TSTP Solution File: ITP339_1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n015.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 : Sun May  5 06:55:57 EDT 2024

% Result   : Theorem 0.58s 0.79s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  276
% Syntax   : Number of formulae    :  287 (  15 unt; 272 typ;   0 def)
%            Number of atoms       :   15 (  14 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   2 avg)
%            Maximal term depth    :   14 (   3 avg)
%            Number of FOOLs       :    1 (   1 fml;   0 var)
%            Number arithmetic     :  156 (   0 atm;  47 fun; 109 num;   0 var)
%            Number of types       :   50 (  48 usr;   1 ari)
%            Number of type conns  :  304 ( 196   >; 108   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-3 aty)
%            Number of functors    :  212 ( 208 usr;  31 con; 0-3 aty)
%            Number of variables   :    4 (   4   !;   0   ?;   4   :)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(type_def_30,type,
    tlbool: $tType ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(func_def_0,type,
    'snd$g': 'Int_nat_prod$' > 'Nat$' ).

tff(func_def_1,type,
    'foldl$a': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'Nat_list$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).

tff(func_def_2,type,
    'b$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).

tff(func_def_3,type,
    'fun_app$l': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$' * 'A_c_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod_bool_fun$' ).

tff(func_def_4,type,
    'gauss_Jordan_in_ij_iarrays_PA$': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'Nat$' * 'Nat$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_5,type,
    'pair$b': ( 'Nat$' * 'A_iarray_iarray$' ) > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_6,type,
    'fst$f': 'Nat_int_prod$' > 'Nat$' ).

tff(func_def_7,type,
    'ncols$a': 'A_c_vec_c_vec$' > 'Nat$' ).

tff(func_def_8,type,
    'fun_app$z': ( 'Int_int_fun$' * $int ) > $int ).

tff(func_def_9,type,
    'plus$h': ( 'Int_nat_prod$' * 'Int_nat_prod$' ) > 'Int_nat_prod$' ).

tff(func_def_10,type,
    'pair$d': ( 'A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).

tff(func_def_11,type,
    'mat$': 'A$' > 'A_c_vec_c_vec$' ).

tff(func_def_12,type,
    'gauss_Jordan_column_k_PA$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' ).

tff(func_def_13,type,
    'gauss_Jordan_upt_k_PA$': ( 'A_b_vec_c_vec$' * 'Nat$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).

tff(func_def_14,type,
    'fun_app$q': ( 'Nat_a_b_vec_c_vec_bool_fun_fun$' * 'Nat$' ) > 'A_b_vec_c_vec_bool_fun$' ).

tff(func_def_15,type,
    'a$a': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_16,type,
    'fst$l': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_17,type,
    'pair$e': ( 'Nat$' * 'Nat$' ) > 'Nat_nat_prod$' ).

tff(func_def_18,type,
    'snd$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_19,type,
    'pair$h': ( $int * $int ) > 'Int_int_prod$' ).

tff(func_def_20,type,
    'fun_app$o': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_bool_fun$' ).

tff(func_def_21,type,
    'pair$a': ( 'Nat$' * 'A_b_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_22,type,
    'snd$h': 'Int_int_prod$' > $int ).

tff(func_def_23,type,
    'fst$e': 'Nat_nat_prod$' > 'Nat$' ).

tff(func_def_24,type,
    'fst$k': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_25,type,
    'fun_app$': ( 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_26,type,
    'foldl$': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_list$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_27,type,
    'nrows$': 'A_b_vec_c_vec$' > 'Nat$' ).

tff(func_def_28,type,
    'pair$f': ( 'Nat$' * $int ) > 'Nat_int_prod$' ).

tff(func_def_29,type,
    'snd$e': 'Nat_nat_prod$' > 'Nat$' ).

tff(func_def_30,type,
    'zero$a': 'A_c_vec_c_vec$' ).

tff(func_def_31,type,
    'fun_app$r': ( 'Nat_a_iarray_iarray_bool_fun_fun$' * 'Nat$' ) > 'A_iarray_iarray_bool_fun$' ).

tff(func_def_32,type,
    'fun_app$m': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'Nat_a_iarray_iarray_prod_bool_fun$' ).

tff(func_def_33,type,
    'pair$l': ( 'A_c_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).

tff(func_def_34,type,
    'fun_app$t': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).

tff(func_def_35,type,
    'snd$a': 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).

tff(func_def_36,type,
    'pair$j': ( 'A_c_vec_c_vec$' * 'Nat_a_c_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).

tff(func_def_37,type,
    'of_nat$': 'Nat_int_fun$' ).

