ( ~ $less('of_nat$'(sK49(X0)),'of_nat$'(X4))
            | ~ 'fun_app$s'(X0,X4) )
        & 'fun_app$s'(X0,sK49(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1676,plain,
    ! [X0: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( ? [X5: 'Nat$'] :
          ( $less('of_nat$'(X2),'of_nat$'(X5))
          & 'fun_app$s'(X0,X5) )
     => ( $less('of_nat$'(X2),'of_nat$'(sK50(X0,X2)))
        & 'fun_app$s'(X0,sK50(X0,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1674,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( ! [X4: 'Nat$'] :
              ( ~ $less('of_nat$'(X3),'of_nat$'(X4))
              | ~ 'fun_app$s'(X0,X4) )
          & 'fun_app$s'(X0,X3) )
      | ? [X5: 'Nat$'] :
          ( $less('of_nat$'(X2),'of_nat$'(X5))
          & 'fun_app$s'(X0,X5) )
      | ~ 'fun_app$s'(X0,X1) ),
    inference(rectify,[],[f1156]) ).

tff(f1156,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ? [X4: 'Nat$'] :
          ( ! [X5: 'Nat$'] :
              ( ~ $less('of_nat$'(X4),'of_nat$'(X5))
              | ~ 'fun_app$s'(X0,X5) )
          & 'fun_app$s'(X0,X4) )
      | ? [X3: 'Nat$'] :
          ( $less('of_nat$'(X2),'of_nat$'(X3))
          & 'fun_app$s'(X0,X3) )
      | ~ 'fun_app$s'(X0,X1) ),
    inference(flattening,[],[f1155]) ).

tff(f1155,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ? [X4: 'Nat$'] :
          ( ! [X5: 'Nat$'] :
              ( ~ $less('of_nat$'(X4),'of_nat$'(X5))
              | ~ 'fun_app$s'(X0,X5) )
          & 'fun_app$s'(X0,X4) )
      | ? [X3: 'Nat$'] :
          ( $less('of_nat$'(X2),'of_nat$'(X3))
          & 'fun_app$s'(X0,X3) )
      | ~ 'fun_app$s'(X0,X1) ),
    inference(ennf_transformation,[],[f938]) ).

tff(f938,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
           => ~ $less('of_nat$'(X2),'of_nat$'(X3)) )
        & 'fun_app$s'(X0,X1) )
     => ? [X4: 'Nat$'] :
          ( ! [X5: 'Nat$'] :
              ( 'fun_app$s'(X0,X5)
             => ~ $less('of_nat$'(X4),'of_nat$'(X5)) )
          & 'fun_app$s'(X0,X4) ) ),
    inference(rectify,[],[f773]) ).

tff(f773,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
           => ~ $less('of_nat$'(X2),'of_nat$'(X3)) )
        & 'fun_app$s'(X0,X1) )
     => ? [X3: 'Nat$'] :
          ( ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X0,X4)
             => ~ $less('of_nat$'(X3),'of_nat$'(X4)) )
          & 'fun_app$s'(X0,X3) ) ),
    inference(theory_normalization,[],[f147]) ).

tff(f147,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
           => $lesseq('of_nat$'(X3),'of_nat$'(X2)) )
        & 'fun_app$s'(X0,X1) )
     => ? [X3: 'Nat$'] :
          ( ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X0,X4)
             => $lesseq('of_nat$'(X4),'of_nat$'(X3)) )
          & 'fun_app$s'(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).

tff(f6764,plain,
    spl173_380,
    inference(avatar_split_clause,[],[f2226,f6762]) ).

tff(f6762,plain,
    ( spl173_380
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ $less('of_nat$'(X1),'of_nat$'(sK40(X0,X1)))
        | 'fun_app$s'(X0,'nat$'(0))
        | ~ 'fun_app$s'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_380])]) ).

tff(f2226,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ $less('of_nat$'(X1),'of_nat$'(sK40(X0,X1)))
      | 'fun_app$s'(X0,'nat$'(0))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f1496,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( 'fun_app$s'(X0,sK40(X0,X1))
        & ! [X3: 'Nat$'] :
            ( ~ 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK40(X0,X1))) )
        & ~ $less('of_nat$'(X1),'of_nat$'(sK40(X0,X1))) )
      | 'fun_app$s'(X0,'nat$'(0))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1077,f1495]) ).

tff(f1495,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( ~ 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) )
     => ( 'fun_app$s'(X0,sK40(X0,X1))
        & ! [X3: 'Nat$'] :
            ( ~ 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK40(X0,X1))) )
        & ~ $less('of_nat$'(X1),'of_nat$'(sK40(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f1077,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( ~ 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) )
      | 'fun_app$s'(X0,'nat$'(0))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(flattening,[],[f1076]) ).

tff(f1076,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( ~ 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) )
      | 'fun_app$s'(X0,'nat$'(0))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(ennf_transformation,[],[f707]) ).

tff(f707,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ~ 'fun_app$s'(X0,'nat$'(0))
        & 'fun_app$s'(X0,X1) )
     => ? [X2: 'Nat$'] :
          ( 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( $less('of_nat$'(X3),'of_nat$'(X2))
             => ~ 'fun_app$s'(X0,X3) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) ) ),
    inference(theory_normalization,[],[f386]) ).

tff(f386,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ~ 'fun_app$s'(X0,'nat$'(0))
        & 'fun_app$s'(X0,X1) )
     => ? [X2: 'Nat$'] :
          ( 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( $less('of_nat$'(X3),'of_nat$'(X2))
             => ~ 'fun_app$s'(X0,X3) )
          & $lesseq('of_nat$'(X2),'of_nat$'(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).

tff(f6760,plain,
    spl173_379,
    inference(avatar_split_clause,[],[f2201,f6758]) ).

tff(f6758,plain,
    ( spl173_379
  <=> ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] :
        ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('gauss_Jordan$a'(X0)),X1) )
        | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_379])]) ).

tff(f2201,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] :
      ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('gauss_Jordan$a'(X0)),X1) )
      | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$'(X0))) ),
    inference(cnf_transformation,[],[f1036]) ).

tff(f1036,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] :
      ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('gauss_Jordan$a'(X0)),X1) )
      | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$'(X0))) ),
    inference(ennf_transformation,[],[f704]) ).

tff(f704,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] :
      ( ~ $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$'(X0)))
     => ( 'zero$a' = 'fun_app$e'('vec_nth$a'('gauss_Jordan$a'(X0)),X1) ) ),
    inference(theory_normalization,[],[f134]) ).

tff(f134,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] :
      ( $lesseq('of_nat$'('rank$'(X0)),'of_nat$'('to_nat$'(X1)))
     => ( 'zero$a' = 'fun_app$e'('vec_nth$a'('gauss_Jordan$a'(X0)),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom132) ).

tff(f6756,plain,
    spl173_378,
    inference(avatar_split_clause,[],[f2200,f6754]) ).

tff(f6754,plain,
    ( spl173_378
  <=> ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] :
        ( ( 'zero$' = 'fun_app$d'('vec_nth$'('gauss_Jordan$'(X0)),X1) )
        | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$b'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_378])]) ).

tff(f2200,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] :
      ( ( 'zero$' = 'fun_app$d'('vec_nth$'('gauss_Jordan$'(X0)),X1) )
      | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$b'(X0))) ),
    inference(cnf_transformation,[],[f1035]) ).

tff(f1035,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] :
      ( ( 'zero$' = 'fun_app$d'('vec_nth$'('gauss_Jordan$'(X0)),X1) )
      | $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$b'(X0))) ),
    inference(ennf_transformation,[],[f703]) ).

tff(f703,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] :
      ( ~ $less('of_nat$'('to_nat$'(X1)),'of_nat$'('rank$b'(X0)))
     => ( 'zero$' = 'fun_app$d'('vec_nth$'('gauss_Jordan$'(X0)),X1) ) ),
    inference(theory_normalization,[],[f133]) ).

tff(f133,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] :
      ( $lesseq('of_nat$'('rank$b'(X0)),'of_nat$'('to_nat$'(X1)))
     => ( 'zero$' = 'fun_app$d'('vec_nth$'('gauss_Jordan$'(X0)),X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom131) ).

tff(f6751,plain,
    spl173_377,
    inference(avatar_split_clause,[],[f1901,f6748]) ).

tff(f1901,plain,
    'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'vector_matrix_mult$'('row$'('i$','p_Gauss_Jordan$'('a$')),'a$'),
    inference(cnf_transformation,[],[f5]) ).

tff(f5,axiom,
    'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'vector_matrix_mult$'('row$'('i$','p_Gauss_Jordan$'('a$')),'a$'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).

tff(f6688,plain,
    ( ~ spl173_376
    | spl173_5
    | ~ spl173_359 ),
    inference(avatar_split_clause,[],[f6575,f6433,f3124,f6685]) ).

tff(f3124,plain,
    ( spl173_5
  <=> ( 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') = 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_5])]) ).

tff(f6433,plain,
    ( spl173_359
  <=> ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_359])]) ).

tff(f6575,plain,
    ( ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') != 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) )
    | spl173_5
    | ~ spl173_359 ),
    inference(superposition,[],[f3126,f6434]) ).

tff(f6434,plain,
    ( ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'(X0,X2)),X1) )
    | ~ spl173_359 ),
    inference(avatar_component_clause,[],[f6433]) ).

tff(f3126,plain,
    ( ( 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') != 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) )
    | spl173_5 ),
    inference(avatar_component_clause,[],[f3124]) ).

tff(f6568,plain,
    ( spl173_375
    | ~ spl173_55
    | ~ spl173_188 ),
    inference(avatar_split_clause,[],[f5017,f4236,f3349,f6566]) ).

tff(f6566,plain,
    ( spl173_375
  <=> ! [X0: $real] : ~ $less($sum(X0,1.0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_375])]) ).

tff(f3349,plain,
    ( spl173_55
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_55])]) ).

tff(f4236,plain,
    ( spl173_188
  <=> ! [X0: $real] : $less(X0,$sum(X0,1.0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_188])]) ).

tff(f5017,plain,
    ( ! [X0: $real] : ~ $less($sum(X0,1.0),X0)
    | ~ spl173_55
    | ~ spl173_188 ),
    inference(resolution,[],[f4237,f3350]) ).

tff(f3350,plain,
    ( ! [X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | ~ $less(X0,X1) )
    | ~ spl173_55 ),
    inference(avatar_component_clause,[],[f3349]) ).

tff(f4237,plain,
    ( ! [X0: $real] : $less(X0,$sum(X0,1.0))
    | ~ spl173_188 ),
    inference(avatar_component_clause,[],[f4236]) ).

tff(f6495,plain,
    spl173_374,
    inference(avatar_split_clause,[],[f2878,f6493]) ).

tff(f6493,plain,
    ( spl173_374
  <=> ! [X2: $int,X0: $int,X3: $int] :
        ( ( 0 = X0 )
        | ( $product(X0,X2) != $product(X0,X3) )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_374])]) ).

tff(f2878,plain,
    ! [X2: $int,X3: $int,X0: $int] :
      ( ( 0 = X0 )
      | ( $product(X0,X2) != $product(X0,X3) )
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f853]) ).

tff(f853,plain,
    ! [X2: $int,X3: $int,X0: $int,X1: $int] :
      ( ( 0 = X0 )
      | ( $product(X0,X2) != X1 )
      | ( $product(X0,X3) != X1 )
      | ( X2 = X3 ) ),
    introduced(theory_axiom_151,[]) ).

tff(f6491,plain,
    spl173_373,
    inference(avatar_split_clause,[],[f2877,f6489]) ).

tff(f6489,plain,
    ( spl173_373
  <=> ! [X2: $real,X0: $real,X3: $real] :
        ( ( 0.0 = X0 )
        | ( $product(X0,X2) != $product(X0,X3) )
        | ( X2 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_373])]) ).

tff(f2877,plain,
    ! [X2: $real,X3: $real,X0: $real] :
      ( ( 0.0 = X0 )
      | ( $product(X0,X2) != $product(X0,X3) )
      | ( X2 = X3 ) ),
    inference(equality_resolution,[],[f871]) ).

tff(f871,plain,
    ! [X2: $real,X3: $real,X0: $real,X1: $real] :
      ( ( 0.0 = X0 )
      | ( $product(X0,X2) != X1 )
      | ( $product(X0,X3) != X1 )
      | ( X2 = X3 ) ),
    introduced(theory_axiom_151,[]) ).

tff(f6487,plain,
    spl173_372,
    inference(avatar_split_clause,[],[f2738,f6485]) ).

tff(f6485,plain,
    ( spl173_372
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2))
        | ~ sP16(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_372])]) ).

tff(f2738,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2))
      | ~ sP16(X1,X2,X0) ),
    inference(cnf_transformation,[],[f1752]) ).

tff(f1752,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2))
        | ~ sP16(X1,X2,X0) )
      & ( sP16(X1,X2,X0)
        | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2)) ) ),
    inference(nnf_transformation,[],[f1390]) ).

tff(f1390,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2))
    <=> sP16(X1,X2,X0) ),
    inference(definition_folding,[],[f547,f1389]) ).

tff(f1389,plain,
    ! [X1: $int,X2: $int,X0: $int] :
      ( sP16(X1,X2,X0)
    <=> ( ( $less(X2,X1)
          & $less(X0,0) )
        | ( $less(X1,X2)
          & $less(0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).

tff(f547,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2))
    <=> ( ( $less(X2,X1)
          & $less(X0,0) )
        | ( $less(X1,X2)
          & $less(0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).

tff(f6483,plain,
    spl173_371,
    inference(avatar_split_clause,[],[f2737,f6481]) ).

tff(f6481,plain,
    ( spl173_371
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP16(X1,X2,X0)
        | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_371])]) ).

tff(f2737,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP16(X1,X2,X0)
      | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X0),X2)) ),
    inference(cnf_transformation,[],[f1752]) ).

tff(f6479,plain,
    spl173_370,
    inference(avatar_split_clause,[],[f2730,f6477]) ).

tff(f6477,plain,
    ( spl173_370
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1))
        | ~ sP15(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_370])]) ).

tff(f2730,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1))
      | ~ sP15(X0,X2,X1) ),
    inference(cnf_transformation,[],[f1748]) ).

tff(f1748,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1))
        | ~ sP15(X0,X2,X1) )
      & ( sP15(X0,X2,X1)
        | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1)) ) ),
    inference(nnf_transformation,[],[f1388]) ).

tff(f1388,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1))
    <=> sP15(X0,X2,X1) ),
    inference(definition_folding,[],[f553,f1387]) ).

tff(f1387,plain,
    ! [X0: $int,X2: $int,X1: $int] :
      ( sP15(X0,X2,X1)
    <=> ( ( $less(X2,X0)
          & $less(X1,0) )
        | ( $less(X0,X2)
          & $less(0,X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).

tff(f553,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1))
    <=> ( ( $less(X2,X0)
          & $less(X1,0) )
        | ( $less(X0,X2)
          & $less(0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).

tff(f6475,plain,
    ( spl173_369
    | ~ spl173_78
    | ~ spl173_180 ),
    inference(avatar_split_clause,[],[f4967,f4204,f3501,f6473]) ).

tff(f6473,plain,
    ( spl173_369
  <=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_369])]) ).

tff(f3501,plain,
    ( spl173_78
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_78])]) ).

tff(f4204,plain,
    ( spl173_180
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_180])]) ).

tff(f4967,plain,
    ( ! [X0: $int] : $less(X0,$sum(1,X0))
    | ~ spl173_78
    | ~ spl173_180 ),
    inference(superposition,[],[f4205,f3502]) ).

tff(f3502,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl173_78 ),
    inference(avatar_component_clause,[],[f3501]) ).

tff(f4205,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl173_180 ),
    inference(avatar_component_clause,[],[f4204]) ).

tff(f6471,plain,
    spl173_368,
    inference(avatar_split_clause,[],[f2729,f6469]) ).

tff(f6469,plain,
    ( spl173_368
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP15(X0,X2,X1)
        | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_368])]) ).

tff(f2729,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP15(X0,X2,X1)
      | ~ $less('fun_app$o'('times$a'(X0),X1),'fun_app$o'('times$a'(X2),X1)) ),
    inference(cnf_transformation,[],[f1748]) ).

tff(f6467,plain,
    spl173_367,
    inference(avatar_split_clause,[],[f2722,f6465]) ).

tff(f6465,plain,
    ( spl173_367
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1))
        | ~ sP14(X0,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_367])]) ).

tff(f2722,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1))
      | ~ sP14(X0,X2,X1) ),
    inference(cnf_transformation,[],[f1744]) ).

tff(f1744,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1))
        | ~ sP14(X0,X2,X1) )
      & ( sP14(X0,X2,X1)
        | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1)) ) ),
    inference(nnf_transformation,[],[f1386]) ).

tff(f1386,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1))
    <=> sP14(X0,X2,X1) ),
    inference(definition_folding,[],[f554,f1385]) ).

tff(f1385,plain,
    ! [X0: $real,X2: $real,X1: $real] :
      ( sP14(X0,X2,X1)
    <=> ( ( $less(X2,X0)
          & $less(X1,0.0) )
        | ( $less(X0,X2)
          & $less(0.0,X1) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).

tff(f554,axiom,
    ! [X0: $real,X1: $real,X2: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1))
    <=> ( ( $less(X2,X0)
          & $less(X1,0.0) )
        | ( $less(X0,X2)
          & $less(0.0,X1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).

tff(f6463,plain,
    spl173_366,
    inference(avatar_split_clause,[],[f2721,f6461]) ).

tff(f6461,plain,
    ( spl173_366
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP14(X0,X2,X1)
        | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_366])]) ).

tff(f2721,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP14(X0,X2,X1)
      | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X2),X1)) ),
    inference(cnf_transformation,[],[f1744]) ).

tff(f6459,plain,
    spl173_365,
    inference(avatar_split_clause,[],[f2714,f6457]) ).

tff(f6457,plain,
    ( spl173_365
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2))
        | ~ sP13(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_365])]) ).

tff(f2714,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2))
      | ~ sP13(X1,X2,X0) ),
    inference(cnf_transformation,[],[f1740]) ).

tff(f1740,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2))
        | ~ sP13(X1,X2,X0) )
      & ( sP13(X1,X2,X0)
        | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2)) ) ),
    inference(nnf_transformation,[],[f1384]) ).

tff(f1384,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2))
    <=> sP13(X1,X2,X0) ),
    inference(definition_folding,[],[f548,f1383]) ).

tff(f1383,plain,
    ! [X1: $real,X2: $real,X0: $real] :
      ( sP13(X1,X2,X0)
    <=> ( ( $less(X2,X1)
          & $less(X0,0.0) )
        | ( $less(X1,X2)
          & $less(0.0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).

tff(f548,axiom,
    ! [X0: $real,X1: $real,X2: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2))
    <=> ( ( $less(X2,X1)
          & $less(X0,0.0) )
        | ( $less(X1,X2)
          & $less(0.0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).

tff(f6455,plain,
    spl173_364,
    inference(avatar_split_clause,[],[f2713,f6453]) ).

tff(f6453,plain,
    ( spl173_364
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP13(X1,X2,X0)
        | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_364])]) ).

tff(f2713,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP13(X1,X2,X0)
      | ~ $less('fun_app$r'('times$'(X0),X1),'fun_app$r'('times$'(X0),X2)) ),
    inference(cnf_transformation,[],[f1740]) ).

tff(f6451,plain,
    spl173_363,
    inference(avatar_split_clause,[],[f2669,f6449]) ).

tff(f6449,plain,
    ( spl173_363
  <=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$s'(X1,X2)
        | sP12(X1,X0)
        | $less('of_nat$'(X0),'of_nat$'(sK56(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_363])]) ).

tff(f2669,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$s'(X1,X2)
      | sP12(X1,X0)
      | $less('of_nat$'(X0),'of_nat$'(sK56(X0,X1))) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f1708,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( 'fun_app$s'(X1,X2)
      | sP12(X1,X0)
      | ( ~ 'fun_app$s'(X1,sK56(X0,X1))
        & $less('of_nat$'(X0),'of_nat$'(sK56(X0,X1))) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f1706,f1707]) ).

tff(f1707,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & $less('of_nat$'(X0),'of_nat$'(X3)) )
     => ( ~ 'fun_app$s'(X1,sK56(X0,X1))
        & $less('of_nat$'(X0),'of_nat$'(sK56(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f1706,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( 'fun_app$s'(X1,X2)
      | sP12(X1,X0)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & $less('of_nat$'(X0),'of_nat$'(X3)) ) ),
    inference(rectify,[],[f1382]) ).

tff(f1382,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( 'fun_app$s'(X1,X2)
      | sP12(X1,X0)
      | ? [X5: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X5)
          & $less('of_nat$'(X0),'of_nat$'(X5)) ) ),
    inference(definition_folding,[],[f1246,f1381]) ).

tff(f1381,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X1,X4)
              | ~ $less('of_nat$'(X3),'of_nat$'(X4)) )
          & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
      | ~ sP12(X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).

tff(f1246,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( 'fun_app$s'(X1,X2)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X1,X4)
              | ~ $less('of_nat$'(X3),'of_nat$'(X4)) )
          & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
      | ? [X5: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X5)
          & $less('of_nat$'(X0),'of_nat$'(X5)) ) ),
    inference(flattening,[],[f1245]) ).

tff(f1245,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( 'fun_app$s'(X1,X2)
      | ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X1,X4)
              | ~ $less('of_nat$'(X3),'of_nat$'(X4)) )
          & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
      | ? [X5: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X5)
          & $less('of_nat$'(X0),'of_nat$'(X5)) ) ),
    inference(ennf_transformation,[],[f942]) ).

tff(f942,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( ( ! [X4: 'Nat$'] :
                  ( $less('of_nat$'(X3),'of_nat$'(X4))
                 => 'fun_app$s'(X1,X4) )
              & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
           => 'fun_app$s'(X1,X3) )
        & ! [X5: 'Nat$'] :
            ( $less('of_nat$'(X0),'of_nat$'(X5))
           => 'fun_app$s'(X1,X5) ) )
     => 'fun_app$s'(X1,X2) ),
    inference(rectify,[],[f801]) ).

tff(f801,plain,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( ( ! [X4: 'Nat$'] :
                  ( $less('of_nat$'(X3),'of_nat$'(X4))
                 => 'fun_app$s'(X1,X4) )
              & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
           => 'fun_app$s'(X1,X3) )
        & ! [X3: 'Nat$'] :
            ( $less('of_nat$'(X0),'of_nat$'(X3))
           => 'fun_app$s'(X1,X3) ) )
     => 'fun_app$s'(X1,X2) ),
    inference(theory_normalization,[],[f399]) ).

tff(f399,axiom,
    ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X2: 'Nat$'] :
      ( ( ! [X3: 'Nat$'] :
            ( ( ! [X4: 'Nat$'] :
                  ( $less('of_nat$'(X3),'of_nat$'(X4))
                 => 'fun_app$s'(X1,X4) )
              & $lesseq('of_nat$'(X3),'of_nat$'(X0)) )
           => 'fun_app$s'(X1,X3) )
        & ! [X3: 'Nat$'] :
            ( $less('of_nat$'(X0),'of_nat$'(X3))
           => 'fun_app$s'(X1,X3) ) )
     => 'fun_app$s'(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).

tff(f6447,plain,
    spl173_362,
    inference(avatar_split_clause,[],[f2667,f6445]) ).

tff(f6445,plain,
    ( spl173_362
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
        ( 'fun_app$s'(X0,X3)
        | ~ $less('of_nat$'(sK55(X0,X1)),'of_nat$'(X3))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_362])]) ).

tff(f2667,plain,
    ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X3)
      | ~ $less('of_nat$'(sK55(X0,X1)),'of_nat$'(X3))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f1705]) ).

tff(f1705,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ~ 'fun_app$s'(X0,sK55(X0,X1))
        & ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(sK55(X0,X1)),'of_nat$'(X3)) )
        & ~ $less('of_nat$'(X1),'of_nat$'(sK55(X0,X1))) )
      | ~ sP12(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1703,f1704]) ).

tff(f1704,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X2),'of_nat$'(X3)) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) )
     => ( ~ 'fun_app$s'(X0,sK55(X0,X1))
        & ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(sK55(X0,X1)),'of_nat$'(X3)) )
        & ~ $less('of_nat$'(X1),'of_nat$'(sK55(X0,X1))) ) ),
    introduced(choice_axiom,[]) ).

tff(f1703,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X2),'of_nat$'(X3)) )
          & ~ $less('of_nat$'(X1),'of_nat$'(X2)) )
      | ~ sP12(X0,X1) ),
    inference(rectify,[],[f1702]) ).

tff(f1702,plain,
    ! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
      ( ? [X3: 'Nat$'] :
          ( ~ 'fun_app$s'(X1,X3)
          & ! [X4: 'Nat$'] :
              ( 'fun_app$s'(X1,X4)
              | ~ $less('of_nat$'(X3),'of_nat$'(X4)) )
          & ~ $less('of_nat$'(X0),'of_nat$'(X3)) )
      | ~ sP12(X1,X0) ),
    inference(nnf_transformation,[],[f1381]) ).

tff(f6443,plain,
    spl173_361,
    inference(avatar_split_clause,[],[f2548,f6441]) ).

tff(f6441,plain,
    ( spl173_361
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('transpose_row$b'(X0,X1)),X2) = 'fun_app$d'('vec_nth$'('vec_nth$c'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_361])]) ).

tff(f2548,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('transpose_row$b'(X0,X1)),X2) = 'fun_app$d'('vec_nth$'('vec_nth$c'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,axiom,
    ! [X0: 'A_rows_vec_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('transpose_row$b'(X0,X1)),X2) = 'fun_app$d'('vec_nth$'('vec_nth$c'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).

tff(f6439,plain,
    spl173_360,
    inference(avatar_split_clause,[],[f2547,f6437]) ).

tff(f6437,plain,
    ( spl173_360
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('transpose_row$c'(X0,X1)),X2) = 'fun_app$e'('vec_nth$a'('vec_nth$d'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_360])]) ).

tff(f2547,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('transpose_row$c'(X0,X1)),X2) = 'fun_app$e'('vec_nth$a'('vec_nth$d'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,axiom,
    ! [X0: 'A_cols_vec_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('transpose_row$c'(X0,X1)),X2) = 'fun_app$e'('vec_nth$a'('vec_nth$d'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).

tff(f6435,plain,
    spl173_359,
    inference(avatar_split_clause,[],[f2545,f6433]) ).

tff(f2545,plain,
    ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f9]) ).

tff(f9,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).

tff(f6431,plain,
    ( spl173_358
    | ~ spl173_56
    | ~ spl173_180 ),
    inference(avatar_split_clause,[],[f4959,f4204,f3353,f6429]) ).

tff(f6429,plain,
    ( spl173_358
  <=> ! [X0: $int] : ~ $less($sum(X0,1),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_358])]) ).

tff(f3353,plain,
    ( spl173_56
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_56])]) ).

tff(f4959,plain,
    ( ! [X0: $int] : ~ $less($sum(X0,1),X0)
    | ~ spl173_56
    | ~ spl173_180 ),
    inference(resolution,[],[f4205,f3354]) ).

tff(f3354,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,X0)
        | ~ $less(X0,X1) )
    | ~ spl173_56 ),
    inference(avatar_component_clause,[],[f3353]) ).

tff(f6427,plain,
    spl173_357,
    inference(avatar_split_clause,[],[f2544,f6425]) ).

tff(f6425,plain,
    ( spl173_357
  <=> ! [X2: 'A_rows_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$a'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$a'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_357])]) ).

tff(f2544,plain,
    ! [X2: 'A_rows_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$a'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$a'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f6]) ).

tff(f6,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$a'('fun_app$d'('vec_nth$'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$a'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).

tff(f6423,plain,
    spl173_356,
    inference(avatar_split_clause,[],[f2543,f6421]) ).

tff(f6421,plain,
    ( spl173_356
  <=> ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$c'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$c'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_356])]) ).

tff(f2543,plain,
    ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$c'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$c'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f8]) ).

tff(f8,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$',X2: 'A_cols_vec_cols_vec$'] : ( 'vector_matrix_mult$c'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$c'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).

tff(f6419,plain,
    spl173_355,
    inference(avatar_split_clause,[],[f2542,f6417]) ).

tff(f6417,plain,
    ( spl173_355
  <=> ! [X2: 'A_rows_vec_cols_vec$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$b'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$b'(X0,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_355])]) ).

tff(f2542,plain,
    ! [X2: 'A_rows_vec_cols_vec$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'vector_matrix_mult$b'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$b'(X0,X2)),X1) ),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$',X2: 'A_rows_vec_cols_vec$'] : ( 'vector_matrix_mult$b'('fun_app$e'('vec_nth$a'(X0),X1),X2) = 'fun_app$d'('vec_nth$'('matrix_matrix_mult$b'(X0,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).

tff(f6415,plain,
    spl173_354,
    inference(avatar_split_clause,[],[f870,f6413]) ).

tff(f6413,plain,
    ( spl173_354
  <=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_354])]) ).

tff(f870,plain,
    ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
    introduced(theory_axiom_150,[]) ).

tff(f6411,plain,
    spl173_353,
    inference(avatar_split_clause,[],[f852,f6409]) ).

tff(f6409,plain,
    ( spl173_353
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_353])]) ).

tff(f852,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
    introduced(theory_axiom_150,[]) ).

tff(f6137,plain,
    ( spl173_352
    | ~ spl173_62
    | ~ spl173_321 ),
    inference(avatar_split_clause,[],[f5814,f5811,f3377,f6135]) ).

tff(f6135,plain,
    ( spl173_352
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,X1)
        | $less(0,'of_nat$'(sK42(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_352])]) ).

tff(f3377,plain,
    ( spl173_62
  <=> ( 'rank$'('zero$c') = 'nat$'(0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_62])]) ).

tff(f5811,plain,
    ( spl173_321
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | $less(0,'of_nat$'(sK42(X0)))
        | ~ 'fun_app$s'(X0,'nat$'(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_321])]) ).

tff(f5814,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,X1)
        | $less(0,'of_nat$'(sK42(X0))) )
    | ~ spl173_62
    | ~ spl173_321 ),
    inference(forward_demodulation,[],[f5812,f3379]) ).

tff(f3379,plain,
    ( ( 'rank$'('zero$c') = 'nat$'(0) )
    | ~ spl173_62 ),
    inference(avatar_component_clause,[],[f3377]) ).

tff(f5812,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | $less(0,'of_nat$'(sK42(X0)))
        | ~ 'fun_app$s'(X0,'nat$'(0)) )
    | ~ spl173_321 ),
    inference(avatar_component_clause,[],[f5811]) ).

tff(f6133,plain,
    ( spl173_351
    | ~ spl173_62
    | ~ spl173_320 ),
    inference(avatar_split_clause,[],[f5809,f5806,f3377,f6131]) ).

tff(f6131,plain,
    ( spl173_351
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,sK40(X0,X1))
        | ~ 'fun_app$s'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_351])]) ).

tff(f5806,plain,
    ( spl173_320
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,sK40(X0,X1))
        | 'fun_app$s'(X0,'nat$'(0))
        | ~ 'fun_app$s'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_320])]) ).

tff(f5809,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,sK40(X0,X1))
        | ~ 'fun_app$s'(X0,X1) )
    | ~ spl173_62
    | ~ spl173_320 ),
    inference(forward_demodulation,[],[f5807,f3379]) ).

tff(f5807,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,sK40(X0,X1))
        | 'fun_app$s'(X0,'nat$'(0))
        | ~ 'fun_app$s'(X0,X1) )
    | ~ spl173_320 ),
    inference(avatar_component_clause,[],[f5806]) ).

tff(f6052,plain,
    ( spl173_350
    | ~ spl173_33
    | ~ spl173_296 ),
    inference(avatar_split_clause,[],[f5705,f5439,f3244,f6050]) ).

tff(f6050,plain,
    ( spl173_350
  <=> ! [X1: 'A_cols_vec_cols_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$c'('zero$c',X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_350])]) ).

tff(f3244,plain,
    ( spl173_33
  <=> ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('zero$b',X0) = 'zero$c' ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_33])]) ).

tff(f5439,plain,
    ( spl173_296
  <=> ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) = 'matrix_matrix_mult$c'('matrix_matrix_mult$'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_296])]) ).

tff(f5705,plain,
    ( ! [X1: 'A_cols_vec_cols_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$c'('zero$c',X1) )
    | ~ spl173_33
    | ~ spl173_296 ),
    inference(forward_demodulation,[],[f5702,f3245]) ).

tff(f3245,plain,
    ( ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('zero$b',X0) = 'zero$c' )
    | ~ spl173_33 ),
    inference(avatar_component_clause,[],[f3244]) ).

tff(f5702,plain,
    ( ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_cols_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$c'('matrix_matrix_mult$'('zero$b',X0),X1) )
    | ~ spl173_33
    | ~ spl173_296 ),
    inference(superposition,[],[f5440,f3245]) ).

tff(f5440,plain,
    ( ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) = 'matrix_matrix_mult$c'('matrix_matrix_mult$'(X0,X1),X2) )
    | ~ spl173_296 ),
    inference(avatar_component_clause,[],[f5439]) ).

tff(f5935,plain,
    spl173_349,
    inference(avatar_split_clause,[],[f3073,f5933]) ).

tff(f5933,plain,
    ( spl173_349
  <=> ! [X0: $real] :
        ( ( -1.0 = X0 )
        | ( 1.0 = X0 )
        | ( 1.0 != 'fun_app$r'('times$'(X0),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_349])]) ).

tff(f3073,plain,
    ! [X0: $real] :
      ( ( -1.0 = X0 )
      | ( 1.0 = X0 )
      | ( 1.0 != 'fun_app$r'('times$'(X0),X0) ) ),
    inference(evaluation,[],[f2085]) ).

tff(f2085,plain,
    ! [X0: $real] :
      ( ( $uminus(1.0) = X0 )
      | ( 1.0 = X0 )
      | ( 1.0 != 'fun_app$r'('times$'(X0),X0) ) ),
    inference(cnf_transformation,[],[f1454]) ).

tff(f1454,plain,
    ! [X0: $real] :
      ( ( ( 1.0 = 'fun_app$r'('times$'(X0),X0) )
        | ( ( $uminus(1.0) != X0 )
          & ( 1.0 != X0 ) ) )
      & ( ( $uminus(1.0) = X0 )
        | ( 1.0 = X0 )
        | ( 1.0 != 'fun_app$r'('times$'(X0),X0) ) ) ),
    inference(flattening,[],[f1453]) ).

tff(f1453,plain,
    ! [X0: $real] :
      ( ( ( 1.0 = 'fun_app$r'('times$'(X0),X0) )
        | ( ( $uminus(1.0) != X0 )
          & ( 1.0 != X0 ) ) )
      & ( ( $uminus(1.0) = X0 )
        | ( 1.0 = X0 )
        | ( 1.0 != 'fun_app$r'('times$'(X0),X0) ) ) ),
    inference(nnf_transformation,[],[f582]) ).

tff(f582,axiom,
    ! [X0: $real] :
      ( ( 1.0 = 'fun_app$r'('times$'(X0),X0) )
    <=> ( ( $uminus(1.0) = X0 )
        | ( 1.0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom580) ).

tff(f5931,plain,
    ( spl173_348
    | ~ spl173_27
    | ~ spl173_28
    | ~ spl173_295 ),
    inference(avatar_split_clause,[],[f5695,f5435,f3224,f3220,f5929]) ).

tff(f5929,plain,
    ( spl173_348
  <=> ! [X0: 'Rows$'] : ( 'zero$a' = 'row$a'(X0,'zero$c') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_348])]) ).

