%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP343_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:33:39 AM UTC 2026
% Result : Theorem 4.77s 1.72s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 31
% Syntax : Number of formulae : 144 ( 66 unt; 0 typ; 25 def)
% Number of atoms : 264 ( 164 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 218 ( 98 ~; 82 |; 21 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 127 ( 125 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 46 ( 44 usr; 7 prp; 0-5 aty)
% Number of functors : 358 ( 357 usr; 63 con; 0-4 aty)
% Number of variables : 21 ( 0 sgn 19 !; 2 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_bool_fun$': $tType ).
tff(type_def_6,type,
'A_iarray_a_iarray_a_iarray_prod_set_fun$': $tType ).
tff(type_def_7,type,
'A_iarray_list_bool_fun$': $tType ).
tff(type_def_8,type,
'A_iarray_iarray_list_a_iarray_iarray_list_prod$': $tType ).
tff(type_def_9,type,
'Int_int_prod_a_n_vec_n_vec_prod$': $tType ).
tff(type_def_10,type,
'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$': $tType ).
tff(type_def_11,type,
'Int_int_int_prod_set_fun$': $tType ).
tff(type_def_12,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_13,type,
'Int_int_prod_set$': $tType ).
tff(type_def_14,type,
'Int_int_prod_bool_fun$': $tType ).
tff(type_def_15,type,
'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$': $tType ).
tff(type_def_16,type,
'Int_a_n_vec_n_vec_prod$': $tType ).
tff(type_def_17,type,
'Nat_a_iarray_fun$': $tType ).
tff(type_def_18,type,
'A_iarray_a_iarray_bool_fun_fun$': $tType ).
tff(type_def_19,type,
'A_iarray_iarray_a_iarray_iarray_prod$': $tType ).
tff(type_def_20,type,
'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$': $tType ).
tff(type_def_21,type,
'Nat_a_iarray_prod_list_nat_fun$': $tType ).
tff(type_def_22,type,
'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$': $tType ).
tff(type_def_23,type,
'A_iarray_iarray$': $tType ).
tff(type_def_24,type,
'A_iarray_iarray_int_prod$': $tType ).
tff(type_def_25,type,
'Int_int_prod$': $tType ).
tff(type_def_26,type,
'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$': $tType ).
tff(type_def_27,type,
'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$': $tType ).
tff(type_def_28,type,
'A_n_vec_iarray$': $tType ).
tff(type_def_29,type,
'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$': $tType ).
tff(type_def_30,type,
'Nat_a_iarray_prod_list$': $tType ).
tff(type_def_31,type,
'A_iarray_iarray_nat_fun$': $tType ).
tff(type_def_32,type,
'A_n_vec_n_vec_int_int_prod_prod$': $tType ).
tff(type_def_33,type,
'A_iarray_a_iarray_fun$': $tType ).
tff(type_def_34,type,
'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun_a_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun_fun$': $tType ).
tff(type_def_35,type,
'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$': $tType ).
tff(type_def_36,type,
'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$': $tType ).
tff(type_def_37,type,
'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$': $tType ).
tff(type_def_38,type,
'A_n_vec_n_vec_bool_fun$': $tType ).
tff(type_def_39,type,
'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$': $tType ).
tff(type_def_40,type,
'Int_int_prod_int_int_prod_prod$': $tType ).
tff(type_def_41,type,
'Int_set$': $tType ).
tff(type_def_42,type,
'Int_int_fun$': $tType ).
tff(type_def_43,type,
'Int_set_set$': $tType ).
tff(type_def_44,type,
'A_iarray_a_iarray_prod_set$': $tType ).
tff(type_def_45,type,
'A_n_vec_n_vec$': $tType ).
tff(type_def_46,type,
'Int_int_prod_int_fun$': $tType ).
tff(type_def_47,type,
'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$': $tType ).
tff(type_def_48,type,
'Nat_a_iarray_prod_nat_a_iarray_prod_prod$': $tType ).
tff(type_def_49,type,
'A_n_vec_n_vec_option$': $tType ).
tff(type_def_50,type,
'Int_int_prod_int_prod$': $tType ).
tff(type_def_51,type,
'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$': $tType ).
tff(type_def_52,type,
'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$': $tType ).
tff(type_def_53,type,
'A_iarray_list_nat_fun$': $tType ).
tff(type_def_54,type,
'A_iarray_list_list$': $tType ).
tff(type_def_55,type,
'A_iarray_iarray_set$': $tType ).
tff(type_def_56,type,
'Int_a_iarray_iarray_prod$': $tType ).
tff(type_def_57,type,
'Int_nat_fun$': $tType ).
tff(type_def_58,type,
'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$': $tType ).
tff(type_def_59,type,
'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$': $tType ).
tff(type_def_60,type,
'Int_set_int_prod$': $tType ).
tff(type_def_61,type,
'A_iarray_list_a_iarray_list_bool_fun_fun$': $tType ).
tff(type_def_62,type,
'Nat$': $tType ).
tff(type_def_63,type,
'A_n_vec_n_vec_set$': $tType ).
tff(type_def_64,type,
'N$': $tType ).
tff(type_def_65,type,
'Int_a_iarray_fun$': $tType ).
tff(type_def_66,type,
'Nat_a_iarray_list_prod_list$': $tType ).
tff(type_def_67,type,
'A_iarray_list_a_iarray_list_prod_set$': $tType ).
tff(type_def_68,type,
'A_iarray_iarray_bool_fun$': $tType ).
tff(type_def_69,type,
'A_iarray_list_list_a_iarray_list_list_prod_set$': $tType ).
tff(type_def_70,type,
'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$': $tType ).
tff(type_def_71,type,
'A_iarray_iarray_option_bool_fun$': $tType ).
tff(type_def_72,type,
'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$': $tType ).
tff(type_def_73,type,
'A_iarray_iarray_a_iarray_iarray_bool_fun_fun_a_iarray_iarray_a_iarray_iarray_prod_bool_fun_fun$': $tType ).
tff(type_def_74,type,
'Int_int_prod_int_int_prod_prod_set$': $tType ).
tff(type_def_75,type,
'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$': $tType ).
tff(type_def_76,type,
'Int_int_bool_fun_fun_int_int_prod_bool_fun_fun$': $tType ).
tff(type_def_77,type,
'Int_set_int_set_prod$': $tType ).
tff(type_def_78,type,
'A_n_vec_n_vec_nat_fun$': $tType ).
tff(type_def_79,type,
tlbool: $tType ).
tff(type_def_80,type,
'A_n_vec_n_vec_int_prod$': $tType ).
tff(type_def_81,type,
'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$': $tType ).
tff(type_def_82,type,
'Int_list_int_list_prod$': $tType ).
tff(type_def_83,type,
'A_iarray_a_iarray_prod_bool_fun$': $tType ).
tff(type_def_84,type,
'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$': $tType ).
tff(type_def_85,type,
'Int_int_prod_int_int_prod_fun$': $tType ).
tff(type_def_86,type,
'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$': $tType ).
tff(type_def_87,type,
'A_iarray_nat_fun$': $tType ).
tff(type_def_88,type,
'Int_list$': $tType ).
tff(type_def_89,type,
'A_iarray_bool_fun$': $tType ).
tff(type_def_90,type,
'Nat_nat_a_iarray_prod_prod_list$': $tType ).
tff(type_def_91,type,
'A_iarray_list_a_iarray_list_prod_bool_fun$': $tType ).
tff(type_def_92,type,
'Int_int_set_prod$': $tType ).
tff(type_def_93,type,
'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$': $tType ).
tff(type_def_94,type,
'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$': $tType ).
tff(type_def_95,type,
'Nat_a_iarray_list_fun$': $tType ).
tff(type_def_96,type,
'A_iarray_iarray_option$': $tType ).
tff(type_def_97,type,
'A_iarray_a_iarray_prod$': $tType ).
tff(type_def_98,type,
'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$': $tType ).
tff(type_def_99,type,
'A_iarray_list_a_iarray_list_prod$': $tType ).
tff(type_def_100,type,
'Bool_bool_fun$': $tType ).
tff(type_def_101,type,
'A_iarray_list$': $tType ).
tff(type_def_102,type,
'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$': $tType ).
tff(type_def_103,type,
'A_iarray_iarray_option_nat_fun$': $tType ).
tff(type_def_104,type,
'A_n_vec_n_vec_option_nat_fun$': $tType ).
tff(type_def_105,type,
'A_iarray_int_fun$': $tType ).
tff(type_def_106,type,
'Nat_a_iarray_iarray_fun$': $tType ).
tff(type_def_107,type,
'Int_a_iarray_iarray_fun$': $tType ).
tff(type_def_108,type,
'Nat_a_iarray_prod_bool_fun$': $tType ).
tff(type_def_109,type,
'A_iarray_set$': $tType ).
tff(type_def_110,type,
'A_iarray_list_list_nat_fun$': $tType ).
tff(type_def_111,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_112,type,
'A_iarray$': $tType ).
tff(type_def_113,type,
'Int_int_int_prod_prod$': $tType ).
tff(type_def_114,type,
'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$': $tType ).
tff(type_def_115,type,
'A_iarray_list_set$': $tType ).
tff(type_def_116,type,
'Nat_a_iarray_prod$': $tType ).
tff(type_def_117,type,
'A_iarray_list_a_iarray_list_fun$': $tType ).
tff(type_def_118,type,
'Nat_bool_fun$': $tType ).
tff(type_def_119,type,
'A_iarray_list_int_fun$': $tType ).