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

tff(func_def_39,type,
    'upt$': ( 'Nat$' * 'Nat$' ) > 'Nat_list$' ).

tff(func_def_40,type,
    'nrows$a': 'A_c_vec_c_vec$' > 'Nat$' ).

tff(func_def_41,type,
    'fst$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_42,type,
    'fst$a': 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).

tff(func_def_43,type,
    'snd$b': 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_44,type,
    'fst$g': 'Int_nat_prod$' > $int ).

tff(func_def_45,type,
    'zero$b': 'Int_nat_prod$' ).

tff(func_def_46,type,
    'less$': 'Nat_nat_bool_fun_fun$' ).

tff(func_def_47,type,
    'nrows_iarray$': 'A_iarray_iarray$' > 'Nat$' ).

tff(func_def_48,type,
    'pair$i': ( 'Nat$' * 'A_iarray$' ) > 'Nat_a_iarray_prod$' ).

tff(func_def_49,type,
    tltrue: tlbool ).

tff(func_def_50,type,
    'gauss_Jordan_column_k_PA$a': ( 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).

tff(func_def_51,type,
    'plus$f': ( 'Nat_a_iarray_iarray_prod$' * 'Nat_a_iarray_iarray_prod$' ) > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_52,type,
    'plus$': 'Nat$' > 'Nat_nat_fun$' ).

tff(func_def_53,type,
    'fun_app$a': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' ).

tff(func_def_54,type,
    'snd$f': 'Nat_int_prod$' > $int ).

tff(func_def_55,type,
    'pair$c': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_56,type,
    'plus$k': ( 'Nat_nat_prod$' * 'Nat_nat_prod$' ) > 'Nat_nat_prod$' ).

tff(func_def_57,type,
    'gauss_Jordan_column_k_iarrays_PA$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' ).

tff(func_def_58,type,
    'one$a': 'Nat$' ).

tff(func_def_59,type,
    'fst$i': 'Nat_a_iarray_prod$' > 'Nat$' ).

tff(func_def_60,type,
    'plus$j': ( 'Nat_int_prod$' * 'Nat_int_prod$' ) > 'Nat_int_prod$' ).

tff(func_def_61,type,
    'zero$i': 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_62,type,
    'fun_app$v': ( 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' * 'Nat$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).

tff(func_def_63,type,
    'fst$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_64,type,
    'fun_app$y': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).

tff(func_def_65,type,
    'fst$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).

tff(func_def_66,type,
    'ncols$': 'A_b_vec_c_vec$' > 'Nat$' ).

tff(func_def_67,type,
    'fst$b': 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).

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

tff(func_def_69,type,
    'vector_all_zero_from_index$': 'Nat_a_iarray_prod_bool_fun$' ).

tff(func_def_70,type,
    'plus$l': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_71,type,
    'plus$c': ( 'Nat_a_b_vec_c_vec_prod$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_72,type,
    'matrix_to_iarray$a': 'A_b_vec_c_vec$' > 'A_iarray_iarray$' ).

tff(func_def_73,type,
    'plus$d': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).

tff(func_def_74,type,
    'zero$h': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_75,type,
    'pair$k': ( 'Nat$' * 'A_c_vec_c_vec$' ) > 'Nat_a_c_vec_c_vec_prod$' ).

tff(func_def_76,type,
    'column_iarray$': ( 'Nat$' * 'A_iarray_iarray$' ) > 'A_iarray$' ).

tff(func_def_77,type,
    'fun_app$w': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' ).

tff(func_def_78,type,
    'zero$j': 'A_b_vec_c_vec$' ).

tff(func_def_79,type,
    'divides_aux$': 'Int_int_prod_bool_fun$' ).

tff(func_def_80,type,
    'less_eq$': 'Nat_nat_bool_fun_fun$' ).

tff(func_def_81,type,
    'snd$i': 'Nat_a_iarray_prod$' > 'A_iarray$' ).

tff(func_def_82,type,
    'plus$e': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).

tff(func_def_83,type,
    'zero$c': 'Nat_a_c_vec_c_vec_prod$' ).