tff(f3220,plain,
    ( spl173_27
  <=> ! [X0: 'A_rows_vec$'] : ( 'zero$a' = 'vector_matrix_mult$'(X0,'zero$c') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_27])]) ).

tff(f3224,plain,
    ( spl173_28
  <=> ! [X0: 'A_rows_vec_rows_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$'(X0,'zero$c') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_28])]) ).

tff(f5695,plain,
    ( ! [X0: 'Rows$'] : ( 'zero$a' = 'row$a'(X0,'zero$c') )
    | ~ spl173_27
    | ~ spl173_28
    | ~ spl173_295 ),
    inference(forward_demodulation,[],[f5689,f3225]) ).

tff(f3225,plain,
    ( ! [X0: 'A_rows_vec_rows_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$'(X0,'zero$c') )
    | ~ spl173_28 ),
    inference(avatar_component_clause,[],[f3224]) ).

tff(f5689,plain,
    ( ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'zero$a' = 'row$a'(X0,'matrix_matrix_mult$'(X1,'zero$c')) )
    | ~ spl173_27
    | ~ spl173_295 ),
    inference(superposition,[],[f5436,f3221]) ).

tff(f3221,plain,
    ( ! [X0: 'A_rows_vec$'] : ( 'zero$a' = 'vector_matrix_mult$'(X0,'zero$c') )
    | ~ spl173_27 ),
    inference(avatar_component_clause,[],[f3220]) ).

tff(f5927,plain,
    spl173_347,
    inference(avatar_split_clause,[],[f3071,f5925]) ).

tff(f5925,plain,
    ( spl173_347
  <=> ! [X0: $int] :
        ( ( -1 = X0 )
        | ( 1 = X0 )
        | ( 1 != 'fun_app$o'('times$a'(X0),X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_347])]) ).

tff(f3071,plain,
    ! [X0: $int] :
      ( ( -1 = X0 )
      | ( 1 = X0 )
      | ( 1 != 'fun_app$o'('times$a'(X0),X0) ) ),
    inference(evaluation,[],[f2088]) ).

tff(f2088,plain,
    ! [X0: $int] :
      ( ( $uminus(1) = X0 )
      | ( 1 = X0 )
      | ( 1 != 'fun_app$o'('times$a'(X0),X0) ) ),
    inference(cnf_transformation,[],[f1456]) ).

tff(f1456,plain,
    ! [X0: $int] :
      ( ( ( 1 = 'fun_app$o'('times$a'(X0),X0) )
        | ( ( $uminus(1) != X0 )
          & ( 1 != X0 ) ) )
      & ( ( $uminus(1) = X0 )
        | ( 1 = X0 )
        | ( 1 != 'fun_app$o'('times$a'(X0),X0) ) ) ),
    inference(flattening,[],[f1455]) ).

tff(f1455,plain,
    ! [X0: $int] :
      ( ( ( 1 = 'fun_app$o'('times$a'(X0),X0) )
        | ( ( $uminus(1) != X0 )
          & ( 1 != X0 ) ) )
      & ( ( $uminus(1) = X0 )
        | ( 1 = X0 )
        | ( 1 != 'fun_app$o'('times$a'(X0),X0) ) ) ),
    inference(nnf_transformation,[],[f583]) ).

tff(f583,axiom,
    ! [X0: $int] :
      ( ( 1 = 'fun_app$o'('times$a'(X0),X0) )
    <=> ( ( $uminus(1) = X0 )
        | ( 1 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).

tff(f5923,plain,
    spl173_346,
    inference(avatar_split_clause,[],[f2624,f5921]) ).

tff(f5921,plain,
    ( spl173_346
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X2,X1)
        | $less(X2,sK52(X0,X1,X2))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_346])]) ).

tff(f2624,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X2,X1)
      | $less(X2,sK52(X0,X1,X2))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1681]) ).

tff(f1681,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X2,X1)
      | ( $less(X2,sK52(X0,X1,X2))
        & $less(sK52(X0,X1,X2),X1)
        & $less(X0,sK52(X0,X1,X2)) )
      | ~ $less(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f1214,f1680]) ).

tff(f1680,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ? [X3: $real] :
          ( $less(X2,X3)
          & $less(X3,X1)
          & $less(X0,X3) )
     => ( $less(X2,sK52(X0,X1,X2))
        & $less(sK52(X0,X1,X2),X1)
        & $less(X0,sK52(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1214,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X2,X1)
      | ? [X3: $real] :
          ( $less(X2,X3)
          & $less(X3,X1)
          & $less(X0,X3) )
      | ~ $less(X0,X1) ),
    inference(flattening,[],[f1213]) ).

tff(f1213,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X2,X1)
      | ? [X3: $real] :
          ( $less(X2,X3)
          & $less(X3,X1)
          & $less(X0,X3) )
      | ~ $less(X0,X1) ),
    inference(ennf_transformation,[],[f793]) ).

tff(f793,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ! [X3: $real] :
            ( ( $less(X3,X1)
              & $less(X0,X3) )
           => ~ $less(X2,X3) )
        & $less(X0,X1) )
     => ~ $less(X2,X1) ),
    inference(theory_normalization,[],[f312]) ).

tff(f312,axiom,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ! [X3: $real] :
            ( ( $less(X3,X1)
              & $less(X0,X3) )
           => $lesseq(X3,X2) )
        & $less(X0,X1) )
     => $lesseq(X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom310) ).

tff(f5919,plain,
    spl173_345,
    inference(avatar_split_clause,[],[f2623,f5917]) ).

tff(f5917,plain,
    ( spl173_345
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X2,X1)
        | $less(sK52(X0,X1,X2),X1)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_345])]) ).

tff(f2623,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X2,X1)
      | $less(sK52(X0,X1,X2),X1)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1681]) ).

tff(f5915,plain,
    spl173_344,
    inference(avatar_split_clause,[],[f2622,f5913]) ).

tff(f5913,plain,
    ( spl173_344
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X2,X1)
        | $less(X0,sK52(X0,X1,X2))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_344])]) ).

tff(f2622,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X2,X1)
      | $less(X0,sK52(X0,X1,X2))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1681]) ).

tff(f5911,plain,
    spl173_343,
    inference(avatar_split_clause,[],[f2621,f5909]) ).

tff(f5909,plain,
    ( spl173_343
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | $less(sK51(X0,X1,X2),X2)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_343])]) ).

tff(f2621,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | $less(sK51(X0,X1,X2),X2)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1679]) ).

tff(f1679,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X0,X2)
      | ( $less(sK51(X0,X1,X2),X2)
        & $less(sK51(X0,X1,X2),X1)
        & $less(X0,sK51(X0,X1,X2)) )
      | ~ $less(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1212,f1678]) ).

tff(f1678,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ? [X3: $real] :
          ( $less(X3,X2)
          & $less(X3,X1)
          & $less(X0,X3) )
     => ( $less(sK51(X0,X1,X2),X2)
        & $less(sK51(X0,X1,X2),X1)
        & $less(X0,sK51(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1212,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X0,X2)
      | ? [X3: $real] :
          ( $less(X3,X2)
          & $less(X3,X1)
          & $less(X0,X3) )
      | ~ $less(X0,X1) ),
    inference(flattening,[],[f1211]) ).

tff(f1211,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X0,X2)
      | ? [X3: $real] :
          ( $less(X3,X2)
          & $less(X3,X1)
          & $less(X0,X3) )
      | ~ $less(X0,X1) ),
    inference(ennf_transformation,[],[f792]) ).

tff(f792,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ! [X3: $real] :
            ( ( $less(X3,X1)
              & $less(X0,X3) )
           => ~ $less(X3,X2) )
        & $less(X0,X1) )
     => ~ $less(X0,X2) ),
    inference(theory_normalization,[],[f311]) ).

tff(f311,axiom,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ! [X3: $real] :
            ( ( $less(X3,X1)
              & $less(X0,X3) )
           => $lesseq(X2,X3) )
        & $less(X0,X1) )
     => $lesseq(X2,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom309) ).

tff(f5907,plain,
    spl173_342,
    inference(avatar_split_clause,[],[f2620,f5905]) ).

tff(f5905,plain,
    ( spl173_342
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | $less(sK51(X0,X1,X2),X1)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_342])]) ).

tff(f2620,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | $less(sK51(X0,X1,X2),X1)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1679]) ).

tff(f5903,plain,
    spl173_341,
    inference(avatar_split_clause,[],[f2619,f5901]) ).

tff(f5901,plain,
    ( spl173_341
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | $less(X0,sK51(X0,X1,X2))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_341])]) ).

tff(f2619,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | $less(X0,sK51(X0,X1,X2))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1679]) ).

tff(f5899,plain,
    spl173_340,
    inference(avatar_split_clause,[],[f2588,f5897]) ).

tff(f5897,plain,
    ( spl173_340
  <=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,sK49(X0))
        | 'fun_app$s'(X0,sK50(X0,X2))
        | ~ 'fun_app$s'(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_340])]) ).

tff(f2588,plain,
    ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,sK49(X0))
      | 'fun_app$s'(X0,sK50(X0,X2))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(cnf_transformation,[],[f1677]) ).

tff(f5895,plain,
    spl173_339,
    inference(avatar_split_clause,[],[f2541,f5893]) ).

tff(f5893,plain,
    ( spl173_339
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Cols$'] : ( 'vec_nth$b'('transpose_row$a'(X0,X1),X2) = 'vec_nth$e'('fun_app$e'('vec_nth$a'(X0),X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_339])]) ).

tff(f2541,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Cols$'] : ( 'vec_nth$b'('transpose_row$a'(X0,X1),X2) = 'vec_nth$e'('fun_app$e'('vec_nth$a'(X0),X2),X1) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Cols$',X2: 'Rows$'] : ( 'vec_nth$b'('transpose_row$a'(X0,X1),X2) = 'vec_nth$e'('fun_app$e'('vec_nth$a'(X0),X2),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).

tff(f5891,plain,
    spl173_338,
    inference(avatar_split_clause,[],[f2540,f5889]) ).

tff(f5889,plain,
    ( spl173_338
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_338])]) ).

tff(f2540,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X2) ),
    inference(cnf_transformation,[],[f48]) ).

tff(f48,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).

tff(f5878,plain,
    spl173_337,
    inference(avatar_split_clause,[],[f2539,f5876]) ).

tff(f5876,plain,
    ( spl173_337
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X2) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_337])]) ).

tff(f2539,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X2) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f50]) ).

tff(f50,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X2) = 'fun_app$d'('vec_nth$'('interchange_rows$'(X0,X1,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).

tff(f5874,plain,
    spl173_336,
    inference(avatar_split_clause,[],[f2538,f5872]) ).

tff(f5872,plain,
    ( spl173_336
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_336])]) ).

tff(f2538,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X2) ),
    inference(cnf_transformation,[],[f49]) ).

tff(f49,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).

tff(f5870,plain,
    spl173_335,
    inference(avatar_split_clause,[],[f2537,f5868]) ).

tff(f5868,plain,
    ( spl173_335
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X2) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_335])]) ).

tff(f2537,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X2) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X1) ),
    inference(cnf_transformation,[],[f51]) ).

tff(f51,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X2) = 'fun_app$e'('vec_nth$a'('interchange_rows$a'(X0,X1,X2)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).

tff(f5866,plain,
    spl173_334,
    inference(avatar_split_clause,[],[f2520,f5864]) ).

tff(f5864,plain,
    ( spl173_334
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'fun_app$t'('of_nat$a',X0) = 'fun_app$t'('of_nat$a',X1) )
        | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_334])]) ).

tff(f2520,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$t'('of_nat$a',X0) = 'fun_app$t'('of_nat$a',X1) )
      | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ),
    inference(cnf_transformation,[],[f1663]) ).

tff(f1663,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 'fun_app$t'('of_nat$a',X0) = 'fun_app$t'('of_nat$a',X1) )
        | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) )
      & ( ( 'of_nat$'(X0) = 'of_nat$'(X1) )
        | ( 'fun_app$t'('of_nat$a',X0) != 'fun_app$t'('of_nat$a',X1) ) ) ),
    inference(nnf_transformation,[],[f163]) ).

tff(f163,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'fun_app$t'('of_nat$a',X0) = 'fun_app$t'('of_nat$a',X1) )
    <=> ( 'of_nat$'(X0) = 'of_nat$'(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).

tff(f5862,plain,
    spl173_333,
    inference(avatar_split_clause,[],[f2519,f5860]) ).

tff(f5860,plain,
    ( spl173_333
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'of_nat$'(X0) = 'of_nat$'(X1) )
        | ( 'fun_app$t'('of_nat$a',X0) != 'fun_app$t'('of_nat$a',X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_333])]) ).

tff(f2519,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'of_nat$'(X0) = 'of_nat$'(X1) )
      | ( 'fun_app$t'('of_nat$a',X0) != 'fun_app$t'('of_nat$a',X1) ) ),
    inference(cnf_transformation,[],[f1663]) ).

tff(f5858,plain,
    spl173_332,
    inference(avatar_split_clause,[],[f2476,f5856]) ).

tff(f5856,plain,
    ( spl173_332
  <=> ! [X0: $real,X1: $real] :
        ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_332])]) ).

tff(f2476,plain,
    ! [X0: $real,X1: $real] :
      ( ( 1.0 = X1 )
      | ( 0.0 = X0 )
      | ( 'fun_app$r'('times$'(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f1641]) ).

tff(f1641,plain,
    ! [X0: $real,X1: $real] :
      ( ( ( 'fun_app$r'('times$'(X0),X1) = X0 )
        | ( ( 1.0 != X1 )
          & ( 0.0 != X0 ) ) )
      & ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X0),X1) != X0 ) ) ),
    inference(flattening,[],[f1640]) ).

tff(f1640,plain,
    ! [X0: $real,X1: $real] :
      ( ( ( 'fun_app$r'('times$'(X0),X1) = X0 )
        | ( ( 1.0 != X1 )
          & ( 0.0 != X0 ) ) )
      & ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X0),X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f505]) ).

tff(f505,axiom,
    ! [X0: $real,X1: $real] :
      ( ( 'fun_app$r'('times$'(X0),X1) = X0 )
    <=> ( ( 1.0 = X1 )
        | ( 0.0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).

tff(f5854,plain,
    spl173_331,
    inference(avatar_split_clause,[],[f2473,f5852]) ).

tff(f5852,plain,
    ( spl173_331
  <=> ! [X0: $real,X1: $real] :
        ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X1),X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_331])]) ).

tff(f2473,plain,
    ! [X0: $real,X1: $real] :
      ( ( 1.0 = X1 )
      | ( 0.0 = X0 )
      | ( 'fun_app$r'('times$'(X1),X0) != X0 ) ),
    inference(cnf_transformation,[],[f1639]) ).

tff(f1639,plain,
    ! [X0: $real,X1: $real] :
      ( ( ( 'fun_app$r'('times$'(X1),X0) = X0 )
        | ( ( 1.0 != X1 )
          & ( 0.0 != X0 ) ) )
      & ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X1),X0) != X0 ) ) ),
    inference(flattening,[],[f1638]) ).

tff(f1638,plain,
    ! [X0: $real,X1: $real] :
      ( ( ( 'fun_app$r'('times$'(X1),X0) = X0 )
        | ( ( 1.0 != X1 )
          & ( 0.0 != X0 ) ) )
      & ( ( 1.0 = X1 )
        | ( 0.0 = X0 )
        | ( 'fun_app$r'('times$'(X1),X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f503]) ).

tff(f503,axiom,
    ! [X0: $real,X1: $real] :
      ( ( 'fun_app$r'('times$'(X1),X0) = X0 )
    <=> ( ( 1.0 = X1 )
        | ( 0.0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).

tff(f5850,plain,
    spl173_330,
    inference(avatar_split_clause,[],[f2464,f5848]) ).

tff(f5848,plain,
    ( spl173_330
  <=> ! [X0: $int,X1: $int] :
        ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X0),X1) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_330])]) ).

tff(f2464,plain,
    ! [X0: $int,X1: $int] :
      ( ( 1 = X1 )
      | ( 0 = X0 )
      | ( 'fun_app$o'('times$a'(X0),X1) != X0 ) ),
    inference(cnf_transformation,[],[f1633]) ).

tff(f1633,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( 'fun_app$o'('times$a'(X0),X1) = X0 )
        | ( ( 1 != X1 )
          & ( 0 != X0 ) ) )
      & ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X0),X1) != X0 ) ) ),
    inference(flattening,[],[f1632]) ).

tff(f1632,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( 'fun_app$o'('times$a'(X0),X1) = X0 )
        | ( ( 1 != X1 )
          & ( 0 != X0 ) ) )
      & ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X0),X1) != X0 ) ) ),
    inference(nnf_transformation,[],[f504]) ).

tff(f504,axiom,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$o'('times$a'(X0),X1) = X0 )
    <=> ( ( 1 = X1 )
        | ( 0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).

tff(f5846,plain,
    spl173_329,
    inference(avatar_split_clause,[],[f2461,f5844]) ).

tff(f5844,plain,
    ( spl173_329
  <=> ! [X0: $int,X1: $int] :
        ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X1),X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_329])]) ).

tff(f2461,plain,
    ! [X0: $int,X1: $int] :
      ( ( 1 = X1 )
      | ( 0 = X0 )
      | ( 'fun_app$o'('times$a'(X1),X0) != X0 ) ),
    inference(cnf_transformation,[],[f1631]) ).

tff(f1631,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( 'fun_app$o'('times$a'(X1),X0) = X0 )
        | ( ( 1 != X1 )
          & ( 0 != X0 ) ) )
      & ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X1),X0) != X0 ) ) ),
    inference(flattening,[],[f1630]) ).

tff(f1630,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( 'fun_app$o'('times$a'(X1),X0) = X0 )
        | ( ( 1 != X1 )
          & ( 0 != X0 ) ) )
      & ( ( 1 = X1 )
        | ( 0 = X0 )
        | ( 'fun_app$o'('times$a'(X1),X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f502]) ).

tff(f502,axiom,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$o'('times$a'(X1),X0) = X0 )
    <=> ( ( 1 = X1 )
        | ( 0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).

tff(f5842,plain,
    spl173_328,
    inference(avatar_split_clause,[],[f2269,f5840]) ).

tff(f5840,plain,
    ( spl173_328
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | 'fun_app$s'(X0,X3)
        | ~ $less('of_nat$'(X3),'of_nat$'(sK46(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_328])]) ).

tff(f2269,plain,
    ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | 'fun_app$s'(X0,X3)
      | ~ $less('of_nat$'(X3),'of_nat$'(sK46(X0))) ),
    inference(cnf_transformation,[],[f1508]) ).

tff(f1508,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ( ~ 'fun_app$s'(X0,sK46(X0))
        & ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK46(X0))) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1127,f1507]) ).

tff(f1507,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ~ 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) ) )
     => ( ~ 'fun_app$s'(X0,sK46(X0))
        & ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK46(X0))) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f1127,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ~ 'fun_app$s'(X0,X2)
          & ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) ) ) ),
    inference(ennf_transformation,[],[f194]) ).

tff(f194,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ! [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( $less('of_nat$'(X3),'of_nat$'(X2))
             => 'fun_app$s'(X0,X3) )
         => 'fun_app$s'(X0,X2) )
     => 'fun_app$s'(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).

tff(f5838,plain,
    ( spl173_327
    | ~ spl173_32
    | ~ spl173_292 ),
    inference(avatar_split_clause,[],[f5670,f5423,f3240,f5836]) ).

tff(f5836,plain,
    ( spl173_327
  <=> ! [X1: 'A_cols_vec_cols_vec$'] : ( 'zero$a' = 'vector_matrix_mult$c'('zero$a',X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_327])]) ).

tff(f3240,plain,
    ( spl173_32
  <=> ! [X0: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('zero$',X0) = 'zero$a' ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_32])]) ).

tff(f5423,plain,
    ( spl173_292
  <=> ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$c'('vector_matrix_mult$'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_292])]) ).

tff(f5670,plain,
    ( ! [X1: 'A_cols_vec_cols_vec$'] : ( 'zero$a' = 'vector_matrix_mult$c'('zero$a',X1) )
    | ~ spl173_32
    | ~ spl173_292 ),
    inference(forward_demodulation,[],[f5668,f3241]) ).

tff(f3241,plain,
    ( ! [X0: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('zero$',X0) = 'zero$a' )
    | ~ spl173_32 ),
    inference(avatar_component_clause,[],[f3240]) ).

tff(f5668,plain,
    ( ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_cols_vec$'] : ( 'zero$a' = 'vector_matrix_mult$c'('vector_matrix_mult$'('zero$',X0),X1) )
    | ~ spl173_32
    | ~ spl173_292 ),
    inference(superposition,[],[f5424,f3241]) ).

tff(f5424,plain,
    ( ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$c'('vector_matrix_mult$'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) )
    | ~ spl173_292 ),
    inference(avatar_component_clause,[],[f5423]) ).

tff(f5834,plain,
    spl173_326,
    inference(avatar_split_clause,[],[f2264,f5832]) ).

tff(f5832,plain,
    ( spl173_326
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | 'fun_app$s'(X0,X3)
        | ~ $less('of_nat$'(X3),'of_nat$'(sK43(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_326])]) ).

tff(f2264,plain,
    ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | 'fun_app$s'(X0,X3)
      | ~ $less('of_nat$'(X3),'of_nat$'(sK43(X0))) ),
    inference(cnf_transformation,[],[f1502]) ).

tff(f1502,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK43(X0))) )
        & ~ 'fun_app$s'(X0,sK43(X0)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f1124,f1501]) ).

tff(f1501,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ 'fun_app$s'(X0,X2) )
     => ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK43(X0))) )
        & ~ 'fun_app$s'(X0,sK43(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1124,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ 'fun_app$s'(X0,X2) ) ),
    inference(ennf_transformation,[],[f193]) ).

tff(f193,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ! [X2: 'Nat$'] :
          ( ~ 'fun_app$s'(X0,X2)
         => ? [X3: 'Nat$'] :
              ( ~ 'fun_app$s'(X0,X3)
              & $less('of_nat$'(X3),'of_nat$'(X2)) ) )
     => 'fun_app$s'(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).

tff(f5830,plain,
    spl173_325,
    inference(avatar_split_clause,[],[f2256,f5828]) ).

tff(f5828,plain,
    ( spl173_325
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X0)
        | ~ $less(0,X1)
        | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_325])]) ).

tff(f2256,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X0)
      | ~ $less(0,X1)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(cnf_transformation,[],[f1118]) ).

tff(f1118,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X0)
      | ~ $less(0,X1)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(flattening,[],[f1117]) ).

tff(f1117,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X0)
      | ~ $less(0,X1)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(ennf_transformation,[],[f537]) ).

tff(f537,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(0,X1)
        & $less(0,'fun_app$o'('times$a'(X0),X1)) )
     => $less(0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).

tff(f5826,plain,
    spl173_324,
    inference(avatar_split_clause,[],[f2255,f5824]) ).

tff(f5824,plain,
    ( spl173_324
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X1)
        | ~ $less(0,X0)
        | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_324])]) ).

tff(f2255,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X1)
      | ~ $less(0,X0)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(cnf_transformation,[],[f1116]) ).

tff(f1116,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X1)
      | ~ $less(0,X0)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(flattening,[],[f1115]) ).

tff(f1115,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X1)
      | ~ $less(0,X0)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(ennf_transformation,[],[f535]) ).

tff(f535,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(0,X0)
        & $less(0,'fun_app$o'('times$a'(X0),X1)) )
     => $less(0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).

tff(f5822,plain,
    spl173_323,
    inference(avatar_split_clause,[],[f2254,f5820]) ).

tff(f5820,plain,
    ( spl173_323
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,X0)
        | ~ $less(0.0,X1)
        | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_323])]) ).

tff(f2254,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X0)
      | ~ $less(0.0,X1)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(cnf_transformation,[],[f1114]) ).

tff(f1114,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X0)
      | ~ $less(0.0,X1)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(flattening,[],[f1113]) ).

tff(f1113,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X0)
      | ~ $less(0.0,X1)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(ennf_transformation,[],[f538]) ).

tff(f538,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,X1)
        & $less(0.0,'fun_app$r'('times$'(X0),X1)) )
     => $less(0.0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom536) ).

tff(f5818,plain,
    spl173_322,
    inference(avatar_split_clause,[],[f2253,f5816]) ).

tff(f5816,plain,
    ( spl173_322
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,X1)
        | ~ $less(0.0,X0)
        | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_322])]) ).

tff(f2253,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X1)
      | ~ $less(0.0,X0)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(cnf_transformation,[],[f1112]) ).

tff(f1112,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X1)
      | ~ $less(0.0,X0)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(flattening,[],[f1111]) ).

tff(f1111,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X1)
      | ~ $less(0.0,X0)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(ennf_transformation,[],[f536]) ).

tff(f536,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,X0)
        & $less(0.0,'fun_app$r'('times$'(X0),X1)) )
     => $less(0.0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).

tff(f5813,plain,
    spl173_321,
    inference(avatar_split_clause,[],[f2247,f5811]) ).

tff(f2247,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | $less(0,'of_nat$'(sK42(X0)))
      | ~ 'fun_app$s'(X0,'nat$'(0)) ),
    inference(cnf_transformation,[],[f1500]) ).

tff(f1500,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK42(X0))) )
        & ~ 'fun_app$s'(X0,sK42(X0))
        & $less(0,'of_nat$'(sK42(X0))) )
      | ~ 'fun_app$s'(X0,'nat$'(0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f1105,f1499]) ).

tff(f1499,plain,
    ! [X0: 'Nat_bool_fun$'] :
      ( ? [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ 'fun_app$s'(X0,X2)
          & $less(0,'of_nat$'(X2)) )
     => ( ! [X3: 'Nat$'] :
            ( 'fun_app$s'(X0,X3)
            | ~ $less('of_nat$'(X3),'of_nat$'(sK42(X0))) )
        & ~ 'fun_app$s'(X0,sK42(X0))
        & $less(0,'of_nat$'(sK42(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f1105,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ 'fun_app$s'(X0,X2)
          & $less(0,'of_nat$'(X2)) )
      | ~ 'fun_app$s'(X0,'nat$'(0)) ),
    inference(flattening,[],[f1104]) ).

tff(f1104,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ? [X2: 'Nat$'] :
          ( ! [X3: 'Nat$'] :
              ( 'fun_app$s'(X0,X3)
              | ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
          & ~ 'fun_app$s'(X0,X2)
          & $less(0,'of_nat$'(X2)) )
      | ~ 'fun_app$s'(X0,'nat$'(0)) ),
    inference(ennf_transformation,[],[f369]) ).

tff(f369,axiom,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ( ! [X2: 'Nat$'] :
            ( ( ~ 'fun_app$s'(X0,X2)
              & $less(0,'of_nat$'(X2)) )
           => ? [X3: 'Nat$'] :
                ( ~ 'fun_app$s'(X0,X3)
                & $less('of_nat$'(X3),'of_nat$'(X2)) ) )
        & 'fun_app$s'(X0,'nat$'(0)) )
     => 'fun_app$s'(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).

tff(f5808,plain,
    spl173_320,
    inference(avatar_split_clause,[],[f2228,f5806]) ).

tff(f2228,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,sK40(X0,X1))
      | 'fun_app$s'(X0,'nat$'(0))
      | ~ 'fun_app$s'(X0,X1) ),
    inference(cnf_transformation,[],[f1496]) ).

tff(f5804,plain,
    spl173_319,
    inference(avatar_split_clause,[],[f2225,f5802]) ).

tff(f5802,plain,
    ( spl173_319
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,'fun_app$o'('times$a'(X0),X1))
        | ~ $less(0,X1)
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_319])]) ).

tff(f2225,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(0,X1)
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1075]) ).

tff(f1075,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(0,X1)
      | ~ $less(0,X0) ),
    inference(flattening,[],[f1074]) ).

tff(f1074,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(0,X1)
      | ~ $less(0,X0) ),
    inference(ennf_transformation,[],[f529]) ).

tff(f529,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(0,X1)
        & $less(0,X0) )
     => $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).

tff(f5800,plain,
    spl173_318,
    inference(avatar_split_clause,[],[f2223,f5798]) ).

tff(f5798,plain,
    ( spl173_318
  <=> ! [X0: $int,X1: $int] :
        ( $less('fun_app$o'('times$a'(X0),X1),0)
        | ~ $less(X1,0)
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_318])]) ).

tff(f2223,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(X1,0)
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1071]) ).

tff(f1071,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(X1,0)
      | ~ $less(0,X0) ),
    inference(flattening,[],[f1070]) ).

tff(f1070,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(X1,0)
      | ~ $less(0,X0) ),
    inference(ennf_transformation,[],[f527]) ).

tff(f527,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(X1,0)
        & $less(0,X0) )
     => $less('fun_app$o'('times$a'(X0),X1),0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom525) ).

tff(f5796,plain,
    spl173_317,
    inference(avatar_split_clause,[],[f2222,f5794]) ).

tff(f5794,plain,
    ( spl173_317
  <=> ! [X0: $int,X1: $int] :
        ( $less(1,'fun_app$o'('times$a'(X0),X1))
        | ~ $less(1,X1)
        | ~ $less(1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_317])]) ).

tff(f2222,plain,
    ! [X0: $int,X1: $int] :
      ( $less(1,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(1,X1)
      | ~ $less(1,X0) ),
    inference(cnf_transformation,[],[f1069]) ).

tff(f1069,plain,
    ! [X0: $int,X1: $int] :
      ( $less(1,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(1,X1)
      | ~ $less(1,X0) ),
    inference(flattening,[],[f1068]) ).

tff(f1068,plain,
    ! [X0: $int,X1: $int] :
      ( $less(1,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(1,X1)
      | ~ $less(1,X0) ),
    inference(ennf_transformation,[],[f557]) ).

tff(f557,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(1,X1)
        & $less(1,X0) )
     => $less(1,'fun_app$o'('times$a'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).

tff(f5789,plain,
    spl173_316,
    inference(avatar_split_clause,[],[f2221,f5787]) ).

tff(f5787,plain,
    ( spl173_316
  <=> ! [X0: $int,X1: $int] :
        ( $less('fun_app$o'('times$a'(X0),X1),0)
        | ~ $less(0,X1)
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_316])]) ).

tff(f2221,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(0,X1)
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1067]) ).

tff(f1067,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(0,X1)
      | ~ $less(X0,0) ),
    inference(flattening,[],[f1066]) ).

tff(f1066,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ $less(0,X1)
      | ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f525]) ).

tff(f525,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(0,X1)
        & $less(X0,0) )
     => $less('fun_app$o'('times$a'(X0),X1),0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).

tff(f5785,plain,
    spl173_315,
    inference(avatar_split_clause,[],[f2220,f5783]) ).

tff(f5783,plain,
    ( spl173_315
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,'fun_app$o'('times$a'(X0),X1))
        | ~ $less(X1,0)
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_315])]) ).

tff(f2220,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1065]) ).

tff(f1065,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(flattening,[],[f1064]) ).

tff(f1064,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ $less(X1,0)
      | ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f519]) ).

tff(f519,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $less(X1,0)
        & $less(X0,0) )
     => $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).

tff(f5781,plain,
    spl173_314,
    inference(avatar_split_clause,[],[f2216,f5779]) ).

tff(f5779,plain,
    ( spl173_314
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,'fun_app$r'('times$'(X0),X1))
        | ~ $less(0.0,X1)
        | ~ $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_314])]) ).

tff(f2216,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1061]) ).

tff(f1061,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(flattening,[],[f1060]) ).

tff(f1060,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(ennf_transformation,[],[f530]) ).

tff(f530,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,X1)
        & $less(0.0,X0) )
     => $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).

tff(f5777,plain,
    spl173_313,
    inference(avatar_split_clause,[],[f2215,f5775]) ).

tff(f5775,plain,
    ( spl173_313
  <=> ! [X0: $real,X1: $real] :
        ( $less('fun_app$r'('times$'(X0),X1),0.0)
        | ~ $less(X1,0.0)
        | ~ $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_313])]) ).

tff(f2215,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(X1,0.0)
      | ~ $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1059]) ).

tff(f1059,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(X1,0.0)
      | ~ $less(0.0,X0) ),
    inference(flattening,[],[f1058]) ).

tff(f1058,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(X1,0.0)
      | ~ $less(0.0,X0) ),
    inference(ennf_transformation,[],[f528]) ).

tff(f528,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(X1,0.0)
        & $less(0.0,X0) )
     => $less('fun_app$r'('times$'(X0),X1),0.0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom526) ).

tff(f5773,plain,
    spl173_312,
    inference(avatar_split_clause,[],[f2213,f5771]) ).

tff(f5771,plain,
    ( spl173_312
  <=> ! [X0: $real,X1: $real] :
        ( $less(1.0,'fun_app$r'('times$'(X0),X1))
        | ~ $less(1.0,X1)
        | ~ $less(1.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_312])]) ).

tff(f2213,plain,
    ! [X0: $real,X1: $real] :
      ( $less(1.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(1.0,X1)
      | ~ $less(1.0,X0) ),
    inference(cnf_transformation,[],[f1055]) ).

tff(f1055,plain,
    ! [X0: $real,X1: $real] :
      ( $less(1.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(1.0,X1)
      | ~ $less(1.0,X0) ),
    inference(flattening,[],[f1054]) ).

tff(f1054,plain,
    ! [X0: $real,X1: $real] :
      ( $less(1.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(1.0,X1)
      | ~ $less(1.0,X0) ),
    inference(ennf_transformation,[],[f558]) ).

tff(f558,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(1.0,X1)
        & $less(1.0,X0) )
     => $less(1.0,'fun_app$r'('times$'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).

tff(f5769,plain,
    spl173_311,
    inference(avatar_split_clause,[],[f2212,f5767]) ).

tff(f5767,plain,
    ( spl173_311
  <=> ! [X0: $real,X1: $real] :
        ( $less('fun_app$r'('times$'(X0),X1),0.0)
        | ~ $less(0.0,X1)
        | ~ $less(X0,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_311])]) ).

tff(f2212,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(0.0,X1)
      | ~ $less(X0,0.0) ),
    inference(cnf_transformation,[],[f1053]) ).

tff(f1053,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(0.0,X1)
      | ~ $less(X0,0.0) ),
    inference(flattening,[],[f1052]) ).

tff(f1052,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ $less(0.0,X1)
      | ~ $less(X0,0.0) ),
    inference(ennf_transformation,[],[f526]) ).

tff(f526,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,X1)
        & $less(X0,0.0) )
     => $less('fun_app$r'('times$'(X0),X1),0.0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).

tff(f5765,plain,
    spl173_310,
    inference(avatar_split_clause,[],[f2211,f5763]) ).

tff(f5763,plain,
    ( spl173_310
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,'fun_app$r'('times$'(X0),X1))
        | ~ $less(X1,0.0)
        | ~ $less(X0,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_310])]) ).

tff(f2211,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(X1,0.0)
      | ~ $less(X0,0.0) ),
    inference(cnf_transformation,[],[f1051]) ).

tff(f1051,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(X1,0.0)
      | ~ $less(X0,0.0) ),
    inference(flattening,[],[f1050]) ).

tff(f1050,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ $less(X1,0.0)
      | ~ $less(X0,0.0) ),
    inference(ennf_transformation,[],[f520]) ).

tff(f520,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(X1,0.0)
        & $less(X0,0.0) )
     => $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).

tff(f5761,plain,
    spl173_309,
    inference(avatar_split_clause,[],[f2199,f5759]) ).

tff(f5759,plain,
    ( spl173_309
  <=> ! [X0: $int,X1: $int] :
        ( ( 0 = X1 )
        | ( 0 = X0 )
        | ( 0 != 'fun_app$o'('times$a'(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_309])]) ).