tff(type_def_120,type,
'A_iarray_iarray_a_iarray_iarray_prod_set$': $tType ).
tff(type_def_121,type,
'A_iarray_iarray_int_set_prod$': $tType ).
tff(type_def_122,type,
'A_iarray_list_list_a_iarray_list_list_prod$': $tType ).
tff(type_def_123,type,
'Int_list_int_list_prod_set$': $tType ).
tff(type_def_124,type,
'Nat_set$': $tType ).
tff(type_def_125,type,
'A_n_vec_n_vec_a_n_vec_n_vec_prod$': $tType ).
tff(type_def_126,type,
'Nat_int_fun$': $tType ).
tff(type_def_127,type,
'A_n_vec_n_vec_option_bool_fun$': $tType ).
tff(type_def_128,type,
'A_iarray_iarray_list$': $tType ).
tff(type_def_129,type,
'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$': $tType ).
tff(func_def_0,type,
'snd$': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' ).
tff(func_def_1,type,
'size$a': 'Nat_a_iarray_prod_list_nat_fun$' ).
tff(func_def_2,type,
'append$': 'Nat_a_iarray_prod_list$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$' ).
tff(func_def_3,type,
'pair$o': ( 'Int_int_prod$' * 'A_n_vec_n_vec$' ) > 'Int_int_prod_a_n_vec_n_vec_prod$' ).
tff(func_def_4,type,
'zero$d': 'Int_int_int_prod_prod$' ).
tff(func_def_5,type,
'collect$f': 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).
tff(func_def_6,type,
'image2$d': ( 'Nat_set$' * 'Nat_a_iarray_fun$' * 'Nat_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).
tff(func_def_7,type,
'fun_app$az': ( 'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).
tff(func_def_8,type,
'fun_app$r': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).
tff(func_def_9,type,
'image2$g': ( 'Nat_set$' * 'Nat_a_iarray_iarray_fun$' * 'Nat_a_iarray_iarray_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).
tff(func_def_10,type,
'case_option$': ( tlbool * 'A_n_vec_n_vec_bool_fun$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).
tff(func_def_11,type,
'gauss_Jordan_upt_k_PA$': ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_12,type,
'lexord$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).
tff(func_def_13,type,
'invertible$': 'A_n_vec_n_vec_bool_fun$' ).
tff(func_def_14,type,
'listrel1$b': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).
tff(func_def_15,type,
'fst$e': 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_16,type,
'uug$': 'A_iarray_iarray_bool_fun$' ).
tff(func_def_17,type,
'size$c': 'A_iarray_iarray_option$' > 'Nat$' ).
tff(func_def_18,type,
def_3: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_19,type,
def_1: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > tlbool ).
tff(func_def_20,type,
'inverse_matrix_iarray$': 'A_iarray_iarray$' > 'A_iarray_iarray_option$' ).
tff(func_def_21,type,
'same_fst$c': ( 'A_iarray_bool_fun$' * 'A_iarray_a_iarray_a_iarray_prod_set_fun$' ) > 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$' ).
tff(func_def_22,type,
'size$f': 'A_iarray_iarray_list$' > 'Nat$' ).
tff(func_def_23,type,
'none$': 'A_iarray_iarray_option$' ).
tff(func_def_24,type,
'collect$e': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$' ).
tff(func_def_25,type,
def_5: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).
tff(func_def_26,type,
'listrel1$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).
tff(func_def_27,type,
'lexn$b': ( 'A_iarray_a_iarray_prod_set$' * 'Nat$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_28,type,
'enumerate$': ( 'Nat$' * 'A_iarray_list$' ) > 'Nat_a_iarray_prod_list$' ).
tff(func_def_29,type,
'fun_app$ap': ( 'Nat_a_iarray_iarray_fun$' * 'Nat$' ) > 'A_iarray_iarray$' ).
tff(func_def_30,type,
'fun_app$ai': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_31,type,
'nths$': ( 'A_iarray_list$' * 'Nat_set$' ) > 'A_iarray_list$' ).
tff(func_def_32,type,
'gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_33,type,
'fun_app$aa': ( 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec$' ) > 'Nat$' ).
tff(func_def_34,type,
'pair$m': ( $int * 'A_n_vec_n_vec$' ) > 'Int_a_n_vec_n_vec_prod$' ).
tff(func_def_35,type,
'enumerate$a': ( 'Nat$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_nat_a_iarray_prod_prod_list$' ).
tff(func_def_36,type,
'gen_length$b': 'Nat$' > 'A_iarray_list_nat_fun$' ).
tff(func_def_37,type,
'fun_app$av': ( 'Int_int_bool_fun_fun_int_int_prod_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_bool_fun$' ).
tff(func_def_38,type,
'fun_app$aq': ( 'Int_a_iarray_iarray_fun$' * $int ) > 'A_iarray_iarray$' ).
tff(func_def_39,type,
def_4: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).
tff(func_def_40,type,
'lexord$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).
tff(func_def_41,type,
'fst$c': 'Int_int_set_prod$' > $int ).
tff(func_def_42,type,
'fstOp$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_int_int_prod_fun$' ).
tff(func_def_43,type,
'fst$k': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).
tff(func_def_44,type,
'collect$d': 'A_iarray_bool_fun$' > 'A_iarray_set$' ).
tff(func_def_45,type,
'append$c': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).
tff(func_def_46,type,
'sndOp$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_prod_int_int_prod_fun$' ).
tff(func_def_47,type,
'lex$a': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ).
tff(func_def_48,type,
'lexord$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).
tff(func_def_49,type,
'plus$o': ( 'Int_int_set_prod$' * 'Int_int_set_prod$' ) > 'Int_int_set_prod$' ).
tff(func_def_50,type,
'snd$k': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list$' ).
tff(func_def_51,type,
'product_lists$': 'A_iarray_list_list$' > 'A_iarray_list_list$' ).
tff(func_def_52,type,
'plus$n': ( 'Int_int_prod_set$' * 'Int_int_prod_set$' ) > 'Int_int_prod_set$' ).
tff(func_def_53,type,
'same_fst$a': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_a_iarray_iarray_prod_set_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$' ).
tff(func_def_54,type,
'lexn$': ( 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' * 'Nat$' ) > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).
tff(func_def_55,type,
'fun_app$ad': ( 'A_iarray_a_iarray_fun$' * 'A_iarray$' ) > 'A_iarray$' ).
tff(func_def_56,type,
'splice$b': ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_57,type,
'plus$s': ( 'Int_int_int_prod_prod$' * 'Int_int_int_prod_prod$' ) > 'Int_int_int_prod_prod$' ).
tff(func_def_58,type,
'listrel1$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).
tff(func_def_59,type,
'relcompp$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).
tff(func_def_60,type,
'swap$b': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_61,type,
'image2$': ( 'Nat_set$' * 'Nat_int_fun$' * 'Nat_int_fun$' ) > 'Int_int_prod_set$' ).
tff(func_def_62,type,
'nat$': 'Int_nat_fun$' ).
tff(func_def_63,type,
'pair$e': ( 'Int_set$' * $int ) > 'Int_set_int_prod$' ).
tff(func_def_64,type,
'snd$h': 'A_iarray_iarray_int_prod$' > $int ).
tff(func_def_65,type,
'fst$d': 'Int_set_int_prod$' > 'Int_set$' ).
tff(func_def_66,type,
'size$': 'A_iarray_list_nat_fun$' ).
tff(func_def_67,type,
'listrel1$d': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).
tff(func_def_68,type,
'snd$c': 'Int_int_set_prod$' > 'Int_set$' ).
tff(func_def_69,type,
'size$b': 'A_iarray_list_list_nat_fun$' ).
tff(func_def_70,type,
'plus$w': ( 'A_iarray_iarray_int_set_prod$' * 'A_iarray_iarray_int_set_prod$' ) > 'A_iarray_iarray_int_set_prod$' ).
tff(func_def_71,type,
'plus$x': ( 'A_n_vec_iarray$' * 'A_n_vec_iarray$' ) > 'A_n_vec_iarray$' ).
tff(func_def_72,type,
'collect$': 'A_iarray_list_a_iarray_list_prod_bool_fun$' > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_73,type,
'plus$q': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray_a_iarray_prod$' ).
tff(func_def_74,type,
'pair$j': ( 'Int_int_prod$' * $int ) > 'Int_int_prod_int_prod$' ).
tff(func_def_75,type,
'pair$b': ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_prod$' ).
tff(func_def_76,type,
'cons$a': ( 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).
tff(func_def_77,type,
'collect$c': 'Nat_bool_fun$' > 'Nat_set$' ).
tff(func_def_78,type,
'set$a': 'A_iarray_list_list$' > 'A_iarray_list_set$' ).
tff(func_def_79,type,
'cons$': ( 'A_iarray$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_80,type,
'zero$': 'Int_set$' ).
tff(func_def_81,type,
'n_lists$': ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray_list_list$' ).
tff(func_def_82,type,
'pick_middlep$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_83,type,
'fun_app$ax': ( 'A_n_vec_n_vec_option_nat_fun$' * 'A_n_vec_n_vec_option$' ) > 'Nat$' ).
tff(func_def_84,type,
'gauss_Jordan_in_ij_PA$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_85,type,
'image2$e': ( 'Int_set$' * 'Int_a_iarray_fun$' * 'Int_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).
tff(func_def_86,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_87,type,
'sndOp$b': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ).
tff(func_def_88,type,
'pair$x': ( 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$' ).
tff(func_def_89,type,
'uuh$': 'A_n_vec_n_vec_bool_fun$' ).