tff(func_def_84,type,
    'zero$': 'A$' ).

tff(func_def_85,type,
    'matrix_to_iarray$': 'A_c_vec_c_vec$' > 'A_iarray_iarray$' ).

tff(func_def_86,type,
    'plus$i': ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_b_vec_c_vec$' ).

tff(func_def_87,type,
    'plus$g': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).

tff(func_def_88,type,
    tlfalse: tlbool ).

tff(func_def_89,type,
    'zero$g': 'Int_int_prod$' ).

tff(func_def_90,type,
    'nat$': $int > 'Nat$' ).

tff(func_def_91,type,
    'fst$h': 'Int_int_prod$' > $int ).

tff(func_def_92,type,
    'zero$e': 'Nat_nat_prod$' ).

tff(func_def_93,type,
    'zero$f': 'Nat_int_prod$' ).

tff(func_def_94,type,
    'snd$l': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).

tff(func_def_95,type,
    'pair$': ( 'A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_96,type,
    'gauss_Jordan_upt_k_iarrays_PA$': ( 'A_iarray_iarray$' * 'Nat$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).

tff(func_def_97,type,
    'suc$': 'Nat_nat_fun$' ).

tff(func_def_98,type,
    'plus$a': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).

tff(func_def_99,type,
    'pair$g': ( $int * 'Nat$' ) > 'Int_nat_prod$' ).

tff(func_def_100,type,
    'fun_app$b': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).

tff(func_def_101,type,
    'fst$j': 'Nat_a_c_vec_c_vec_prod$' > 'Nat$' ).

tff(func_def_102,type,
    'zero$d': 'Nat$' ).

tff(func_def_103,type,
    'a$': 'A_b_vec_c_vec$' ).

tff(func_def_104,type,
    'ka$': 'Nat$' ).

tff(func_def_105,type,
    'snd$j': 'Nat_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_106,type,
    'plus$b': ( 'A_c_vec_c_vec$' * 'A_c_vec_c_vec$' ) > 'A_c_vec_c_vec$' ).

tff(func_def_107,type,
    'mat_iarray$': ( 'A$' * 'Nat$' ) > 'A_iarray_iarray$' ).

tff(func_def_108,type,
    'k$': 'Nat$' ).

tff(func_def_109,type,
    'snd$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_110,type,
    'snd$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_111,type,
    'snd$k': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$' ).

tff(func_def_116,type,
    sK3: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_117,type,
    sK4: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$' ).

tff(func_def_118,type,
    sK5: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$' ).

tff(func_def_119,type,
    sK6: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).

tff(func_def_120,type,
    sK7: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).

tff(func_def_121,type,
    sK8: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).

tff(func_def_122,type,
    sK9: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).

tff(func_def_123,type,
    sK10: ( 'A_b_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'Nat$' ).

tff(func_def_124,type,
    sK11: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_125,type,
    sK12: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_126,type,
    sK13: ( 'Nat$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_b_vec_c_vec$' ).

tff(func_def_127,type,
    sK14: ( 'A_c_vec_c_vec$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_128,type,
    sK15: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_129,type,
    sK16: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_130,type,
    sK17: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_131,type,
    sK18: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_132,type,
    sK19: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_133,type,
    sK20: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_134,type,
    sK21: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_135,type,
    sK22: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_136,type,
    sK23: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_137,type,
    sK24: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_138,type,
    sK25: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_139,type,
    sK26: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_140,type,
    sK27: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_141,type,
    sK28: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_142,type,
    sK29: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_143,type,
    sK30: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_144,type,
    sK31: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_145,type,
    sK32: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_146,type,
    sK33: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_147,type,
    sK34: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_148,type,
    sK35: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_149,type,
    sK36: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_150,type,
    sK37: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_151,type,
    sK38: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_152,type,
    sK39: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_153,type,
    sK40: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_154,type,
    sK41: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_155,type,
    sK42: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_156,type,
    sK43: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).

tff(func_def_157,type,
    sK44: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_158,type,
    sK45: 'Nat_int_fun$' > 'Nat$' ).

tff(func_def_159,type,
    sK46: 'Nat_int_fun$' > 'Nat$' ).

tff(func_def_160,type,
    sK47: 'Nat_int_fun$' > 'Nat$' ).

tff(func_def_161,type,
    sK48: 'Nat_int_fun$' > 'Nat$' ).