tff(f2199,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X1 )
      | ( 0 = X0 )
      | ( 0 != 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1034]) ).

tff(f1034,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X1 )
      | ( 0 = X0 )
      | ( 0 != 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(flattening,[],[f1033]) ).

tff(f1033,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 = X1 )
      | ( 0 = X0 )
      | ( 0 != 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(ennf_transformation,[],[f562]) ).

tff(f562,axiom,
    ! [X0: $int,X1: $int] :
      ( ( 0 = 'fun_app$o'('times$a'(X0),X1) )
     => ( ( 0 = X1 )
        | ( 0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).

tff(f5757,plain,
    spl173_308,
    inference(avatar_split_clause,[],[f2198,f5755]) ).

tff(f5755,plain,
    ( spl173_308
  <=> ! [X0: $real,X1: $real] :
        ( ( 0.0 = X1 )
        | ( 0.0 = X0 )
        | ( 0.0 != 'fun_app$r'('times$'(X0),X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_308])]) ).

tff(f2198,plain,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 = X1 )
      | ( 0.0 = X0 )
      | ( 0.0 != 'fun_app$r'('times$'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1032]) ).

tff(f1032,plain,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 = X1 )
      | ( 0.0 = X0 )
      | ( 0.0 != 'fun_app$r'('times$'(X0),X1) ) ),
    inference(flattening,[],[f1031]) ).

tff(f1031,plain,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 = X1 )
      | ( 0.0 = X0 )
      | ( 0.0 != 'fun_app$r'('times$'(X0),X1) ) ),
    inference(ennf_transformation,[],[f563]) ).

tff(f563,axiom,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 = 'fun_app$r'('times$'(X0),X1) )
     => ( ( 0.0 = X1 )
        | ( 0.0 = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).

tff(f5753,plain,
    spl173_307,
    inference(avatar_split_clause,[],[f2193,f5751]) ).

tff(f5751,plain,
    ( spl173_307
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( $less('fun_app$t'('of_nat$a',X0),'fun_app$t'('of_nat$a',X1))
        | ~ $less('of_nat$'(X0),'of_nat$'(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_307])]) ).

tff(f2193,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$t'('of_nat$a',X0),'fun_app$t'('of_nat$a',X1))
      | ~ $less('of_nat$'(X0),'of_nat$'(X1)) ),
    inference(cnf_transformation,[],[f1028]) ).

tff(f1028,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('fun_app$t'('of_nat$a',X0),'fun_app$t'('of_nat$a',X1))
      | ~ $less('of_nat$'(X0),'of_nat$'(X1)) ),
    inference(ennf_transformation,[],[f203]) ).

tff(f203,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $less('of_nat$'(X0),'of_nat$'(X1))
     => $less('fun_app$t'('of_nat$a',X0),'fun_app$t'('of_nat$a',X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom201) ).

tff(f5746,plain,
    spl173_306,
    inference(avatar_split_clause,[],[f2186,f5744]) ).

tff(f5744,plain,
    ( spl173_306
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ~ $less('fun_app$t'('of_nat$a',X1),'fun_app$t'('of_nat$a',X0))
        | $less('of_nat$'(X1),'of_nat$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_306])]) ).

tff(f2186,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less('fun_app$t'('of_nat$a',X1),'fun_app$t'('of_nat$a',X0))
      | $less('of_nat$'(X1),'of_nat$'(X0)) ),
    inference(cnf_transformation,[],[f1021]) ).

tff(f1021,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less('fun_app$t'('of_nat$a',X1),'fun_app$t'('of_nat$a',X0))
      | $less('of_nat$'(X1),'of_nat$'(X0)) ),
    inference(ennf_transformation,[],[f701]) ).

tff(f701,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
     => ~ $less('fun_app$t'('of_nat$a',X1),'fun_app$t'('of_nat$a',X0)) ),
    inference(theory_normalization,[],[f385]) ).

tff(f385,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( $lesseq('of_nat$'(X0),'of_nat$'(X1))
     => $lesseq('fun_app$t'('of_nat$a',X0),'fun_app$t'('of_nat$a',X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).

tff(f5676,plain,
    ( spl173_305
    | ~ spl173_53
    | ~ spl173_196 ),
    inference(avatar_split_clause,[],[f4654,f4268,f3341,f5673]) ).

tff(f5673,plain,
    ( spl173_305
  <=> $less(0,'of_nat$'(sK37(0.0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_305])]) ).

tff(f3341,plain,
    ( spl173_53
  <=> ! [X0: $real] : $less(X0,'fun_app$t'('of_nat$a',sK37(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_53])]) ).

tff(f4268,plain,
    ( spl173_196
  <=> ! [X0: 'Nat$'] :
        ( $less(0,'of_nat$'(X0))
        | ~ $less(0.0,'fun_app$t'('of_nat$a',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_196])]) ).

tff(f4654,plain,
    ( $less(0,'of_nat$'(sK37(0.0)))
    | ~ spl173_53
    | ~ spl173_196 ),
    inference(resolution,[],[f4269,f3342]) ).

tff(f3342,plain,
    ( ! [X0: $real] : $less(X0,'fun_app$t'('of_nat$a',sK37(X0)))
    | ~ spl173_53 ),
    inference(avatar_component_clause,[],[f3341]) ).

tff(f4269,plain,
    ( ! [X0: 'Nat$'] :
        ( ~ $less(0.0,'fun_app$t'('of_nat$a',X0))
        | $less(0,'of_nat$'(X0)) )
    | ~ spl173_196 ),
    inference(avatar_component_clause,[],[f4268]) ).

tff(f5667,plain,
    ( spl173_304
    | ~ spl173_62
    | ~ spl173_289 ),
    inference(avatar_split_clause,[],[f5413,f5410,f3377,f5665]) ).

tff(f5665,plain,
    ( spl173_304
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK42(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_304])]) ).

tff(f5410,plain,
    ( spl173_289
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK42(X0))
        | ~ 'fun_app$s'(X0,'nat$'(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_289])]) ).

tff(f5413,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$s'(X0,'rank$'('zero$c'))
        | 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK42(X0)) )
    | ~ spl173_62
    | ~ spl173_289 ),
    inference(forward_demodulation,[],[f5411,f3379]) ).

tff(f5411,plain,
    ( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK42(X0))
        | ~ 'fun_app$s'(X0,'nat$'(0)) )
    | ~ spl173_289 ),
    inference(avatar_component_clause,[],[f5410]) ).

tff(f5588,plain,
    ( ~ spl173_303
    | ~ spl173_52
    | ~ spl173_192 ),
    inference(avatar_split_clause,[],[f4615,f4252,f3337,f5585]) ).

tff(f5585,plain,
    ( spl173_303
  <=> $less('of_nat$'(sK36(1.0)),1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_303])]) ).

tff(f3337,plain,
    ( spl173_52
  <=> ! [X0: $real] : ~ $less('fun_app$t'('of_nat$a',sK36(X0)),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_52])]) ).

tff(f4252,plain,
    ( spl173_192
  <=> ! [X0: 'Nat$'] :
        ( ~ $less('of_nat$'(X0),1)
        | $less('fun_app$t'('of_nat$a',X0),1.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_192])]) ).

tff(f4615,plain,
    ( ~ $less('of_nat$'(sK36(1.0)),1)
    | ~ spl173_52
    | ~ spl173_192 ),
    inference(resolution,[],[f4253,f3338]) ).

tff(f3338,plain,
    ( ! [X0: $real] : ~ $less('fun_app$t'('of_nat$a',sK36(X0)),X0)
    | ~ spl173_52 ),
    inference(avatar_component_clause,[],[f3337]) ).

tff(f4253,plain,
    ( ! [X0: 'Nat$'] :
        ( $less('fun_app$t'('of_nat$a',X0),1.0)
        | ~ $less('of_nat$'(X0),1) )
    | ~ spl173_192 ),
    inference(avatar_component_clause,[],[f4252]) ).

tff(f5579,plain,
    ( spl173_302
    | ~ spl173_281 ),
    inference(avatar_split_clause,[],[f5351,f5348,f5577]) ).

tff(f5577,plain,
    ( spl173_302
  <=> ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),$uminus(X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_302])]) ).

tff(f5348,plain,
    ( spl173_281
  <=> ! [X0: $real,X1: $real] : ( $uminus('fun_app$r'('times$'(X0),X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_281])]) ).

tff(f5351,plain,
    ( ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),$uminus(X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) )
    | ~ spl173_281 ),
    inference(forward_demodulation,[],[f5349,f2119]) ).

tff(f2119,plain,
    ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),$uminus(X1)) = $uminus('fun_app$r'('times$'(X0),X1)) ),
    inference(cnf_transformation,[],[f476]) ).

tff(f476,axiom,
    ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),$uminus(X1)) = $uminus('fun_app$r'('times$'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).

tff(f5349,plain,
    ( ! [X0: $real,X1: $real] : ( $uminus('fun_app$r'('times$'(X0),X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) )
    | ~ spl173_281 ),
    inference(avatar_component_clause,[],[f5348]) ).

tff(f5462,plain,
    spl173_301,
    inference(avatar_split_clause,[],[f2670,f5460]) ).

tff(f5460,plain,
    ( spl173_301
  <=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
        ( 'fun_app$s'(X1,X2)
        | sP12(X1,X0)
        | ~ 'fun_app$s'(X1,sK56(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_301])]) ).

tff(f2670,plain,
    ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
      ( 'fun_app$s'(X1,X2)
      | sP12(X1,X0)
      | ~ 'fun_app$s'(X1,sK56(X0,X1)) ),
    inference(cnf_transformation,[],[f1708]) ).

tff(f5458,plain,
    spl173_300,
    inference(avatar_split_clause,[],[f2559,f5456]) ).

tff(f5456,plain,
    ( spl173_300
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec$',X1: 'Rows$'] :
        ( ( 'zero$' = 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_300])]) ).

tff(f2559,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec$',X1: 'Rows$'] :
      ( ( 'zero$' = 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f1129]) ).

tff(f1129,plain,
    ! [X0: 'A_rows_vec$',X1: 'Rows$',X2: 'Rows$'] :
      ( ( ( 'zero$' = 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) )
        | ( X1 = X2 ) )
      & ( ( 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) = X0 )
        | ( X1 != X2 ) ) ),
    inference(ennf_transformation,[],[f66]) ).

tff(f66,axiom,
    ! [X0: 'A_rows_vec$',X1: 'Rows$',X2: 'Rows$'] :
      ( ( ( X1 != X2 )
       => ( 'zero$' = 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) ) )
      & ( ( X1 = X2 )
       => ( 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).

tff(f5454,plain,
    ( spl173_299
    | ~ spl173_53
    | ~ spl173_185 ),
    inference(avatar_split_clause,[],[f4555,f4224,f3341,f5451]) ).

tff(f5451,plain,
    ( spl173_299
  <=> $less(1,'of_nat$'(sK37(1.0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_299])]) ).

tff(f4224,plain,
    ( spl173_185
  <=> ! [X0: 'Nat$'] :
        ( $less(1,'of_nat$'(X0))
        | ~ $less(1.0,'fun_app$t'('of_nat$a',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_185])]) ).

tff(f4555,plain,
    ( $less(1,'of_nat$'(sK37(1.0)))
    | ~ spl173_53
    | ~ spl173_185 ),
    inference(resolution,[],[f4225,f3342]) ).

tff(f4225,plain,
    ( ! [X0: 'Nat$'] :
        ( ~ $less(1.0,'fun_app$t'('of_nat$a',X0))
        | $less(1,'of_nat$'(X0)) )
    | ~ spl173_185 ),
    inference(avatar_component_clause,[],[f4224]) ).

tff(f5449,plain,
    spl173_298,
    inference(avatar_split_clause,[],[f2557,f5447]) ).

tff(f5447,plain,
    ( spl173_298
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec$',X1: 'Rows$'] :
        ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) )
        | ( X1 = X2 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_298])]) ).

tff(f2557,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec$',X1: 'Rows$'] :
      ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) )
      | ( X1 = X2 ) ),
    inference(cnf_transformation,[],[f1128]) ).

tff(f1128,plain,
    ! [X0: 'A_cols_vec$',X1: 'Rows$',X2: 'Rows$'] :
      ( ( ( 'zero$a' = 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) )
        | ( X1 = X2 ) )
      & ( ( 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) = X0 )
        | ( X1 != X2 ) ) ),
    inference(ennf_transformation,[],[f67]) ).

tff(f67,axiom,
    ! [X0: 'A_cols_vec$',X1: 'Rows$',X2: 'Rows$'] :
      ( ( ( X1 != X2 )
       => ( 'zero$a' = 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) ) )
      & ( ( X1 = X2 )
       => ( 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).

tff(f5445,plain,
    spl173_297,
    inference(avatar_split_clause,[],[f2536,f5443]) ).

tff(f5443,plain,
    ( spl173_297
  <=> ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_297])]) ).

tff(f2536,plain,
    ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$',X2: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) = 'matrix_matrix_mult$'('matrix_matrix_mult$a'(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).

tff(f5441,plain,
    spl173_296,
    inference(avatar_split_clause,[],[f2535,f5439]) ).

tff(f2535,plain,
    ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) = 'matrix_matrix_mult$c'('matrix_matrix_mult$'(X0,X1),X2) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$',X2: 'A_cols_vec_cols_vec$'] : ( 'matrix_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) = 'matrix_matrix_mult$c'('matrix_matrix_mult$'(X0,X1),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).

tff(f5437,plain,
    spl173_295,
    inference(avatar_split_clause,[],[f2534,f5435]) ).

tff(f2534,plain,
    ! [X2: 'A_cols_vec_rows_vec$',X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$'('row$'(X0,X1),X2) = 'row$a'(X0,'matrix_matrix_mult$'(X1,X2)) ),
    inference(cnf_transformation,[],[f36]) ).

tff(f36,axiom,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$',X2: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('row$'(X0,X1),X2) = 'row$a'(X0,'matrix_matrix_mult$'(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom34) ).

tff(f5433,plain,
    spl173_294,
    inference(avatar_split_clause,[],[f2533,f5431]) ).

tff(f5431,plain,
    ( spl173_294
  <=> ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$'('vector_matrix_mult$a'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_294])]) ).

tff(f2533,plain,
    ! [X2: 'A_cols_vec_rows_vec$',X0: 'A_rows_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$'('vector_matrix_mult$a'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) ),
    inference(cnf_transformation,[],[f11]) ).

tff(f11,axiom,
    ! [X0: 'A_rows_vec$',X1: 'A_rows_vec_rows_vec$',X2: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('vector_matrix_mult$a'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$'(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).

tff(f5429,plain,
    spl173_293,
    inference(avatar_split_clause,[],[f2532,f5427]) ).

tff(f5427,plain,
    ( spl173_293
  <=> ! [X2: 'A_rows_vec_rows_vec$',X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$a'('row$'(X0,X1),X2) = 'row$'(X0,'matrix_matrix_mult$a'(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_293])]) ).

tff(f2532,plain,
    ! [X2: 'A_rows_vec_rows_vec$',X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$a'('row$'(X0,X1),X2) = 'row$'(X0,'matrix_matrix_mult$a'(X1,X2)) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,axiom,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$',X2: 'A_rows_vec_rows_vec$'] : ( 'vector_matrix_mult$a'('row$'(X0,X1),X2) = 'row$'(X0,'matrix_matrix_mult$a'(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).

tff(f5425,plain,
    spl173_292,
    inference(avatar_split_clause,[],[f2531,f5423]) ).

tff(f2531,plain,
    ! [X2: 'A_cols_vec_cols_vec$',X0: 'A_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$c'('vector_matrix_mult$'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) ),
    inference(cnf_transformation,[],[f10]) ).

tff(f10,axiom,
    ! [X0: 'A_rows_vec$',X1: 'A_cols_vec_rows_vec$',X2: 'A_cols_vec_cols_vec$'] : ( 'vector_matrix_mult$c'('vector_matrix_mult$'(X0,X1),X2) = 'vector_matrix_mult$'(X0,'matrix_matrix_mult$c'(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).

tff(f5421,plain,
    spl173_291,
    inference(avatar_split_clause,[],[f2530,f5419]) ).

tff(f5419,plain,
    ( spl173_291
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('columnvector_row$'(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_291])]) ).

tff(f2530,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('columnvector_row$'(X0,X1)),X2) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$d'('vec_nth$'(X0),X1) = 'fun_app$d'('vec_nth$'('columnvector_row$'(X0,X1)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).

tff(f5417,plain,
    spl173_290,
    inference(avatar_split_clause,[],[f2529,f5415]) ).

tff(f5415,plain,
    ( spl173_290
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('columnvector_row$a'(X0,X1)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_290])]) ).

tff(f2529,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('columnvector_row$a'(X0,X1)),X2) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f40,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$',X2: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'(X0),X1) = 'fun_app$e'('vec_nth$a'('columnvector_row$a'(X0,X1)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).

tff(f5412,plain,
    spl173_289,
    inference(avatar_split_clause,[],[f2248,f5410]) ).

tff(f2248,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ~ 'fun_app$s'(X0,sK42(X0))
      | ~ 'fun_app$s'(X0,'nat$'(0)) ),
    inference(cnf_transformation,[],[f1500]) ).

tff(f5379,plain,
    spl173_288,
    inference(avatar_split_clause,[],[f2219,f5377]) ).

tff(f5377,plain,
    ( spl173_288
  <=> ! [X0: $real,X1: $real] :
        ( $less(sK39(X0,X1),X1)
        | ~ $less(0.0,X1)
        | ~ $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_288])]) ).

tff(f2219,plain,
    ! [X0: $real,X1: $real] :
      ( $less(sK39(X0,X1),X1)
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f1494,plain,
    ! [X0: $real,X1: $real] :
      ( ( $less(sK39(X0,X1),X1)
        & $less(sK39(X0,X1),X0)
        & $less(0.0,sK39(X0,X1)) )
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1063,f1493]) ).

tff(f1493,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X2,X0)
          & $less(0.0,X2) )
     => ( $less(sK39(X0,X1),X1)
        & $less(sK39(X0,X1),X0)
        & $less(0.0,sK39(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1063,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X2,X0)
          & $less(0.0,X2) )
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(flattening,[],[f1062]) ).

tff(f1062,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X2,X0)
          & $less(0.0,X2) )
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(ennf_transformation,[],[f431]) ).

tff(f431,axiom,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,X1)
        & $less(0.0,X0) )
     => ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X2,X0)
          & $less(0.0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).

tff(f5375,plain,
    spl173_287,
    inference(avatar_split_clause,[],[f2218,f5373]) ).

tff(f5373,plain,
    ( spl173_287
  <=> ! [X0: $real,X1: $real] :
        ( $less(sK39(X0,X1),X0)
        | ~ $less(0.0,X1)
        | ~ $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_287])]) ).

tff(f2218,plain,
    ! [X0: $real,X1: $real] :
      ( $less(sK39(X0,X1),X0)
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f5371,plain,
    spl173_286,
    inference(avatar_split_clause,[],[f2217,f5369]) ).

tff(f5369,plain,
    ( spl173_286
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,sK39(X0,X1))
        | ~ $less(0.0,X1)
        | ~ $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_286])]) ).

tff(f2217,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,sK39(X0,X1))
      | ~ $less(0.0,X1)
      | ~ $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1494]) ).

tff(f5367,plain,
    spl173_285,
    inference(avatar_split_clause,[],[f2119,f5365]) ).

tff(f5365,plain,
    ( spl173_285
  <=> ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),$uminus(X1)) = $uminus('fun_app$r'('times$'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_285])]) ).

tff(f5363,plain,
    spl173_284,
    inference(avatar_split_clause,[],[f2118,f5361]) ).

tff(f5361,plain,
    ( spl173_284
  <=> ! [X0: 'Nat$',X1: $int] : ( 'fun_app$o'('times$a'('of_nat$'(X0)),X1) = 'fun_app$o'('times$a'(X1),'of_nat$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_284])]) ).

tff(f2118,plain,
    ! [X0: 'Nat$',X1: $int] : ( 'fun_app$o'('times$a'('of_nat$'(X0)),X1) = 'fun_app$o'('times$a'(X1),'of_nat$'(X0)) ),
    inference(cnf_transformation,[],[f604]) ).

tff(f604,axiom,
    ! [X0: 'Nat$',X1: $int] : ( 'fun_app$o'('times$a'('of_nat$'(X0)),X1) = 'fun_app$o'('times$a'(X1),'of_nat$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).

tff(f5359,plain,
    spl173_283,
    inference(avatar_split_clause,[],[f2117,f5357]) ).

tff(f5357,plain,
    ( spl173_283
  <=> ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'(X0)),X1) = 'uminus$a'('fun_app$d'('vec_nth$'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_283])]) ).

tff(f2117,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'(X0)),X1) = 'uminus$a'('fun_app$d'('vec_nth$'(X0),X1)) ),
    inference(cnf_transformation,[],[f482]) ).

tff(f482,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'(X0)),X1) = 'uminus$a'('fun_app$d'('vec_nth$'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).

tff(f5355,plain,
    spl173_282,
    inference(avatar_split_clause,[],[f2116,f5353]) ).

tff(f5353,plain,
    ( spl173_282
  <=> ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'(X0)),X1) = 'uminus$c'('fun_app$e'('vec_nth$a'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_282])]) ).

tff(f2116,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'(X0)),X1) = 'uminus$c'('fun_app$e'('vec_nth$a'(X0),X1)) ),
    inference(cnf_transformation,[],[f483]) ).

tff(f483,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'(X0)),X1) = 'uminus$c'('fun_app$e'('vec_nth$a'(X0),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).

tff(f5350,plain,
    spl173_281,
    inference(avatar_split_clause,[],[f2115,f5348]) ).

tff(f2115,plain,
    ! [X0: $real,X1: $real] : ( $uminus('fun_app$r'('times$'(X0),X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) ),
    inference(cnf_transformation,[],[f477]) ).

tff(f477,axiom,
    ! [X0: $real,X1: $real] : ( $uminus('fun_app$r'('times$'(X0),X1)) = 'fun_app$r'('times$'($uminus(X0)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).

tff(f5346,plain,
    spl173_280,
    inference(avatar_split_clause,[],[f1981,f5344]) ).

tff(f5344,plain,
    ( spl173_280
  <=> ! [X0: $int] :
        ( ( $uminus('of_nat$'(sK22(X0))) = X0 )
        | ( 'of_nat$'(sK23(X0)) = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_280])]) ).

tff(f1981,plain,
    ! [X0: $int] :
      ( ( $uminus('of_nat$'(sK22(X0))) = X0 )
      | ( 'of_nat$'(sK23(X0)) = X0 ) ),
    inference(cnf_transformation,[],[f1403]) ).

tff(f1403,plain,
    ! [X0: $int] :
      ( ( $uminus('of_nat$'(sK22(X0))) = X0 )
      | ( 'of_nat$'(sK23(X0)) = X0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f972,f1402,f1401]) ).

tff(f1401,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( $uminus('of_nat$'(X1)) = X0 )
     => ( $uminus('of_nat$'(sK22(X0))) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f1402,plain,
    ! [X0: $int] :
      ( ? [X2: 'Nat$'] : ( 'of_nat$'(X2) = X0 )
     => ( 'of_nat$'(sK23(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f972,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( $uminus('of_nat$'(X1)) = X0 )
      | ? [X2: 'Nat$'] : ( 'of_nat$'(X2) = X0 ) ),
    inference(ennf_transformation,[],[f888]) ).

tff(f888,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] : ( $uminus('of_nat$'(X1)) != X0 )
        & ! [X2: 'Nat$'] : ( 'of_nat$'(X2) != X0 ) ),
    inference(flattening,[],[f887]) ).

tff(f887,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] :
            ( ~ $uminus('of_nat$'(X1)) = X0 )
        & ! [X2: 'Nat$'] :
            ( ~ 'of_nat$'(X2) = X0 ) ),
    inference(true_and_false_elimination,[],[f886]) ).

tff(f886,plain,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( $uminus('of_nat$'(X1)) = X0 )
           => $false )
        & ! [X2: 'Nat$'] :
            ( ( 'of_nat$'(X2) = X0 )
           => $false ) )
     => $false ),
    inference(rectify,[],[f606]) ).

tff(f606,axiom,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( $uminus('of_nat$'(X1)) = X0 )
           => $false )
        & ! [X1: 'Nat$'] :
            ( ( 'of_nat$'(X1) = X0 )
           => $false ) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).

tff(f5342,plain,
    spl173_279,
    inference(avatar_split_clause,[],[f867,f5340]) ).

tff(f5340,plain,
    ( spl173_279
  <=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_279])]) ).

tff(f867,plain,
    ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f5309,plain,
    spl173_278,
    inference(avatar_split_clause,[],[f856,f5307]) ).

tff(f5307,plain,
    ( spl173_278
  <=> ! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_278])]) ).

tff(f856,plain,
    ! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f5305,plain,
    spl173_277,
    inference(avatar_split_clause,[],[f849,f5303]) ).

tff(f5303,plain,
    ( spl173_277
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_277])]) ).

tff(f849,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f5301,plain,
    spl173_276,
    inference(avatar_split_clause,[],[f838,f5299]) ).

tff(f5299,plain,
    ( spl173_276
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_276])]) ).

tff(f838,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f5181,plain,
    ( spl173_275
    | ~ spl173_20
    | ~ spl173_247 ),
    inference(avatar_split_clause,[],[f5177,f4933,f3186,f5179]) ).

tff(f5179,plain,
    ( spl173_275
  <=> ! [X0: 'Nat$'] : ( 'of_nat$'(X0) != -1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_275])]) ).

tff(f3186,plain,
    ( spl173_20
  <=> ( 1 = 'of_nat$'('to_nat$'('one$e')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_20])]) ).

tff(f4933,plain,
    ( spl173_247
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X0) )
        | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_247])]) ).

tff(f5177,plain,
    ( ! [X0: 'Nat$'] : ( 'of_nat$'(X0) != -1 )
    | ~ spl173_20
    | ~ spl173_247 ),
    inference(evaluation,[],[f5168]) ).

tff(f5168,plain,
    ( ! [X0: 'Nat$'] :
        ( ( 'of_nat$'(X0) != $uminus(1) )
        | ( 0 = 1 ) )
    | ~ spl173_20
    | ~ spl173_247 ),
    inference(superposition,[],[f4934,f3188]) ).

tff(f3188,plain,
    ( ( 1 = 'of_nat$'('to_nat$'('one$e')) )
    | ~ spl173_20 ),
    inference(avatar_component_clause,[],[f3186]) ).

tff(f4934,plain,
    ( ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) )
        | ( 0 = 'of_nat$'(X0) ) )
    | ~ spl173_247 ),
    inference(avatar_component_clause,[],[f4933]) ).

tff(f5091,plain,
    spl173_274,
    inference(avatar_split_clause,[],[f2736,f5089]) ).

tff(f5089,plain,
    ( spl173_274
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP16(X0,X1,X2)
        | ~ $less(X1,X0)
        | ~ $less(X2,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_274])]) ).

tff(f2736,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP16(X0,X1,X2)
      | ~ $less(X1,X0)
      | ~ $less(X2,0) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f1751,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( sP16(X0,X1,X2)
        | ( ( ~ $less(X1,X0)
            | ~ $less(X2,0) )
          & ( ~ $less(X0,X1)
            | ~ $less(0,X2) ) ) )
      & ( ( $less(X1,X0)
          & $less(X2,0) )
        | ( $less(X0,X1)
          & $less(0,X2) )
        | ~ sP16(X0,X1,X2) ) ),
    inference(rectify,[],[f1750]) ).

tff(f1750,plain,
    ! [X1: $int,X2: $int,X0: $int] :
      ( ( sP16(X1,X2,X0)
        | ( ( ~ $less(X2,X1)
            | ~ $less(X0,0) )
          & ( ~ $less(X1,X2)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(X2,X1)
          & $less(X0,0) )
        | ( $less(X1,X2)
          & $less(0,X0) )
        | ~ sP16(X1,X2,X0) ) ),
    inference(flattening,[],[f1749]) ).

tff(f1749,plain,
    ! [X1: $int,X2: $int,X0: $int] :
      ( ( sP16(X1,X2,X0)
        | ( ( ~ $less(X2,X1)
            | ~ $less(X0,0) )
          & ( ~ $less(X1,X2)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(X2,X1)
          & $less(X0,0) )
        | ( $less(X1,X2)
          & $less(0,X0) )
        | ~ sP16(X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1389]) ).

tff(f5087,plain,
    spl173_273,
    inference(avatar_split_clause,[],[f2735,f5085]) ).

tff(f5085,plain,
    ( spl173_273
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP16(X0,X1,X2)
        | ~ $less(X0,X1)
        | ~ $less(0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_273])]) ).

tff(f2735,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP16(X0,X1,X2)
      | ~ $less(X0,X1)
      | ~ $less(0,X2) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f5067,plain,
    spl173_272,
    inference(avatar_split_clause,[],[f2734,f5065]) ).

tff(f5065,plain,
    ( spl173_272
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | $less(X0,X1)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_272])]) ).

tff(f2734,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f5063,plain,
    spl173_271,
    inference(avatar_split_clause,[],[f2733,f5061]) ).

tff(f5061,plain,
    ( spl173_271
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | $less(0,X2)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_271])]) ).

tff(f2733,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(0,X2)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f5059,plain,
    spl173_270,
    inference(avatar_split_clause,[],[f2732,f5057]) ).

tff(f5057,plain,
    ( spl173_270
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X2,0)
        | $less(X0,X1)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_270])]) ).

tff(f2732,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X2,0)
      | $less(X0,X1)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f5055,plain,
    spl173_269,
    inference(avatar_split_clause,[],[f2731,f5053]) ).

tff(f5053,plain,
    ( spl173_269
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X2,0)
        | $less(0,X2)
        | ~ sP16(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_269])]) ).

tff(f2731,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X2,0)
      | $less(0,X2)
      | ~ sP16(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1751]) ).

tff(f5051,plain,
    spl173_268,
    inference(avatar_split_clause,[],[f2728,f5049]) ).

tff(f5049,plain,
    ( spl173_268
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP15(X0,X1,X2)
        | ~ $less(X1,X0)
        | ~ $less(X2,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_268])]) ).

tff(f2728,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP15(X0,X1,X2)
      | ~ $less(X1,X0)
      | ~ $less(X2,0) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f1747,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( sP15(X0,X1,X2)
        | ( ( ~ $less(X1,X0)
            | ~ $less(X2,0) )
          & ( ~ $less(X0,X1)
            | ~ $less(0,X2) ) ) )
      & ( ( $less(X1,X0)
          & $less(X2,0) )
        | ( $less(X0,X1)
          & $less(0,X2) )
        | ~ sP15(X0,X1,X2) ) ),
    inference(rectify,[],[f1746]) ).

tff(f1746,plain,
    ! [X0: $int,X2: $int,X1: $int] :
      ( ( sP15(X0,X2,X1)
        | ( ( ~ $less(X2,X0)
            | ~ $less(X1,0) )
          & ( ~ $less(X0,X2)
            | ~ $less(0,X1) ) ) )
      & ( ( $less(X2,X0)
          & $less(X1,0) )
        | ( $less(X0,X2)
          & $less(0,X1) )
        | ~ sP15(X0,X2,X1) ) ),
    inference(flattening,[],[f1745]) ).

tff(f1745,plain,
    ! [X0: $int,X2: $int,X1: $int] :
      ( ( sP15(X0,X2,X1)
        | ( ( ~ $less(X2,X0)
            | ~ $less(X1,0) )
          & ( ~ $less(X0,X2)
            | ~ $less(0,X1) ) ) )
      & ( ( $less(X2,X0)
          & $less(X1,0) )
        | ( $less(X0,X2)
          & $less(0,X1) )
        | ~ sP15(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f1387]) ).

tff(f5047,plain,
    spl173_267,
    inference(avatar_split_clause,[],[f2727,f5045]) ).

tff(f5045,plain,
    ( spl173_267
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( sP15(X0,X1,X2)
        | ~ $less(X0,X1)
        | ~ $less(0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_267])]) ).

tff(f2727,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( sP15(X0,X1,X2)
      | ~ $less(X0,X1)
      | ~ $less(0,X2) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f5043,plain,
    spl173_266,
    inference(avatar_split_clause,[],[f2726,f5041]) ).

tff(f5041,plain,
    ( spl173_266
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | $less(X0,X1)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_266])]) ).

tff(f2726,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f5039,plain,
    spl173_265,
    inference(avatar_split_clause,[],[f2725,f5037]) ).

tff(f5037,plain,
    ( spl173_265
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | $less(0,X2)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_265])]) ).

tff(f2725,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X1,X0)
      | $less(0,X2)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f5035,plain,
    spl173_264,
    inference(avatar_split_clause,[],[f2724,f5033]) ).

tff(f5033,plain,
    ( spl173_264
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X2,0)
        | $less(X0,X1)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_264])]) ).

tff(f2724,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X2,0)
      | $less(X0,X1)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f5031,plain,
    spl173_263,
    inference(avatar_split_clause,[],[f2723,f5029]) ).

tff(f5029,plain,
    ( spl173_263
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X2,0)
        | $less(0,X2)
        | ~ sP15(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_263])]) ).

tff(f2723,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( $less(X2,0)
      | $less(0,X2)
      | ~ sP15(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1747]) ).

tff(f5014,plain,
    spl173_262,
    inference(avatar_split_clause,[],[f2720,f5012]) ).

tff(f5012,plain,
    ( spl173_262
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP14(X0,X1,X2)
        | ~ $less(X1,X0)
        | ~ $less(X2,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_262])]) ).

tff(f2720,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP14(X0,X1,X2)
      | ~ $less(X1,X0)
      | ~ $less(X2,0.0) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f1743,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( sP14(X0,X1,X2)
        | ( ( ~ $less(X1,X0)
            | ~ $less(X2,0.0) )
          & ( ~ $less(X0,X1)
            | ~ $less(0.0,X2) ) ) )
      & ( ( $less(X1,X0)
          & $less(X2,0.0) )
        | ( $less(X0,X1)
          & $less(0.0,X2) )
        | ~ sP14(X0,X1,X2) ) ),
    inference(rectify,[],[f1742]) ).

tff(f1742,plain,
    ! [X0: $real,X2: $real,X1: $real] :
      ( ( sP14(X0,X2,X1)
        | ( ( ~ $less(X2,X0)
            | ~ $less(X1,0.0) )
          & ( ~ $less(X0,X2)
            | ~ $less(0.0,X1) ) ) )
      & ( ( $less(X2,X0)
          & $less(X1,0.0) )
        | ( $less(X0,X2)
          & $less(0.0,X1) )
        | ~ sP14(X0,X2,X1) ) ),
    inference(flattening,[],[f1741]) ).

tff(f1741,plain,
    ! [X0: $real,X2: $real,X1: $real] :
      ( ( sP14(X0,X2,X1)
        | ( ( ~ $less(X2,X0)
            | ~ $less(X1,0.0) )
          & ( ~ $less(X0,X2)
            | ~ $less(0.0,X1) ) ) )
      & ( ( $less(X2,X0)
          & $less(X1,0.0) )
        | ( $less(X0,X2)
          & $less(0.0,X1) )
        | ~ sP14(X0,X2,X1) ) ),
    inference(nnf_transformation,[],[f1385]) ).

tff(f5010,plain,
    spl173_261,
    inference(avatar_split_clause,[],[f2719,f5008]) ).

tff(f5008,plain,
    ( spl173_261
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP14(X0,X1,X2)
        | ~ $less(X0,X1)
        | ~ $less(0.0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_261])]) ).