tff(func_def_90,type,
'snd$d': 'Int_set_int_prod$' > $int ).
tff(func_def_91,type,
'matrix_inv$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_92,type,
'fun_app$bf': ( 'A_iarray_list_a_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' ).
tff(func_def_93,type,
'plus$e': 'A_iarray$' > 'A_iarray_a_iarray_fun$' ).
tff(func_def_94,type,
'fst$g': 'Int_int_int_prod_prod$' > $int ).
tff(func_def_95,type,
'fst$a': 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' ).
tff(func_def_96,type,
'nil$': 'A_iarray_list$' ).
tff(func_def_97,type,
'fun_app$g': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_98,type,
'uuk$': 'A_iarray_list_set$' > 'A_iarray_list_bool_fun$' ).
tff(func_def_99,type,
'filter$': 'A_iarray_bool_fun$' > 'A_iarray_list_a_iarray_list_fun$' ).
tff(func_def_100,type,
'uu$': 'A_iarray_bool_fun$' ).
tff(func_def_101,type,
'equivalent_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).
tff(func_def_102,type,
'fun_app$k': ( 'Int_nat_fun$' * $int ) > 'Nat$' ).
tff(func_def_103,type,
'fun_app$bc': ( 'A_iarray_nat_fun$' * 'A_iarray$' ) > 'Nat$' ).
tff(func_def_104,type,
'image2$i': ( 'Nat_set$' * 'Nat_a_iarray_list_fun$' * 'Nat_a_iarray_list_fun$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_105,type,
'collect$a': 'A_iarray_list_bool_fun$' > 'A_iarray_list_set$' ).
tff(func_def_106,type,
'fun_app$as': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_107,type,
'set$': 'A_iarray_list$' > 'A_iarray_set$' ).
tff(func_def_108,type,
'pair$h': ( 'A_iarray_iarray$' * $int ) > 'A_iarray_iarray_int_prod$' ).
tff(func_def_109,type,
'pair$q': ( 'A_n_vec_n_vec$' * 'Int_int_prod$' ) > 'A_n_vec_n_vec_int_int_prod_prod$' ).
tff(func_def_110,type,
'lexord$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_111,type,
'fun_app$w': ( 'A_n_vec_n_vec_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).
tff(func_def_112,type,
tltrue: tlbool ).
tff(func_def_113,type,
'uuo$': 'Int_int_prod_set$' > 'Int_int_bool_fun_fun$' ).
tff(func_def_114,type,
'cons$b': ( 'A_iarray_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).
tff(func_def_115,type,
'zero$a': 'Int_int_prod$' ).
tff(func_def_116,type,
'swap$a': 'A_iarray_a_iarray_prod$' > 'A_iarray_a_iarray_prod$' ).
tff(func_def_117,type,
'image2$f': ( 'A_iarray_set$' * 'A_iarray_a_iarray_fun$' * 'A_iarray_a_iarray_fun$' ) > 'A_iarray_a_iarray_prod_set$' ).
tff(func_def_118,type,
'plus$h': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_119,type,
'pair$t': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod$' ) > 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$' ).
tff(func_def_120,type,
'rank$': 'A_n_vec_n_vec_nat_fun$' ).
tff(func_def_121,type,
'gauss_Jordan_upt_k$': ( 'A_n_vec_n_vec$' * 'Nat$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_122,type,
'fun_app$bb': ( 'A_iarray_a_iarray_a_iarray_prod_set_fun$' * 'A_iarray$' ) > 'A_iarray_a_iarray_prod_set$' ).
tff(func_def_123,type,
'gauss_Jordan_in_ij$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_124,type,
'size_prod$': ( 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_nat_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'Nat$' ).
tff(func_def_125,type,
'fun_app$aj': ( 'Int_int_prod_int_int_prod_fun$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).
tff(func_def_126,type,
'fun_app$v': ( 'A_iarray_list_list_nat_fun$' * 'A_iarray_list_list$' ) > 'Nat$' ).
tff(func_def_127,type,
'plus$i': ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).
tff(func_def_128,type,
'pair$y': ( 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod$' ) > 'Nat_a_iarray_prod_nat_a_iarray_prod_prod$' ).
tff(func_def_129,type,
'filter$a': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).
tff(func_def_130,type,
'uuj$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_prod_bool_fun$' ).
tff(func_def_131,type,
'fun_app$h': ( 'A_iarray_a_iarray_bool_fun_fun$' * 'A_iarray$' ) > 'A_iarray_bool_fun$' ).
tff(func_def_132,type,
'filter$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).
tff(func_def_133,type,
'fun_app$ar': ( 'Nat_a_iarray_list_fun$' * 'Nat$' ) > 'A_iarray_list$' ).
tff(func_def_134,type,
'relcompp$a': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ).
tff(func_def_135,type,
'list_of$': 'A_iarray_iarray$' > 'A_iarray_list$' ).
tff(func_def_136,type,
'fun_app$ba': ( 'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_137,type,
'snd$e': 'A_iarray_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_138,type,
'a$': 'A_n_vec_n_vec$' ).
tff(func_def_139,type,
'fun_app$ao': ( 'Int_a_iarray_fun$' * $int ) > 'A_iarray$' ).
tff(func_def_140,type,
'uuq$': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_a_iarray_list_bool_fun_fun$' ).
tff(func_def_141,type,
'lex$d': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_142,type,
'pair$': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_143,type,
'sndOp$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ).
tff(func_def_144,type,
'rank_iarray$': 'A_iarray_iarray_nat_fun$' ).
tff(func_def_145,type,
'fun_app$ah': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_bool_fun$' ).
tff(func_def_146,type,
'listrel1$c': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_147,type,
'p_Gauss_Jordan$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_148,type,
'gauss_Jordan_iarrays_PA$': 'A_iarray_iarray$' > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_149,type,
'some$a': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$' ).
tff(func_def_150,type,
'matrix_to_iarray$': 'A_n_vec_n_vec$' > 'A_iarray_iarray$' ).
tff(func_def_151,type,
'uuu$': ( 'A_iarray_bool_fun$' * 'A_iarray_list$' ) > 'A_iarray_bool_fun$' ).
tff(func_def_152,type,
'reduced_row_echelon_form$': 'A_n_vec_n_vec_bool_fun$' ).
tff(func_def_153,type,
'lexn$a': ( 'A_iarray_list_a_iarray_list_prod_set$' * 'Nat$' ) > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).
tff(func_def_154,type,
'swap$d': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_155,type,
'fun_app$at': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun_a_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_bool_fun$' ).
tff(func_def_156,type,
'append$b': ( 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list$' ).
tff(func_def_157,type,
'plus$l': ( 'Int_set_set$' * 'Int_set_set$' ) > 'Int_set_set$' ).
tff(func_def_158,type,
'uua$': ( 'A_iarray_bool_fun$' * 'A_iarray_bool_fun$' ) > 'A_iarray_bool_fun$' ).
tff(func_def_159,type,
'uur$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_a_iarray_bool_fun_fun$' ).
tff(func_def_160,type,
'pair$n': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod_int_int_prod_prod$' ).
tff(func_def_161,type,
'gen_length$a': 'Nat$' > 'A_iarray_list_list_nat_fun$' ).
tff(func_def_162,type,
'size$e': 'Int_list$' > 'Nat$' ).
tff(func_def_163,type,
'pair$p': ( 'A_n_vec_n_vec$' * $int ) > 'A_n_vec_n_vec_int_prod$' ).
tff(func_def_164,type,
'pick_middlep$a': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' * $int ) > 'Int_int_fun$' ).
tff(func_def_165,type,
'pair$d': ( $int * 'Int_set$' ) > 'Int_int_set_prod$' ).
tff(func_def_166,type,
'snd$f': 'Int_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_167,type,
'append$d': 'A_iarray_list$' > 'A_iarray_list_a_iarray_list_fun$' ).
tff(func_def_168,type,
'uus$': ( 'A_iarray_list_set$' * 'A_iarray$' ) > 'A_iarray_list_bool_fun$' ).
tff(func_def_169,type,
'gauss_Jordan_PA$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_170,type,
'fun_app$au': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun_a_iarray_iarray_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' ).
tff(func_def_171,type,
def_2: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).
tff(func_def_172,type,
'plus$t': ( 'A_iarray_iarray_int_prod$' * 'A_iarray_iarray_int_prod$' ) > 'A_iarray_iarray_int_prod$' ).
tff(func_def_173,type,
'cons$d': ( 'A_iarray_iarray$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list$' ).
tff(func_def_174,type,
'image2$b': ( 'A_iarray_set$' * 'A_iarray_int_fun$' * 'A_iarray_int_fun$' ) > 'Int_int_prod_set$' ).
tff(func_def_175,type,
'none$a': 'A_n_vec_n_vec_option$' ).
tff(func_def_176,type,
'uut$': ( 'A_iarray_list$' * 'Nat_set$' ) > 'Nat_bool_fun$' ).
tff(func_def_177,type,
'lex$c': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).
tff(func_def_178,type,
'uue$': ( 'Bool_bool_fun$' * 'A_iarray_iarray_bool_fun$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_179,type,
'plus$m': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec_set$' ).
tff(func_def_180,type,
'fun_app$ay': ( 'Int_int_int_prod_set_fun$' * $int ) > 'Int_int_prod_set$' ).
tff(func_def_181,type,
'pair$k': ( 'A_iarray_iarray$' * 'Int_set$' ) > 'A_iarray_iarray_int_set_prod$' ).