tff(func_def_162,type,
    sK49: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_163,type,
    sK50: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_164,type,
    sK51: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).

tff(func_def_165,type,
    sK52: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).

tff(func_def_166,type,
    sK53: ( 'Nat_a_b_vec_c_vec_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'A_c_vec_c_vec$' ).

tff(func_def_167,type,
    sK54: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_168,type,
    sK55: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_169,type,
    sK56: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_170,type,
    sK57: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_171,type,
    sK58: 'Nat$' > 'Nat$' ).

tff(func_def_172,type,
    sK59: 'Nat$' > 'Nat$' ).

tff(func_def_173,type,
    sK60: 'Nat$' > 'Nat$' ).

tff(func_def_174,type,
    sK61: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_175,type,
    sK62: 'Nat$' > 'Nat$' ).

tff(func_def_176,type,
    sK63: 'Nat$' > 'Nat$' ).

tff(func_def_177,type,
    sK64: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_178,type,
    sK65: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_179,type,
    sK66: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_180,type,
    sK67: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).

tff(func_def_181,type,
    sK68: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat$' ).

tff(func_def_182,type,
    sK69: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).

tff(func_def_183,type,
    sK70: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).

tff(func_def_184,type,
    sK71: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_185,type,
    sK72: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).

tff(func_def_186,type,
    sK73: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).

tff(func_def_187,type,
    sK74: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).

tff(func_def_188,type,
    sK75: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_189,type,
    sK76: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).

tff(func_def_190,type,
    sK77: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_191,type,
    sK78: $int > $int ).

tff(func_def_192,type,
    sK79: $int > $int ).

tff(func_def_193,type,
    sK80: ( 'A_iarray_iarray$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'Nat_a_iarray_iarray_prod$' ).

tff(func_def_194,type,
    sK81: ( 'A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$' ) > 'Nat$' ).

tff(func_def_195,type,
    sK82: ( 'Nat_a_iarray_iarray_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_196,type,
    sK83: ( 'Nat$' * 'Nat_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_197,type,
    sK84: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_198,type,
    sK85: 'Nat_nat_fun$' > 'Nat$' ).

tff(func_def_199,type,
    sK86: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_200,type,
    sK87: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_201,type,
    sK88: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).

tff(func_def_202,type,
    sK89: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_203,type,
    sK90: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_204,type,
    sK91: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_205,type,
    sK92: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).

tff(func_def_206,type,
    sK93: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_207,type,
    sK94: 'Nat_bool_fun$' > 'Nat$' ).

tff(func_def_208,type,
    sK95: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$' ).

tff(func_def_209,type,
    sK96: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$' ).

tff(func_def_210,type,
    sK97: ( 'A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(func_def_211,type,
    sK98: ( 'A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).

tff(pred_def_1,type,
    'fun_app$n': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > $o ).

tff(pred_def_2,type,
    'fun_app$f': ( 'Int_nat_prod_bool_fun$' * 'Int_nat_prod$' ) > $o ).

tff(pred_def_3,type,
    'fun_app$p': ( 'A_b_vec_c_vec_bool_fun$' * 'A_b_vec_c_vec$' ) > $o ).

tff(pred_def_4,type,
    'fun_app$g': ( 'Int_int_prod_bool_fun$' * 'Int_int_prod$' ) > $o ).

tff(pred_def_5,type,
    'fun_app$j': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > $o ).

tff(pred_def_6,type,
    'fun_app$d': ( 'Nat_nat_prod_bool_fun$' * 'Nat_nat_prod$' ) > $o ).

tff(pred_def_7,type,
    'fun_app$e': ( 'Nat_int_prod_bool_fun$' * 'Nat_int_prod$' ) > $o ).

tff(pred_def_8,type,
    'fun_app$i': ( 'Nat_a_b_vec_c_vec_prod_bool_fun$' * 'Nat_a_b_vec_c_vec_prod$' ) > $o ).

tff(pred_def_9,type,
    'fun_app$k': ( 'Nat_a_iarray_iarray_prod_bool_fun$' * 'Nat_a_iarray_iarray_prod$' ) > $o ).

tff(pred_def_10,type,
    'fun_app$x': ( 'Int_bool_fun$' * $int ) > $o ).

tff(pred_def_11,type,
    'fun_app$h': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > $o ).