tff(f2719,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP14(X0,X1,X2)
      | ~ $less(X0,X1)
      | ~ $less(0.0,X2) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f5006,plain,
    spl173_260,
    inference(avatar_split_clause,[],[f2718,f5004]) ).

tff(f5004,plain,
    ( spl173_260
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X1,X0)
        | $less(X0,X1)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_260])]) ).

tff(f2718,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f5002,plain,
    spl173_259,
    inference(avatar_split_clause,[],[f2717,f5000]) ).

tff(f5000,plain,
    ( spl173_259
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X1,X0)
        | $less(0.0,X2)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_259])]) ).

tff(f2717,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X1,X0)
      | $less(0.0,X2)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f4998,plain,
    spl173_258,
    inference(avatar_split_clause,[],[f2716,f4996]) ).

tff(f4996,plain,
    ( spl173_258
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X2,0.0)
        | $less(X0,X1)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_258])]) ).

tff(f2716,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X2,0.0)
      | $less(X0,X1)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f4994,plain,
    spl173_257,
    inference(avatar_split_clause,[],[f2715,f4992]) ).

tff(f4992,plain,
    ( spl173_257
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X2,0.0)
        | $less(0.0,X2)
        | ~ sP14(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_257])]) ).

tff(f2715,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X2,0.0)
      | $less(0.0,X2)
      | ~ sP14(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1743]) ).

tff(f4990,plain,
    spl173_256,
    inference(avatar_split_clause,[],[f2712,f4988]) ).

tff(f4988,plain,
    ( spl173_256
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP13(X0,X1,X2)
        | ~ $less(X1,X0)
        | ~ $less(X2,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_256])]) ).

tff(f2712,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP13(X0,X1,X2)
      | ~ $less(X1,X0)
      | ~ $less(X2,0.0) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f1739,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( sP13(X0,X1,X2)
        | ( ( ~ $less(X1,X0)
            | ~ $less(X2,0.0) )
          & ( ~ $less(X0,X1)
            | ~ $less(0.0,X2) ) ) )
      & ( ( $less(X1,X0)
          & $less(X2,0.0) )
        | ( $less(X0,X1)
          & $less(0.0,X2) )
        | ~ sP13(X0,X1,X2) ) ),
    inference(rectify,[],[f1738]) ).

tff(f1738,plain,
    ! [X1: $real,X2: $real,X0: $real] :
      ( ( sP13(X1,X2,X0)
        | ( ( ~ $less(X2,X1)
            | ~ $less(X0,0.0) )
          & ( ~ $less(X1,X2)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(X2,X1)
          & $less(X0,0.0) )
        | ( $less(X1,X2)
          & $less(0.0,X0) )
        | ~ sP13(X1,X2,X0) ) ),
    inference(flattening,[],[f1737]) ).

tff(f1737,plain,
    ! [X1: $real,X2: $real,X0: $real] :
      ( ( sP13(X1,X2,X0)
        | ( ( ~ $less(X2,X1)
            | ~ $less(X0,0.0) )
          & ( ~ $less(X1,X2)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(X2,X1)
          & $less(X0,0.0) )
        | ( $less(X1,X2)
          & $less(0.0,X0) )
        | ~ sP13(X1,X2,X0) ) ),
    inference(nnf_transformation,[],[f1383]) ).

tff(f4986,plain,
    spl173_255,
    inference(avatar_split_clause,[],[f2711,f4984]) ).

tff(f4984,plain,
    ( spl173_255
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( sP13(X0,X1,X2)
        | ~ $less(X0,X1)
        | ~ $less(0.0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_255])]) ).

tff(f2711,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( sP13(X0,X1,X2)
      | ~ $less(X0,X1)
      | ~ $less(0.0,X2) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f4982,plain,
    spl173_254,
    inference(avatar_split_clause,[],[f2710,f4980]) ).

tff(f4980,plain,
    ( spl173_254
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X1,X0)
        | $less(X0,X1)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_254])]) ).

tff(f2710,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X1,X0)
      | $less(X0,X1)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f4978,plain,
    spl173_253,
    inference(avatar_split_clause,[],[f2709,f4976]) ).

tff(f4976,plain,
    ( spl173_253
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X1,X0)
        | $less(0.0,X2)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_253])]) ).

tff(f2709,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X1,X0)
      | $less(0.0,X2)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f4955,plain,
    spl173_252,
    inference(avatar_split_clause,[],[f2708,f4953]) ).

tff(f4953,plain,
    ( spl173_252
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X2,0.0)
        | $less(X0,X1)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_252])]) ).

tff(f2708,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X2,0.0)
      | $less(X0,X1)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f4951,plain,
    spl173_251,
    inference(avatar_split_clause,[],[f2707,f4949]) ).

tff(f4949,plain,
    ( spl173_251
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( $less(X2,0.0)
        | $less(0.0,X2)
        | ~ sP13(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_251])]) ).

tff(f2707,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( $less(X2,0.0)
      | $less(0.0,X2)
      | ~ sP13(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1739]) ).

tff(f4947,plain,
    spl173_250,
    inference(avatar_split_clause,[],[f2666,f4945]) ).

tff(f4945,plain,
    ( spl173_250
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ $less('of_nat$'(X1),'of_nat$'(sK55(X0,X1)))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_250])]) ).

tff(f2666,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ $less('of_nat$'(X1),'of_nat$'(sK55(X0,X1)))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f1705]) ).

tff(f4943,plain,
    spl173_249,
    inference(avatar_split_clause,[],[f2517,f4941]) ).

tff(f4941,plain,
    ( spl173_249
  <=> ! [X0: 'Rows$',X1: 'Rows$'] :
        ( ( X0 = X1 )
        | ( 'of_nat$'('to_nat$'(X0)) != 'of_nat$'('to_nat$'(X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_249])]) ).

tff(f2517,plain,
    ! [X0: 'Rows$',X1: 'Rows$'] :
      ( ( X0 = X1 )
      | ( 'of_nat$'('to_nat$'(X0)) != 'of_nat$'('to_nat$'(X1)) ) ),
    inference(cnf_transformation,[],[f1662]) ).

tff(f1662,plain,
    ! [X0: 'Rows$',X1: 'Rows$'] :
      ( ( ( 'of_nat$'('to_nat$'(X0)) = 'of_nat$'('to_nat$'(X1)) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'of_nat$'('to_nat$'(X0)) != 'of_nat$'('to_nat$'(X1)) ) ) ),
    inference(nnf_transformation,[],[f65]) ).

tff(f65,axiom,
    ! [X0: 'Rows$',X1: 'Rows$'] :
      ( ( 'of_nat$'('to_nat$'(X0)) = 'of_nat$'('to_nat$'(X1)) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).

tff(f4939,plain,
    spl173_248,
    inference(avatar_split_clause,[],[f2459,f4937]) ).

tff(f4937,plain,
    ( spl173_248
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X1) )
        | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_248])]) ).

tff(f2459,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X1) )
      | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ),
    inference(cnf_transformation,[],[f1629]) ).

tff(f1629,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 'of_nat$'(X1) = $uminus('of_nat$'(X0)) )
        | ( 0 != 'of_nat$'(X1) )
        | ( 0 != 'of_nat$'(X0) ) )
      & ( ( ( 0 = 'of_nat$'(X1) )
          & ( 0 = 'of_nat$'(X0) ) )
        | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ) ),
    inference(flattening,[],[f1628]) ).

tff(f1628,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( ( 'of_nat$'(X1) = $uminus('of_nat$'(X0)) )
        | ( 0 != 'of_nat$'(X1) )
        | ( 0 != 'of_nat$'(X0) ) )
      & ( ( ( 0 = 'of_nat$'(X1) )
          & ( 0 = 'of_nat$'(X0) ) )
        | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ) ),
    inference(nnf_transformation,[],[f512]) ).

tff(f512,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'of_nat$'(X1) = $uminus('of_nat$'(X0)) )
    <=> ( ( 0 = 'of_nat$'(X1) )
        & ( 0 = 'of_nat$'(X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).

tff(f4935,plain,
    spl173_247,
    inference(avatar_split_clause,[],[f2458,f4933]) ).

tff(f2458,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | ( 'of_nat$'(X1) != $uminus('of_nat$'(X0)) ) ),
    inference(cnf_transformation,[],[f1629]) ).

tff(f4931,plain,
    spl173_246,
    inference(avatar_split_clause,[],[f2184,f4929]) ).

tff(f4929,plain,
    ( spl173_246
  <=> ! [X0: 'Nat$',X1: 'Nat$'] :
        ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
        | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_246])]) ).

tff(f2184,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
      | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ),
    inference(cnf_transformation,[],[f1019]) ).

tff(f1019,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
      | ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ),
    inference(ennf_transformation,[],[f699]) ).

tff(f699,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'of_nat$'(X0) = 'of_nat$'(X1) )
     => ~ $less('of_nat$'(X1),'of_nat$'(X0)) ),
    inference(theory_normalization,[],[f150]) ).

tff(f150,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] :
      ( ( 'of_nat$'(X0) = 'of_nat$'(X1) )
     => $lesseq('of_nat$'(X0),'of_nat$'(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).

tff(f4927,plain,
    spl173_245,
    inference(avatar_split_clause,[],[f2114,f4925]) ).

tff(f4925,plain,
    ( spl173_245
  <=> ! [X0: 'A_rows_vec_cols_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'transpose$a'('matrix_matrix_mult$d'(X0,X1)) = 'matrix_matrix_mult$'('transpose$'(X1),'transpose$a'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_245])]) ).

tff(f2114,plain,
    ! [X0: 'A_rows_vec_cols_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'transpose$a'('matrix_matrix_mult$d'(X0,X1)) = 'matrix_matrix_mult$'('transpose$'(X1),'transpose$a'(X0)) ),
    inference(cnf_transformation,[],[f60]) ).

tff(f60,axiom,
    ! [X0: 'A_rows_vec_cols_vec$',X1: 'A_rows_vec_rows_vec$'] : ( 'transpose$a'('matrix_matrix_mult$d'(X0,X1)) = 'matrix_matrix_mult$'('transpose$'(X1),'transpose$a'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).

tff(f4923,plain,
    spl173_244,
    inference(avatar_split_clause,[],[f2113,f4921]) ).

tff(f4921,plain,
    ( spl173_244
  <=> ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'transpose$b'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult$d'('transpose$b'(X1),'transpose$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_244])]) ).

tff(f2113,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'transpose$b'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult$d'('transpose$b'(X1),'transpose$'(X0)) ),
    inference(cnf_transformation,[],[f61]) ).

tff(f61,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] : ( 'transpose$b'('matrix_matrix_mult$'(X0,X1)) = 'matrix_matrix_mult$d'('transpose$b'(X1),'transpose$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).

tff(f4919,plain,
    spl173_243,
    inference(avatar_split_clause,[],[f863,f4917]) ).

tff(f4917,plain,
    ( spl173_243
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_243])]) ).

tff(f863,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f4909,plain,
    spl173_242,
    inference(avatar_split_clause,[],[f858,f4907]) ).

tff(f4907,plain,
    ( spl173_242
  <=> ! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_242])]) ).

tff(f858,plain,
    ! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f4905,plain,
    spl173_241,
    inference(avatar_split_clause,[],[f845,f4903]) ).

tff(f4903,plain,
    ( spl173_241
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_241])]) ).

tff(f845,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f4901,plain,
    spl173_240,
    inference(avatar_split_clause,[],[f840,f4899]) ).

tff(f4899,plain,
    ( spl173_240
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_240])]) ).

tff(f840,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f4810,plain,
    ( spl173_239
    | ~ spl173_66
    | ~ spl173_224 ),
    inference(avatar_split_clause,[],[f4805,f4383,f3394,f4807]) ).

tff(f4807,plain,
    ( spl173_239
  <=> sP2(-1,-1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_239])]) ).

tff(f3394,plain,
    ( spl173_66
  <=> ( 1 = 'fun_app$o'('times$a'(-1),-1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_66])]) ).

tff(f4383,plain,
    ( spl173_224
  <=> ! [X0: $int,X1: $int] :
        ( sP2(X1,X0)
        | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_224])]) ).

tff(f4805,plain,
    ( sP2(-1,-1)
    | ~ spl173_66
    | ~ spl173_224 ),
    inference(evaluation,[],[f4804]) ).

tff(f4804,plain,
    ( ~ $less(0,1)
    | sP2(-1,-1)
    | ~ spl173_66
    | ~ spl173_224 ),
    inference(superposition,[],[f4384,f3396]) ).

tff(f3396,plain,
    ( ( 1 = 'fun_app$o'('times$a'(-1),-1) )
    | ~ spl173_66 ),
    inference(avatar_component_clause,[],[f3394]) ).

tff(f4384,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(0,'fun_app$o'('times$a'(X0),X1))
        | sP2(X1,X0) )
    | ~ spl173_224 ),
    inference(avatar_component_clause,[],[f4383]) ).

tff(f4730,plain,
    ( spl173_238
    | ~ spl173_67
    | ~ spl173_206 ),
    inference(avatar_split_clause,[],[f4725,f4309,f3399,f4727]) ).

tff(f4727,plain,
    ( spl173_238
  <=> sP0(-1.0,-1.0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_238])]) ).

tff(f3399,plain,
    ( spl173_67
  <=> ( 1.0 = 'fun_app$r'('times$'(-1.0),-1.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_67])]) ).

tff(f4309,plain,
    ( spl173_206
  <=> ! [X0: $real,X1: $real] :
        ( sP0(X1,X0)
        | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_206])]) ).

tff(f4725,plain,
    ( sP0(-1.0,-1.0)
    | ~ spl173_67
    | ~ spl173_206 ),
    inference(evaluation,[],[f4724]) ).

tff(f4724,plain,
    ( ~ $less(0.0,1.0)
    | sP0(-1.0,-1.0)
    | ~ spl173_67
    | ~ spl173_206 ),
    inference(superposition,[],[f4310,f3401]) ).

tff(f3401,plain,
    ( ( 1.0 = 'fun_app$r'('times$'(-1.0),-1.0) )
    | ~ spl173_67 ),
    inference(avatar_component_clause,[],[f3399]) ).

tff(f4310,plain,
    ( ! [X0: $real,X1: $real] :
        ( ~ $less(0.0,'fun_app$r'('times$'(X0),X1))
        | sP0(X1,X0) )
    | ~ spl173_206 ),
    inference(avatar_component_clause,[],[f4309]) ).

tff(f4438,plain,
    spl173_237,
    inference(avatar_split_clause,[],[f2863,f4436]) ).

tff(f4436,plain,
    ( spl173_237
  <=> ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,X1) = 'row$'(X0,'transpose$'('transpose$'(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_237])]) ).

tff(f2863,plain,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,X1) = 'row$'(X0,'transpose$'('transpose$'(X1))) ),
    inference(definition_unfolding,[],[f2105,f2107]) ).

tff(f2107,plain,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,'transpose$'(X1)) = 'column$'(X0,X1) ),
    inference(cnf_transformation,[],[f158]) ).

tff(f158,axiom,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,'transpose$'(X1)) = 'column$'(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).

tff(f2105,plain,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,X1) = 'column$'(X0,'transpose$'(X1)) ),
    inference(cnf_transformation,[],[f157]) ).

tff(f157,axiom,
    ! [X0: 'Rows$',X1: 'A_rows_vec_rows_vec$'] : ( 'row$'(X0,X1) = 'column$'(X0,'transpose$'(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).

tff(f4434,plain,
    spl173_236,
    inference(avatar_split_clause,[],[f2601,f4432]) ).

tff(f4432,plain,
    ( spl173_236
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X2)
        | $less(X0,X2)
        | $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_236])]) ).

tff(f2601,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(cnf_transformation,[],[f1176]) ).

tff(f1176,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(flattening,[],[f1175]) ).

tff(f1175,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(ennf_transformation,[],[f783]) ).

tff(f783,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( ~ $less(X0,X2)
        & ~ $less(X1,X0) )
     => ~ $less(X1,X2) ),
    inference(theory_normalization,[],[f98]) ).

tff(f98,axiom,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( $lesseq(X2,X0)
        & $lesseq(X0,X1) )
     => $lesseq(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).

tff(f4430,plain,
    spl173_235,
    inference(avatar_split_clause,[],[f2593,f4428]) ).

tff(f4428,plain,
    ( spl173_235
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X1,X2)
        | $less(X0,X2)
        | $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_235])]) ).

tff(f2593,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(cnf_transformation,[],[f1160]) ).

tff(f1160,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(flattening,[],[f1159]) ).

tff(f1159,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ~ $less(X1,X2)
      | $less(X0,X2)
      | $less(X1,X0) ),
    inference(ennf_transformation,[],[f775]) ).

tff(f775,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ~ $less(X0,X2)
        & ~ $less(X1,X0) )
     => ~ $less(X1,X2) ),
    inference(theory_normalization,[],[f99]) ).

tff(f99,axiom,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( $lesseq(X2,X0)
        & $lesseq(X0,X1) )
     => $lesseq(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).

tff(f4426,plain,
    spl173_234,
    inference(avatar_split_clause,[],[f2516,f4424]) ).

tff(f4424,plain,
    ( spl173_234
  <=> ! [X0: $int,X1: $int] :
        ( $less('fun_app$o'('times$a'(X0),X1),0)
        | ~ sP3(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_234])]) ).

tff(f2516,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
      | ~ sP3(X1,X0) ),
    inference(cnf_transformation,[],[f1661]) ).

tff(f1661,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less('fun_app$o'('times$a'(X0),X1),0)
        | ~ sP3(X1,X0) )
      & ( sP3(X1,X0)
        | ~ $less('fun_app$o'('times$a'(X0),X1),0) ) ),
    inference(nnf_transformation,[],[f1370]) ).

tff(f1370,plain,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
    <=> sP3(X1,X0) ),
    inference(definition_folding,[],[f523,f1369]) ).

tff(f1369,plain,
    ! [X1: $int,X0: $int] :
      ( sP3(X1,X0)
    <=> ( ( $less(0,X1)
          & $less(X0,0) )
        | ( $less(X1,0)
          & $less(0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

tff(f523,axiom,
    ! [X0: $int,X1: $int] :
      ( $less('fun_app$o'('times$a'(X0),X1),0)
    <=> ( ( $less(0,X1)
          & $less(X0,0) )
        | ( $less(X1,0)
          & $less(0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).

tff(f4422,plain,
    spl173_233,
    inference(avatar_split_clause,[],[f2515,f4420]) ).

tff(f4420,plain,
    ( spl173_233
  <=> ! [X0: $int,X1: $int] :
        ( sP3(X1,X0)
        | ~ $less('fun_app$o'('times$a'(X0),X1),0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_233])]) ).

tff(f2515,plain,
    ! [X0: $int,X1: $int] :
      ( sP3(X1,X0)
      | ~ $less('fun_app$o'('times$a'(X0),X1),0) ),
    inference(cnf_transformation,[],[f1661]) ).

tff(f4418,plain,
    ( spl173_232
    | ~ spl173_49
    | ~ spl173_145 ),
    inference(avatar_split_clause,[],[f4103,f3841,f3323,f4415]) ).

tff(f4415,plain,
    ( spl173_232
  <=> ( 1 = 'of_nat$'(sK21(1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_232])]) ).

tff(f3323,plain,
    ( spl173_49
  <=> ! [X0: $int] :
        ( $less(0,X0)
        | $less(X0,1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_49])]) ).

tff(f3841,plain,
    ( spl173_145
  <=> ! [X0: $int] :
        ( ( 'of_nat$'(sK21(X0)) = X0 )
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_145])]) ).

tff(f4103,plain,
    ( ( 1 = 'of_nat$'(sK21(1)) )
    | ~ spl173_49
    | ~ spl173_145 ),
    inference(evaluation,[],[f4099]) ).

tff(f4099,plain,
    ( ( 1 = 'of_nat$'(sK21(1)) )
    | $less(0,0)
    | ~ spl173_49
    | ~ spl173_145 ),
    inference(resolution,[],[f3842,f3324]) ).

tff(f3324,plain,
    ( ! [X0: $int] :
        ( $less(0,X0)
        | $less(X0,1) )
    | ~ spl173_49 ),
    inference(avatar_component_clause,[],[f3323]) ).

tff(f3842,plain,
    ( ! [X0: $int] :
        ( ~ $less(0,X0)
        | ( 'of_nat$'(sK21(X0)) = X0 ) )
    | ~ spl173_145 ),
    inference(avatar_component_clause,[],[f3841]) ).

tff(f4413,plain,
    spl173_231,
    inference(avatar_split_clause,[],[f2514,f4411]) ).

tff(f4411,plain,
    ( spl173_231
  <=> ! [X0: $int,X1: $int] :
        ( sP3(X0,X1)
        | ~ $less(0,X0)
        | ~ $less(X1,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_231])]) ).

tff(f2514,plain,
    ! [X0: $int,X1: $int] :
      ( sP3(X0,X1)
      | ~ $less(0,X0)
      | ~ $less(X1,0) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f1660,plain,
    ! [X0: $int,X1: $int] :
      ( ( sP3(X0,X1)
        | ( ( ~ $less(0,X0)
            | ~ $less(X1,0) )
          & ( ~ $less(X0,0)
            | ~ $less(0,X1) ) ) )
      & ( ( $less(0,X0)
          & $less(X1,0) )
        | ( $less(X0,0)
          & $less(0,X1) )
        | ~ sP3(X0,X1) ) ),
    inference(rectify,[],[f1659]) ).

tff(f1659,plain,
    ! [X1: $int,X0: $int] :
      ( ( sP3(X1,X0)
        | ( ( ~ $less(0,X1)
            | ~ $less(X0,0) )
          & ( ~ $less(X1,0)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(0,X1)
          & $less(X0,0) )
        | ( $less(X1,0)
          & $less(0,X0) )
        | ~ sP3(X1,X0) ) ),
    inference(flattening,[],[f1658]) ).

tff(f1658,plain,
    ! [X1: $int,X0: $int] :
      ( ( sP3(X1,X0)
        | ( ( ~ $less(0,X1)
            | ~ $less(X0,0) )
          & ( ~ $less(X1,0)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(0,X1)
          & $less(X0,0) )
        | ( $less(X1,0)
          & $less(0,X0) )
        | ~ sP3(X1,X0) ) ),
    inference(nnf_transformation,[],[f1369]) ).

tff(f4409,plain,
    spl173_230,
    inference(avatar_split_clause,[],[f2513,f4407]) ).

tff(f4407,plain,
    ( spl173_230
  <=> ! [X0: $int,X1: $int] :
        ( sP3(X0,X1)
        | ~ $less(X0,0)
        | ~ $less(0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_230])]) ).

tff(f2513,plain,
    ! [X0: $int,X1: $int] :
      ( sP3(X0,X1)
      | ~ $less(X0,0)
      | ~ $less(0,X1) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f4405,plain,
    spl173_229,
    inference(avatar_split_clause,[],[f2512,f4403]) ).

tff(f4403,plain,
    ( spl173_229
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X0)
        | $less(X0,0)
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_229])]) ).

tff(f2512,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X0)
      | $less(X0,0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f4401,plain,
    spl173_228,
    inference(avatar_split_clause,[],[f2511,f4399]) ).

tff(f4399,plain,
    ( spl173_228
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,X0)
        | $less(0,X1)
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_228])]) ).

tff(f2511,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,X0)
      | $less(0,X1)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f4397,plain,
    spl173_227,
    inference(avatar_split_clause,[],[f2510,f4395]) ).

tff(f4395,plain,
    ( spl173_227
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,0)
        | $less(X0,0)
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_227])]) ).

tff(f2510,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,0)
      | $less(X0,0)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f4393,plain,
    spl173_226,
    inference(avatar_split_clause,[],[f2509,f4391]) ).

tff(f4391,plain,
    ( spl173_226
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,0)
        | $less(0,X1)
        | ~ sP3(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_226])]) ).

tff(f2509,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,0)
      | $less(0,X1)
      | ~ sP3(X0,X1) ),
    inference(cnf_transformation,[],[f1660]) ).

tff(f4389,plain,
    spl173_225,
    inference(avatar_split_clause,[],[f2508,f4387]) ).

tff(f4387,plain,
    ( spl173_225
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,'fun_app$o'('times$a'(X0),X1))
        | ~ sP2(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_225])]) ).

tff(f2508,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
      | ~ sP2(X1,X0) ),
    inference(cnf_transformation,[],[f1657]) ).

tff(f1657,plain,
    ! [X0: $int,X1: $int] :
      ( ( $less(0,'fun_app$o'('times$a'(X0),X1))
        | ~ sP2(X1,X0) )
      & ( sP2(X1,X0)
        | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ) ),
    inference(nnf_transformation,[],[f1368]) ).

tff(f1368,plain,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
    <=> sP2(X1,X0) ),
    inference(definition_folding,[],[f533,f1367]) ).

tff(f1367,plain,
    ! [X1: $int,X0: $int] :
      ( sP2(X1,X0)
    <=> ( ( $less(X1,0)
          & $less(X0,0) )
        | ( $less(0,X1)
          & $less(0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

tff(f533,axiom,
    ! [X0: $int,X1: $int] :
      ( $less(0,'fun_app$o'('times$a'(X0),X1))
    <=> ( ( $less(X1,0)
          & $less(X0,0) )
        | ( $less(0,X1)
          & $less(0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).

tff(f4385,plain,
    spl173_224,
    inference(avatar_split_clause,[],[f2507,f4383]) ).

tff(f2507,plain,
    ! [X0: $int,X1: $int] :
      ( sP2(X1,X0)
      | ~ $less(0,'fun_app$o'('times$a'(X0),X1)) ),
    inference(cnf_transformation,[],[f1657]) ).

tff(f4381,plain,
    spl173_223,
    inference(avatar_split_clause,[],[f2506,f4379]) ).

tff(f4379,plain,
    ( spl173_223
  <=> ! [X0: $int,X1: $int] :
        ( sP2(X0,X1)
        | ~ $less(X0,0)
        | ~ $less(X1,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_223])]) ).

tff(f2506,plain,
    ! [X0: $int,X1: $int] :
      ( sP2(X0,X1)
      | ~ $less(X0,0)
      | ~ $less(X1,0) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f1656,plain,
    ! [X0: $int,X1: $int] :
      ( ( sP2(X0,X1)
        | ( ( ~ $less(X0,0)
            | ~ $less(X1,0) )
          & ( ~ $less(0,X0)
            | ~ $less(0,X1) ) ) )
      & ( ( $less(X0,0)
          & $less(X1,0) )
        | ( $less(0,X0)
          & $less(0,X1) )
        | ~ sP2(X0,X1) ) ),
    inference(rectify,[],[f1655]) ).

tff(f1655,plain,
    ! [X1: $int,X0: $int] :
      ( ( sP2(X1,X0)
        | ( ( ~ $less(X1,0)
            | ~ $less(X0,0) )
          & ( ~ $less(0,X1)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(X1,0)
          & $less(X0,0) )
        | ( $less(0,X1)
          & $less(0,X0) )
        | ~ sP2(X1,X0) ) ),
    inference(flattening,[],[f1654]) ).

tff(f1654,plain,
    ! [X1: $int,X0: $int] :
      ( ( sP2(X1,X0)
        | ( ( ~ $less(X1,0)
            | ~ $less(X0,0) )
          & ( ~ $less(0,X1)
            | ~ $less(0,X0) ) ) )
      & ( ( $less(X1,0)
          & $less(X0,0) )
        | ( $less(0,X1)
          & $less(0,X0) )
        | ~ sP2(X1,X0) ) ),
    inference(nnf_transformation,[],[f1367]) ).

tff(f4377,plain,
    spl173_222,
    inference(avatar_split_clause,[],[f2505,f4375]) ).

tff(f4375,plain,
    ( spl173_222
  <=> ! [X0: $int,X1: $int] :
        ( sP2(X0,X1)
        | ~ $less(0,X0)
        | ~ $less(0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_222])]) ).

tff(f2505,plain,
    ! [X0: $int,X1: $int] :
      ( sP2(X0,X1)
      | ~ $less(0,X0)
      | ~ $less(0,X1) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f4373,plain,
    ( spl173_221
    | ~ spl173_1
    | ~ spl173_143 ),
    inference(avatar_split_clause,[],[f4073,f3833,f3104,f4370]) ).

tff(f4370,plain,
    ( spl173_221
  <=> ( 0 = 'of_nat$'(sK19(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_221])]) ).

tff(f3104,plain,
    ( spl173_1
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_1])]) ).

tff(f3833,plain,
    ( spl173_143
  <=> ! [X0: $int] :
        ( ( 'of_nat$'(sK19(X0)) = X0 )
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_143])]) ).

tff(f4073,plain,
    ( ( 0 = 'of_nat$'(sK19(0)) )
    | ~ spl173_1
    | ~ spl173_143 ),
    inference(resolution,[],[f3834,f3105]) ).

tff(f3105,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl173_1 ),
    inference(avatar_component_clause,[],[f3104]) ).

tff(f3834,plain,
    ( ! [X0: $int] :
        ( $less(X0,0)
        | ( 'of_nat$'(sK19(X0)) = X0 ) )
    | ~ spl173_143 ),
    inference(avatar_component_clause,[],[f3833]) ).

tff(f4368,plain,
    spl173_220,
    inference(avatar_split_clause,[],[f2504,f4366]) ).

tff(f4366,plain,
    ( spl173_220
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,0)
        | $less(0,X0)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_220])]) ).

tff(f2504,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,0)
      | $less(0,X0)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f4364,plain,
    spl173_219,
    inference(avatar_split_clause,[],[f2503,f4362]) ).

tff(f4362,plain,
    ( spl173_219
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,0)
        | $less(0,X1)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_219])]) ).

tff(f2503,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,0)
      | $less(0,X1)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f4360,plain,
    spl173_218,
    inference(avatar_split_clause,[],[f2502,f4358]) ).

tff(f4358,plain,
    ( spl173_218
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,0)
        | $less(0,X0)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_218])]) ).

tff(f2502,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,0)
      | $less(0,X0)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f4356,plain,
    spl173_217,
    inference(avatar_split_clause,[],[f2501,f4354]) ).

tff(f4354,plain,
    ( spl173_217
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,0)
        | $less(0,X1)
        | ~ sP2(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_217])]) ).

tff(f2501,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X1,0)
      | $less(0,X1)
      | ~ sP2(X0,X1) ),
    inference(cnf_transformation,[],[f1656]) ).

tff(f4352,plain,
    spl173_216,
    inference(avatar_split_clause,[],[f2500,f4350]) ).

tff(f4350,plain,
    ( spl173_216
  <=> ! [X0: $real,X1: $real] :
        ( $less('fun_app$r'('times$'(X0),X1),0.0)
        | ~ sP1(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_216])]) ).

tff(f2500,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
      | ~ sP1(X1,X0) ),
    inference(cnf_transformation,[],[f1653]) ).

tff(f1653,plain,
    ! [X0: $real,X1: $real] :
      ( ( $less('fun_app$r'('times$'(X0),X1),0.0)
        | ~ sP1(X1,X0) )
      & ( sP1(X1,X0)
        | ~ $less('fun_app$r'('times$'(X0),X1),0.0) ) ),
    inference(nnf_transformation,[],[f1366]) ).

tff(f1366,plain,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
    <=> sP1(X1,X0) ),
    inference(definition_folding,[],[f524,f1365]) ).

tff(f1365,plain,
    ! [X1: $real,X0: $real] :
      ( sP1(X1,X0)
    <=> ( ( $less(0.0,X1)
          & $less(X0,0.0) )
        | ( $less(X1,0.0)
          & $less(0.0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

tff(f524,axiom,
    ! [X0: $real,X1: $real] :
      ( $less('fun_app$r'('times$'(X0),X1),0.0)
    <=> ( ( $less(0.0,X1)
          & $less(X0,0.0) )
        | ( $less(X1,0.0)
          & $less(0.0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).

tff(f4348,plain,
    spl173_215,
    inference(avatar_split_clause,[],[f2499,f4346]) ).

tff(f4346,plain,
    ( spl173_215
  <=> ! [X0: $real,X1: $real] :
        ( sP1(X1,X0)
        | ~ $less('fun_app$r'('times$'(X0),X1),0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_215])]) ).

tff(f2499,plain,
    ! [X0: $real,X1: $real] :
      ( sP1(X1,X0)
      | ~ $less('fun_app$r'('times$'(X0),X1),0.0) ),
    inference(cnf_transformation,[],[f1653]) ).

tff(f4344,plain,
    spl173_214,
    inference(avatar_split_clause,[],[f2498,f4342]) ).

tff(f4342,plain,
    ( spl173_214
  <=> ! [X0: $real,X1: $real] :
        ( sP1(X0,X1)
        | ~ $less(0.0,X0)
        | ~ $less(X1,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_214])]) ).

tff(f2498,plain,
    ! [X0: $real,X1: $real] :
      ( sP1(X0,X1)
      | ~ $less(0.0,X0)
      | ~ $less(X1,0.0) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f1652,plain,
    ! [X0: $real,X1: $real] :
      ( ( sP1(X0,X1)
        | ( ( ~ $less(0.0,X0)
            | ~ $less(X1,0.0) )
          & ( ~ $less(X0,0.0)
            | ~ $less(0.0,X1) ) ) )
      & ( ( $less(0.0,X0)
          & $less(X1,0.0) )
        | ( $less(X0,0.0)
          & $less(0.0,X1) )
        | ~ sP1(X0,X1) ) ),
    inference(rectify,[],[f1651]) ).

tff(f1651,plain,
    ! [X1: $real,X0: $real] :
      ( ( sP1(X1,X0)
        | ( ( ~ $less(0.0,X1)
            | ~ $less(X0,0.0) )
          & ( ~ $less(X1,0.0)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(0.0,X1)
          & $less(X0,0.0) )
        | ( $less(X1,0.0)
          & $less(0.0,X0) )
        | ~ sP1(X1,X0) ) ),
    inference(flattening,[],[f1650]) ).

tff(f1650,plain,
    ! [X1: $real,X0: $real] :
      ( ( sP1(X1,X0)
        | ( ( ~ $less(0.0,X1)
            | ~ $less(X0,0.0) )
          & ( ~ $less(X1,0.0)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(0.0,X1)
          & $less(X0,0.0) )
        | ( $less(X1,0.0)
          & $less(0.0,X0) )
        | ~ sP1(X1,X0) ) ),
    inference(nnf_transformation,[],[f1365]) ).

tff(f4340,plain,
    spl173_213,
    inference(avatar_split_clause,[],[f2497,f4338]) ).

tff(f4338,plain,
    ( spl173_213
  <=> ! [X0: $real,X1: $real] :
        ( sP1(X0,X1)
        | ~ $less(X0,0.0)
        | ~ $less(0.0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_213])]) ).

tff(f2497,plain,
    ! [X0: $real,X1: $real] :
      ( sP1(X0,X1)
      | ~ $less(X0,0.0)
      | ~ $less(0.0,X1) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f4336,plain,
    spl173_212,
    inference(avatar_split_clause,[],[f2496,f4334]) ).

tff(f4334,plain,
    ( spl173_212
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,X0)
        | $less(X0,0.0)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_212])]) ).

tff(f2496,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X0)
      | $less(X0,0.0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f4332,plain,
    spl173_211,
    inference(avatar_split_clause,[],[f2495,f4330]) ).

tff(f4330,plain,
    ( spl173_211
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,X0)
        | $less(0.0,X1)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_211])]) ).

tff(f2495,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,X0)
      | $less(0.0,X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f4328,plain,
    ( spl173_210
    | ~ spl173_49
    | ~ spl173_140 ),
    inference(avatar_split_clause,[],[f4060,f3820,f3323,f4325]) ).

tff(f4325,plain,
    ( spl173_210
  <=> ( 1 = 'of_nat$'(sK18(1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_210])]) ).