tff(func_def_182,type,
'same_fst$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list_a_iarray_list_a_iarray_list_prod_set_fun$' ) > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$' ).
tff(func_def_183,type,
'plus$a': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_184,type,
'fun_app$bd': ( 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).
tff(func_def_185,type,
'pair$g': ( $int * 'Int_int_prod$' ) > 'Int_int_int_prod_prod$' ).
tff(func_def_186,type,
'collect$b': 'Int_bool_fun$' > 'Int_set$' ).
tff(func_def_187,type,
'plus$p': ( 'Int_set_int_prod$' * 'Int_set_int_prod$' ) > 'Int_set_int_prod$' ).
tff(func_def_188,type,
'cons$c': ( $int * 'Int_list$' ) > 'Int_list$' ).
tff(func_def_189,type,
'fun_app$m': ( 'A_iarray_list_nat_fun$' * 'A_iarray_list$' ) > 'Nat$' ).
tff(func_def_190,type,
'matrix_matrix_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_191,type,
'plus$r': ( 'Int_a_iarray_iarray_prod$' * 'Int_a_iarray_iarray_prod$' ) > 'Int_a_iarray_iarray_prod$' ).
tff(func_def_192,type,
'snd$i': 'Int_set_int_set_prod$' > 'Int_set$' ).
tff(func_def_193,type,
'matrix_to_iarray_option$': 'A_n_vec_n_vec_option$' > 'A_iarray_iarray_option$' ).
tff(func_def_194,type,
'plus$j': ( 'A_iarray_iarray_set$' * 'A_iarray_iarray_set$' ) > 'A_iarray_iarray_set$' ).
tff(func_def_195,type,
'fun_app$ab': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec$' ).
tff(func_def_196,type,
'lenlex$': 'A_iarray_a_iarray_prod_set$' > 'A_iarray_list_a_iarray_list_prod_set$' ).
tff(func_def_197,type,
'zero$i': 'A_n_vec_n_vec_int_prod$' ).
tff(func_def_198,type,
'uul$': 'Int_set$' > 'Int_bool_fun$' ).
tff(func_def_199,type,
'size$g': 'Nat_nat_a_iarray_prod_prod_list$' > 'Nat$' ).
tff(func_def_200,type,
'fun_app$an': ( 'Nat_a_iarray_fun$' * 'Nat$' ) > 'A_iarray$' ).
tff(func_def_201,type,
'fun_app$al': ( 'A_iarray_int_fun$' * 'A_iarray$' ) > $int ).
tff(func_def_202,type,
'snd$a': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' ).
tff(func_def_203,type,
'fst$f': 'Int_a_iarray_iarray_prod$' > $int ).
tff(func_def_204,type,
'uuf$': 'A_n_vec_n_vec_bool_fun$' ).
tff(func_def_205,type,
'size$h': 'Nat_a_iarray_list_prod_list$' > 'Nat$' ).
tff(func_def_206,type,
'fstOp$': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ).
tff(func_def_207,type,
'uui$': 'A_iarray_iarray_bool_fun$' ).
tff(func_def_208,type,
'plus$b': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).
tff(func_def_209,type,
'zero$j': 'A_n_vec_n_vec_int_int_prod_prod$' ).
tff(func_def_210,type,
'plus$u': ( 'Int_set_int_set_prod$' * 'Int_set_int_set_prod$' ) > 'Int_set_int_set_prod$' ).
tff(func_def_211,type,
'shift$': ( 'A_iarray_list_set$' * 'A_iarray$' ) > 'A_iarray_list_set$' ).
tff(func_def_212,type,
def_7: ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).
tff(func_def_213,type,
'uuc$': 'A_iarray_list_bool_fun$' > 'A_iarray_list_bool_fun$' ).
tff(func_def_214,type,
'zero$h': 'Int_int_prod_a_n_vec_n_vec_prod$' ).
tff(func_def_215,type,
'pair$a': ( 'A_iarray$' * 'A_iarray$' ) > 'A_iarray_a_iarray_prod$' ).
tff(func_def_216,type,
'snd$j': 'Int_int_prod_int_prod$' > $int ).
tff(func_def_217,type,
'gauss_Jordan_iarrays$': 'A_iarray_iarray$' > 'A_iarray_iarray$' ).
tff(func_def_218,type,
'divides_aux$': 'Int_int_prod_bool_fun$' ).
tff(func_def_219,type,
'same_fst$': ( 'Int_bool_fun$' * 'Int_int_int_prod_set_fun$' ) > 'Int_int_prod_int_int_prod_prod_set$' ).
tff(func_def_220,type,
'fun_app$l': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_221,type,
'fst$b': 'Int_int_prod_int_fun$' ).
tff(func_def_222,type,
'plus$k': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_223,type,
'fun_app$j': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_224,type,
'size_prod$b': ( 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'Nat$' ).
tff(func_def_225,type,
'image2$c': ( 'A_iarray_list_set$' * 'A_iarray_list_int_fun$' * 'A_iarray_list_int_fun$' ) > 'Int_int_prod_set$' ).
tff(func_def_226,type,
'uum$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_227,type,
'zero$b': 'A_n_vec_n_vec$' ).
tff(func_def_228,type,
def_6: ( tlbool * 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray_option$' ) > tlbool ).
tff(func_def_229,type,
'plus$d': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_230,type,
'relcompp$b': ( 'Int_int_bool_fun_fun$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_bool_fun_fun$' ).
tff(func_def_231,type,
'invertible_iarray$': 'A_iarray_iarray_bool_fun$' ).
tff(func_def_232,type,
'uud$': 'A_iarray_bool_fun$' > 'A_iarray_bool_fun$' ).
tff(func_def_233,type,
'pair$c': ( $int * $int ) > 'Int_int_prod$' ).
tff(func_def_234,type,
tlfalse: tlbool ).
tff(func_def_235,type,
'fun_app$x': ( 'A_n_vec_n_vec_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_n_vec_n_vec_option$' ) > 'A_iarray_iarray_option_bool_fun$' ).
tff(func_def_236,type,
'gen_length$': 'Nat$' > 'Nat_a_iarray_prod_list_nat_fun$' ).
tff(func_def_237,type,
'plus$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_238,type,
'lex$': 'Int_int_prod_set$' > 'Int_list_int_list_prod_set$' ).
tff(func_def_239,type,
'fst$h': 'A_iarray_iarray_int_prod$' > 'A_iarray_iarray$' ).
tff(func_def_240,type,
'swap$': 'A_iarray_list_a_iarray_list_prod$' > 'A_iarray_list_a_iarray_list_prod$' ).
tff(func_def_241,type,
'pair$z': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list_a_iarray_list_list_prod$' ).
tff(func_def_242,type,
'id_upt_k$': 'A_n_vec_n_vec$' > 'Nat_bool_fun$' ).
tff(func_def_243,type,
'fst$j': 'Int_int_prod_int_prod$' > 'Int_int_prod$' ).
tff(func_def_244,type,
'fun_app$ak': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_245,type,
'collect$g': 'Int_int_prod_bool_fun$' > 'Int_int_prod_set$' ).
tff(func_def_246,type,
'pair$s': ( 'A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod$' ) > 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$' ).
tff(func_def_247,type,
'plus$v': ( 'Int_int_prod_int_prod$' * 'Int_int_prod_int_prod$' ) > 'Int_int_prod_int_prod$' ).
tff(func_def_248,type,
'splice$a': ( 'A_iarray_list_list$' * 'A_iarray_list_list$' ) > 'A_iarray_list_list$' ).
tff(func_def_249,type,
'pair$w': ( 'A_iarray_iarray_list$' * 'A_iarray_iarray_list$' ) > 'A_iarray_iarray_list_a_iarray_iarray_list_prod$' ).
tff(func_def_250,type,
'lex$b': 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' > 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ).
tff(func_def_251,type,
'pair$v': ( 'Int_list$' * 'Int_list$' ) > 'Int_list_int_list_prod$' ).
tff(func_def_252,type,
'is_zero_iarray$': 'A_iarray_bool_fun$' ).
tff(func_def_253,type,
'size_prod$a': ( 'Int_nat_fun$' * 'Int_nat_fun$' * 'Int_int_prod$' ) > 'Nat$' ).
tff(func_def_254,type,
'fun_app$be': ( 'A_iarray_list_a_iarray_list_a_iarray_list_bool_fun_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_a_iarray_list_bool_fun_fun$' ).
tff(func_def_255,type,
'iarray_to_matrix$': 'A_iarray_iarray$' > 'A_n_vec_n_vec$' ).
tff(func_def_256,type,
'fun_app$am': ( 'A_iarray_list_int_fun$' * 'A_iarray_list$' ) > $int ).
tff(func_def_257,type,
'pair$l': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_258,type,
'inverse_matrix$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec_option$' ).
tff(func_def_259,type,
'fst$i': 'Int_set_int_set_prod$' > 'Int_set$' ).
tff(func_def_260,type,
'fst$': 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' ).
tff(func_def_261,type,
'nrows_iarray$': 'A_iarray_iarray_nat_fun$' ).
tff(func_def_262,type,
'fun_app$z': ( 'A_iarray_iarray_option_a_iarray_iarray_option_bool_fun_fun$' * 'A_iarray_iarray_option$' ) > 'A_iarray_iarray_option_bool_fun$' ).
tff(func_def_263,type,
'pair$f': ( $int * 'A_iarray_iarray$' ) > 'Int_a_iarray_iarray_prod$' ).