tff(pred_def_12,type,
    'fun_app$c': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$' ) > $o ).

tff(pred_def_13,type,
    'fun_app$s': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff(pred_def_16,type,
    sP0: ( $int * $int * $int ) > $o ).

tff(pred_def_17,type,
    sP1: ( $int * $int * $int ) > $o ).

tff(pred_def_18,type,
    sP2: ( $int * $int * $int ) > $o ).

tff(f2471,plain,
    $false,
    inference(subsumption_resolution,[],[f2470,f2466]) ).

tff(f2466,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(2,'fun_app$b'('of_nat$','ka$'))))))),
    inference(evaluation,[],[f1582]) ).

tff(f1582,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum($sum('fun_app$b'('of_nat$','ka$'),1),1)))))),
    inference(cnf_transformation,[],[f3]) ).

tff(f3,axiom,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum($sum('fun_app$b'('of_nat$','ka$'),1),1)))))),
    file('/export/starexec/sandbox/tmp/tmp.dB63t5HSOO/Vampire---4.8_15424',axiom1) ).

tff(f2470,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(2,'fun_app$b'('of_nat$','ka$'))))))),
    inference(backward_demodulation,[],[f2469,f1651]) ).

tff(f1651,plain,
    ! [X0: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : ( 'pair$'('fst$'(X0),'snd$'(X0)) = X0 ),
    inference(cnf_transformation,[],[f133]) ).

tff(f133,axiom,
    ! [X0: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$'] : ( 'pair$'('fst$'(X0),'snd$'(X0)) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.dB63t5HSOO/Vampire---4.8_15424',axiom131) ).

tff(f2469,plain,
    'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(2,'fun_app$b'('of_nat$','ka$'))))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
    inference(backward_demodulation,[],[f2468,f1585]) ).

tff(f1585,plain,
    ! [X0: 'Nat_a_b_vec_c_vec_prod$'] : ( 'pair$a'('fst$a'(X0),'snd$a'(X0)) = X0 ),
    inference(cnf_transformation,[],[f136]) ).

tff(f136,axiom,
    ! [X0: 'Nat_a_b_vec_c_vec_prod$'] : ( 'pair$a'('fst$a'(X0),'snd$a'(X0)) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.dB63t5HSOO/Vampire---4.8_15424',axiom134) ).

tff(f2468,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum(2,'fun_app$b'('of_nat$','ka$'))))))),
    inference(backward_demodulation,[],[f1566,f2466]) ).

tff(f1566,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
    inference(cnf_transformation,[],[f811]) ).

tff(f811,plain,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
    inference(flattening,[],[f2]) ).