tff(f3820,plain,
    ( spl173_140
  <=> ! [X0: $int] :
        ( ( 'of_nat$'(sK18(X0)) = X0 )
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_140])]) ).

tff(f4060,plain,
    ( ( 1 = 'of_nat$'(sK18(1)) )
    | ~ spl173_49
    | ~ spl173_140 ),
    inference(evaluation,[],[f4056]) ).

tff(f4056,plain,
    ( ( 1 = 'of_nat$'(sK18(1)) )
    | $less(0,0)
    | ~ spl173_49
    | ~ spl173_140 ),
    inference(resolution,[],[f3821,f3324]) ).

tff(f3821,plain,
    ( ! [X0: $int] :
        ( ~ $less(0,X0)
        | ( 'of_nat$'(sK18(X0)) = X0 ) )
    | ~ spl173_140 ),
    inference(avatar_component_clause,[],[f3820]) ).

tff(f4323,plain,
    spl173_209,
    inference(avatar_split_clause,[],[f2494,f4321]) ).

tff(f4321,plain,
    ( spl173_209
  <=> ! [X0: $real,X1: $real] :
        ( $less(X1,0.0)
        | $less(X0,0.0)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_209])]) ).

tff(f2494,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X1,0.0)
      | $less(X0,0.0)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f4319,plain,
    spl173_208,
    inference(avatar_split_clause,[],[f2493,f4317]) ).

tff(f4317,plain,
    ( spl173_208
  <=> ! [X0: $real,X1: $real] :
        ( $less(X1,0.0)
        | $less(0.0,X1)
        | ~ sP1(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_208])]) ).

tff(f2493,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X1,0.0)
      | $less(0.0,X1)
      | ~ sP1(X0,X1) ),
    inference(cnf_transformation,[],[f1652]) ).

tff(f4315,plain,
    spl173_207,
    inference(avatar_split_clause,[],[f2492,f4313]) ).

tff(f4313,plain,
    ( spl173_207
  <=> ! [X0: $real,X1: $real] :
        ( $less(0.0,'fun_app$r'('times$'(X0),X1))
        | ~ sP0(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_207])]) ).

tff(f2492,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
      | ~ sP0(X1,X0) ),
    inference(cnf_transformation,[],[f1649]) ).

tff(f1649,plain,
    ! [X0: $real,X1: $real] :
      ( ( $less(0.0,'fun_app$r'('times$'(X0),X1))
        | ~ sP0(X1,X0) )
      & ( sP0(X1,X0)
        | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ) ),
    inference(nnf_transformation,[],[f1364]) ).

tff(f1364,plain,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
    <=> sP0(X1,X0) ),
    inference(definition_folding,[],[f534,f1363]) ).

tff(f1363,plain,
    ! [X1: $real,X0: $real] :
      ( sP0(X1,X0)
    <=> ( ( $less(X1,0.0)
          & $less(X0,0.0) )
        | ( $less(0.0,X1)
          & $less(0.0,X0) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f534,axiom,
    ! [X0: $real,X1: $real] :
      ( $less(0.0,'fun_app$r'('times$'(X0),X1))
    <=> ( ( $less(X1,0.0)
          & $less(X0,0.0) )
        | ( $less(0.0,X1)
          & $less(0.0,X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).

tff(f4311,plain,
    spl173_206,
    inference(avatar_split_clause,[],[f2491,f4309]) ).

tff(f2491,plain,
    ! [X0: $real,X1: $real] :
      ( sP0(X1,X0)
      | ~ $less(0.0,'fun_app$r'('times$'(X0),X1)) ),
    inference(cnf_transformation,[],[f1649]) ).

tff(f4307,plain,
    spl173_205,
    inference(avatar_split_clause,[],[f2490,f4305]) ).

tff(f4305,plain,
    ( spl173_205
  <=> ! [X0: $real,X1: $real] :
        ( sP0(X0,X1)
        | ~ $less(X0,0.0)
        | ~ $less(X1,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_205])]) ).

tff(f2490,plain,
    ! [X0: $real,X1: $real] :
      ( sP0(X0,X1)
      | ~ $less(X0,0.0)
      | ~ $less(X1,0.0) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f1648,plain,
    ! [X0: $real,X1: $real] :
      ( ( sP0(X0,X1)
        | ( ( ~ $less(X0,0.0)
            | ~ $less(X1,0.0) )
          & ( ~ $less(0.0,X0)
            | ~ $less(0.0,X1) ) ) )
      & ( ( $less(X0,0.0)
          & $less(X1,0.0) )
        | ( $less(0.0,X0)
          & $less(0.0,X1) )
        | ~ sP0(X0,X1) ) ),
    inference(rectify,[],[f1647]) ).

tff(f1647,plain,
    ! [X1: $real,X0: $real] :
      ( ( sP0(X1,X0)
        | ( ( ~ $less(X1,0.0)
            | ~ $less(X0,0.0) )
          & ( ~ $less(0.0,X1)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(X1,0.0)
          & $less(X0,0.0) )
        | ( $less(0.0,X1)
          & $less(0.0,X0) )
        | ~ sP0(X1,X0) ) ),
    inference(flattening,[],[f1646]) ).

tff(f1646,plain,
    ! [X1: $real,X0: $real] :
      ( ( sP0(X1,X0)
        | ( ( ~ $less(X1,0.0)
            | ~ $less(X0,0.0) )
          & ( ~ $less(0.0,X1)
            | ~ $less(0.0,X0) ) ) )
      & ( ( $less(X1,0.0)
          & $less(X0,0.0) )
        | ( $less(0.0,X1)
          & $less(0.0,X0) )
        | ~ sP0(X1,X0) ) ),
    inference(nnf_transformation,[],[f1363]) ).

tff(f4303,plain,
    spl173_204,
    inference(avatar_split_clause,[],[f2489,f4301]) ).

tff(f4301,plain,
    ( spl173_204
  <=> ! [X0: $real,X1: $real] :
        ( sP0(X0,X1)
        | ~ $less(0.0,X0)
        | ~ $less(0.0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_204])]) ).

tff(f2489,plain,
    ! [X0: $real,X1: $real] :
      ( sP0(X0,X1)
      | ~ $less(0.0,X0)
      | ~ $less(0.0,X1) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f4299,plain,
    spl173_203,
    inference(avatar_split_clause,[],[f2488,f4297]) ).

tff(f4297,plain,
    ( spl173_203
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,0.0)
        | $less(0.0,X0)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_203])]) ).

tff(f2488,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,0.0)
      | $less(0.0,X0)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f4295,plain,
    spl173_202,
    inference(avatar_split_clause,[],[f2487,f4293]) ).

tff(f4293,plain,
    ( spl173_202
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,0.0)
        | $less(0.0,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_202])]) ).

tff(f2487,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,0.0)
      | $less(0.0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f4291,plain,
    spl173_201,
    inference(avatar_split_clause,[],[f2486,f4289]) ).

tff(f4289,plain,
    ( spl173_201
  <=> ! [X0: $real,X1: $real] :
        ( $less(X1,0.0)
        | $less(0.0,X0)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_201])]) ).

tff(f2486,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X1,0.0)
      | $less(0.0,X0)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f4287,plain,
    spl173_200,
    inference(avatar_split_clause,[],[f2485,f4285]) ).

tff(f4285,plain,
    ( spl173_200
  <=> ! [X0: $real,X1: $real] :
        ( $less(X1,0.0)
        | $less(0.0,X1)
        | ~ sP0(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_200])]) ).

tff(f2485,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X1,0.0)
      | $less(0.0,X1)
      | ~ sP0(X0,X1) ),
    inference(cnf_transformation,[],[f1648]) ).

tff(f4283,plain,
    ( spl173_199
    | ~ spl173_1
    | ~ spl173_138 ),
    inference(avatar_split_clause,[],[f4036,f3812,f3104,f4280]) ).

tff(f4280,plain,
    ( spl173_199
  <=> ( 0 = 'of_nat$'(sK17(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_199])]) ).

tff(f3812,plain,
    ( spl173_138
  <=> ! [X0: $int] :
        ( ( 'of_nat$'(sK17(X0)) = X0 )
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_138])]) ).

tff(f4036,plain,
    ( ( 0 = 'of_nat$'(sK17(0)) )
    | ~ spl173_1
    | ~ spl173_138 ),
    inference(resolution,[],[f3813,f3105]) ).

tff(f3813,plain,
    ( ! [X0: $int] :
        ( $less(X0,0)
        | ( 'of_nat$'(sK17(X0)) = X0 ) )
    | ~ spl173_138 ),
    inference(avatar_component_clause,[],[f3812]) ).

tff(f4278,plain,
    spl173_198,
    inference(avatar_split_clause,[],[f2112,f4276]) ).

tff(f4276,plain,
    ( spl173_198
  <=> ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),X1) = 'fun_app$r'('times$'(X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_198])]) ).

tff(f2112,plain,
    ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),X1) = 'fun_app$r'('times$'(X1),X0) ),
    inference(cnf_transformation,[],[f599]) ).

tff(f599,axiom,
    ! [X0: $real,X1: $real] : ( 'fun_app$r'('times$'(X0),X1) = 'fun_app$r'('times$'(X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).

tff(f4274,plain,
    spl173_197,
    inference(avatar_split_clause,[],[f2084,f4272]) ).

tff(f4272,plain,
    ( spl173_197
  <=> ! [X0: 'Nat$'] :
        ( $less(0.0,'fun_app$t'('of_nat$a',X0))
        | ~ $less(0,'of_nat$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_197])]) ).

tff(f2084,plain,
    ! [X0: 'Nat$'] :
      ( $less(0.0,'fun_app$t'('of_nat$a',X0))
      | ~ $less(0,'of_nat$'(X0)) ),
    inference(cnf_transformation,[],[f1452]) ).

tff(f1452,plain,
    ! [X0: 'Nat$'] :
      ( ( $less(0.0,'fun_app$t'('of_nat$a',X0))
        | ~ $less(0,'of_nat$'(X0)) )
      & ( $less(0,'of_nat$'(X0))
        | ~ $less(0.0,'fun_app$t'('of_nat$a',X0)) ) ),
    inference(nnf_transformation,[],[f187]) ).

tff(f187,axiom,
    ! [X0: 'Nat$'] :
      ( $less(0.0,'fun_app$t'('of_nat$a',X0))
    <=> $less(0,'of_nat$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).

tff(f4270,plain,
    spl173_196,
    inference(avatar_split_clause,[],[f2083,f4268]) ).

tff(f2083,plain,
    ! [X0: 'Nat$'] :
      ( $less(0,'of_nat$'(X0))
      | ~ $less(0.0,'fun_app$t'('of_nat$a',X0)) ),
    inference(cnf_transformation,[],[f1452]) ).

tff(f4266,plain,
    spl173_195,
    inference(avatar_split_clause,[],[f2082,f4264]) ).

tff(f4264,plain,
    ( spl173_195
  <=> ! [X0: 'Nat$'] :
        ( ~ $less(0.0,'fun_app$t'('of_nat$a',X0))
        | ( 0 != 'of_nat$'(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_195])]) ).

tff(f2082,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less(0.0,'fun_app$t'('of_nat$a',X0))
      | ( 0 != 'of_nat$'(X0) ) ),
    inference(cnf_transformation,[],[f1451]) ).

tff(f1451,plain,
    ! [X0: 'Nat$'] :
      ( ( ~ $less(0.0,'fun_app$t'('of_nat$a',X0))
        | ( 0 != 'of_nat$'(X0) ) )
      & ( ( 0 = 'of_nat$'(X0) )
        | $less(0.0,'fun_app$t'('of_nat$a',X0)) ) ),
    inference(nnf_transformation,[],[f664]) ).

tff(f664,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less(0.0,'fun_app$t'('of_nat$a',X0))
    <=> ( 0 = 'of_nat$'(X0) ) ),
    inference(theory_normalization,[],[f161]) ).

tff(f161,axiom,
    ! [X0: 'Nat$'] :
      ( $lesseq('fun_app$t'('of_nat$a',X0),0.0)
    <=> ( 0 = 'of_nat$'(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).

tff(f4262,plain,
    spl173_194,
    inference(avatar_split_clause,[],[f2081,f4260]) ).

tff(f4260,plain,
    ( spl173_194
  <=> ! [X0: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X0) )
        | $less(0.0,'fun_app$t'('of_nat$a',X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_194])]) ).

tff(f2081,plain,
    ! [X0: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | $less(0.0,'fun_app$t'('of_nat$a',X0)) ),
    inference(cnf_transformation,[],[f1451]) ).

tff(f4258,plain,
    spl173_193,
    inference(avatar_split_clause,[],[f2080,f4256]) ).

tff(f4256,plain,
    ( spl173_193
  <=> ! [X0: 'Nat$'] :
        ( ~ $less('fun_app$t'('of_nat$a',X0),1.0)
        | $less('of_nat$'(X0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_193])]) ).

tff(f2080,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less('fun_app$t'('of_nat$a',X0),1.0)
      | $less('of_nat$'(X0),1) ),
    inference(cnf_transformation,[],[f1450]) ).

tff(f1450,plain,
    ! [X0: 'Nat$'] :
      ( ( ~ $less('fun_app$t'('of_nat$a',X0),1.0)
        | $less('of_nat$'(X0),1) )
      & ( ~ $less('of_nat$'(X0),1)
        | $less('fun_app$t'('of_nat$a',X0),1.0) ) ),
    inference(nnf_transformation,[],[f663]) ).

tff(f663,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less('fun_app$t'('of_nat$a',X0),1.0)
    <=> ~ $less('of_nat$'(X0),1) ),
    inference(theory_normalization,[],[f404]) ).

tff(f404,axiom,
    ! [X0: 'Nat$'] :
      ( $lesseq(1.0,'fun_app$t'('of_nat$a',X0))
    <=> $lesseq(1,'of_nat$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).

tff(f4254,plain,
    spl173_192,
    inference(avatar_split_clause,[],[f2079,f4252]) ).

tff(f2079,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less('of_nat$'(X0),1)
      | $less('fun_app$t'('of_nat$a',X0),1.0) ),
    inference(cnf_transformation,[],[f1450]) ).

tff(f4250,plain,
    spl173_191,
    inference(avatar_split_clause,[],[f2076,f4248]) ).

tff(f4248,plain,
    ( spl173_191
  <=> ! [X0: 'Nat$'] :
        ( ( 'fun_app$t'('of_nat$a',X0) = 1.0 )
        | ( 'of_nat$'(X0) != 1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_191])]) ).

tff(f2076,plain,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$t'('of_nat$a',X0) = 1.0 )
      | ( 'of_nat$'(X0) != 1 ) ),
    inference(cnf_transformation,[],[f1448]) ).

tff(f1448,plain,
    ! [X0: 'Nat$'] :
      ( ( ( 'fun_app$t'('of_nat$a',X0) = 1.0 )
        | ( 'of_nat$'(X0) != 1 ) )
      & ( ( 'of_nat$'(X0) = 1 )
        | ( 'fun_app$t'('of_nat$a',X0) != 1.0 ) ) ),
    inference(nnf_transformation,[],[f169]) ).

tff(f169,axiom,
    ! [X0: 'Nat$'] :
      ( ( 'fun_app$t'('of_nat$a',X0) = 1.0 )
    <=> ( 'of_nat$'(X0) = 1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).

tff(f4246,plain,
    spl173_190,
    inference(avatar_split_clause,[],[f2075,f4244]) ).

tff(f4244,plain,
    ( spl173_190
  <=> ! [X0: 'Nat$'] :
        ( ( 'of_nat$'(X0) = 1 )
        | ( 'fun_app$t'('of_nat$a',X0) != 1.0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_190])]) ).

tff(f2075,plain,
    ! [X0: 'Nat$'] :
      ( ( 'of_nat$'(X0) = 1 )
      | ( 'fun_app$t'('of_nat$a',X0) != 1.0 ) ),
    inference(cnf_transformation,[],[f1448]) ).

tff(f4242,plain,
    spl173_189,
    inference(avatar_split_clause,[],[f2070,f4240]) ).

tff(f4240,plain,
    ( spl173_189
  <=> ! [X0: 'Nat$'] :
        ( ( 0.0 = 'fun_app$t'('of_nat$a',X0) )
        | ( 0 != 'of_nat$'(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_189])]) ).

tff(f2070,plain,
    ! [X0: 'Nat$'] :
      ( ( 0.0 = 'fun_app$t'('of_nat$a',X0) )
      | ( 0 != 'of_nat$'(X0) ) ),
    inference(cnf_transformation,[],[f1445]) ).

tff(f1445,plain,
    ! [X0: 'Nat$'] :
      ( ( ( 0.0 = 'fun_app$t'('of_nat$a',X0) )
        | ( 0 != 'of_nat$'(X0) ) )
      & ( ( 0 = 'of_nat$'(X0) )
        | ( 0.0 != 'fun_app$t'('of_nat$a',X0) ) ) ),
    inference(nnf_transformation,[],[f181]) ).

tff(f181,axiom,
    ! [X0: 'Nat$'] :
      ( ( 0.0 = 'fun_app$t'('of_nat$a',X0) )
    <=> ( 0 = 'of_nat$'(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).

tff(f4238,plain,
    ( spl173_188
    | ~ spl173_2
    | ~ spl173_129 ),
    inference(avatar_split_clause,[],[f3988,f3775,f3108,f4236]) ).

tff(f3108,plain,
    ( spl173_2
  <=> ! [X0: $real] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_2])]) ).

tff(f3775,plain,
    ( spl173_129
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1.0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_129])]) ).

tff(f3988,plain,
    ( ! [X0: $real] : $less(X0,$sum(X0,1.0))
    | ~ spl173_2
    | ~ spl173_129 ),
    inference(resolution,[],[f3776,f3109]) ).

tff(f3109,plain,
    ( ! [X0: $real] : ~ $less(X0,X0)
    | ~ spl173_2 ),
    inference(avatar_component_clause,[],[f3108]) ).

tff(f3776,plain,
    ( ! [X0: $real,X1: $real] :
        ( $less(X1,$sum(X0,1.0))
        | $less(X0,X1) )
    | ~ spl173_129 ),
    inference(avatar_component_clause,[],[f3775]) ).

tff(f4234,plain,
    spl173_187,
    inference(avatar_split_clause,[],[f2069,f4232]) ).

tff(f4232,plain,
    ( spl173_187
  <=> ! [X0: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X0) )
        | ( 0.0 != 'fun_app$t'('of_nat$a',X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_187])]) ).

tff(f2069,plain,
    ! [X0: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | ( 0.0 != 'fun_app$t'('of_nat$a',X0) ) ),
    inference(cnf_transformation,[],[f1445]) ).

tff(f4230,plain,
    spl173_186,
    inference(avatar_split_clause,[],[f1976,f4228]) ).

tff(f4228,plain,
    ( spl173_186
  <=> ! [X0: $int] :
        ( ( $uminus('of_nat$'(sK20(X0))) = X0 )
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_186])]) ).

tff(f1976,plain,
    ! [X0: $int] :
      ( ( $uminus('of_nat$'(sK20(X0))) = X0 )
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1398]) ).

tff(f1398,plain,
    ! [X0: $int] :
      ( ( $less(0,'of_nat$'(sK20(X0)))
        & ( $uminus('of_nat$'(sK20(X0))) = X0 ) )
      | ~ $less(X0,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f969,f1397]) ).

tff(f1397,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( $less(0,'of_nat$'(X1))
          & ( $uminus('of_nat$'(X1)) = X0 ) )
     => ( $less(0,'of_nat$'(sK20(X0)))
        & ( $uminus('of_nat$'(sK20(X0))) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f969,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( $less(0,'of_nat$'(X1))
          & ( $uminus('of_nat$'(X1)) = X0 ) )
      | ~ $less(X0,0) ),
    inference(ennf_transformation,[],[f882]) ).

tff(f882,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] :
            ~ ( $less(0,'of_nat$'(X1))
              & ( $uminus('of_nat$'(X1)) = X0 ) )
        & $less(X0,0) ),
    inference(true_and_false_elimination,[],[f439]) ).

tff(f439,axiom,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( $less(0,'of_nat$'(X1))
              & ( $uminus('of_nat$'(X1)) = X0 ) )
           => $false )
        & $less(X0,0) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).

tff(f4226,plain,
    spl173_185,
    inference(avatar_split_clause,[],[f1973,f4224]) ).

tff(f1973,plain,
    ! [X0: 'Nat$'] :
      ( $less(1,'of_nat$'(X0))
      | ~ $less(1.0,'fun_app$t'('of_nat$a',X0)) ),
    inference(cnf_transformation,[],[f967]) ).

tff(f967,plain,
    ! [X0: 'Nat$'] :
      ( $less(1,'of_nat$'(X0))
      | ~ $less(1.0,'fun_app$t'('of_nat$a',X0)) ),
    inference(ennf_transformation,[],[f388]) ).

tff(f388,axiom,
    ! [X0: 'Nat$'] :
      ( $less(1.0,'fun_app$t'('of_nat$a',X0))
     => $less(1,'of_nat$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).

tff(f4222,plain,
    spl173_184,
    inference(avatar_split_clause,[],[f862,f4220]) ).

tff(f4220,plain,
    ( spl173_184
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_184])]) ).

tff(f862,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f4218,plain,
    spl173_183,
    inference(avatar_split_clause,[],[f861,f4216]) ).

tff(f4216,plain,
    ( spl173_183
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_183])]) ).

tff(f861,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f4214,plain,
    spl173_182,
    inference(avatar_split_clause,[],[f844,f4212]) ).

tff(f4212,plain,
    ( spl173_182
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_182])]) ).

tff(f844,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f4210,plain,
    spl173_181,
    inference(avatar_split_clause,[],[f843,f4208]) ).

tff(f4208,plain,
    ( spl173_181
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_181])]) ).

tff(f843,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f4206,plain,
    ( spl173_180
    | ~ spl173_1
    | ~ spl173_127 ),
    inference(avatar_split_clause,[],[f3975,f3767,f3104,f4204]) ).

tff(f3767,plain,
    ( spl173_127
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_127])]) ).

tff(f3975,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl173_1
    | ~ spl173_127 ),
    inference(resolution,[],[f3768,f3105]) ).

tff(f3768,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl173_127 ),
    inference(avatar_component_clause,[],[f3767]) ).

tff(f4160,plain,
    ( spl173_179
    | ~ spl173_24
    | ~ spl173_54 ),
    inference(avatar_split_clause,[],[f3445,f3345,f3206,f4158]) ).

tff(f4158,plain,
    ( spl173_179
  <=> ! [X0: 'Nat$'] : ~ $less(0,$uminus('of_nat$'(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_179])]) ).

tff(f3206,plain,
    ( spl173_24
  <=> ( 0 = 'of_nat$'('to_nat$'('zero$d')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_24])]) ).

tff(f3345,plain,
    ( spl173_54
  <=> ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less('of_nat$'(X0),$uminus('of_nat$'(X1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_54])]) ).

tff(f3445,plain,
    ( ! [X0: 'Nat$'] : ~ $less(0,$uminus('of_nat$'(X0)))
    | ~ spl173_24
    | ~ spl173_54 ),
    inference(superposition,[],[f3346,f3208]) ).

tff(f3208,plain,
    ( ( 0 = 'of_nat$'('to_nat$'('zero$d')) )
    | ~ spl173_24 ),
    inference(avatar_component_clause,[],[f3206]) ).

tff(f3346,plain,
    ( ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less('of_nat$'(X0),$uminus('of_nat$'(X1)))
    | ~ spl173_54 ),
    inference(avatar_component_clause,[],[f3345]) ).

tff(f4125,plain,
    ( spl173_178
    | ~ spl173_20
    | ~ spl173_54 ),
    inference(avatar_split_clause,[],[f3444,f3345,f3186,f4123]) ).

tff(f4123,plain,
    ( spl173_178
  <=> ! [X0: 'Nat$'] : ~ $less(1,$uminus('of_nat$'(X0))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_178])]) ).

tff(f3444,plain,
    ( ! [X0: 'Nat$'] : ~ $less(1,$uminus('of_nat$'(X0)))
    | ~ spl173_20
    | ~ spl173_54 ),
    inference(superposition,[],[f3346,f3188]) ).

tff(f3974,plain,
    spl173_177,
    inference(avatar_split_clause,[],[f2992,f3972]) ).

tff(f3972,plain,
    ( spl173_177
  <=> ! [X2: 'Rows$',X0: 'A_rows_vec$'] : ( 'fun_app$d'('vec_nth$'('mat_row$'(X0,X2)),X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_177])]) ).

tff(f2992,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec$'] : ( 'fun_app$d'('vec_nth$'('mat_row$'(X0,X2)),X2) = X0 ),
    inference(equality_resolution,[],[f2558]) ).

tff(f2558,plain,
    ! [X2: 'Rows$',X0: 'A_rows_vec$',X1: 'Rows$'] :
      ( ( 'fun_app$d'('vec_nth$'('mat_row$'(X0,X1)),X2) = X0 )
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f1129]) ).

tff(f3970,plain,
    spl173_176,
    inference(avatar_split_clause,[],[f2991,f3968]) ).

tff(f3968,plain,
    ( spl173_176
  <=> ! [X2: 'Rows$',X0: 'A_cols_vec$'] : ( 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X2)),X2) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_176])]) ).

tff(f2991,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec$'] : ( 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X2)),X2) = X0 ),
    inference(equality_resolution,[],[f2556]) ).

tff(f2556,plain,
    ! [X2: 'Rows$',X0: 'A_cols_vec$',X1: 'Rows$'] :
      ( ( 'fun_app$e'('vec_nth$a'('mat_row$a'(X0,X1)),X2) = X0 )
      | ( X1 != X2 ) ),
    inference(cnf_transformation,[],[f1128]) ).

tff(f3966,plain,
    spl173_175,
    inference(avatar_split_clause,[],[f2668,f3964]) ).

tff(f3964,plain,
    ( spl173_175
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( ~ 'fun_app$s'(X0,sK55(X0,X1))
        | ~ sP12(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_175])]) ).

tff(f2668,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( ~ 'fun_app$s'(X0,sK55(X0,X1))
      | ~ sP12(X0,X1) ),
    inference(cnf_transformation,[],[f1705]) ).

tff(f3962,plain,
    spl173_174,
    inference(avatar_split_clause,[],[f2424,f3960]) ).

tff(f3960,plain,
    ( spl173_174
  <=> ! [X0: $int,X1: $int] :
        ( 'fun_app$b'('fun_app$c'('uu$',X0),X1)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_174])]) ).

tff(f2424,plain,
    ! [X0: $int,X1: $int] :
      ( 'fun_app$b'('fun_app$c'('uu$',X0),X1)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1608]) ).

tff(f1608,plain,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$b'('fun_app$c'('uu$',X0),X1)
        | ~ $less(X0,X1) )
      & ( $less(X0,X1)
        | ~ 'fun_app$b'('fun_app$c'('uu$',X0),X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: $int,X1: $int] :
      ( 'fun_app$b'('fun_app$c'('uu$',X0),X1)
    <=> $less(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).

tff(f3958,plain,
    spl173_173,
    inference(avatar_split_clause,[],[f2423,f3956]) ).

tff(f3956,plain,
    ( spl173_173
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | ~ 'fun_app$b'('fun_app$c'('uu$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_173])]) ).

tff(f2423,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | ~ 'fun_app$b'('fun_app$c'('uu$',X0),X1) ),
    inference(cnf_transformation,[],[f1608]) ).

tff(f3954,plain,
    spl173_172,
    inference(avatar_split_clause,[],[f2422,f3952]) ).

tff(f3952,plain,
    ( spl173_172
  <=> ! [X0: $real,X1: $real] :
        ( 'fun_app$'('fun_app$a'('uua$',X0),X1)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_172])]) ).

tff(f2422,plain,
    ! [X0: $real,X1: $real] :
      ( 'fun_app$'('fun_app$a'('uua$',X0),X1)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f1607,plain,
    ! [X0: $real,X1: $real] :
      ( ( 'fun_app$'('fun_app$a'('uua$',X0),X1)
        | ~ $less(X0,X1) )
      & ( $less(X0,X1)
        | ~ 'fun_app$'('fun_app$a'('uua$',X0),X1) ) ),
    inference(nnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $real,X1: $real] :
      ( 'fun_app$'('fun_app$a'('uua$',X0),X1)
    <=> $less(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).

tff(f3950,plain,
    spl173_171,
    inference(avatar_split_clause,[],[f2421,f3948]) ).

tff(f3948,plain,
    ( spl173_171
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,X1)
        | ~ 'fun_app$'('fun_app$a'('uua$',X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_171])]) ).

tff(f2421,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,X1)
      | ~ 'fun_app$'('fun_app$a'('uua$',X0),X1) ),
    inference(cnf_transformation,[],[f1607]) ).

tff(f3946,plain,
    spl173_170,
    inference(avatar_split_clause,[],[f2413,f3944]) ).

tff(f3944,plain,
    ( spl173_170
  <=> ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] :
        ( ( X0 = X1 )
        | ( 'vec_nth$'(X0) != 'vec_nth$'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_170])]) ).

tff(f2413,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] :
      ( ( X0 = X1 )
      | ( 'vec_nth$'(X0) != 'vec_nth$'(X1) ) ),
    inference(cnf_transformation,[],[f1603]) ).

tff(f1603,plain,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] :
      ( ( ( 'vec_nth$'(X0) = 'vec_nth$'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'vec_nth$'(X0) != 'vec_nth$'(X1) ) ) ),
    inference(nnf_transformation,[],[f20]) ).

tff(f20,axiom,
    ! [X0: 'A_rows_vec_rows_vec$',X1: 'A_rows_vec_rows_vec$'] :
      ( ( 'vec_nth$'(X0) = 'vec_nth$'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).

tff(f3942,plain,
    spl173_169,
    inference(avatar_split_clause,[],[f2411,f3940]) ).

tff(f3940,plain,
    ( spl173_169
  <=> ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] :
        ( ( X0 = X1 )
        | ( 'vec_nth$a'(X0) != 'vec_nth$a'(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_169])]) ).

tff(f2411,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] :
      ( ( X0 = X1 )
      | ( 'vec_nth$a'(X0) != 'vec_nth$a'(X1) ) ),
    inference(cnf_transformation,[],[f1602]) ).

tff(f1602,plain,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] :
      ( ( ( 'vec_nth$a'(X0) = 'vec_nth$a'(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( 'vec_nth$a'(X0) != 'vec_nth$a'(X1) ) ) ),
    inference(nnf_transformation,[],[f21]) ).

tff(f21,axiom,
    ! [X0: 'A_cols_vec_rows_vec$',X1: 'A_cols_vec_rows_vec$'] :
      ( ( 'vec_nth$a'(X0) = 'vec_nth$a'(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).

tff(f3938,plain,
    spl173_168,
    inference(avatar_split_clause,[],[f2409,f3936]) ).

tff(f3936,plain,
    ( spl173_168
  <=> ! [X0: $int,X1: $int] :
        ( ( X0 = X1 )
        | ( $uminus(X0) != $uminus(X1) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_168])]) ).

tff(f2409,plain,
    ! [X0: $int,X1: $int] :
      ( ( X0 = X1 )
      | ( $uminus(X0) != $uminus(X1) ) ),
    inference(cnf_transformation,[],[f1601]) ).

tff(f1601,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( $uminus(X0) = $uminus(X1) )
        | ( X0 != X1 ) )
      & ( ( X0 = X1 )
        | ( $uminus(X0) != $uminus(X1) ) ) ),
    inference(nnf_transformation,[],[f440]) ).

tff(f440,axiom,
    ! [X0: $int,X1: $int] :
      ( ( $uminus(X0) = $uminus(X1) )
    <=> ( X0 = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).

tff(f3934,plain,
    spl173_167,
    inference(avatar_split_clause,[],[f2397,f3932]) ).

tff(f3932,plain,
    ( spl173_167
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$uminus(X0))
        | $less(X0,$uminus(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_167])]) ).

tff(f2397,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$uminus(X0))
      | $less(X0,$uminus(X1)) ),
    inference(cnf_transformation,[],[f1594]) ).

tff(f1594,plain,
    ! [X0: $int,X1: $int] :
      ( ( ~ $less(X1,$uminus(X0))
        | $less(X0,$uminus(X1)) )
      & ( ~ $less(X0,$uminus(X1))
        | $less(X1,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f762]) ).

tff(f762,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,$uminus(X0))
    <=> ~ $less(X0,$uminus(X1)) ),
    inference(theory_normalization,[],[f586]) ).

tff(f586,axiom,
    ! [X0: $int,X1: $int] :
      ( $lesseq($uminus(X0),X1)
    <=> $lesseq($uminus(X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).

tff(f3930,plain,
    spl173_166,
    inference(avatar_split_clause,[],[f2395,f3928]) ).

tff(f3928,plain,
    ( spl173_166
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less($uminus(X1),X0)
        | $less($uminus(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_166])]) ).

tff(f2395,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less($uminus(X1),X0)
      | $less($uminus(X0),X1) ),
    inference(cnf_transformation,[],[f1593]) ).

tff(f1593,plain,
    ! [X0: $int,X1: $int] :
      ( ( ~ $less($uminus(X1),X0)
        | $less($uminus(X0),X1) )
      & ( ~ $less($uminus(X0),X1)
        | $less($uminus(X1),X0) ) ),
    inference(nnf_transformation,[],[f761]) ).

tff(f761,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less($uminus(X1),X0)
    <=> ~ $less($uminus(X0),X1) ),
    inference(theory_normalization,[],[f588]) ).

tff(f588,axiom,
    ! [X0: $int,X1: $int] :
      ( $lesseq(X0,$uminus(X1))
    <=> $lesseq(X1,$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).

tff(f3926,plain,
    spl173_165,
    inference(avatar_split_clause,[],[f2393,f3924]) ).

tff(f3924,plain,
    ( spl173_165
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X1,$uminus(X0))
        | $less(X0,$uminus(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_165])]) ).

tff(f2393,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,$uminus(X0))
      | $less(X0,$uminus(X1)) ),
    inference(cnf_transformation,[],[f1592]) ).

tff(f1592,plain,
    ! [X0: $real,X1: $real] :
      ( ( ~ $less(X1,$uminus(X0))
        | $less(X0,$uminus(X1)) )
      & ( ~ $less(X0,$uminus(X1))
        | $less(X1,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f760]) ).

tff(f760,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,$uminus(X0))
    <=> ~ $less(X0,$uminus(X1)) ),
    inference(theory_normalization,[],[f587]) ).

tff(f587,axiom,
    ! [X0: $real,X1: $real] :
      ( $lesseq($uminus(X0),X1)
    <=> $lesseq($uminus(X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).

tff(f3922,plain,
    spl173_164,
    inference(avatar_split_clause,[],[f2391,f3920]) ).

tff(f3920,plain,
    ( spl173_164
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less($uminus(X1),X0)
        | $less($uminus(X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_164])]) ).

tff(f2391,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less($uminus(X1),X0)
      | $less($uminus(X0),X1) ),
    inference(cnf_transformation,[],[f1591]) ).

tff(f1591,plain,
    ! [X0: $real,X1: $real] :
      ( ( ~ $less($uminus(X1),X0)
        | $less($uminus(X0),X1) )
      & ( ~ $less($uminus(X0),X1)
        | $less($uminus(X1),X0) ) ),
    inference(nnf_transformation,[],[f759]) ).

tff(f759,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less($uminus(X1),X0)
    <=> ~ $less($uminus(X0),X1) ),
    inference(theory_normalization,[],[f589]) ).

tff(f589,axiom,
    ! [X0: $real,X1: $real] :
      ( $lesseq(X0,$uminus(X1))
    <=> $lesseq(X1,$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).