tff(func_def_264,type,
'fun_app$aw': ( 'A_iarray_iarray_option_nat_fun$' * 'A_iarray_iarray_option$' ) > 'Nat$' ).
tff(func_def_265,type,
'uun$': 'A_iarray_set$' > 'A_iarray_bool_fun$' ).
tff(func_def_266,type,
'uub$': 'Nat_a_iarray_prod_bool_fun$' > 'Nat_a_iarray_prod_bool_fun$' ).
tff(func_def_267,type,
'similar_matrices$': 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ).
tff(func_def_268,type,
'case_option$a': ( tlbool * 'A_iarray_iarray_bool_fun$' ) > 'A_iarray_iarray_option_bool_fun$' ).
tff(func_def_269,type,
'zero$g': 'Int_int_prod_int_int_prod_prod$' ).
tff(func_def_270,type,
'pair$u': ( 'Nat$' * 'A_iarray$' ) > 'Nat_a_iarray_prod$' ).
tff(func_def_271,type,
'image2$a': ( 'Int_set$' * 'Int_int_fun$' * 'Int_int_fun$' ) > 'Int_int_prod_set$' ).
tff(func_def_272,type,
'uup$': 'A_iarray_iarray_a_iarray_iarray_prod_set$' > 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' ).
tff(func_def_273,type,
'the$a': 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).
tff(func_def_274,type,
'some$': 'A_iarray_iarray$' > 'A_iarray_iarray_option$' ).
tff(func_def_275,type,
'size_option$': 'A_iarray_iarray_nat_fun$' > 'A_iarray_iarray_option_nat_fun$' ).
tff(func_def_276,type,
'zero$e': 'Int_a_n_vec_n_vec_prod$' ).
tff(func_def_277,type,
'fun_app$y': ( 'A_iarray_iarray_option_a_n_vec_n_vec_option_bool_fun_fun$' * 'A_iarray_iarray_option$' ) > 'A_n_vec_n_vec_option_bool_fun$' ).
tff(func_def_278,type,
'pair$r': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$' ).
tff(func_def_279,type,
'zero$c': 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_280,type,
'image2$h': ( 'Int_set$' * 'Int_a_iarray_iarray_fun$' * 'Int_a_iarray_iarray_fun$' ) > 'A_iarray_iarray_a_iarray_iarray_prod_set$' ).
tff(func_def_281,type,
'fun_app$q': ( 'A_iarray_iarray_nat_fun$' * 'A_iarray_iarray$' ) > 'Nat$' ).
tff(func_def_282,type,
'fun_app$p': ( 'A_iarray_list_a_iarray_list_fun$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_283,type,
'fun_app$ac': ( 'Int_int_prod_int_fun$' * 'Int_int_prod$' ) > $int ).
tff(func_def_284,type,
'swap$c': 'Int_int_prod$' > 'Int_int_prod$' ).
tff(func_def_285,type,
'zero$f': 'Int_int_prod_int_prod$' ).
tff(func_def_286,type,
'append$a': ( 'Int_list$' * 'Int_list$' ) > 'Int_list$' ).
tff(func_def_287,type,
'size_option$a': 'A_n_vec_n_vec_nat_fun$' > 'A_n_vec_n_vec_option_nat_fun$' ).
tff(func_def_288,type,
'nil$a': 'Nat_a_iarray_prod_list$' ).
tff(func_def_289,type,
'fstOp$b': ( 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_bool_fun_fun$' ) > 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ).
tff(func_def_290,type,
'fun_app$i': ( 'A_iarray_list_a_iarray_list_bool_fun_fun$' * 'A_iarray_list$' ) > 'A_iarray_list_bool_fun$' ).
tff(func_def_291,type,
'the$': 'A_n_vec_n_vec_option$' > 'A_n_vec_n_vec$' ).
tff(func_def_292,type,
'size$d': 'A_n_vec_n_vec_option$' > 'Nat$' ).
tff(func_def_293,type,
'plus$g': ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_294,type,
'enumerate$b': ( 'Nat$' * 'A_iarray_list_list$' ) > 'Nat_a_iarray_list_prod_list$' ).
tff(func_def_295,type,
'plus$f': ( 'A_iarray_set$' * 'A_iarray_set$' ) > 'A_iarray_set$' ).
tff(func_def_296,type,
'matrix_matrix_mult_iarray$': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_297,type,
'splice$': ( 'Nat_a_iarray_prod_list$' * 'Nat_a_iarray_prod_list$' ) > 'Nat_a_iarray_prod_list$' ).
tff(func_def_298,type,
'fun_app$u': ( 'Nat_a_iarray_prod_list_nat_fun$' * 'Nat_a_iarray_prod_list$' ) > 'Nat$' ).
tff(func_def_299,type,
'vec_to_iarray$': 'A_n_vec_n_vec$' > 'A_n_vec_iarray$' ).
tff(func_def_300,type,
'snd$g': 'Int_int_int_prod_prod$' > 'Int_int_prod$' ).
tff(func_def_301,type,
'pair$i': ( 'Int_set$' * 'Int_set$' ) > 'Int_set_int_set_prod$' ).
tff(func_def_302,type,
'lexord$b': 'A_iarray_list_a_iarray_list_prod_set$' > 'A_iarray_list_list_a_iarray_list_list_prod_set$' ).
tff(func_def_303,type,
'snd$b': 'Int_int_prod_int_fun$' ).
tff(func_def_304,type,
'plus$c': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_305,type,
'size_list$': ( 'A_iarray_nat_fun$' * 'A_iarray_list$' ) > 'Nat$' ).
tff(func_def_309,type,
sK1: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_310,type,
sK2: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_311,type,
sK3: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray$' ).
tff(func_def_312,type,
sK4: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_313,type,
sK5: ( 'A_iarray_list$' * 'A_iarray_list$' ) > 'A_iarray$' ).
tff(func_def_314,type,
sK6: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_315,type,
sK7: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_316,type,
sK8: 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).
tff(func_def_317,type,
sK9: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).
tff(func_def_318,type,
sK10: 'Nat$' > 'Nat$' ).
tff(func_def_319,type,
sK11: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_320,type,
sK12: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).
tff(func_def_321,type,
sK13: 'Nat$' > 'Nat$' ).
tff(func_def_322,type,
sK14: 'A_iarray_iarray_option$' > 'A_iarray_iarray$' ).
tff(func_def_323,type,
sK15: 'Nat$' > 'Nat$' ).
tff(func_def_324,type,
sK16: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_325,type,
sK17: ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_326,type,
sK18: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_327,type,
sK19: 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_328,type,
sK20: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_329,type,
sK21: 'Nat$' > 'A_iarray_list$' ).
tff(func_def_330,type,
sK22: ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray_list$' ).
tff(func_def_331,type,
sK23: ( 'Nat$' * 'A_iarray_list$' ) > 'A_iarray$' ).
tff(func_def_332,type,
sK24: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_333,type,
sK25: 'Nat$' > 'Nat$' ).
tff(func_def_334,type,
sK26: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_335,type,
sK27: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray_list$' ).
tff(func_def_336,type,
sK28: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray$' ).
tff(func_def_337,type,
sK29: ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_338,type,
sK30: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_339,type,
sK31: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray_list$' ).
tff(func_def_340,type,
sK32: ( 'A_iarray_list$' * 'Nat$' ) > 'A_iarray$' ).
tff(func_def_341,type,
sF33: 'A_iarray_iarray$' ).
tff(func_def_342,type,
sF34: 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_343,type,
sF35: 'A_iarray_iarray$' ).
tff(func_def_344,type,
sF36: 'A_iarray_iarray_option$' ).
tff(func_def_345,type,
sF37: 'Nat$' ).
tff(func_def_346,type,
sF38: $int ).
tff(func_def_347,type,
sF39: 'A_iarray_list_a_iarray_list_fun$' ).
tff(func_def_348,type,
sF40: 'A_n_vec_n_vec_a_n_vec_n_vec_prod$' ).
tff(func_def_349,type,
sF41: 'A_n_vec_n_vec$' ).
tff(func_def_350,type,
sF42: 'A_iarray_iarray$' ).
tff(func_def_351,type,
sF43: 'A_iarray_list$' ).
tff(func_def_352,type,
sF44: 'A_iarray_list$' ).
tff(func_def_353,type,
sF45: 'Nat$' ).
tff(func_def_354,type,
sF46: $int ).
tff(func_def_355,type,
sF47: 'A_iarray_iarray$' ).
tff(func_def_356,type,
sF48: 'A_iarray_list$' ).
tff(func_def_357,type,
sF49: 'A_iarray_list$' ).
tff(func_def_358,type,
sF50: 'Nat$' ).
tff(func_def_359,type,
sF51: $int ).
tff(func_def_361,type,
2: $int > $int ).
tff(pred_def_1,type,
'fun_app$s': ( 'A_n_vec_n_vec_option_bool_fun$' * 'A_n_vec_n_vec_option$' ) > $o ).
tff(pred_def_2,type,
'fun_app$o': ( 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$' ) > $o ).
tff(pred_def_3,type,
'member$q': ( 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod$' * 'Nat_a_iarray_prod_list_nat_a_iarray_prod_list_prod_set$' ) > $o ).
tff(pred_def_4,type,
'member$p': ( 'A_iarray_iarray_list_a_iarray_iarray_list_prod$' * 'A_iarray_iarray_list_a_iarray_iarray_list_prod_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$f': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > $o ).