tff(f2,negated_conjecture,
    ( ~ 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
    file('/export/starexec/sandbox/tmp/tmp.dB63t5HSOO/Vampire---4.8_15424',conjecture0) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.06/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35  % Computer : n015.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Fri May  3 19:04:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a TF0_THM_EQU_ARI problem
% 0.13/0.35  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.dB63t5HSOO/Vampire---4.8_15424
% 0.57/0.76  % (15532)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.57/0.76  % (15534)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.76  % (15537)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.57/0.76  % (15535)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.57/0.76  % (15539)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.57/0.76  % (15533)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.57/0.76  % (15538)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.57/0.76  % (15536)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.58/0.77  % (15532)Instruction limit reached!
% 0.58/0.77  % (15532)------------------------------
% 0.58/0.77  % (15532)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.77  % (15532)Termination reason: Unknown
% 0.58/0.77  % (15532)Termination phase: Preprocessing 3
% 0.58/0.77  
% 0.58/0.77  % (15532)Memory used [KB]: 1594
% 0.58/0.77  % (15532)Time elapsed: 0.010 s
% 0.58/0.77  % (15532)Instructions burned: 34 (million)
% 0.58/0.77  % (15532)------------------------------
% 0.58/0.77  % (15532)------------------------------
% 0.58/0.78  % (15540)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2995ds/55Mi)
% 0.58/0.78  % (15535)Instruction limit reached!
% 0.58/0.78  % (15535)------------------------------
% 0.58/0.78  % (15535)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (15535)Termination reason: Unknown
% 0.58/0.78  % (15535)Termination phase: Preprocessing 3
% 0.58/0.78  
% 0.58/0.78  % (15535)Memory used [KB]: 1562
% 0.58/0.78  % (15535)Time elapsed: 0.015 s
% 0.58/0.78  % (15535)Instructions burned: 33 (million)
% 0.58/0.78  % (15535)------------------------------
% 0.58/0.78  % (15535)------------------------------
% 0.58/0.78  % (15536)Instruction limit reached!
% 0.58/0.78  % (15536)------------------------------
% 0.58/0.78  % (15536)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (15536)Termination reason: Unknown
% 0.58/0.78  % (15536)Termination phase: Preprocessing 2
% 0.58/0.78  
% 0.58/0.78  % (15536)Memory used [KB]: 1579
% 0.58/0.78  % (15536)Time elapsed: 0.016 s
% 0.58/0.78  % (15536)Instructions burned: 34 (million)
% 0.58/0.78  % (15536)------------------------------
% 0.58/0.78  % (15536)------------------------------
% 0.58/0.78  % (15537)Instruction limit reached!
% 0.58/0.78  % (15537)------------------------------
% 0.58/0.78  % (15537)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (15537)Termination reason: Unknown
% 0.58/0.78  % (15537)Termination phase: Property scanning
% 0.58/0.78  
% 0.58/0.78  % (15537)Memory used [KB]: 2004
% 0.58/0.78  % (15537)Time elapsed: 0.019 s
% 0.58/0.78  % (15537)Instructions burned: 45 (million)
% 0.58/0.78  % (15537)------------------------------
% 0.58/0.78  % (15537)------------------------------
% 0.58/0.78  % (15542)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.58/0.78  % (15533)Instruction limit reached!
% 0.58/0.78  % (15533)------------------------------
% 0.58/0.78  % (15533)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (15533)Termination reason: Unknown
% 0.58/0.78  % (15533)Termination phase: Property scanning
% 0.58/0.78  
% 0.58/0.78  % (15533)Memory used [KB]: 2160
% 0.58/0.78  % (15533)Time elapsed: 0.021 s
% 0.58/0.78  % (15533)Instructions burned: 51 (million)
% 0.58/0.78  % (15533)------------------------------
% 0.58/0.78  % (15533)------------------------------
% 0.58/0.78  % (15543)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.58/0.78  % (15539)Instruction limit reached!
% 0.58/0.78  % (15539)------------------------------
% 0.58/0.78  % (15539)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.78  % (15539)Termination reason: Unknown
% 0.58/0.78  % (15539)Termination phase: Equality proxy
% 0.58/0.78  
% 0.58/0.78  % (15539)Memory used [KB]: 2040
% 0.58/0.78  % (15539)Time elapsed: 0.023 s
% 0.58/0.78  % (15539)Instructions burned: 58 (million)
% 0.58/0.78  % (15539)------------------------------
% 0.58/0.78  % (15539)------------------------------
% 0.58/0.79  % (15544)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.58/0.79  % (15540)Instruction limit reached!
% 0.58/0.79  % (15540)------------------------------
% 0.58/0.79  % (15540)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.79  % (15540)Termination reason: Unknown
% 0.58/0.79  % (15540)Termination phase: Property scanning
% 0.58/0.79  
% 0.58/0.79  % (15540)Memory used [KB]: 2165
% 0.58/0.79  % (15540)Time elapsed: 0.014 s
% 0.58/0.79  % (15540)Instructions burned: 56 (million)
% 0.58/0.79  % (15540)------------------------------
% 0.58/0.79  % (15540)------------------------------
% 0.58/0.79  % (15541)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2995ds/50Mi)
% 0.58/0.79  % (15545)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.58/0.79  % (15534)First to succeed.
% 0.58/0.79  % (15534)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-15531"
% 0.58/0.79  % (15534)Refutation found. Thanks to Tanya!
% 0.58/0.79  % SZS status Theorem for Vampire---4
% 0.58/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.58/0.79  % (15534)------------------------------
% 0.58/0.79  % (15534)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.58/0.79  % (15534)Termination reason: Refutation
% 0.58/0.79  
% 0.58/0.79  % (15534)Memory used [KB]: 2086
% 0.58/0.79  % (15534)Time elapsed: 0.031 s
% 0.58/0.79  % (15534)Instructions burned: 76 (million)
% 0.58/0.79  % (15531)Success in time 0.429 s
% 0.58/0.80  % Vampire---4.8 exiting
%------------------------------------------------------------------------------