tff(f3918,plain,
    ( ~ spl173_163
    | ~ spl173_56
    | ~ spl173_142 ),
    inference(avatar_split_clause,[],[f3873,f3828,f3353,f3915]) ).

tff(f3915,plain,
    ( spl173_163
  <=> $less(sK34(1),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_163])]) ).

tff(f3828,plain,
    ( spl173_142
  <=> $less(0,sK34(1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_142])]) ).

tff(f3873,plain,
    ( ~ $less(sK34(1),0)
    | ~ spl173_56
    | ~ spl173_142 ),
    inference(resolution,[],[f3830,f3354]) ).

tff(f3830,plain,
    ( $less(0,sK34(1))
    | ~ spl173_142 ),
    inference(avatar_component_clause,[],[f3828]) ).

tff(f3913,plain,
    spl173_162,
    inference(avatar_split_clause,[],[f2268,f3911]) ).

tff(f3911,plain,
    ( spl173_162
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | $less(X1,sK45(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_162])]) ).

tff(f2268,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | $less(X1,sK45(X0,X1)) ),
    inference(cnf_transformation,[],[f1506]) ).

tff(f1506,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ( $less(X1,sK45(X0,X1))
        & $less(sK45(X0,X1),X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1126,f1505]) ).

tff(f1505,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X1,X2)
          & $less(X2,X0) )
     => ( $less(X1,sK45(X0,X1))
        & $less(sK45(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

tff(f1126,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ? [X2: $real] :
          ( $less(X1,X2)
          & $less(X2,X0) ) ),
    inference(ennf_transformation,[],[f723]) ).

tff(f723,plain,
    ! [X0: $real,X1: $real] :
      ( ! [X2: $real] :
          ( $less(X2,X0)
         => ~ $less(X1,X2) )
     => ~ $less(X1,X0) ),
    inference(theory_normalization,[],[f296]) ).

tff(f296,axiom,
    ! [X0: $real,X1: $real] :
      ( ! [X2: $real] :
          ( $less(X2,X0)
         => $lesseq(X2,X1) )
     => $lesseq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).

tff(f3909,plain,
    spl173_161,
    inference(avatar_split_clause,[],[f2267,f3907]) ).

tff(f3907,plain,
    ( spl173_161
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | $less(sK45(X0,X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_161])]) ).

tff(f2267,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | $less(sK45(X0,X1),X0) ),
    inference(cnf_transformation,[],[f1506]) ).

tff(f3905,plain,
    spl173_160,
    inference(avatar_split_clause,[],[f2266,f3903]) ).

tff(f3903,plain,
    ( spl173_160
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X0,X1)
        | $less(sK44(X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_160])]) ).

tff(f2266,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | $less(sK44(X0,X1),X1) ),
    inference(cnf_transformation,[],[f1504]) ).

tff(f1504,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | ( $less(sK44(X0,X1),X1)
        & $less(X0,sK44(X0,X1)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1125,f1503]) ).

tff(f1503,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X0,X2) )
     => ( $less(sK44(X0,X1),X1)
        & $less(X0,sK44(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1125,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X0,X2) ) ),
    inference(ennf_transformation,[],[f722]) ).

tff(f722,plain,
    ! [X0: $real,X1: $real] :
      ( ! [X2: $real] :
          ( $less(X0,X2)
         => ~ $less(X2,X1) )
     => ~ $less(X0,X1) ),
    inference(theory_normalization,[],[f295]) ).

tff(f295,axiom,
    ! [X0: $real,X1: $real] :
      ( ! [X2: $real] :
          ( $less(X0,X2)
         => $lesseq(X1,X2) )
     => $lesseq(X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).

tff(f3901,plain,
    spl173_159,
    inference(avatar_split_clause,[],[f2265,f3899]) ).

tff(f3899,plain,
    ( spl173_159
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less(X0,X1)
        | $less(X0,sK44(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_159])]) ).

tff(f2265,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | $less(X0,sK44(X0,X1)) ),
    inference(cnf_transformation,[],[f1504]) ).

tff(f3897,plain,
    spl173_158,
    inference(avatar_split_clause,[],[f2180,f3895]) ).

tff(f3895,plain,
    ( spl173_158
  <=> ! [X0: $int,X1: $int] :
        ( $less($uminus(X1),$uminus(X0))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_158])]) ).

tff(f2180,plain,
    ! [X0: $int,X1: $int] :
      ( $less($uminus(X1),$uminus(X0))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1015]) ).

tff(f1015,plain,
    ! [X0: $int,X1: $int] :
      ( $less($uminus(X1),$uminus(X0))
      | ~ $less(X0,X1) ),
    inference(ennf_transformation,[],[f612]) ).

tff(f612,axiom,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
     => $less($uminus(X1),$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).

tff(f3893,plain,
    spl173_157,
    inference(avatar_split_clause,[],[f2172,f3891]) ).

tff(f3891,plain,
    ( spl173_157
  <=> ! [X0: $real,X1: $real] :
        ( $less(sK38(X0,X1),X1)
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_157])]) ).

tff(f2172,plain,
    ! [X0: $real,X1: $real] :
      ( $less(sK38(X0,X1),X1)
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1492]) ).

tff(f1492,plain,
    ! [X0: $real,X1: $real] :
      ( ( $less(sK38(X0,X1),X1)
        & $less(X0,sK38(X0,X1)) )
      | ~ $less(X0,X1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1007,f1491]) ).

tff(f1491,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X0,X2) )
     => ( $less(sK38(X0,X1),X1)
        & $less(X0,sK38(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f1007,plain,
    ! [X0: $real,X1: $real] :
      ( ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X0,X2) )
      | ~ $less(X0,X1) ),
    inference(ennf_transformation,[],[f280]) ).

tff(f280,axiom,
    ! [X0: $real,X1: $real] :
      ( $less(X0,X1)
     => ? [X2: $real] :
          ( $less(X2,X1)
          & $less(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).

tff(f3889,plain,
    spl173_156,
    inference(avatar_split_clause,[],[f2171,f3887]) ).

tff(f3887,plain,
    ( spl173_156
  <=> ! [X0: $real,X1: $real] :
        ( $less(X0,sK38(X0,X1))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_156])]) ).

tff(f2171,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,sK38(X0,X1))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1492]) ).

tff(f3885,plain,
    spl173_155,
    inference(avatar_split_clause,[],[f2167,f3883]) ).

tff(f3883,plain,
    ( spl173_155
  <=> ! [X0: $real,X1: $real] :
        ( $less($uminus(X1),$uminus(X0))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_155])]) ).

tff(f2167,plain,
    ! [X0: $real,X1: $real] :
      ( $less($uminus(X1),$uminus(X0))
      | ~ $less(X0,X1) ),
    inference(cnf_transformation,[],[f1003]) ).

tff(f1003,plain,
    ! [X0: $real,X1: $real] :
      ( $less($uminus(X1),$uminus(X0))
      | ~ $less(X0,X1) ),
    inference(ennf_transformation,[],[f611]) ).

tff(f611,axiom,
    ! [X0: $real,X1: $real] :
      ( $less(X0,X1)
     => $less($uminus(X1),$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom609) ).

tff(f3881,plain,
    spl173_154,
    inference(avatar_split_clause,[],[f2154,f3879]) ).

tff(f3879,plain,
    ( spl173_154
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less($uminus(X0),$uminus(X1))
        | $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_154])]) ).

tff(f2154,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less($uminus(X0),$uminus(X1))
      | $less(X1,X0) ),
    inference(cnf_transformation,[],[f991]) ).

tff(f991,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less($uminus(X0),$uminus(X1))
      | $less(X1,X0) ),
    inference(ennf_transformation,[],[f689]) ).

tff(f689,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X1,X0)
     => ~ $less($uminus(X0),$uminus(X1)) ),
    inference(theory_normalization,[],[f584]) ).

tff(f584,axiom,
    ! [X0: $int,X1: $int] :
      ( $lesseq(X0,X1)
     => $lesseq($uminus(X1),$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom582) ).

tff(f3877,plain,
    spl173_153,
    inference(avatar_split_clause,[],[f2147,f3875]) ).

tff(f3875,plain,
    ( spl173_153
  <=> ! [X0: $real,X1: $real] :
        ( ~ $less($uminus(X0),$uminus(X1))
        | $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_153])]) ).

tff(f2147,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less($uminus(X0),$uminus(X1))
      | $less(X1,X0) ),
    inference(cnf_transformation,[],[f985]) ).

tff(f985,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less($uminus(X0),$uminus(X1))
      | $less(X1,X0) ),
    inference(ennf_transformation,[],[f684]) ).

tff(f684,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
     => ~ $less($uminus(X0),$uminus(X1)) ),
    inference(theory_normalization,[],[f585]) ).

tff(f585,axiom,
    ! [X0: $real,X1: $real] :
      ( $lesseq(X0,X1)
     => $lesseq($uminus(X1),$uminus(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom583) ).

tff(f3871,plain,
    spl173_152,
    inference(avatar_split_clause,[],[f2111,f3869]) ).

tff(f3869,plain,
    ( spl173_152
  <=> ! [X0: 'Rows$',X1: 'A_rows_vec$'] : ( 'fun_app$d'('vec_nth$'('axis$'(X0,X1)),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_152])]) ).

tff(f2111,plain,
    ! [X0: 'Rows$',X1: 'A_rows_vec$'] : ( 'fun_app$d'('vec_nth$'('axis$'(X0,X1)),X0) = X1 ),
    inference(cnf_transformation,[],[f46]) ).

tff(f46,axiom,
    ! [X0: 'Rows$',X1: 'A_rows_vec$'] : ( 'fun_app$d'('vec_nth$'('axis$'(X0,X1)),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).

tff(f3867,plain,
    spl173_151,
    inference(avatar_split_clause,[],[f2110,f3865]) ).

tff(f3865,plain,
    ( spl173_151
  <=> ! [X0: 'Rows$',X1: 'A_cols_vec$'] : ( 'fun_app$e'('vec_nth$a'('axis$a'(X0,X1)),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_151])]) ).

tff(f2110,plain,
    ! [X0: 'Rows$',X1: 'A_cols_vec$'] : ( 'fun_app$e'('vec_nth$a'('axis$a'(X0,X1)),X0) = X1 ),
    inference(cnf_transformation,[],[f47]) ).

tff(f47,axiom,
    ! [X0: 'Rows$',X1: 'A_cols_vec$'] : ( 'fun_app$e'('vec_nth$a'('axis$a'(X0,X1)),X0) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).

tff(f3863,plain,
    spl173_150,
    inference(avatar_split_clause,[],[f2109,f3861]) ).

tff(f3861,plain,
    ( spl173_150
  <=> ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('of_nat$b'(X0)),X1) = 'of_nat$c'(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_150])]) ).

tff(f2109,plain,
    ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('of_nat$b'(X0)),X1) = 'of_nat$c'(X0) ),
    inference(cnf_transformation,[],[f208]) ).

tff(f208,axiom,
    ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('of_nat$b'(X0)),X1) = 'of_nat$c'(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).

tff(f3859,plain,
    spl173_149,
    inference(avatar_split_clause,[],[f2108,f3857]) ).

tff(f3857,plain,
    ( spl173_149
  <=> ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('of_nat$d'(X0)),X1) = 'of_nat$e'(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_149])]) ).

tff(f2108,plain,
    ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('of_nat$d'(X0)),X1) = 'of_nat$e'(X0) ),
    inference(cnf_transformation,[],[f209]) ).

tff(f209,axiom,
    ! [X0: 'Nat$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('of_nat$d'(X0)),X1) = 'of_nat$e'(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).

tff(f3855,plain,
    spl173_148,
    inference(avatar_split_clause,[],[f2073,f3853]) ).

tff(f3853,plain,
    ( spl173_148
  <=> ! [X0: 'Rows$'] :
        ( ( 'zero$d' = X0 )
        | ( 'of_nat$'('to_nat$'(X0)) != 0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_148])]) ).

tff(f2073,plain,
    ! [X0: 'Rows$'] :
      ( ( 'zero$d' = X0 )
      | ( 'of_nat$'('to_nat$'(X0)) != 0 ) ),
    inference(cnf_transformation,[],[f1447]) ).

tff(f1447,plain,
    ! [X0: 'Rows$'] :
      ( ( ( 'of_nat$'('to_nat$'(X0)) = 0 )
        | ( 'zero$d' != X0 ) )
      & ( ( 'zero$d' = X0 )
        | ( 'of_nat$'('to_nat$'(X0)) != 0 ) ) ),
    inference(nnf_transformation,[],[f74]) ).

tff(f74,axiom,
    ! [X0: 'Rows$'] :
      ( ( 'of_nat$'('to_nat$'(X0)) = 0 )
    <=> ( 'zero$d' = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).

tff(f3851,plain,
    spl173_147,
    inference(avatar_split_clause,[],[f2056,f3849]) ).

tff(f3849,plain,
    ( spl173_147
  <=> ! [X0: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X0) )
        | ~ $less('of_nat$'(X0),1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_147])]) ).

tff(f2056,plain,
    ! [X0: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | ~ $less('of_nat$'(X0),1) ),
    inference(cnf_transformation,[],[f1439]) ).

tff(f1439,plain,
    ! [X0: 'Nat$'] :
      ( ( $less('of_nat$'(X0),1)
        | ( 0 != 'of_nat$'(X0) ) )
      & ( ( 0 = 'of_nat$'(X0) )
        | ~ $less('of_nat$'(X0),1) ) ),
    inference(nnf_transformation,[],[f172]) ).

tff(f172,axiom,
    ! [X0: 'Nat$'] :
      ( $less('of_nat$'(X0),1)
    <=> ( 0 = 'of_nat$'(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).

tff(f3847,plain,
    spl173_146,
    inference(avatar_split_clause,[],[f1979,f3845]) ).

tff(f3845,plain,
    ( spl173_146
  <=> ! [X0: $int] :
        ( $less(0,'of_nat$'(sK21(X0)))
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_146])]) ).

tff(f1979,plain,
    ! [X0: $int] :
      ( $less(0,'of_nat$'(sK21(X0)))
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f1400,plain,
    ! [X0: $int] :
      ( ( $less(0,'of_nat$'(sK21(X0)))
        & ( 'of_nat$'(sK21(X0)) = X0 ) )
      | ~ $less(0,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f970,f1399]) ).

tff(f1399,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( $less(0,'of_nat$'(X1))
          & ( 'of_nat$'(X1) = X0 ) )
     => ( $less(0,'of_nat$'(sK21(X0)))
        & ( 'of_nat$'(sK21(X0)) = X0 ) ) ),
    introduced(choice_axiom,[]) ).

tff(f970,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( $less(0,'of_nat$'(X1))
          & ( 'of_nat$'(X1) = X0 ) )
      | ~ $less(0,X0) ),
    inference(ennf_transformation,[],[f883]) ).

tff(f883,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] :
            ~ ( $less(0,'of_nat$'(X1))
              & ( 'of_nat$'(X1) = X0 ) )
        & $less(0,X0) ),
    inference(true_and_false_elimination,[],[f405]) ).

tff(f405,axiom,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( $less(0,'of_nat$'(X1))
              & ( 'of_nat$'(X1) = X0 ) )
           => $false )
        & $less(0,X0) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).

tff(f3843,plain,
    spl173_145,
    inference(avatar_split_clause,[],[f1978,f3841]) ).

tff(f1978,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK21(X0)) = X0 )
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1400]) ).

tff(f3839,plain,
    spl173_144,
    inference(avatar_split_clause,[],[f1977,f3837]) ).

tff(f3837,plain,
    ( spl173_144
  <=> ! [X0: $int] :
        ( $less(0,'of_nat$'(sK20(X0)))
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_144])]) ).

tff(f1977,plain,
    ! [X0: $int] :
      ( $less(0,'of_nat$'(sK20(X0)))
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f1398]) ).

tff(f3835,plain,
    spl173_143,
    inference(avatar_split_clause,[],[f1975,f3833]) ).

tff(f1975,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK19(X0)) = X0 )
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f1396]) ).

tff(f1396,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK19(X0)) = X0 )
      | $less(X0,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f968,f1395]) ).

tff(f1395,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 )
     => ( 'of_nat$'(sK19(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f968,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 )
      | $less(X0,0) ),
    inference(ennf_transformation,[],[f881]) ).

tff(f881,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] : ( 'of_nat$'(X1) != X0 )
        & ~ $less(X0,0) ),
    inference(flattening,[],[f880]) ).

tff(f880,plain,
    ! [X0: $int] :
      ~ ( ! [X1: 'Nat$'] :
            ( ~ 'of_nat$'(X1) = X0 )
        & ~ $less(X0,0) ),
    inference(true_and_false_elimination,[],[f649]) ).

tff(f649,plain,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( 'of_nat$'(X1) = X0 )
           => $false )
        & ~ $less(X0,0) )
     => $false ),
    inference(theory_normalization,[],[f409]) ).

tff(f409,axiom,
    ! [X0: $int] :
      ( ( ! [X1: 'Nat$'] :
            ( ( 'of_nat$'(X1) = X0 )
           => $false )
        & $lesseq(0,X0) )
     => $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom407) ).

tff(f3831,plain,
    ( spl173_142
    | ~ spl173_49
    | ~ spl173_105 ),
    inference(avatar_split_clause,[],[f3765,f3610,f3323,f3828]) ).

tff(f3610,plain,
    ( spl173_105
  <=> ! [X0: $int] : ~ $less(sK34(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_105])]) ).

tff(f3765,plain,
    ( $less(0,sK34(1))
    | ~ spl173_49
    | ~ spl173_105 ),
    inference(resolution,[],[f3611,f3324]) ).

tff(f3611,plain,
    ( ! [X0: $int] : ~ $less(sK34(X0),X0)
    | ~ spl173_105 ),
    inference(avatar_component_clause,[],[f3610]) ).

tff(f3826,plain,
    spl173_141,
    inference(avatar_split_clause,[],[f1970,f3824]) ).

tff(f3824,plain,
    ( spl173_141
  <=> ! [X0: 'Nat$'] :
        ( ( 0 = 'of_nat$'(X0) )
        | $less(0,'of_nat$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_141])]) ).

tff(f1970,plain,
    ! [X0: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | $less(0,'of_nat$'(X0)) ),
    inference(cnf_transformation,[],[f965]) ).

tff(f965,plain,
    ! [X0: 'Nat$'] :
      ( ( 0 = 'of_nat$'(X0) )
      | $less(0,'of_nat$'(X0)) ),
    inference(ennf_transformation,[],[f648]) ).

tff(f648,plain,
    ! [X0: 'Nat$'] :
      ( ~ $less(0,'of_nat$'(X0))
     => ( 0 = 'of_nat$'(X0) ) ),
    inference(theory_normalization,[],[f137]) ).

tff(f137,axiom,
    ! [X0: 'Nat$'] :
      ( $lesseq('of_nat$'(X0),0)
     => ( 0 = 'of_nat$'(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).

tff(f3822,plain,
    spl173_140,
    inference(avatar_split_clause,[],[f1969,f3820]) ).

tff(f1969,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK18(X0)) = X0 )
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1394]) ).

tff(f1394,plain,
    ! [X0: $int] :
      ( ( ( 'of_nat$'(sK18(X0)) = X0 )
        & $less(0,'of_nat$'(sK18(X0))) )
      | ~ $less(0,X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f964,f1393]) ).

tff(f1393,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( ( 'of_nat$'(X1) = X0 )
          & $less(0,'of_nat$'(X1)) )
     => ( ( 'of_nat$'(sK18(X0)) = X0 )
        & $less(0,'of_nat$'(sK18(X0))) ) ),
    introduced(choice_axiom,[]) ).

tff(f964,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] :
          ( ( 'of_nat$'(X1) = X0 )
          & $less(0,'of_nat$'(X1)) )
      | ~ $less(0,X0) ),
    inference(ennf_transformation,[],[f406]) ).

tff(f406,axiom,
    ! [X0: $int] :
      ( $less(0,X0)
     => ? [X1: 'Nat$'] :
          ( ( 'of_nat$'(X1) = X0 )
          & $less(0,'of_nat$'(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).

tff(f3818,plain,
    spl173_139,
    inference(avatar_split_clause,[],[f1968,f3816]) ).

tff(f3816,plain,
    ( spl173_139
  <=> ! [X0: $int] :
        ( $less(0,'of_nat$'(sK18(X0)))
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_139])]) ).

tff(f1968,plain,
    ! [X0: $int] :
      ( $less(0,'of_nat$'(sK18(X0)))
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1394]) ).

tff(f3814,plain,
    spl173_138,
    inference(avatar_split_clause,[],[f1967,f3812]) ).

tff(f1967,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK17(X0)) = X0 )
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f1392]) ).

tff(f1392,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'(sK17(X0)) = X0 )
      | $less(X0,0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f963,f1391]) ).

tff(f1391,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 )
     => ( 'of_nat$'(sK17(X0)) = X0 ) ),
    introduced(choice_axiom,[]) ).

tff(f963,plain,
    ! [X0: $int] :
      ( ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 )
      | $less(X0,0) ),
    inference(ennf_transformation,[],[f647]) ).

tff(f647,plain,
    ! [X0: $int] :
      ( ~ $less(X0,0)
     => ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 ) ),
    inference(theory_normalization,[],[f408]) ).

tff(f408,axiom,
    ! [X0: $int] :
      ( $lesseq(0,X0)
     => ? [X1: 'Nat$'] : ( 'of_nat$'(X1) = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom406) ).

tff(f3810,plain,
    spl173_137,
    inference(avatar_split_clause,[],[f1966,f3808]) ).

tff(f3808,plain,
    ( spl173_137
  <=> ! [X0: 'A_cols_vec_rows_vec$'] :
        ( $less(0,'of_nat$'('rank$'(X0)))
        | ( 'zero$c' = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_137])]) ).

tff(f1966,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] :
      ( $less(0,'of_nat$'('rank$'(X0)))
      | ( 'zero$c' = X0 ) ),
    inference(cnf_transformation,[],[f962]) ).

tff(f962,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] :
      ( $less(0,'of_nat$'('rank$'(X0)))
      | ( 'zero$c' = X0 ) ),
    inference(ennf_transformation,[],[f159]) ).

tff(f159,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] :
      ( ( 'zero$c' != X0 )
     => $less(0,'of_nat$'('rank$'(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom157) ).

tff(f3806,plain,
    spl173_136,
    inference(avatar_split_clause,[],[f1964,f3804]) ).

tff(f3804,plain,
    ( spl173_136
  <=> ! [X0: $int] :
        ( ( 0 = 'of_nat$'('nat$'(X0)) )
        | ~ $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_136])]) ).

tff(f1964,plain,
    ! [X0: $int] :
      ( ( 0 = 'of_nat$'('nat$'(X0)) )
      | ~ $less(X0,0) ),
    inference(cnf_transformation,[],[f961]) ).

tff(f961,plain,
    ! [X0: $int] :
      ( ( ( 0 = 'of_nat$'('nat$'(X0)) )
        | ~ $less(X0,0) )
      & ( ( 'of_nat$'('nat$'(X0)) = X0 )
        | $less(X0,0) ) ),
    inference(ennf_transformation,[],[f646]) ).

tff(f646,plain,
    ! [X0: $int] :
      ( ( $less(X0,0)
       => ( 0 = 'of_nat$'('nat$'(X0)) ) )
      & ( ~ $less(X0,0)
       => ( 'of_nat$'('nat$'(X0)) = X0 ) ) ),
    inference(theory_normalization,[],[f616]) ).

tff(f616,axiom,
    ! [X0: $int] :
      ( ( ~ $lesseq(0,X0)
       => ( 0 = 'of_nat$'('nat$'(X0)) ) )
      & ( $lesseq(0,X0)
       => ( 'of_nat$'('nat$'(X0)) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).

tff(f3802,plain,
    spl173_135,
    inference(avatar_split_clause,[],[f1963,f3800]) ).

tff(f3800,plain,
    ( spl173_135
  <=> ! [X0: $int] :
        ( ( 'of_nat$'('nat$'(X0)) = X0 )
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_135])]) ).

tff(f1963,plain,
    ! [X0: $int] :
      ( ( 'of_nat$'('nat$'(X0)) = X0 )
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f961]) ).

tff(f3798,plain,
    spl173_134,
    inference(avatar_split_clause,[],[f1962,f3796]) ).

tff(f3796,plain,
    ( spl173_134
  <=> ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'('one$a')),X0) = 'uminus$a'('one$b') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_134])]) ).

tff(f1962,plain,
    ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'('one$a')),X0) = 'uminus$a'('one$b') ),
    inference(cnf_transformation,[],[f517]) ).

tff(f517,axiom,
    ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('uminus$'('one$a')),X0) = 'uminus$a'('one$b') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).

tff(f3794,plain,
    spl173_133,
    inference(avatar_split_clause,[],[f1961,f3792]) ).

tff(f3792,plain,
    ( spl173_133
  <=> ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'('one$c')),X0) = 'uminus$c'('one$d') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_133])]) ).

tff(f1961,plain,
    ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'('one$c')),X0) = 'uminus$c'('one$d') ),
    inference(cnf_transformation,[],[f518]) ).

tff(f518,axiom,
    ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('uminus$b'('one$c')),X0) = 'uminus$c'('one$d') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).

tff(f3790,plain,
    spl173_132,
    inference(avatar_split_clause,[],[f1960,f3788]) ).

tff(f3788,plain,
    ( spl173_132
  <=> ! [X0: 'A_rows_vec_cols_vec$'] : ( 'of_nat$'('rank$'('transpose$a'(X0))) = 'of_nat$'('rank$a'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_132])]) ).

tff(f1960,plain,
    ! [X0: 'A_rows_vec_cols_vec$'] : ( 'of_nat$'('rank$'('transpose$a'(X0))) = 'of_nat$'('rank$a'(X0)) ),
    inference(cnf_transformation,[],[f73]) ).

tff(f73,axiom,
    ! [X0: 'A_rows_vec_cols_vec$'] : ( 'of_nat$'('rank$'('transpose$a'(X0))) = 'of_nat$'('rank$a'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).

tff(f3785,plain,
    spl173_131,
    inference(avatar_split_clause,[],[f1959,f3783]) ).

tff(f3783,plain,
    ( spl173_131
  <=> ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$a'('transpose$b'(X0))) = 'of_nat$'('rank$'(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_131])]) ).

tff(f1959,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$a'('transpose$b'(X0))) = 'of_nat$'('rank$'(X0)) ),
    inference(cnf_transformation,[],[f72]) ).

tff(f72,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$a'('transpose$b'(X0))) = 'of_nat$'('rank$'(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).

tff(f3781,plain,
    spl173_130,
    inference(avatar_split_clause,[],[f1958,f3779]) ).

tff(f3779,plain,
    ( spl173_130
  <=> ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$'(X0)) = 'of_nat$'('rank$'('gauss_Jordan$a'(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_130])]) ).

tff(f1958,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$'(X0)) = 'of_nat$'('rank$'('gauss_Jordan$a'(X0))) ),
    inference(cnf_transformation,[],[f145]) ).

tff(f145,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'of_nat$'('rank$'(X0)) = 'of_nat$'('rank$'('gauss_Jordan$a'(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).

tff(f3777,plain,
    spl173_129,
    inference(avatar_split_clause,[],[f864,f3775]) ).

tff(f864,plain,
    ! [X0: $real,X1: $real] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1.0)) ),
    introduced(theory_axiom_147,[]) ).

tff(f3773,plain,
    spl173_128,
    inference(avatar_split_clause,[],[f854,f3771]) ).

tff(f3771,plain,
    ( spl173_128
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_128])]) ).

tff(f854,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f3769,plain,
    spl173_127,
    inference(avatar_split_clause,[],[f846,f3767]) ).

tff(f846,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f3696,plain,
    spl173_126,
    inference(avatar_split_clause,[],[f2657,f3694]) ).

tff(f3694,plain,
    ( spl173_126
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X0)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_126])]) ).

tff(f2657,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X0)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1697]) ).

tff(f1697,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP8(X0,X1,X2) ),
    inference(rectify,[],[f1696]) ).

tff(f1696,plain,
    ! [X1: $int,X2: $int,X0: $int] :
      ( ( ~ $less(X2,X1)
        & ~ $less(X1,X0) )
      | ~ sP8(X1,X2,X0) ),
    inference(nnf_transformation,[],[f1376]) ).

tff(f1376,plain,
    ! [X1: $int,X2: $int,X0: $int] :
      ( ( ~ $less(X2,X1)
        & ~ $less(X1,X0) )
      | ~ sP8(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).

tff(f3692,plain,
    spl173_125,
    inference(avatar_split_clause,[],[f2656,f3690]) ).

tff(f3690,plain,
    ( spl173_125
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X2)
        | ~ sP8(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_125])]) ).

tff(f2656,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X2)
      | ~ sP8(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1697]) ).

tff(f3688,plain,
    spl173_124,
    inference(avatar_split_clause,[],[f2655,f3686]) ).

tff(f3686,plain,
    ( spl173_124
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X0)
        | ~ sP9(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_124])]) ).

tff(f2655,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X0)
      | ~ sP9(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1695]) ).

tff(f1695,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP9(X0,X1,X2) ),
    inference(rectify,[],[f1694]) ).

tff(f1694,plain,
    ! [X0: $int,X2: $int,X1: $int] :
      ( ( ~ $less(X2,X0)
        & ~ $less(X0,X1) )
      | ~ sP9(X0,X2,X1) ),
    inference(nnf_transformation,[],[f1377]) ).

tff(f1377,plain,
    ! [X0: $int,X2: $int,X1: $int] :
      ( ( ~ $less(X2,X0)
        & ~ $less(X0,X1) )
      | ~ sP9(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).

tff(f3684,plain,
    spl173_123,
    inference(avatar_split_clause,[],[f2654,f3682]) ).

tff(f3682,plain,
    ( spl173_123
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X2)
        | ~ sP9(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_123])]) ).

tff(f2654,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X2)
      | ~ sP9(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1695]) ).

tff(f3680,plain,
    spl173_122,
    inference(avatar_split_clause,[],[f2653,f3678]) ).

tff(f3678,plain,
    ( spl173_122
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X0)
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_122])]) ).

tff(f2653,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X0)
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1693]) ).

tff(f1693,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP10(X0,X1,X2) ),
    inference(rectify,[],[f1692]) ).

tff(f1692,plain,
    ! [X2: $int,X1: $int,X0: $int] :
      ( ( ~ $less(X1,X2)
        & ~ $less(X2,X0) )
      | ~ sP10(X2,X1,X0) ),
    inference(nnf_transformation,[],[f1378]) ).

tff(f1378,plain,
    ! [X2: $int,X1: $int,X0: $int] :
      ( ( ~ $less(X1,X2)
        & ~ $less(X2,X0) )
      | ~ sP10(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).

tff(f3676,plain,
    spl173_121,
    inference(avatar_split_clause,[],[f2652,f3674]) ).

tff(f3674,plain,
    ( spl173_121
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X2)
        | ~ sP10(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_121])]) ).

tff(f2652,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X2)
      | ~ sP10(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1693]) ).

tff(f3672,plain,
    spl173_120,
    inference(avatar_split_clause,[],[f2651,f3670]) ).

tff(f3670,plain,
    ( spl173_120
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X0)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_120])]) ).

tff(f2651,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X1,X0)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1691]) ).

tff(f1691,plain,
    ! [X0: $int,X1: $int,X2: $int] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP11(X0,X1,X2) ),
    inference(rectify,[],[f1690]) ).

tff(f1690,plain,
    ! [X1: $int,X0: $int,X2: $int] :
      ( ( ~ $less(X0,X1)
        & ~ $less(X1,X2) )
      | ~ sP11(X1,X0,X2) ),
    inference(nnf_transformation,[],[f1379]) ).

tff(f1379,plain,
    ! [X1: $int,X0: $int,X2: $int] :
      ( ( ~ $less(X0,X1)
        & ~ $less(X1,X2) )
      | ~ sP11(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).

tff(f3668,plain,
    spl173_119,
    inference(avatar_split_clause,[],[f2650,f3666]) ).

tff(f3666,plain,
    ( spl173_119
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X2)
        | ~ sP11(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_119])]) ).

tff(f2650,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X2)
      | ~ sP11(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1691]) ).

tff(f3664,plain,
    spl173_118,
    inference(avatar_split_clause,[],[f2645,f3662]) ).

tff(f3662,plain,
    ( spl173_118
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_118])]) ).

tff(f2645,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1689]) ).

tff(f1689,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP4(X0,X1,X2) ),
    inference(rectify,[],[f1688]) ).

tff(f1688,plain,
    ! [X1: $real,X2: $real,X0: $real] :
      ( ( ~ $less(X2,X1)
        & ~ $less(X1,X0) )
      | ~ sP4(X1,X2,X0) ),
    inference(nnf_transformation,[],[f1371]) ).

tff(f1371,plain,
    ! [X1: $real,X2: $real,X0: $real] :
      ( ( ~ $less(X2,X1)
        & ~ $less(X1,X0) )
      | ~ sP4(X1,X2,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).

tff(f3660,plain,
    spl173_117,
    inference(avatar_split_clause,[],[f2644,f3658]) ).

tff(f3658,plain,
    ( spl173_117
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | ~ sP4(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_117])]) ).

tff(f2644,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | ~ sP4(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1689]) ).

tff(f3656,plain,
    ( spl173_116
    | ~ spl173_10
    | ~ spl173_56 ),
    inference(avatar_split_clause,[],[f3464,f3353,f3145,f3654]) ).

tff(f3654,plain,
    ( spl173_116
  <=> ! [X0: $int] : ~ $less(X0,sK35(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_116])]) ).

tff(f3145,plain,
    ( spl173_10
  <=> ! [X0: $int] : $less(sK35(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_10])]) ).

tff(f3464,plain,
    ( ! [X0: $int] : ~ $less(X0,sK35(X0))
    | ~ spl173_10
    | ~ spl173_56 ),
    inference(resolution,[],[f3354,f3146]) ).

tff(f3146,plain,
    ( ! [X0: $int] : $less(sK35(X0),X0)
    | ~ spl173_10 ),
    inference(avatar_component_clause,[],[f3145]) ).

tff(f3652,plain,
    spl173_115,
    inference(avatar_split_clause,[],[f2643,f3650]) ).

tff(f3650,plain,
    ( spl173_115
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | ~ sP5(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_115])]) ).

tff(f2643,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1687]) ).

tff(f1687,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP5(X0,X1,X2) ),
    inference(rectify,[],[f1686]) ).

tff(f1686,plain,
    ! [X0: $real,X2: $real,X1: $real] :
      ( ( ~ $less(X2,X0)
        & ~ $less(X0,X1) )
      | ~ sP5(X0,X2,X1) ),
    inference(nnf_transformation,[],[f1372]) ).

tff(f1372,plain,
    ! [X0: $real,X2: $real,X1: $real] :
      ( ( ~ $less(X2,X0)
        & ~ $less(X0,X1) )
      | ~ sP5(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).

tff(f3648,plain,
    spl173_114,
    inference(avatar_split_clause,[],[f2642,f3646]) ).

tff(f3646,plain,
    ( spl173_114
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | ~ sP5(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_114])]) ).

tff(f2642,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | ~ sP5(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1687]) ).

tff(f3644,plain,
    spl173_113,
    inference(avatar_split_clause,[],[f2641,f3642]) ).

tff(f3642,plain,
    ( spl173_113
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_113])]) ).

tff(f2641,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f1685,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP6(X0,X1,X2) ),
    inference(rectify,[],[f1684]) ).

tff(f1684,plain,
    ! [X2: $real,X1: $real,X0: $real] :
      ( ( ~ $less(X1,X2)
        & ~ $less(X2,X0) )
      | ~ sP6(X2,X1,X0) ),
    inference(nnf_transformation,[],[f1373]) ).