tff(pred_def_6,type,
'csquare$': ( 'A_n_vec_n_vec_a_n_vec_n_vec_prod_set$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' * 'A_n_vec_n_vec_a_n_vec_n_vec_prod_a_n_vec_n_vec_a_n_vec_n_vec_prod_fun$' ) > $o ).
tff(pred_def_7,type,
'fun_app$c': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_8,type,
'fun_app$ae': ( 'Int_int_prod_bool_fun$' * 'Int_int_prod$' ) > $o ).
tff(pred_def_9,type,
'member$r': ( 'Nat_a_iarray_prod_nat_a_iarray_prod_prod$' * 'Nat_a_iarray_prod_nat_a_iarray_prod_prod_set$' ) > $o ).
tff(pred_def_10,type,
'member$c': ( 'Nat$' * 'Nat_set$' ) > $o ).
tff(pred_def_11,type,
'member$a': ( 'A_iarray$' * 'A_iarray_set$' ) > $o ).
tff(pred_def_12,type,
'member$l': ( 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_prod_set$' ) > $o ).
tff(pred_def_13,type,
'member$e': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod_set$' ) > $o ).
tff(pred_def_14,type,
'fun_app$d': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_15,type,
'member$m': ( 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod$' * 'A_iarray_list_a_iarray_list_prod_a_iarray_list_a_iarray_list_prod_prod_set$' ) > $o ).
tff(pred_def_16,type,
'csquare$b': ( 'Int_int_prod_set$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_fun$' * 'Int_int_prod_int_int_prod_fun$' * 'Int_int_prod_int_int_prod_fun$' ) > $o ).
tff(pred_def_17,type,
'fun_app$a': ( 'A_iarray_list_a_iarray_list_prod_bool_fun$' * 'A_iarray_list_a_iarray_list_prod$' ) > $o ).
tff(pred_def_18,type,
'member$d': ( $int * 'Int_set$' ) > $o ).
tff(pred_def_19,type,
'fun_app$': ( 'A_iarray_bool_fun$' * 'A_iarray$' ) > $o ).
tff(pred_def_20,type,
'fun_app$n': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_21,type,
'member$b': ( 'A_iarray_list$' * 'A_iarray_list_set$' ) > $o ).
tff(pred_def_22,type,
'fun_app$af': ( 'A_iarray_iarray_a_iarray_iarray_prod_bool_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > $o ).
tff(pred_def_23,type,
'member$n': ( 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod$' * 'A_iarray_a_iarray_prod_a_iarray_a_iarray_prod_prod_set$' ) > $o ).
tff(pred_def_24,type,
'member$k': ( 'Int_int_prod_int_int_prod_prod$' * 'Int_int_prod_int_int_prod_prod_set$' ) > $o ).
tff(pred_def_25,type,
'fun_app$b': ( 'A_iarray_list_bool_fun$' * 'A_iarray_list$' ) > $o ).
tff(pred_def_26,type,
'member$s': ( 'A_iarray_list_list_a_iarray_list_list_prod$' * 'A_iarray_list_list_a_iarray_list_list_prod_set$' ) > $o ).
tff(pred_def_27,type,
'member$i': ( 'Int_set$' * 'Int_set_set$' ) > $o ).
tff(pred_def_28,type,
'member$j': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' ) > $o ).
tff(pred_def_29,type,
'fun_app$e': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$' ) > $o ).
tff(pred_def_30,type,
'member$g': ( 'Int_int_prod$' * 'Int_int_prod_set$' ) > $o ).
tff(pred_def_31,type,
'member$o': ( 'Int_list_int_list_prod$' * 'Int_list_int_list_prod_set$' ) > $o ).
tff(pred_def_32,type,
'fun_app$t': ( 'A_iarray_iarray_option_bool_fun$' * 'A_iarray_iarray_option$' ) > $o ).
tff(pred_def_33,type,
'csquare$a': ( 'A_iarray_iarray_a_iarray_iarray_prod_set$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' * 'A_iarray_iarray_a_iarray_iarray_prod_a_iarray_iarray_a_iarray_iarray_prod_fun$' ) > $o ).
tff(pred_def_34,type,
'member$f': ( 'A_iarray_a_iarray_prod$' * 'A_iarray_a_iarray_prod_set$' ) > $o ).
tff(pred_def_35,type,
'member$': ( 'A_iarray_list_a_iarray_list_prod$' * 'A_iarray_list_a_iarray_list_prod_set$' ) > $o ).
tff(pred_def_36,type,
'fun_app$ag': ( 'A_iarray_a_iarray_prod_bool_fun$' * 'A_iarray_a_iarray_prod$' ) > $o ).
tff(pred_def_37,type,
'member$h': ( 'A_iarray_iarray$' * 'A_iarray_iarray_set$' ) > $o ).
tff(pred_def_38,type,
'is_zero_iarray$a': 'A_n_vec_iarray$' > $o ).
tff(f23,conjecture,
( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture22) ).
tff(f24,negated_conjecture,
~ ( ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'none$' = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
=> ( ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'none$' ) )
& ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
=> ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) = 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
tff(f195,axiom,
! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).
tff(f206,axiom,
! [X0: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) = 'gauss_Jordan_iarrays$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
tff(f234,axiom,
! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] :
? [X1: 'A_iarray_iarray$',X2: 'A_iarray_iarray$'] : ( X0 = 'pair$'(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).
tff(f253,axiom,
! [X1: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom251) ).
tff(f275,axiom,
! [X0: 'A_n_vec_n_vec$'] : ( 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) = 'gauss_Jordan$'(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
tff(f700,plain,
! [X1: 'A_iarray_iarray$',X0: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X1,X0)) = X0 ),
inference(rectify,[],[f253]) ).
tff(f777,plain,
( ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
& ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ( ( ( ( 'none$' != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) ) ),
inference(ennf_transformation,[],[f24]) ).
tff(f849,definition,
( ( ( ( ( 'none$' != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f850,plain,
( ( ( ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
& ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| sP0 ),
inference(definition_folding,[],[f777,f849]) ).
tff(f857,plain,
! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK6(X0),sK7(X0)) = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X1,sK6(X0)),skolemize(X2,sK7(X0))],[f234]) ).
tff(f877,plain,
! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ),
inference(rectify,[],[f700]) ).
tff(f915,plain,
( ( ( ( ( 'none$' != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) )
| ( ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'none$' )
& ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) ) ) )
& ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) ) )
| ~ sP0 ),
inference(nnf_transformation,[],[f849]) ).
tff(f1055,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'gauss_Jordan$'(X0) = 'fun_app$ab'('snd$','gauss_Jordan_PA$'(X0)) ),
inference(cnf_transformation,[],[f275]) ).
tff(f1064,plain,
! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'pair$'(sK6(X0),sK7(X0)) = X0 ),
inference(cnf_transformation,[],[f857]) ).
tff(f1079,plain,
! [X0: 'A_iarray_iarray$'] : ( 'gauss_Jordan_iarrays$'(X0) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'(X0)) ),
inference(cnf_transformation,[],[f206]) ).
tff(f1096,plain,
! [X0: 'A_iarray_iarray$',X1: 'A_iarray_iarray$'] : ( 'fun_app$r'('snd$a','pair$'(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f877]) ).
tff(f1156,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
| ~ sP0 ),
inference(cnf_transformation,[],[f915]) ).
tff(f1159,plain,
( ( 'none$' != 'none$' )
| ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
| ~ sP0 ),
inference(cnf_transformation,[],[f915]) ).
tff(f1161,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('gauss_Jordan_iarrays$'('matrix_to_iarray$'('a$')))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) )
| sP0 ),
inference(cnf_transformation,[],[f850]) ).
tff(f1162,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('gauss_Jordan$'('a$')))))) )
| ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
| sP0 ),
inference(cnf_transformation,[],[f850]) ).
tff(f1330,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = 'fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
inference(cnf_transformation,[],[f195]) ).
tff(f1374,plain,
( ( 'none$' != 'none$' )
| ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
| ~ sP0 ),
inference(definition_unfolding,[],[f1159,f1055]) ).
tff(f1377,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| ~ sP0 ),
inference(definition_unfolding,[],[f1156,f1079]) ).
tff(f1380,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
| ( 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) != 'some$'('fun_app$r'('fst$','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$')))) )
| sP0 ),
inference(definition_unfolding,[],[f1162,f1055]) ).
tff(f1381,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| sP0 ),
inference(definition_unfolding,[],[f1161,f1079]) ).
tff(f1463,definition,
sF33 = 'matrix_to_iarray$'('a$'),
introduced(definition,[new_symbols(definition,[sF33])],[function_definition]) ).
tff(f1464,plain,
'matrix_to_iarray$'('a$') = sF33,
inference(reorient_equations,[],[f1463]) ).
tff(f1465,definition,
sF34 = 'gauss_Jordan_iarrays_PA$'(sF33),
introduced(definition,[new_symbols(definition,[sF34])],[function_definition]) ).
tff(f1466,plain,
'gauss_Jordan_iarrays_PA$'(sF33) = sF34,
inference(reorient_equations,[],[f1465]) ).
tff(f1467,definition,
sF35 = 'fun_app$r'('fst$',sF34),
introduced(definition,[new_symbols(definition,[sF35])],[function_definition]) ).
tff(f1468,plain,
'fun_app$r'('fst$',sF34) = sF35,
inference(reorient_equations,[],[f1467]) ).
tff(f1469,definition,
sF36 = 'some$'(sF35),
introduced(definition,[new_symbols(definition,[sF36])],[function_definition]) ).