tff(f1373,plain,
    ! [X2: $real,X1: $real,X0: $real] :
      ( ( ~ $less(X1,X2)
        & ~ $less(X2,X0) )
      | ~ sP6(X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).

tff(f3640,plain,
    spl173_112,
    inference(avatar_split_clause,[],[f2640,f3638]) ).

tff(f3638,plain,
    ( spl173_112
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | ~ sP6(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_112])]) ).

tff(f2640,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | ~ sP6(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1685]) ).

tff(f3636,plain,
    spl173_111,
    inference(avatar_split_clause,[],[f2639,f3634]) ).

tff(f3634,plain,
    ( spl173_111
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X1,X0)
        | ~ sP7(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_111])]) ).

tff(f2639,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X1,X0)
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1683]) ).

tff(f1683,plain,
    ! [X0: $real,X1: $real,X2: $real] :
      ( ( ~ $less(X1,X0)
        & ~ $less(X0,X2) )
      | ~ sP7(X0,X1,X2) ),
    inference(rectify,[],[f1682]) ).

tff(f1682,plain,
    ! [X1: $real,X0: $real,X2: $real] :
      ( ( ~ $less(X0,X1)
        & ~ $less(X1,X2) )
      | ~ sP7(X1,X0,X2) ),
    inference(nnf_transformation,[],[f1374]) ).

tff(f1374,plain,
    ! [X1: $real,X0: $real,X2: $real] :
      ( ( ~ $less(X0,X1)
        & ~ $less(X1,X2) )
      | ~ sP7(X1,X0,X2) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).

tff(f3632,plain,
    spl173_110,
    inference(avatar_split_clause,[],[f2638,f3630]) ).

tff(f3630,plain,
    ( spl173_110
  <=> ! [X2: $real,X0: $real,X1: $real] :
        ( ~ $less(X0,X2)
        | ~ sP7(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_110])]) ).

tff(f2638,plain,
    ! [X2: $real,X0: $real,X1: $real] :
      ( ~ $less(X0,X2)
      | ~ sP7(X0,X1,X2) ),
    inference(cnf_transformation,[],[f1683]) ).

tff(f3628,plain,
    spl173_109,
    inference(avatar_split_clause,[],[f2270,f3626]) ).

tff(f3626,plain,
    ( spl173_109
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK46(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_109])]) ).

tff(f2270,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ~ 'fun_app$s'(X0,sK46(X0)) ),
    inference(cnf_transformation,[],[f1508]) ).

tff(f3624,plain,
    spl173_108,
    inference(avatar_split_clause,[],[f2263,f3622]) ).

tff(f3622,plain,
    ( spl173_108
  <=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
        ( 'fun_app$s'(X0,X1)
        | ~ 'fun_app$s'(X0,sK43(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_108])]) ).

tff(f2263,plain,
    ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
      ( 'fun_app$s'(X0,X1)
      | ~ 'fun_app$s'(X0,sK43(X0)) ),
    inference(cnf_transformation,[],[f1502]) ).

tff(f3620,plain,
    spl173_107,
    inference(avatar_split_clause,[],[f2104,f3618]) ).

tff(f3618,plain,
    ( spl173_107
  <=> ! [X0: 'A_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('vec$'(X0)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_107])]) ).

tff(f2104,plain,
    ! [X0: 'A_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('vec$'(X0)),X1) = X0 ),
    inference(cnf_transformation,[],[f53]) ).

tff(f53,axiom,
    ! [X0: 'A_rows_vec$',X1: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('vec$'(X0)),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).

tff(f3616,plain,
    spl173_106,
    inference(avatar_split_clause,[],[f2103,f3614]) ).

tff(f3614,plain,
    ( spl173_106
  <=> ! [X0: 'A_cols_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('vec$a'(X0)),X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_106])]) ).

tff(f2103,plain,
    ! [X0: 'A_cols_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('vec$a'(X0)),X1) = X0 ),
    inference(cnf_transformation,[],[f54]) ).

tff(f54,axiom,
    ! [X0: 'A_cols_vec$',X1: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('vec$a'(X0)),X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).

tff(f3612,plain,
    ( spl173_105
    | ~ spl173_9
    | ~ spl173_56 ),
    inference(avatar_split_clause,[],[f3462,f3353,f3141,f3610]) ).

tff(f3141,plain,
    ( spl173_9
  <=> ! [X0: $int] : $less(X0,sK34(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_9])]) ).

tff(f3462,plain,
    ( ! [X0: $int] : ~ $less(sK34(X0),X0)
    | ~ spl173_9
    | ~ spl173_56 ),
    inference(resolution,[],[f3354,f3142]) ).

tff(f3142,plain,
    ( ! [X0: $int] : $less(X0,sK34(X0))
    | ~ spl173_9 ),
    inference(avatar_component_clause,[],[f3141]) ).

tff(f3608,plain,
    spl173_104,
    inference(avatar_split_clause,[],[f2062,f3606]) ).

tff(f3606,plain,
    ( spl173_104
  <=> ! [X0: $real] :
        ( ~ $less(X0,$uminus(X0))
        | $less(X0,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_104])]) ).

tff(f2062,plain,
    ! [X0: $real] :
      ( ~ $less(X0,$uminus(X0))
      | $less(X0,0.0) ),
    inference(cnf_transformation,[],[f1441]) ).

tff(f1441,plain,
    ! [X0: $real] :
      ( ( ~ $less(X0,$uminus(X0))
        | $less(X0,0.0) )
      & ( ~ $less(X0,0.0)
        | $less(X0,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f662]) ).

tff(f662,plain,
    ! [X0: $real] :
      ( ~ $less(X0,$uminus(X0))
    <=> ~ $less(X0,0.0) ),
    inference(theory_normalization,[],[f491]) ).

tff(f491,axiom,
    ! [X0: $real] :
      ( $lesseq($uminus(X0),X0)
    <=> $lesseq(0.0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).

tff(f3604,plain,
    spl173_103,
    inference(avatar_split_clause,[],[f2061,f3602]) ).

tff(f3602,plain,
    ( spl173_103
  <=> ! [X0: $real] :
        ( ~ $less(X0,0.0)
        | $less(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_103])]) ).

tff(f2061,plain,
    ! [X0: $real] :
      ( ~ $less(X0,0.0)
      | $less(X0,$uminus(X0)) ),
    inference(cnf_transformation,[],[f1441]) ).

tff(f3600,plain,
    spl173_102,
    inference(avatar_split_clause,[],[f2060,f3598]) ).

tff(f3598,plain,
    ( spl173_102
  <=> ! [X0: $real] :
        ( ~ $less($uminus(X0),X0)
        | $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_102])]) ).

tff(f2060,plain,
    ! [X0: $real] :
      ( ~ $less($uminus(X0),X0)
      | $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1440]) ).

tff(f1440,plain,
    ! [X0: $real] :
      ( ( ~ $less($uminus(X0),X0)
        | $less(0.0,X0) )
      & ( ~ $less(0.0,X0)
        | $less($uminus(X0),X0) ) ),
    inference(nnf_transformation,[],[f661]) ).

tff(f661,plain,
    ! [X0: $real] :
      ( ~ $less($uminus(X0),X0)
    <=> ~ $less(0.0,X0) ),
    inference(theory_normalization,[],[f489]) ).

tff(f489,axiom,
    ! [X0: $real] :
      ( $lesseq(X0,$uminus(X0))
    <=> $lesseq(X0,0.0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).

tff(f3596,plain,
    spl173_101,
    inference(avatar_split_clause,[],[f2059,f3594]) ).

tff(f3594,plain,
    ( spl173_101
  <=> ! [X0: $real] :
        ( ~ $less(0.0,X0)
        | $less($uminus(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_101])]) ).

tff(f2059,plain,
    ! [X0: $real] :
      ( ~ $less(0.0,X0)
      | $less($uminus(X0),X0) ),
    inference(cnf_transformation,[],[f1440]) ).

tff(f3592,plain,
    spl173_100,
    inference(avatar_split_clause,[],[f2037,f3590]) ).

tff(f3590,plain,
    ( spl173_100
  <=> ! [X0: $int] :
        ( ~ $less(0,$uminus(X0))
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_100])]) ).

tff(f2037,plain,
    ! [X0: $int] :
      ( ~ $less(0,$uminus(X0))
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f1429]) ).

tff(f1429,plain,
    ! [X0: $int] :
      ( ( ~ $less(0,$uminus(X0))
        | $less(X0,0) )
      & ( ~ $less(X0,0)
        | $less(0,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f657]) ).

tff(f657,plain,
    ! [X0: $int] :
      ( ~ $less(0,$uminus(X0))
    <=> ~ $less(X0,0) ),
    inference(theory_normalization,[],[f486]) ).

tff(f486,axiom,
    ! [X0: $int] :
      ( $lesseq($uminus(X0),0)
    <=> $lesseq(0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).

tff(f3588,plain,
    spl173_99,
    inference(avatar_split_clause,[],[f2036,f3586]) ).

tff(f3586,plain,
    ( spl173_99
  <=> ! [X0: $int] :
        ( ~ $less(X0,0)
        | $less(0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_99])]) ).

tff(f2036,plain,
    ! [X0: $int] :
      ( ~ $less(X0,0)
      | $less(0,$uminus(X0)) ),
    inference(cnf_transformation,[],[f1429]) ).

tff(f3584,plain,
    spl173_98,
    inference(avatar_split_clause,[],[f2035,f3582]) ).

tff(f3582,plain,
    ( spl173_98
  <=> ! [X0: $int] :
        ( ~ $less(X0,$uminus(X0))
        | $less(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_98])]) ).

tff(f2035,plain,
    ! [X0: $int] :
      ( ~ $less(X0,$uminus(X0))
      | $less(X0,0) ),
    inference(cnf_transformation,[],[f1428]) ).

tff(f1428,plain,
    ! [X0: $int] :
      ( ( ~ $less(X0,$uminus(X0))
        | $less(X0,0) )
      & ( ~ $less(X0,0)
        | $less(X0,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f656]) ).

tff(f656,plain,
    ! [X0: $int] :
      ( ~ $less(X0,$uminus(X0))
    <=> ~ $less(X0,0) ),
    inference(theory_normalization,[],[f490]) ).

tff(f490,axiom,
    ! [X0: $int] :
      ( $lesseq($uminus(X0),X0)
    <=> $lesseq(0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).

tff(f3580,plain,
    spl173_97,
    inference(avatar_split_clause,[],[f2034,f3578]) ).

tff(f3578,plain,
    ( spl173_97
  <=> ! [X0: $int] :
        ( ~ $less(X0,0)
        | $less(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_97])]) ).

tff(f2034,plain,
    ! [X0: $int] :
      ( ~ $less(X0,0)
      | $less(X0,$uminus(X0)) ),
    inference(cnf_transformation,[],[f1428]) ).

tff(f3576,plain,
    spl173_96,
    inference(avatar_split_clause,[],[f2032,f3574]) ).

tff(f3574,plain,
    ( spl173_96
  <=> ! [X0: $int] :
        ( ~ $less($uminus(X0),0)
        | $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_96])]) ).

tff(f2032,plain,
    ! [X0: $int] :
      ( ~ $less($uminus(X0),0)
      | $less(0,X0) ),
    inference(cnf_transformation,[],[f1427]) ).

tff(f1427,plain,
    ! [X0: $int] :
      ( ( ~ $less($uminus(X0),0)
        | $less(0,X0) )
      & ( ~ $less(0,X0)
        | $less($uminus(X0),0) ) ),
    inference(nnf_transformation,[],[f654]) ).

tff(f654,plain,
    ! [X0: $int] :
      ( ~ $less($uminus(X0),0)
    <=> ~ $less(0,X0) ),
    inference(theory_normalization,[],[f484]) ).

tff(f484,axiom,
    ! [X0: $int] :
      ( $lesseq(0,$uminus(X0))
    <=> $lesseq(X0,0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).

tff(f3572,plain,
    spl173_95,
    inference(avatar_split_clause,[],[f2031,f3570]) ).

tff(f3570,plain,
    ( spl173_95
  <=> ! [X0: $int] :
        ( ~ $less(0,X0)
        | $less($uminus(X0),0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_95])]) ).

tff(f2031,plain,
    ! [X0: $int] :
      ( ~ $less(0,X0)
      | $less($uminus(X0),0) ),
    inference(cnf_transformation,[],[f1427]) ).

tff(f3568,plain,
    ( spl173_94
    | ~ spl173_8
    | ~ spl173_55 ),
    inference(avatar_split_clause,[],[f3461,f3349,f3137,f3566]) ).

tff(f3566,plain,
    ( spl173_94
  <=> ! [X0: $real] : ~ $less(X0,sK33(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_94])]) ).

tff(f3137,plain,
    ( spl173_8
  <=> ! [X0: $real] : $less(sK33(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_8])]) ).

tff(f3461,plain,
    ( ! [X0: $real] : ~ $less(X0,sK33(X0))
    | ~ spl173_8
    | ~ spl173_55 ),
    inference(resolution,[],[f3350,f3138]) ).

tff(f3138,plain,
    ( ! [X0: $real] : $less(sK33(X0),X0)
    | ~ spl173_8 ),
    inference(avatar_component_clause,[],[f3137]) ).

tff(f3564,plain,
    spl173_93,
    inference(avatar_split_clause,[],[f2030,f3562]) ).

tff(f3562,plain,
    ( spl173_93
  <=> ! [X0: $int] :
        ( ~ $less($uminus(X0),X0)
        | $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_93])]) ).

tff(f2030,plain,
    ! [X0: $int] :
      ( ~ $less($uminus(X0),X0)
      | $less(0,X0) ),
    inference(cnf_transformation,[],[f1426]) ).

tff(f1426,plain,
    ! [X0: $int] :
      ( ( ~ $less($uminus(X0),X0)
        | $less(0,X0) )
      & ( ~ $less(0,X0)
        | $less($uminus(X0),X0) ) ),
    inference(nnf_transformation,[],[f653]) ).

tff(f653,plain,
    ! [X0: $int] :
      ( ~ $less($uminus(X0),X0)
    <=> ~ $less(0,X0) ),
    inference(theory_normalization,[],[f488]) ).

tff(f488,axiom,
    ! [X0: $int] :
      ( $lesseq(X0,$uminus(X0))
    <=> $lesseq(X0,0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).

tff(f3560,plain,
    spl173_92,
    inference(avatar_split_clause,[],[f2029,f3558]) ).

tff(f3558,plain,
    ( spl173_92
  <=> ! [X0: $int] :
        ( ~ $less(0,X0)
        | $less($uminus(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_92])]) ).

tff(f2029,plain,
    ! [X0: $int] :
      ( ~ $less(0,X0)
      | $less($uminus(X0),X0) ),
    inference(cnf_transformation,[],[f1426]) ).

tff(f3556,plain,
    spl173_91,
    inference(avatar_split_clause,[],[f2028,f3554]) ).

tff(f3554,plain,
    ( spl173_91
  <=> ! [X0: $real] :
        ( ~ $less(0.0,$uminus(X0))
        | $less(X0,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_91])]) ).

tff(f2028,plain,
    ! [X0: $real] :
      ( ~ $less(0.0,$uminus(X0))
      | $less(X0,0.0) ),
    inference(cnf_transformation,[],[f1425]) ).

tff(f1425,plain,
    ! [X0: $real] :
      ( ( ~ $less(0.0,$uminus(X0))
        | $less(X0,0.0) )
      & ( ~ $less(X0,0.0)
        | $less(0.0,$uminus(X0)) ) ),
    inference(nnf_transformation,[],[f652]) ).

tff(f652,plain,
    ! [X0: $real] :
      ( ~ $less(0.0,$uminus(X0))
    <=> ~ $less(X0,0.0) ),
    inference(theory_normalization,[],[f487]) ).

tff(f487,axiom,
    ! [X0: $real] :
      ( $lesseq($uminus(X0),0.0)
    <=> $lesseq(0.0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).

tff(f3552,plain,
    spl173_90,
    inference(avatar_split_clause,[],[f2027,f3550]) ).

tff(f3550,plain,
    ( spl173_90
  <=> ! [X0: $real] :
        ( ~ $less(X0,0.0)
        | $less(0.0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_90])]) ).

tff(f2027,plain,
    ! [X0: $real] :
      ( ~ $less(X0,0.0)
      | $less(0.0,$uminus(X0)) ),
    inference(cnf_transformation,[],[f1425]) ).

tff(f3548,plain,
    spl173_89,
    inference(avatar_split_clause,[],[f2026,f3546]) ).

tff(f3546,plain,
    ( spl173_89
  <=> ! [X0: $real] :
        ( ~ $less($uminus(X0),0.0)
        | $less(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_89])]) ).

tff(f2026,plain,
    ! [X0: $real] :
      ( ~ $less($uminus(X0),0.0)
      | $less(0.0,X0) ),
    inference(cnf_transformation,[],[f1424]) ).

tff(f1424,plain,
    ! [X0: $real] :
      ( ( ~ $less($uminus(X0),0.0)
        | $less(0.0,X0) )
      & ( ~ $less(0.0,X0)
        | $less($uminus(X0),0.0) ) ),
    inference(nnf_transformation,[],[f651]) ).

tff(f651,plain,
    ! [X0: $real] :
      ( ~ $less($uminus(X0),0.0)
    <=> ~ $less(0.0,X0) ),
    inference(theory_normalization,[],[f485]) ).

tff(f485,axiom,
    ! [X0: $real] :
      ( $lesseq(0.0,$uminus(X0))
    <=> $lesseq(X0,0.0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).

tff(f3544,plain,
    spl173_88,
    inference(avatar_split_clause,[],[f2025,f3542]) ).

tff(f3542,plain,
    ( spl173_88
  <=> ! [X0: $real] :
        ( ~ $less(0.0,X0)
        | $less($uminus(X0),0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_88])]) ).

tff(f2025,plain,
    ! [X0: $real] :
      ( ~ $less(0.0,X0)
      | $less($uminus(X0),0.0) ),
    inference(cnf_transformation,[],[f1424]) ).

tff(f3540,plain,
    spl173_87,
    inference(avatar_split_clause,[],[f2017,f3538]) ).

tff(f3538,plain,
    ( spl173_87
  <=> ! [X0: $int] :
        ( ( 0 = X0 )
        | ( $uminus(X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_87])]) ).

tff(f2017,plain,
    ! [X0: $int] :
      ( ( 0 = X0 )
      | ( $uminus(X0) != X0 ) ),
    inference(cnf_transformation,[],[f1420]) ).

tff(f1420,plain,
    ! [X0: $int] :
      ( ( ( $uminus(X0) = X0 )
        | ( 0 != X0 ) )
      & ( ( 0 = X0 )
        | ( $uminus(X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f460]) ).

tff(f460,axiom,
    ! [X0: $int] :
      ( ( $uminus(X0) = X0 )
    <=> ( 0 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom458) ).

tff(f3536,plain,
    spl173_86,
    inference(avatar_split_clause,[],[f2013,f3534]) ).

tff(f3534,plain,
    ( spl173_86
  <=> ! [X0: $real] :
        ( ( 0.0 = X0 )
        | ( $uminus(X0) != X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_86])]) ).

tff(f2013,plain,
    ! [X0: $real] :
      ( ( 0.0 = X0 )
      | ( $uminus(X0) != X0 ) ),
    inference(cnf_transformation,[],[f1418]) ).

tff(f1418,plain,
    ! [X0: $real] :
      ( ( ( $uminus(X0) = X0 )
        | ( 0.0 != X0 ) )
      & ( ( 0.0 = X0 )
        | ( $uminus(X0) != X0 ) ) ),
    inference(nnf_transformation,[],[f461]) ).

tff(f461,axiom,
    ! [X0: $real] :
      ( ( $uminus(X0) = X0 )
    <=> ( 0.0 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom459) ).

tff(f3532,plain,
    spl173_85,
    inference(avatar_split_clause,[],[f2005,f3530]) ).

tff(f3530,plain,
    ( spl173_85
  <=> ! [X0: $int] :
        ( ( 0 = X0 )
        | ( 0 != $uminus(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_85])]) ).

tff(f2005,plain,
    ! [X0: $int] :
      ( ( 0 = X0 )
      | ( 0 != $uminus(X0) ) ),
    inference(cnf_transformation,[],[f1414]) ).

tff(f1414,plain,
    ! [X0: $int] :
      ( ( ( 0 = $uminus(X0) )
        | ( 0 != X0 ) )
      & ( ( 0 = X0 )
        | ( 0 != $uminus(X0) ) ) ),
    inference(nnf_transformation,[],[f464]) ).

tff(f464,axiom,
    ! [X0: $int] :
      ( ( 0 = $uminus(X0) )
    <=> ( 0 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).

tff(f3528,plain,
    spl173_84,
    inference(avatar_split_clause,[],[f2001,f3526]) ).

tff(f3526,plain,
    ( spl173_84
  <=> ! [X0: $real] :
        ( ( 0.0 = X0 )
        | ( 0.0 != $uminus(X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_84])]) ).

tff(f2001,plain,
    ! [X0: $real] :
      ( ( 0.0 = X0 )
      | ( 0.0 != $uminus(X0) ) ),
    inference(cnf_transformation,[],[f1412]) ).

tff(f1412,plain,
    ! [X0: $real] :
      ( ( ( 0.0 = $uminus(X0) )
        | ( 0.0 != X0 ) )
      & ( ( 0.0 = X0 )
        | ( 0.0 != $uminus(X0) ) ) ),
    inference(nnf_transformation,[],[f465]) ).

tff(f465,axiom,
    ! [X0: $real] :
      ( ( 0.0 = $uminus(X0) )
    <=> ( 0.0 = X0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).

tff(f3524,plain,
    ( spl173_83
    | ~ spl173_7
    | ~ spl173_55 ),
    inference(avatar_split_clause,[],[f3459,f3349,f3133,f3522]) ).

tff(f3522,plain,
    ( spl173_83
  <=> ! [X0: $real] : ~ $less(sK32(X0),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_83])]) ).

tff(f3133,plain,
    ( spl173_7
  <=> ! [X0: $real] : $less(X0,sK32(X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_7])]) ).

tff(f3459,plain,
    ( ! [X0: $real] : ~ $less(sK32(X0),X0)
    | ~ spl173_7
    | ~ spl173_55 ),
    inference(resolution,[],[f3350,f3134]) ).

tff(f3134,plain,
    ( ! [X0: $real] : $less(X0,sK32(X0))
    | ~ spl173_7 ),
    inference(avatar_component_clause,[],[f3133]) ).

tff(f3520,plain,
    ~ spl173_82,
    inference(avatar_split_clause,[],[f1900,f3517]) ).

tff(f3517,plain,
    ( spl173_82
  <=> $less('of_nat$'('to_nat$'('i$')),'of_nat$'('rank$'('a$'))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_82])]) ).

tff(f1900,plain,
    ~ $less('of_nat$'('to_nat$'('i$')),'of_nat$'('rank$'('a$'))),
    inference(cnf_transformation,[],[f633]) ).

tff(f633,plain,
    ~ $less('of_nat$'('to_nat$'('i$')),'of_nat$'('rank$'('a$'))),
    inference(theory_normalization,[],[f45]) ).

tff(f45,axiom,
    $lesseq('of_nat$'('rank$'('a$')),'of_nat$'('to_nat$'('i$'))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).

tff(f3515,plain,
    spl173_81,
    inference(avatar_split_clause,[],[f866,f3513]) ).

tff(f3513,plain,
    ( spl173_81
  <=> ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_81])]) ).

tff(f866,plain,
    ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f3511,plain,
    spl173_80,
    inference(avatar_split_clause,[],[f855,f3509]) ).

tff(f3509,plain,
    ( spl173_80
  <=> ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_80])]) ).

tff(f855,plain,
    ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f3507,plain,
    spl173_79,
    inference(avatar_split_clause,[],[f848,f3505]) ).

tff(f3505,plain,
    ( spl173_79
  <=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_79])]) ).

tff(f848,plain,
    ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f3503,plain,
    spl173_78,
    inference(avatar_split_clause,[],[f837,f3501]) ).

tff(f837,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f3498,plain,
    ( spl173_77
    | ~ spl173_23
    | ~ spl173_31
    | ~ spl173_51
    | ~ spl173_73 ),
    inference(avatar_split_clause,[],[f3430,f3426,f3331,f3236,f3201,f3495]) ).

tff(f3495,plain,
    ( spl173_77
  <=> ( 0.0 = 'fun_app$t'('of_nat$a','rank$'('zero$c')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_77])]) ).

tff(f3201,plain,
    ( spl173_23
  <=> ( 0 = 'of_nat$'('rank$'('zero$c')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_23])]) ).

tff(f3236,plain,
    ( spl173_31
  <=> ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_31])]) ).

tff(f3331,plain,
    ( spl173_51
  <=> ( 'to_nat$'('zero$d') = 'nat$'(0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_51])]) ).

tff(f3426,plain,
    ( spl173_73
  <=> ( 0.0 = 'fun_app$t'('of_nat$a','to_nat$'('zero$d')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_73])]) ).

tff(f3430,plain,
    ( ( 0.0 = 'fun_app$t'('of_nat$a','rank$'('zero$c')) )
    | ~ spl173_23
    | ~ spl173_31
    | ~ spl173_51
    | ~ spl173_73 ),
    inference(forward_demodulation,[],[f3428,f3335]) ).

tff(f3335,plain,
    ( ( 'rank$'('zero$c') = 'to_nat$'('zero$d') )
    | ~ spl173_23
    | ~ spl173_31
    | ~ spl173_51 ),
    inference(forward_demodulation,[],[f3333,f3264]) ).

tff(f3264,plain,
    ( ( 'rank$'('zero$c') = 'nat$'(0) )
    | ~ spl173_23
    | ~ spl173_31 ),
    inference(superposition,[],[f3237,f3203]) ).

tff(f3203,plain,
    ( ( 0 = 'of_nat$'('rank$'('zero$c')) )
    | ~ spl173_23 ),
    inference(avatar_component_clause,[],[f3201]) ).

tff(f3237,plain,
    ( ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 )
    | ~ spl173_31 ),
    inference(avatar_component_clause,[],[f3236]) ).

tff(f3333,plain,
    ( ( 'to_nat$'('zero$d') = 'nat$'(0) )
    | ~ spl173_51 ),
    inference(avatar_component_clause,[],[f3331]) ).

tff(f3428,plain,
    ( ( 0.0 = 'fun_app$t'('of_nat$a','to_nat$'('zero$d')) )
    | ~ spl173_73 ),
    inference(avatar_component_clause,[],[f3426]) ).

tff(f3488,plain,
    ( spl173_76
    | ~ spl173_20
    | ~ spl173_54 ),
    inference(avatar_split_clause,[],[f3458,f3345,f3186,f3486]) ).

tff(f3486,plain,
    ( spl173_76
  <=> ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),-1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_76])]) ).

tff(f3458,plain,
    ( ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),-1)
    | ~ spl173_20
    | ~ spl173_54 ),
    inference(evaluation,[],[f3449]) ).

tff(f3449,plain,
    ( ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),$uminus(1))
    | ~ spl173_20
    | ~ spl173_54 ),
    inference(superposition,[],[f3346,f3188]) ).

tff(f3472,plain,
    ( ~ spl173_75
    | ~ spl173_9
    | ~ spl173_50 ),
    inference(avatar_split_clause,[],[f3442,f3327,f3141,f3469]) ).

tff(f3469,plain,
    ( spl173_75
  <=> $less(sK34(0),1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_75])]) ).

tff(f3327,plain,
    ( spl173_50
  <=> ! [X0: $int] :
        ( ~ $less(X0,1)
        | ~ $less(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_50])]) ).

tff(f3442,plain,
    ( ~ $less(sK34(0),1)
    | ~ spl173_9
    | ~ spl173_50 ),
    inference(resolution,[],[f3328,f3142]) ).

tff(f3328,plain,
    ( ! [X0: $int] :
        ( ~ $less(0,X0)
        | ~ $less(X0,1) )
    | ~ spl173_50 ),
    inference(avatar_component_clause,[],[f3327]) ).

tff(f3435,plain,
    ( spl173_74
    | ~ spl173_23
    | ~ spl173_31
    | ~ spl173_51 ),
    inference(avatar_split_clause,[],[f3335,f3331,f3236,f3201,f3432]) ).

tff(f3432,plain,
    ( spl173_74
  <=> ( 'rank$'('zero$c') = 'to_nat$'('zero$d') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_74])]) ).

tff(f3429,plain,
    ( spl173_73
    | ~ spl173_24
    | ~ spl173_31
    | ~ spl173_39 ),
    inference(avatar_split_clause,[],[f3284,f3280,f3236,f3206,f3426]) ).

tff(f3280,plain,
    ( spl173_39
  <=> ( 0.0 = 'fun_app$t'('of_nat$a','nat$'(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_39])]) ).

tff(f3284,plain,
    ( ( 0.0 = 'fun_app$t'('of_nat$a','to_nat$'('zero$d')) )
    | ~ spl173_24
    | ~ spl173_31
    | ~ spl173_39 ),
    inference(forward_demodulation,[],[f3282,f3263]) ).

tff(f3263,plain,
    ( ( 'to_nat$'('zero$d') = 'nat$'(0) )
    | ~ spl173_24
    | ~ spl173_31 ),
    inference(superposition,[],[f3237,f3208]) ).

tff(f3282,plain,
    ( ( 0.0 = 'fun_app$t'('of_nat$a','nat$'(0)) )
    | ~ spl173_39 ),
    inference(avatar_component_clause,[],[f3280]) ).

tff(f3424,plain,
    ( spl173_72
    | ~ spl173_20
    | ~ spl173_31
    | ~ spl173_38 ),
    inference(avatar_split_clause,[],[f3278,f3274,f3236,f3186,f3421]) ).

tff(f3421,plain,
    ( spl173_72
  <=> ( 1.0 = 'fun_app$t'('of_nat$a','to_nat$'('one$e')) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_72])]) ).

tff(f3274,plain,
    ( spl173_38
  <=> ( 1.0 = 'fun_app$t'('of_nat$a','nat$'(1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_38])]) ).

tff(f3278,plain,
    ( ( 1.0 = 'fun_app$t'('of_nat$a','to_nat$'('one$e')) )
    | ~ spl173_20
    | ~ spl173_31
    | ~ spl173_38 ),
    inference(forward_demodulation,[],[f3276,f3262]) ).

tff(f3262,plain,
    ( ( 'nat$'(1) = 'to_nat$'('one$e') )
    | ~ spl173_20
    | ~ spl173_31 ),
    inference(superposition,[],[f3237,f3188]) ).

tff(f3276,plain,
    ( ( 1.0 = 'fun_app$t'('of_nat$a','nat$'(1)) )
    | ~ spl173_38 ),
    inference(avatar_component_clause,[],[f3274]) ).

tff(f3418,plain,
    spl173_71,
    inference(avatar_split_clause,[],[f3078,f3416]) ).

tff(f3416,plain,
    ( spl173_71
  <=> ! [X0: $real] : ( $uminus(X0) = $product(X0,-1.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_71])]) ).

tff(f3078,plain,
    ! [X0: $real] : ( $uminus(X0) = $product(X0,-1.0) ),
    inference(evaluation,[],[f1954]) ).

tff(f1954,plain,
    ! [X0: $real] : ( $uminus(X0) = $product(X0,$uminus(1.0)) ),
    inference(cnf_transformation,[],[f508]) ).

tff(f508,axiom,
    ! [X0: $real] : ( $uminus(X0) = $product(X0,$uminus(1.0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).

tff(f3414,plain,
    spl173_70,
    inference(avatar_split_clause,[],[f3077,f3412]) ).

tff(f3412,plain,
    ( spl173_70
  <=> ! [X0: $real] : ( $uminus(X0) = $product(-1.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_70])]) ).

tff(f3077,plain,
    ! [X0: $real] : ( $uminus(X0) = $product(-1.0,X0) ),
    inference(evaluation,[],[f1955]) ).

tff(f1955,plain,
    ! [X0: $real] : ( $uminus(X0) = $product($uminus(1.0),X0) ),
    inference(cnf_transformation,[],[f510]) ).

tff(f510,axiom,
    ! [X0: $real] : ( $uminus(X0) = $product($uminus(1.0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).

tff(f3410,plain,
    spl173_69,
    inference(avatar_split_clause,[],[f3076,f3408]) ).

tff(f3408,plain,
    ( spl173_69
  <=> ! [X0: $int] : ( $uminus(X0) = $product(X0,-1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_69])]) ).

tff(f3076,plain,
    ! [X0: $int] : ( $uminus(X0) = $product(X0,-1) ),
    inference(evaluation,[],[f1956]) ).

tff(f1956,plain,
    ! [X0: $int] : ( $uminus(X0) = $product(X0,$uminus(1)) ),
    inference(cnf_transformation,[],[f509]) ).

tff(f509,axiom,
    ! [X0: $int] : ( $uminus(X0) = $product(X0,$uminus(1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).

tff(f3406,plain,
    spl173_68,
    inference(avatar_split_clause,[],[f3075,f3404]) ).

tff(f3404,plain,
    ( spl173_68
  <=> ! [X0: $int] : ( $uminus(X0) = $product(-1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_68])]) ).

tff(f3075,plain,
    ! [X0: $int] : ( $uminus(X0) = $product(-1,X0) ),
    inference(evaluation,[],[f1957]) ).

tff(f1957,plain,
    ! [X0: $int] : ( $uminus(X0) = $product($uminus(1),X0) ),
    inference(cnf_transformation,[],[f511]) ).

tff(f511,axiom,
    ! [X0: $int] : ( $uminus(X0) = $product($uminus(1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).

tff(f3402,plain,
    spl173_67,
    inference(avatar_split_clause,[],[f3074,f3399]) ).

tff(f3074,plain,
    1.0 = 'fun_app$r'('times$'(-1.0),-1.0),
    inference(evaluation,[],[f2896]) ).

tff(f2896,plain,
    1.0 = 'fun_app$r'('times$'($uminus(1.0)),$uminus(1.0)),
    inference(equality_resolution,[],[f2087]) ).

tff(f2087,plain,
    ! [X0: $real] :
      ( ( 1.0 = 'fun_app$r'('times$'(X0),X0) )
      | ( $uminus(1.0) != X0 ) ),
    inference(cnf_transformation,[],[f1454]) ).

tff(f3397,plain,
    spl173_66,
    inference(avatar_split_clause,[],[f3072,f3394]) ).

tff(f3072,plain,
    1 = 'fun_app$o'('times$a'(-1),-1),
    inference(evaluation,[],[f2898]) ).

tff(f2898,plain,
    1 = 'fun_app$o'('times$a'($uminus(1)),$uminus(1)),
    inference(equality_resolution,[],[f2090]) ).

tff(f2090,plain,
    ! [X0: $int] :
      ( ( 1 = 'fun_app$o'('times$a'(X0),X0) )
      | ( $uminus(1) != X0 ) ),
    inference(cnf_transformation,[],[f1456]) ).

tff(f3392,plain,
    spl173_65,
    inference(avatar_split_clause,[],[f2984,f3390]) ).

tff(f3390,plain,
    ( spl173_65
  <=> ! [X0: $real] : ( 'fun_app$r'('times$'(X0),1.0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_65])]) ).

tff(f2984,plain,
    ! [X0: $real] : ( 'fun_app$r'('times$'(X0),1.0) = X0 ),
    inference(equality_resolution,[],[f2478]) ).

tff(f2478,plain,
    ! [X0: $real,X1: $real] :
      ( ( 'fun_app$r'('times$'(X0),X1) = X0 )
      | ( 1.0 != X1 ) ),
    inference(cnf_transformation,[],[f1641]) ).