tff(f1470,definition,
sF37 = 'fun_app$q'('nrows_iarray$',sF33),
introduced(definition,[new_symbols(definition,[sF37])],[function_definition]) ).
tff(f1471,definition,
sF38 = 'fun_app$l'('of_nat$',sF37),
introduced(definition,[new_symbols(definition,[sF38])],[function_definition]) ).
tff(f1472,plain,
'fun_app$l'('of_nat$',sF37) = sF38,
inference(reorient_equations,[],[f1471]) ).
tff(f1473,definition,
sF39 = 'filter$'('uu$'),
introduced(definition,[new_symbols(definition,[sF39])],[function_definition]) ).
tff(f1474,plain,
'filter$'('uu$') = sF39,
inference(reorient_equations,[],[f1473]) ).
tff(f1475,definition,
sF40 = 'gauss_Jordan_PA$'('a$'),
introduced(definition,[new_symbols(definition,[sF40])],[function_definition]) ).
tff(f1476,definition,
sF41 = 'fun_app$ab'('snd$',sF40),
introduced(definition,[new_symbols(definition,[sF41])],[function_definition]) ).
tff(f1477,definition,
sF42 = 'matrix_to_iarray$'(sF41),
introduced(definition,[new_symbols(definition,[sF42])],[function_definition]) ).
tff(f1478,plain,
'matrix_to_iarray$'(sF41) = sF42,
inference(reorient_equations,[],[f1477]) ).
tff(f1479,definition,
sF43 = 'list_of$'(sF42),
introduced(definition,[new_symbols(definition,[sF43])],[function_definition]) ).
tff(f1480,plain,
'list_of$'(sF42) = sF43,
inference(reorient_equations,[],[f1479]) ).
tff(f1481,definition,
sF44 = 'fun_app$p'(sF39,sF43),
introduced(definition,[new_symbols(definition,[sF44])],[function_definition]) ).
tff(f1482,definition,
sF45 = 'fun_app$m'('size$',sF44),
introduced(definition,[new_symbols(definition,[sF45])],[function_definition]) ).
tff(f1483,plain,
'fun_app$m'('size$',sF44) = sF45,
inference(reorient_equations,[],[f1482]) ).
tff(f1484,definition,
sF46 = 'fun_app$l'('of_nat$',sF45),
introduced(definition,[new_symbols(definition,[sF46])],[function_definition]) ).
tff(f1488,plain,
( ( sF36 != sF36 )
| sP0
| ( sF46 != sF38 ) ),
inference(definition_folding,[],[f1380,f1469,f1468,f1466,f1464,f1469,f1468,f1466,f1464,f1484,f1483,f1481,f1480,f1478,f1476,f1475,f1474,f1472,f1470,f1464]) ).
tff(f1489,definition,
sF47 = 'fun_app$r'('snd$a',sF34),
introduced(definition,[new_symbols(definition,[sF47])],[function_definition]) ).
tff(f1490,definition,
sF48 = 'list_of$'(sF47),
introduced(definition,[new_symbols(definition,[sF48])],[function_definition]) ).
tff(f1491,plain,
'list_of$'(sF47) = sF48,
inference(reorient_equations,[],[f1490]) ).
tff(f1492,definition,
sF49 = 'fun_app$p'(sF39,sF48),
introduced(definition,[new_symbols(definition,[sF49])],[function_definition]) ).
tff(f1493,plain,
'fun_app$p'(sF39,sF48) = sF49,
inference(reorient_equations,[],[f1492]) ).
tff(f1494,definition,
sF50 = 'fun_app$m'('size$',sF49),
introduced(definition,[new_symbols(definition,[sF50])],[function_definition]) ).
tff(f1495,definition,
sF51 = 'fun_app$l'('of_nat$',sF50),
introduced(definition,[new_symbols(definition,[sF51])],[function_definition]) ).
tff(f1496,plain,
'fun_app$l'('of_nat$',sF50) = sF51,
inference(reorient_equations,[],[f1495]) ).
tff(f1497,plain,
( ( sF38 = sF51 )
| sP0 ),
inference(definition_folding,[],[f1381,f1496,f1494,f1493,f1491,f1489,f1466,f1464,f1474,f1472,f1470,f1464]) ).
tff(f1498,plain,
( ( sF46 != sF38 )
| sP0 ),
inference(trivial_inequality_removal,[],[f1488]) ).
tff(f1499,plain,
( ~ sP0
| ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) ) ),
inference(trivial_inequality_removal,[],[f1374]) ).
tff(f1503,definition,
( spl52_1
<=> ( sF46 = sF38 ) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
tff(f1507,definition,
( spl52_2
<=> sP0 ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
tff(f1510,plain,
( ~ spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f1498,f1507,f1503]) ).
tff(f1512,definition,
( spl52_3
<=> ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) ) ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
tff(f1513,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
| spl52_3 ),
inference(avatar_component_clause,[],[f1512]) ).
tff(f1514,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'('a$'))))))) )
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f1512]) ).
tff(f1515,plain,
( spl52_3
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f1499,f1507,f1512]) ).
tff(f1522,definition,
( spl52_5
<=> ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) ) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
tff(f1524,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'('fun_app$r'('snd$a','gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| spl52_5 ),
inference(avatar_component_clause,[],[f1522]) ).
tff(f1525,plain,
( ~ spl52_2
| ~ spl52_5 ),
inference(avatar_split_clause,[],[f1377,f1522,f1507]) ).
tff(f1528,definition,
( spl52_6
<=> ( sF38 = sF51 ) ),
introduced(definition,[new_symbols(definition,[spl52_6])],[avatar_definition]) ).
tff(f1530,plain,
( ( sF38 = sF51 )
| ~ spl52_6 ),
inference(avatar_component_clause,[],[f1528]) ).
tff(f1531,plain,
( spl52_6
| spl52_2 ),
inference(avatar_split_clause,[],[f1497,f1507,f1528]) ).
tff(f1548,plain,
! [X0: 'A_iarray_iarray_a_iarray_iarray_prod$'] : ( 'fun_app$r'('snd$a',X0) = sK7(X0) ),
inference(superposition,[],[f1096,f1064]) ).
tff(f1592,plain,
sF47 = sK7(sF34),
inference(superposition,[],[f1548,f1489]) ).
tff(f2058,plain,
! [X0: 'A_n_vec_n_vec$'] : ( 'matrix_to_iarray$'('fun_app$ab'('snd$','gauss_Jordan_PA$'(X0))) = sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'(X0))) ),
inference(forward_demodulation,[],[f1330,f1548]) ).
tff(f2059,plain,
sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))) = 'matrix_to_iarray$'('fun_app$ab'('snd$',sF40)),
inference(superposition,[],[f2058,f1475]) ).
tff(f2069,plain,
'matrix_to_iarray$'(sF41) = sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))),
inference(forward_demodulation,[],[f2059,f1476]) ).
tff(f2070,plain,
'matrix_to_iarray$'(sF41) = sK7('gauss_Jordan_iarrays_PA$'(sF33)),
inference(forward_demodulation,[],[f2069,f1464]) ).
tff(f2071,plain,
'matrix_to_iarray$'(sF41) = sK7(sF34),
inference(forward_demodulation,[],[f2070,f1466]) ).
tff(f2072,plain,
'matrix_to_iarray$'(sF41) = sF47,
inference(forward_demodulation,[],[f2071,f1592]) ).
tff(f2073,plain,
sF42 = sF47,
inference(superposition,[],[f2072,f1478]) ).
tff(f2090,plain,
'list_of$'(sF47) = sF43,
inference(superposition,[],[f1480,f2073]) ).
tff(f2097,plain,
sF48 = sF43,
inference(forward_demodulation,[],[f2090,f1491]) ).
tff(f2113,plain,
'fun_app$p'(sF39,sF48) = sF44,
inference(superposition,[],[f1481,f2097]) ).
tff(f2114,plain,
sF44 = sF49,
inference(forward_demodulation,[],[f2113,f1493]) ).
tff(f2117,plain,
'fun_app$m'('size$',sF49) = sF45,
inference(superposition,[],[f1483,f2114]) ).
tff(f2118,plain,
sF50 = sF45,
inference(forward_demodulation,[],[f2117,f1494]) ).
tff(f2131,plain,
'fun_app$l'('of_nat$',sF50) = sF46,
inference(superposition,[],[f1484,f2118]) ).
tff(f2152,plain,
sF46 = sF51,
inference(superposition,[],[f2131,f1496]) ).
tff(f3501,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f1514,f2058]) ).
tff(f3502,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) = 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',sF33)) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3501,f1464]) ).
tff(f3503,plain,
( ( 'fun_app$l'('of_nat$',sF37) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3502,f1470]) ).
tff(f3504,plain,
( ( 'fun_app$l'('of_nat$',sF37) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7(sF34))))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3503,f1466]) ).
tff(f3505,plain,
( ( 'fun_app$l'('of_nat$',sF37) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sF47)))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3504,f1592]) ).
tff(f3506,plain,
( ( 'fun_app$l'('of_nat$',sF37) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),sF48))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3505,f1491]) ).
tff(f3507,plain,
( ( 'fun_app$l'('of_nat$',sF37) = 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'(sF39,sF48))) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3506,f1474]) ).
tff(f3508,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) = 'fun_app$l'('of_nat$',sF37) )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3507,f1493]) ).
tff(f3509,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) = sF38 )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3508,f1472]) ).
tff(f3510,plain,
( ( 'fun_app$l'('of_nat$',sF50) = sF38 )
| ~ spl52_3 ),
inference(forward_demodulation,[],[f3509,f1494]) ).