tff(f3388,plain,
    spl173_64,
    inference(avatar_split_clause,[],[f2982,f3386]) ).

tff(f3386,plain,
    ( spl173_64
  <=> ! [X0: $real] : ( 'fun_app$r'('times$'(1.0),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_64])]) ).

tff(f2982,plain,
    ! [X0: $real] : ( 'fun_app$r'('times$'(1.0),X0) = X0 ),
    inference(equality_resolution,[],[f2475]) ).

tff(f2475,plain,
    ! [X0: $real,X1: $real] :
      ( ( 'fun_app$r'('times$'(X1),X0) = X0 )
      | ( 1.0 != X1 ) ),
    inference(cnf_transformation,[],[f1639]) ).

tff(f3384,plain,
    spl173_63,
    inference(avatar_split_clause,[],[f2976,f3382]) ).

tff(f3382,plain,
    ( spl173_63
  <=> ! [X0: $int] : ( 'fun_app$o'('times$a'(X0),1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_63])]) ).

tff(f2976,plain,
    ! [X0: $int] : ( 'fun_app$o'('times$a'(X0),1) = X0 ),
    inference(equality_resolution,[],[f2466]) ).

tff(f2466,plain,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$o'('times$a'(X0),X1) = X0 )
      | ( 1 != X1 ) ),
    inference(cnf_transformation,[],[f1633]) ).

tff(f3380,plain,
    ( spl173_62
    | ~ spl173_23
    | ~ spl173_31 ),
    inference(avatar_split_clause,[],[f3264,f3236,f3201,f3377]) ).

tff(f3375,plain,
    spl173_61,
    inference(avatar_split_clause,[],[f2974,f3373]) ).

tff(f3373,plain,
    ( spl173_61
  <=> ! [X0: $int] : ( 'fun_app$o'('times$a'(1),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_61])]) ).

tff(f2974,plain,
    ! [X0: $int] : ( 'fun_app$o'('times$a'(1),X0) = X0 ),
    inference(equality_resolution,[],[f2463]) ).

tff(f2463,plain,
    ! [X0: $int,X1: $int] :
      ( ( 'fun_app$o'('times$a'(X1),X0) = X0 )
      | ( 1 != X1 ) ),
    inference(cnf_transformation,[],[f1631]) ).

tff(f3371,plain,
    spl173_60,
    inference(avatar_split_clause,[],[f2923,f3369]) ).

tff(f3369,plain,
    ( spl173_60
  <=> ! [X1: $int] : ( 0 = 'fun_app$o'('times$a'(0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_60])]) ).

tff(f2923,plain,
    ! [X1: $int] : ( 0 = 'fun_app$o'('times$a'(0),X1) ),
    inference(equality_resolution,[],[f2196]) ).

tff(f2196,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 != X0 )
      | ( 0 = 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1030]) ).

tff(f1030,plain,
    ! [X0: $int,X1: $int] :
      ( ( ( 0 != X1 )
        & ( 0 != X0 ) )
      | ( 0 = 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(ennf_transformation,[],[f560]) ).

tff(f560,axiom,
    ! [X0: $int,X1: $int] :
      ( ( 0 != 'fun_app$o'('times$a'(X0),X1) )
     => ( ( 0 != X1 )
        & ( 0 != X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).

tff(f3367,plain,
    spl173_59,
    inference(avatar_split_clause,[],[f2922,f3365]) ).

tff(f3365,plain,
    ( spl173_59
  <=> ! [X0: $int] : ( 0 = 'fun_app$o'('times$a'(X0),0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_59])]) ).

tff(f2922,plain,
    ! [X0: $int] : ( 0 = 'fun_app$o'('times$a'(X0),0) ),
    inference(equality_resolution,[],[f2197]) ).

tff(f2197,plain,
    ! [X0: $int,X1: $int] :
      ( ( 0 != X1 )
      | ( 0 = 'fun_app$o'('times$a'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1030]) ).

tff(f3363,plain,
    spl173_58,
    inference(avatar_split_clause,[],[f2921,f3361]) ).

tff(f3361,plain,
    ( spl173_58
  <=> ! [X1: $real] : ( 0.0 = 'fun_app$r'('times$'(0.0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_58])]) ).

tff(f2921,plain,
    ! [X1: $real] : ( 0.0 = 'fun_app$r'('times$'(0.0),X1) ),
    inference(equality_resolution,[],[f2194]) ).

tff(f2194,plain,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 != X0 )
      | ( 0.0 = 'fun_app$r'('times$'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1029]) ).

tff(f1029,plain,
    ! [X0: $real,X1: $real] :
      ( ( ( 0.0 != X1 )
        & ( 0.0 != X0 ) )
      | ( 0.0 = 'fun_app$r'('times$'(X0),X1) ) ),
    inference(ennf_transformation,[],[f561]) ).

tff(f561,axiom,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 != 'fun_app$r'('times$'(X0),X1) )
     => ( ( 0.0 != X1 )
        & ( 0.0 != X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom559) ).

tff(f3359,plain,
    spl173_57,
    inference(avatar_split_clause,[],[f2920,f3357]) ).

tff(f3357,plain,
    ( spl173_57
  <=> ! [X0: $real] : ( 0.0 = 'fun_app$r'('times$'(X0),0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_57])]) ).

tff(f2920,plain,
    ! [X0: $real] : ( 0.0 = 'fun_app$r'('times$'(X0),0.0) ),
    inference(equality_resolution,[],[f2195]) ).

tff(f2195,plain,
    ! [X0: $real,X1: $real] :
      ( ( 0.0 != X1 )
      | ( 0.0 = 'fun_app$r'('times$'(X0),X1) ) ),
    inference(cnf_transformation,[],[f1029]) ).

tff(f3355,plain,
    spl173_56,
    inference(avatar_split_clause,[],[f2127,f3353]) ).

tff(f2127,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(cnf_transformation,[],[f671]) ).

tff(f671,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(theory_normalization,[],[f114]) ).

tff(f114,axiom,
    ! [X0: $int,X1: $int] :
      ( $lesseq(X1,X0)
      | $lesseq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).

tff(f3351,plain,
    spl173_55,
    inference(avatar_split_clause,[],[f2125,f3349]) ).

tff(f2125,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(cnf_transformation,[],[f669]) ).

tff(f669,plain,
    ! [X0: $real,X1: $real] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X0) ),
    inference(theory_normalization,[],[f115]) ).

tff(f115,axiom,
    ! [X0: $real,X1: $real] :
      ( $lesseq(X1,X0)
      | $lesseq(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom113) ).

tff(f3347,plain,
    spl173_54,
    inference(avatar_split_clause,[],[f2101,f3345]) ).

tff(f2101,plain,
    ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less('of_nat$'(X0),$uminus('of_nat$'(X1))),
    inference(cnf_transformation,[],[f559]) ).

tff(f559,axiom,
    ! [X0: 'Nat$',X1: 'Nat$'] : ~ $less('of_nat$'(X0),$uminus('of_nat$'(X1))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).

tff(f3343,plain,
    spl173_53,
    inference(avatar_split_clause,[],[f2100,f3341]) ).

tff(f2100,plain,
    ! [X0: $real] : $less(X0,'fun_app$t'('of_nat$a',sK37(X0))),
    inference(cnf_transformation,[],[f1482]) ).

tff(f1482,plain,
    ! [X0: $real] : $less(X0,'fun_app$t'('of_nat$a',sK37(X0))),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f428,f1481]) ).

tff(f1481,plain,
    ! [X0: $real] :
      ( ? [X1: 'Nat$'] : $less(X0,'fun_app$t'('of_nat$a',X1))
     => $less(X0,'fun_app$t'('of_nat$a',sK37(X0))) ),
    introduced(choice_axiom,[]) ).

tff(f428,axiom,
    ! [X0: $real] :
    ? [X1: 'Nat$'] : $less(X0,'fun_app$t'('of_nat$a',X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).

tff(f3339,plain,
    spl173_52,
    inference(avatar_split_clause,[],[f2099,f3337]) ).

tff(f2099,plain,
    ! [X0: $real] : ~ $less('fun_app$t'('of_nat$a',sK36(X0)),X0),
    inference(cnf_transformation,[],[f1480]) ).

tff(f1480,plain,
    ! [X0: $real] : ~ $less('fun_app$t'('of_nat$a',sK36(X0)),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f665,f1479]) ).

tff(f1479,plain,
    ! [X0: $real] :
      ( ? [X1: 'Nat$'] : ~ $less('fun_app$t'('of_nat$a',X1),X0)
     => ~ $less('fun_app$t'('of_nat$a',sK36(X0)),X0) ),
    introduced(choice_axiom,[]) ).

tff(f665,plain,
    ! [X0: $real] :
    ? [X1: 'Nat$'] : ~ $less('fun_app$t'('of_nat$a',X1),X0),
    inference(theory_normalization,[],[f429]) ).

tff(f429,axiom,
    ! [X0: $real] :
    ? [X1: 'Nat$'] : $lesseq(X0,'fun_app$t'('of_nat$a',X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).

tff(f3334,plain,
    ( spl173_51
    | ~ spl173_24
    | ~ spl173_31 ),
    inference(avatar_split_clause,[],[f3263,f3236,f3206,f3331]) ).

tff(f3329,plain,
    spl173_50,
    inference(avatar_split_clause,[],[f1992,f3327]) ).

tff(f1992,plain,
    ! [X0: $int] :
      ( ~ $less(X0,1)
      | ~ $less(0,X0) ),
    inference(cnf_transformation,[],[f1408]) ).

tff(f1408,plain,
    ! [X0: $int] :
      ( ( ~ $less(X0,1)
        | ~ $less(0,X0) )
      & ( $less(0,X0)
        | $less(X0,1) ) ),
    inference(nnf_transformation,[],[f650]) ).

tff(f650,plain,
    ! [X0: $int] :
      ( ~ $less(X0,1)
    <=> $less(0,X0) ),
    inference(theory_normalization,[],[f407]) ).

tff(f407,axiom,
    ! [X0: $int] :
      ( $lesseq(1,X0)
    <=> $less(0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).

tff(f3325,plain,
    spl173_49,
    inference(avatar_split_clause,[],[f1991,f3323]) ).

tff(f1991,plain,
    ! [X0: $int] :
      ( $less(0,X0)
      | $less(X0,1) ),
    inference(cnf_transformation,[],[f1408]) ).

tff(f3321,plain,
    spl173_48,
    inference(avatar_split_clause,[],[f1965,f3319]) ).

tff(f3319,plain,
    ( spl173_48
  <=> ! [X0: tlbool] :
        ( ( tlfalse = X0 )
        | ( tltrue = X0 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_48])]) ).

tff(f1965,plain,
    ! [X0: tlbool] :
      ( ( tlfalse = X0 )
      | ( tltrue = X0 ) ),
    inference(cnf_transformation,[],[f875]) ).

tff(f875,plain,
    ! [X0: tlbool] :
      ( ( tlfalse = X0 )
      | ( tltrue = X0 ) ),
    inference(rectify,[],[f617]) ).

tff(f617,axiom,
    ! [X6: tlbool] :
      ( ( tlfalse = X6 )
      | ( tltrue = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_616) ).

tff(f3317,plain,
    spl173_47,
    inference(avatar_split_clause,[],[f1953,f3315]) ).

tff(f3315,plain,
    ( spl173_47
  <=> ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('one$a'),X0) = 'one$b' ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_47])]) ).

tff(f1953,plain,
    ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('one$a'),X0) = 'one$b' ),
    inference(cnf_transformation,[],[f164]) ).

tff(f164,axiom,
    ! [X0: 'Rows$'] : ( 'fun_app$d'('vec_nth$'('one$a'),X0) = 'one$b' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).

tff(f3313,plain,
    spl173_46,
    inference(avatar_split_clause,[],[f1952,f3311]) ).

tff(f3311,plain,
    ( spl173_46
  <=> ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('one$c'),X0) = 'one$d' ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_46])]) ).

tff(f1952,plain,
    ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('one$c'),X0) = 'one$d' ),
    inference(cnf_transformation,[],[f165]) ).

tff(f165,axiom,
    ! [X0: 'Rows$'] : ( 'fun_app$e'('vec_nth$a'('one$c'),X0) = 'one$d' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).

tff(f3309,plain,
    spl173_45,
    inference(avatar_split_clause,[],[f1951,f3307]) ).

tff(f3307,plain,
    ( spl173_45
  <=> ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('mat$'('one$'),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_45])]) ).

tff(f1951,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('mat$'('one$'),X0) = X0 ),
    inference(cnf_transformation,[],[f514]) ).

tff(f514,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('mat$'('one$'),X0) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).

tff(f3305,plain,
    spl173_44,
    inference(avatar_split_clause,[],[f1948,f3303]) ).

tff(f3303,plain,
    ( spl173_44
  <=> ! [X0: 'Rows$'] : ( 'zero$' = 'fun_app$d'('vec_nth$'('zero$b'),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_44])]) ).

tff(f1948,plain,
    ! [X0: 'Rows$'] : ( 'zero$' = 'fun_app$d'('vec_nth$'('zero$b'),X0) ),
    inference(cnf_transformation,[],[f58]) ).

tff(f58,axiom,
    ! [X0: 'Rows$'] : ( 'zero$' = 'fun_app$d'('vec_nth$'('zero$b'),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom56) ).

tff(f3301,plain,
    spl173_43,
    inference(avatar_split_clause,[],[f1947,f3299]) ).

tff(f3299,plain,
    ( spl173_43
  <=> ! [X0: 'Rows$'] : ( 'zero$a' = 'fun_app$e'('vec_nth$a'('zero$c'),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_43])]) ).

tff(f1947,plain,
    ! [X0: 'Rows$'] : ( 'zero$a' = 'fun_app$e'('vec_nth$a'('zero$c'),X0) ),
    inference(cnf_transformation,[],[f59]) ).

tff(f59,axiom,
    ! [X0: 'Rows$'] : ( 'zero$a' = 'fun_app$e'('vec_nth$a'('zero$c'),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom57) ).

tff(f3297,plain,
    spl173_42,
    inference(avatar_split_clause,[],[f1946,f3295]) ).

tff(f3295,plain,
    ( spl173_42
  <=> ! [X0: $int] : ~ $less('fun_app$o'('times$a'(X0),X0),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_42])]) ).

tff(f1946,plain,
    ! [X0: $int] : ~ $less('fun_app$o'('times$a'(X0),X0),0),
    inference(cnf_transformation,[],[f521]) ).

tff(f521,axiom,
    ! [X0: $int] : ~ $less('fun_app$o'('times$a'(X0),X0),0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom519) ).

tff(f3293,plain,
    spl173_41,
    inference(avatar_split_clause,[],[f1945,f3291]) ).

tff(f3291,plain,
    ( spl173_41
  <=> ! [X0: $real] : ~ $less('fun_app$r'('times$'(X0),X0),0.0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_41])]) ).

tff(f1945,plain,
    ! [X0: $real] : ~ $less('fun_app$r'('times$'(X0),X0),0.0),
    inference(cnf_transformation,[],[f522]) ).

tff(f522,axiom,
    ! [X0: $real] : ~ $less('fun_app$r'('times$'(X0),X0),0.0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).

tff(f3289,plain,
    ( spl173_40
    | ~ spl173_20
    | ~ spl173_31 ),
    inference(avatar_split_clause,[],[f3262,f3236,f3186,f3286]) ).

tff(f3286,plain,
    ( spl173_40
  <=> ( 'nat$'(1) = 'to_nat$'('one$e') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_40])]) ).

tff(f3283,plain,
    spl173_39,
    inference(avatar_split_clause,[],[f1897,f3280]) ).

tff(f1897,plain,
    0.0 = 'fun_app$t'('of_nat$a','nat$'(0)),
    inference(cnf_transformation,[],[f177]) ).

tff(f177,axiom,
    0.0 = 'fun_app$t'('of_nat$a','nat$'(0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).

tff(f3277,plain,
    spl173_38,
    inference(avatar_split_clause,[],[f1896,f3274]) ).

tff(f1896,plain,
    1.0 = 'fun_app$t'('of_nat$a','nat$'(1)),
    inference(cnf_transformation,[],[f171]) ).

tff(f171,axiom,
    1.0 = 'fun_app$t'('of_nat$a','nat$'(1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).

tff(f3272,plain,
    spl173_37,
    inference(avatar_split_clause,[],[f859,f3270]) ).

tff(f3270,plain,
    ( spl173_37
  <=> ! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_37])]) ).

tff(f859,plain,
    ! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f3268,plain,
    spl173_36,
    inference(avatar_split_clause,[],[f841,f3266]) ).

tff(f3266,plain,
    ( spl173_36
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_36])]) ).

tff(f841,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f3256,plain,
    spl173_35,
    inference(avatar_split_clause,[],[f3080,f3253]) ).

tff(f3253,plain,
    ( spl173_35
  <=> ( -1.0 = 'fun_app$r'('dbl_inc$a',-1.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_35])]) ).

tff(f3080,plain,
    -1.0 = 'fun_app$r'('dbl_inc$a',-1.0),
    inference(evaluation,[],[f1898]) ).

tff(f1898,plain,
    $uminus(1.0) = 'fun_app$r'('dbl_inc$a',$uminus(1.0)),
    inference(cnf_transformation,[],[f515]) ).

tff(f515,axiom,
    $uminus(1.0) = 'fun_app$r'('dbl_inc$a',$uminus(1.0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).

tff(f3251,plain,
    spl173_34,
    inference(avatar_split_clause,[],[f3079,f3248]) ).

tff(f3248,plain,
    ( spl173_34
  <=> ( -1 = 'fun_app$o'('dbl_inc$',-1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_34])]) ).

tff(f3079,plain,
    -1 = 'fun_app$o'('dbl_inc$',-1),
    inference(evaluation,[],[f1899]) ).

tff(f1899,plain,
    $uminus(1) = 'fun_app$o'('dbl_inc$',$uminus(1)),
    inference(cnf_transformation,[],[f516]) ).

tff(f516,axiom,
    $uminus(1) = 'fun_app$o'('dbl_inc$',$uminus(1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).

tff(f3246,plain,
    spl173_33,
    inference(avatar_split_clause,[],[f1942,f3244]) ).

tff(f1942,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('zero$b',X0) = 'zero$c' ),
    inference(cnf_transformation,[],[f55]) ).

tff(f55,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'matrix_matrix_mult$'('zero$b',X0) = 'zero$c' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).

tff(f3242,plain,
    spl173_32,
    inference(avatar_split_clause,[],[f1938,f3240]) ).

tff(f1938,plain,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('zero$',X0) = 'zero$a' ),
    inference(cnf_transformation,[],[f52]) ).

tff(f52,axiom,
    ! [X0: 'A_cols_vec_rows_vec$'] : ( 'vector_matrix_mult$'('zero$',X0) = 'zero$a' ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).

tff(f3238,plain,
    spl173_31,
    inference(avatar_split_clause,[],[f1930,f3236]) ).

tff(f1930,plain,
    ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f615]) ).

tff(f615,axiom,
    ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom613) ).

tff(f3234,plain,
    spl173_30,
    inference(avatar_split_clause,[],[f1929,f3232]) ).

tff(f3232,plain,
    ( spl173_30
  <=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_30])]) ).

tff(f1929,plain,
    ! [X0: $int] : ( 0 = $product(0,X0) ),
    inference(cnf_transformation,[],[f442]) ).

tff(f442,axiom,
    ! [X0: $int] : ( 0 = $product(0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).

tff(f3230,plain,
    spl173_29,
    inference(avatar_split_clause,[],[f1926,f3228]) ).

tff(f3228,plain,
    ( spl173_29
  <=> ! [X0: $real] : ( 0.0 = $product(0.0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_29])]) ).

tff(f1926,plain,
    ! [X0: $real] : ( 0.0 = $product(0.0,X0) ),
    inference(cnf_transformation,[],[f453]) ).

tff(f453,axiom,
    ! [X0: $real] : ( 0.0 = $product(0.0,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).

tff(f3226,plain,
    spl173_28,
    inference(avatar_split_clause,[],[f1923,f3224]) ).

tff(f1923,plain,
    ! [X0: 'A_rows_vec_rows_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$'(X0,'zero$c') ),
    inference(cnf_transformation,[],[f56]) ).

tff(f56,axiom,
    ! [X0: 'A_rows_vec_rows_vec$'] : ( 'zero$c' = 'matrix_matrix_mult$'(X0,'zero$c') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).

tff(f3222,plain,
    spl173_27,
    inference(avatar_split_clause,[],[f1922,f3220]) ).

tff(f1922,plain,
    ! [X0: 'A_rows_vec$'] : ( 'zero$a' = 'vector_matrix_mult$'(X0,'zero$c') ),
    inference(cnf_transformation,[],[f57]) ).

tff(f57,axiom,
    ! [X0: 'A_rows_vec$'] : ( 'zero$a' = 'vector_matrix_mult$'(X0,'zero$c') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).

tff(f3218,plain,
    spl173_26,
    inference(avatar_split_clause,[],[f1920,f3216]) ).

tff(f3216,plain,
    ( spl173_26
  <=> ! [X0: 'Nat$'] : ~ $less('fun_app$t'('of_nat$a',X0),0.0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_26])]) ).

tff(f1920,plain,
    ! [X0: 'Nat$'] : ~ $less('fun_app$t'('of_nat$a',X0),0.0),
    inference(cnf_transformation,[],[f189]) ).

tff(f189,axiom,
    ! [X0: 'Nat$'] : ~ $less('fun_app$t'('of_nat$a',X0),0.0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).

tff(f3214,plain,
    spl173_25,
    inference(avatar_split_clause,[],[f1894,f3211]) ).

tff(f3211,plain,
    ( spl173_25
  <=> ( 0 = 'of_nat$'('nat$'(0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_25])]) ).

tff(f1894,plain,
    0 = 'of_nat$'('nat$'(0)),
    inference(cnf_transformation,[],[f176]) ).

tff(f176,axiom,
    0 = 'of_nat$'('nat$'(0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).

tff(f3209,plain,
    spl173_24,
    inference(avatar_split_clause,[],[f1893,f3206]) ).

tff(f1893,plain,
    0 = 'of_nat$'('to_nat$'('zero$d')),
    inference(cnf_transformation,[],[f130]) ).

tff(f130,axiom,
    0 = 'of_nat$'('to_nat$'('zero$d')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).

tff(f3204,plain,
    spl173_23,
    inference(avatar_split_clause,[],[f1892,f3201]) ).

tff(f1892,plain,
    0 = 'of_nat$'('rank$'('zero$c')),
    inference(cnf_transformation,[],[f75]) ).

tff(f75,axiom,
    0 = 'of_nat$'('rank$'('zero$c')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).

tff(f3199,plain,
    spl173_22,
    inference(avatar_split_clause,[],[f1891,f3196]) ).

tff(f3196,plain,
    ( spl173_22
  <=> ( 1 = 'fun_app$o'('dbl_inc$',0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_22])]) ).

tff(f1891,plain,
    1 = 'fun_app$o'('dbl_inc$',0),
    inference(cnf_transformation,[],[f432]) ).

tff(f432,axiom,
    1 = 'fun_app$o'('dbl_inc$',0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).

tff(f3194,plain,
    spl173_21,
    inference(avatar_split_clause,[],[f1889,f3191]) ).

tff(f3191,plain,
    ( spl173_21
  <=> ( 1 = 'of_nat$'('nat$'(1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_21])]) ).

tff(f1889,plain,
    1 = 'of_nat$'('nat$'(1)),
    inference(cnf_transformation,[],[f426]) ).

tff(f426,axiom,
    1 = 'of_nat$'('nat$'(1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).

tff(f3189,plain,
    spl173_20,
    inference(avatar_split_clause,[],[f1888,f3186]) ).

tff(f1888,plain,
    1 = 'of_nat$'('to_nat$'('one$e')),
    inference(cnf_transformation,[],[f207]) ).

tff(f207,axiom,
    1 = 'of_nat$'('to_nat$'('one$e')),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).

tff(f3184,plain,
    spl173_19,
    inference(avatar_split_clause,[],[f1887,f3181]) ).

tff(f3181,plain,
    ( spl173_19
  <=> ( 1.0 = 'fun_app$r'('dbl_inc$a',0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_19])]) ).

tff(f1887,plain,
    1.0 = 'fun_app$r'('dbl_inc$a',0.0),
    inference(cnf_transformation,[],[f433]) ).

tff(f433,axiom,
    1.0 = 'fun_app$r'('dbl_inc$a',0.0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom431) ).

tff(f3179,plain,
    spl173_18,
    inference(avatar_split_clause,[],[f869,f3177]) ).

tff(f3177,plain,
    ( spl173_18
  <=> ! [X0: $real] : ( 0.0 = $product(X0,0.0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_18])]) ).

tff(f869,plain,
    ! [X0: $real] : ( 0.0 = $product(X0,0.0) ),
    introduced(theory_axiom_149,[]) ).

tff(f3175,plain,
    spl173_17,
    inference(avatar_split_clause,[],[f868,f3173]) ).

tff(f3173,plain,
    ( spl173_17
  <=> ! [X0: $real] : ( $product(X0,1.0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_17])]) ).

tff(f868,plain,
    ! [X0: $real] : ( $product(X0,1.0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f3171,plain,
    spl173_16,
    inference(avatar_split_clause,[],[f865,f3169]) ).

tff(f3169,plain,
    ( spl173_16
  <=> ! [X0: $real] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_16])]) ).

tff(f865,plain,
    ! [X0: $real] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f3167,plain,
    spl173_15,
    inference(avatar_split_clause,[],[f857,f3165]) ).

tff(f3165,plain,
    ( spl173_15
  <=> ! [X0: $real] : ( $sum(X0,0.0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_15])]) ).

tff(f857,plain,
    ! [X0: $real] : ( $sum(X0,0.0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f3163,plain,
    spl173_14,
    inference(avatar_split_clause,[],[f851,f3161]) ).

tff(f3161,plain,
    ( spl173_14
  <=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_14])]) ).

tff(f851,plain,
    ! [X0: $int] : ( 0 = $product(X0,0) ),
    introduced(theory_axiom_149,[]) ).

tff(f3159,plain,
    spl173_13,
    inference(avatar_split_clause,[],[f850,f3157]) ).

tff(f3157,plain,
    ( spl173_13
  <=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_13])]) ).

tff(f850,plain,
    ! [X0: $int] : ( $product(X0,1) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f3155,plain,
    spl173_12,
    inference(avatar_split_clause,[],[f847,f3153]) ).

tff(f3153,plain,
    ( spl173_12
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_12])]) ).

tff(f847,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f3151,plain,
    spl173_11,
    inference(avatar_split_clause,[],[f839,f3149]) ).

tff(f3149,plain,
    ( spl173_11
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_11])]) ).

tff(f839,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f3147,plain,
    spl173_10,
    inference(avatar_split_clause,[],[f2098,f3145]) ).

tff(f2098,plain,
    ! [X0: $int] : $less(sK35(X0),X0),
    inference(cnf_transformation,[],[f1478]) ).

tff(f1478,plain,
    ! [X0: $int] : $less(sK35(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f283,f1477]) ).

tff(f1477,plain,
    ! [X0: $int] :
      ( ? [X1: $int] : $less(X1,X0)
     => $less(sK35(X0),X0) ),
    introduced(choice_axiom,[]) ).

tff(f283,axiom,
    ! [X0: $int] :
    ? [X1: $int] : $less(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).

tff(f3143,plain,
    spl173_9,
    inference(avatar_split_clause,[],[f2097,f3141]) ).

tff(f2097,plain,
    ! [X0: $int] : $less(X0,sK34(X0)),
    inference(cnf_transformation,[],[f1476]) ).

tff(f1476,plain,
    ! [X0: $int] : $less(X0,sK34(X0)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK34])],[f281,f1475]) ).

tff(f1475,plain,
    ! [X0: $int] :
      ( ? [X1: $int] : $less(X0,X1)
     => $less(X0,sK34(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f281,axiom,
    ! [X0: $int] :
    ? [X1: $int] : $less(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom279) ).

tff(f3139,plain,
    spl173_8,
    inference(avatar_split_clause,[],[f2096,f3137]) ).

tff(f2096,plain,
    ! [X0: $real] : $less(sK33(X0),X0),
    inference(cnf_transformation,[],[f1474]) ).

tff(f1474,plain,
    ! [X0: $real] : $less(sK33(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK33])],[f284,f1473]) ).

tff(f1473,plain,
    ! [X0: $real] :
      ( ? [X1: $real] : $less(X1,X0)
     => $less(sK33(X0),X0) ),
    introduced(choice_axiom,[]) ).

tff(f284,axiom,
    ! [X0: $real] :
    ? [X1: $real] : $less(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).

tff(f3135,plain,
    spl173_7,
    inference(avatar_split_clause,[],[f2095,f3133]) ).

tff(f2095,plain,
    ! [X0: $real] : $less(X0,sK32(X0)),
    inference(cnf_transformation,[],[f1472]) ).

tff(f1472,plain,
    ! [X0: $real] : $less(X0,sK32(X0)),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f282,f1471]) ).

tff(f1471,plain,
    ! [X0: $real] :
      ( ? [X1: $real] : $less(X0,X1)
     => $less(X0,sK32(X0)) ),
    introduced(choice_axiom,[]) ).

tff(f282,axiom,
    ! [X0: $real] :
    ? [X1: $real] : $less(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).

tff(f3131,plain,
    spl173_6,
    inference(avatar_split_clause,[],[f1913,f3129]) ).

tff(f3129,plain,
    ( spl173_6
  <=> ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_6])]) ).

tff(f1913,plain,
    ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0),
    inference(cnf_transformation,[],[f188]) ).

tff(f188,axiom,
    ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).

tff(f3127,plain,
    ( ~ spl173_5
    | spl173_4 ),
    inference(avatar_split_clause,[],[f3122,f3117,f3124]) ).

tff(f3117,plain,
    ( spl173_4
  <=> ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_4])]) ).

tff(f3122,plain,
    ( ( 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') != 'row$a'('i$','matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')) )
    | spl173_4 ),
    inference(forward_demodulation,[],[f3121,f2534]) ).

tff(f3121,plain,
    ( ( 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') != 'vector_matrix_mult$'('row$'('i$','p_Gauss_Jordan$'('a$')),'a$') )
    | spl173_4 ),
    inference(forward_demodulation,[],[f3119,f1901]) ).

tff(f3119,plain,
    ( ( 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') != 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') )
    | spl173_4 ),
    inference(avatar_component_clause,[],[f3117]) ).

tff(f3120,plain,
    ~ spl173_4,
    inference(avatar_split_clause,[],[f1849,f3117]) ).

tff(f1849,plain,
    'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') != 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$'),
    inference(cnf_transformation,[],[f872]) ).

tff(f872,plain,
    'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') != 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$'),
    inference(flattening,[],[f4]) ).

tff(f4,negated_conjecture,
    ( ~ 'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$') ),
    inference(negated_conjecture,[],[f3]) ).

tff(f3,conjecture,
    'vector_matrix_mult$'('fun_app$d'('vec_nth$'('p_Gauss_Jordan$'('a$')),'i$'),'a$') = 'fun_app$e'('vec_nth$a'('matrix_matrix_mult$'('p_Gauss_Jordan$'('a$'),'a$')),'i$'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture2) ).

tff(f3115,plain,
    ~ spl173_3,
    inference(avatar_split_clause,[],[f1850,f3112]) ).

tff(f3112,plain,
    ( spl173_3
  <=> ( tltrue = tlfalse ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl173_3])]) ).

tff(f1850,plain,
    tltrue != tlfalse,
    inference(cnf_transformation,[],[f618]) ).

tff(f618,axiom,
    tltrue != tlfalse,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_617) ).

tff(f3110,plain,
    spl173_2,
    inference(avatar_split_clause,[],[f860,f3108]) ).

tff(f860,plain,
    ! [X0: $real] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f3106,plain,
    spl173_1,
    inference(avatar_split_clause,[],[f842,f3104]) ).

tff(f842,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% 0.03/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 18 17:30:08 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (10251)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40  % (10254)WARNING: value z3 for option sas not known
% 0.21/0.40  % (10255)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40  % (10253)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40  % (10254)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)
% 0.21/0.40  % (10256)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)
% 0.21/0.40  % (10257)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)
% 0.21/0.40  % (10258)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)
% 0.21/0.40  % (10252)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.42  % (10253)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42  % (10253)Terminated due to inappropriate strategy.
% 0.21/0.42  % (10253)------------------------------
% 0.21/0.42  % (10253)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.42  % (10253)Termination reason: Inappropriate
% 0.21/0.42  
% 0.21/0.42  % (10253)Memory used [KB]: 2019
% 0.21/0.42  % (10253)Time elapsed: 0.024 s
% 0.21/0.42  % (10253)Instructions burned: 55 (million)
% 0.21/0.42  % (10253)------------------------------
% 0.21/0.42  % (10253)------------------------------
% 0.21/0.42  % (10255)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42  % (10255)Terminated due to inappropriate strategy.
% 0.21/0.42  % (10255)------------------------------
% 0.21/0.42  % (10255)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.42  % (10255)Termination reason: Inappropriate
% 0.21/0.42  
% 0.21/0.42  % (10255)Memory used [KB]: 2013
% 0.21/0.42  % (10255)Time elapsed: 0.025 s
% 0.21/0.42  % (10255)Instructions burned: 57 (million)
% 0.21/0.42  % (10252)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42  % (10252)Terminated due to inappropriate strategy.
% 0.21/0.42  % (10252)------------------------------
% 0.21/0.42  % (10252)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.42  % (10252)Termination reason: Inappropriate
% 0.21/0.42  
% 0.21/0.42  % (10252)Memory used [KB]: 2019
% 0.21/0.42  % (10252)Time elapsed: 0.024 s
% 0.21/0.42  % (10252)Instructions burned: 56 (million)
% 0.21/0.42  % (10255)------------------------------
% 0.21/0.42  % (10255)------------------------------
% 0.21/0.42  % (10252)------------------------------
% 0.21/0.42  % (10252)------------------------------
% 0.21/0.44  % (10259)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.44  % (10260)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)
% 0.21/0.44  % (10261)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)
% 0.21/0.46  % (10259)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.46  % (10259)Terminated due to inappropriate strategy.
% 0.21/0.46  % (10259)------------------------------
% 0.21/0.46  % (10259)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.46  % (10259)Termination reason: Inappropriate
% 0.21/0.46  
% 0.21/0.46  % (10259)Memory used [KB]: 1978
% 0.21/0.46  % (10259)Time elapsed: 0.025 s
% 0.21/0.46  % (10259)Instructions burned: 59 (million)
% 0.21/0.46  % (10259)------------------------------
% 0.21/0.46  % (10259)------------------------------
% 0.21/0.48  % (10262)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)
% 0.21/0.52  % (10256)First to succeed.
% 1.15/0.53  % (10256)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10251"
% 1.15/0.53  % (10256)Refutation found. Thanks to Tanya!
% 1.15/0.53  % SZS status Theorem for theBenchmark
% 1.15/0.53  % SZS output start Proof for theBenchmark
% See solution above
% 1.15/0.54  % (10256)------------------------------
% 1.15/0.54  % (10256)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.15/0.54  % (10256)Termination reason: Refutation
% 1.15/0.54  
% 1.15/0.54  % (10256)Memory used [KB]: 3863
% 1.15/0.54  % (10256)Time elapsed: 0.134 s
% 1.15/0.54  % (10256)Instructions burned: 279 (million)
% 1.15/0.54  % (10251)Success in time 0.172 s
%------------------------------------------------------------------------------