tff(f3513,plain,
( ( sF46 = sF38 )
| ~ spl52_3 ),
inference(superposition,[],[f2131,f3510]) ).
tff(f3558,plain,
( spl52_1
| ~ spl52_3 ),
inference(avatar_split_clause,[],[f3513,f1512,f1503]) ).
tff(f3559,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| spl52_3 ),
inference(forward_demodulation,[],[f1513,f2058]) ).
tff(f3560,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',sF33)) )
| spl52_3 ),
inference(forward_demodulation,[],[f3559,f1464]) ).
tff(f3561,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) )
| spl52_3 ),
inference(forward_demodulation,[],[f3560,f1470]) ).
tff(f3562,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7(sF34))))) )
| spl52_3 ),
inference(forward_demodulation,[],[f3561,f1466]) ).
tff(f3563,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sF47)))) )
| spl52_3 ),
inference(forward_demodulation,[],[f3562,f1592]) ).
tff(f3564,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),sF48))) )
| spl52_3 ),
inference(forward_demodulation,[],[f3563,f1491]) ).
tff(f3565,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'(sF39,sF48))) )
| spl52_3 ),
inference(forward_demodulation,[],[f3564,f1474]) ).
tff(f3566,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) != 'fun_app$l'('of_nat$',sF37) )
| spl52_3 ),
inference(forward_demodulation,[],[f3565,f1493]) ).
tff(f3567,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) != sF38 )
| spl52_3 ),
inference(forward_demodulation,[],[f3566,f1472]) ).
tff(f3568,plain,
( ( 'fun_app$l'('of_nat$',sF50) != sF38 )
| spl52_3 ),
inference(forward_demodulation,[],[f3567,f1494]) ).
tff(f3569,plain,
( ( sF38 != sF51 )
| spl52_3 ),
inference(forward_demodulation,[],[f3568,f1496]) ).
tff(f3570,plain,
( ( sF46 != sF38 )
| spl52_3 ),
inference(forward_demodulation,[],[f3569,f2152]) ).
tff(f3571,plain,
( ~ spl52_1
| spl52_3 ),
inference(avatar_split_clause,[],[f3570,f1512,f1503]) ).
tff(f3572,plain,
( ( sF46 = sF38 )
| ~ spl52_6 ),
inference(superposition,[],[f1530,f2152]) ).
tff(f3585,plain,
( spl52_1
| ~ spl52_6 ),
inference(avatar_split_clause,[],[f3572,f1528,f1503]) ).
tff(f3663,plain,
( ( 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$','matrix_to_iarray$'('a$'))) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'('matrix_to_iarray$'('a$'))))))) )
| spl52_5 ),
inference(forward_demodulation,[],[f1524,f1548]) ).
tff(f3664,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) != 'fun_app$l'('of_nat$','fun_app$q'('nrows_iarray$',sF33)) )
| spl52_5 ),
inference(forward_demodulation,[],[f3663,f1464]) ).
tff(f3665,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7('gauss_Jordan_iarrays_PA$'(sF33)))))) )
| spl52_5 ),
inference(forward_demodulation,[],[f3664,f1470]) ).
tff(f3666,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sK7(sF34))))) )
| spl52_5 ),
inference(forward_demodulation,[],[f3665,f1466]) ).
tff(f3667,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),'list_of$'(sF47)))) )
| spl52_5 ),
inference(forward_demodulation,[],[f3666,f1592]) ).
tff(f3668,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'('filter$'('uu$'),sF48))) )
| spl52_5 ),
inference(forward_demodulation,[],[f3667,f1491]) ).
tff(f3669,plain,
( ( 'fun_app$l'('of_nat$',sF37) != 'fun_app$l'('of_nat$','fun_app$m'('size$','fun_app$p'(sF39,sF48))) )
| spl52_5 ),
inference(forward_demodulation,[],[f3668,f1474]) ).
tff(f3670,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) != 'fun_app$l'('of_nat$',sF37) )
| spl52_5 ),
inference(forward_demodulation,[],[f3669,f1493]) ).
tff(f3671,plain,
( ( 'fun_app$l'('of_nat$','fun_app$m'('size$',sF49)) != sF38 )
| spl52_5 ),
inference(forward_demodulation,[],[f3670,f1472]) ).
tff(f3672,plain,
( ( 'fun_app$l'('of_nat$',sF50) != sF38 )
| spl52_5 ),
inference(forward_demodulation,[],[f3671,f1494]) ).
tff(f3673,plain,
( $false
| ~ spl52_3
| spl52_5 ),
inference(forward_subsumption_resolution,[],[f3672,f3510]) ).
tff(f3674,plain,
( ~ spl52_3
| spl52_5 ),
inference(avatar_contradiction_clause,[],[f3673]) ).
cnf(s1,plain,
( ~ spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f1510]) ).
cnf(s2,plain,
( ~ spl52_2
| spl52_3 ),
inference(sat_conversion,[],[f1515]) ).
cnf(s4,plain,
( ~ spl52_2
| ~ spl52_5 ),
inference(sat_conversion,[],[f1525]) ).
cnf(s6,plain,
( spl52_2
| spl52_6 ),
inference(sat_conversion,[],[f1531]) ).
cnf(s79,plain,
( spl52_1
| ~ spl52_3 ),
inference(sat_conversion,[],[f3558]) ).
cnf(s82,plain,
( ~ spl52_1
| spl52_3 ),
inference(sat_conversion,[],[f3571]) ).
cnf(s86,plain,
( spl52_1
| ~ spl52_6 ),
inference(sat_conversion,[],[f3585]) ).
cnf(s89,plain,
( ~ spl52_3
| spl52_5 ),
inference(sat_conversion,[],[f3674]) ).
cnf(s100,plain,
spl52_1,
inference(rat,[],[s2,s6,s79,s86]) ).
cnf(s101,plain,
spl52_3,
inference(rat,[],[s82,s100]) ).
cnf(s102,plain,
spl52_2,
inference(rat,[],[s1,s100]) ).
cnf(s103,plain,
spl52_5,
inference(rat,[],[s89,s101]) ).
cnf(s106,plain,
$false,
inference(rat,[],[s4,s103,s102]) ).
tff(f3675,plain,
$false,
inference(avatar_sat_refutation,[],[s106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP343_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 12:54:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.16/0.41 Running first-order theorem proving
% 0.16/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.99/1.41 % (3963756)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.99/1.41 % (3963795)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2578037547:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.99/1.41 % (3963795)Instruction limit reached!
% 2.99/1.41 % (3963795)------------------------------
% 2.99/1.41 % (3963795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.41 % (3963795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.41 % (3963795)CaDiCaL version: 2.1.3
% 2.99/1.41 % (3963795)Termination reason: Instruction limit
% 2.99/1.41 % (3963795)Termination phase: Property scanning
% 2.99/1.41 % (3963795)Time elapsed: 0.004 s
% 2.99/1.41 % (3963795)Peak memory usage: 86 MB
% 2.99/1.41 % (3963795)Instructions burned: 15 (million)
% 2.99/1.41 % (3963801)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3577505628:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.99/1.41 % (3963800)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3665332751:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.99/1.41 % (3963796)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2994607117:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.99/1.41 % (3963799)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3043894211:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.99/1.41 % (3963797)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=832693963:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.99/1.41 % (3963799)Instruction limit reached!
% 2.99/1.41 % (3963799)------------------------------
% 2.99/1.41 % (3963799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.41 % (3963799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.41 % (3963799)CaDiCaL version: 2.1.3
% 2.99/1.41 % (3963799)Termination reason: Instruction limit
% 2.99/1.41 % (3963799)Termination phase: Property scanning
% 2.99/1.41 % (3963799)Time elapsed: 0.003 s
% 2.99/1.41 % (3963799)Peak memory usage: 85 MB
% 2.99/1.41 % (3963799)Instructions burned: 4 (million)
% 2.99/1.41 % (3963801)Instruction limit reached!
% 2.99/1.41 % (3963801)------------------------------
% 2.99/1.41 % (3963801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.41 % (3963801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.41 % (3963801)CaDiCaL version: 2.1.3
% 2.99/1.41 % (3963801)Termination reason: Instruction limit
% 2.99/1.41 % (3963801)Termination phase: Preprocessing 3
% 2.99/1.41 % (3963801)Time elapsed: 0.019 s
% 2.99/1.41 % (3963801)Peak memory usage: 88 MB
% 2.99/1.41 % (3963801)Instructions burned: 33 (million)
% 2.99/1.41 % (3963800)Instruction limit reached!
% 2.99/1.41 % (3963800)------------------------------
% 2.99/1.41 % (3963800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.41 % (3963800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.41 % (3963800)CaDiCaL version: 2.1.3
% 2.99/1.41 % (3963800)Termination reason: Instruction limit
% 2.99/1.41 % (3963800)Termination phase: Function definition elimination
% 2.99/1.41 % (3963800)Time elapsed: 0.027 s
% 2.99/1.41 % (3963800)Peak memory usage: 88 MB
% 2.99/1.41 % (3963800)Instructions burned: 47 (million)
% 2.99/1.41 % (3963798)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2684125915:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.99/1.41 % (3963798)Instruction limit reached!
% 2.99/1.41 % (3963798)------------------------------
% 2.99/1.41 % (3963798)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.41 % (3963798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.41 % (3963798)CaDiCaL version: 2.1.3
% 2.99/1.41 % (3963798)Termination reason: Instruction limit
% 2.99/1.41 % (3963798)Termination phase: Property scanning
% 2.99/1.41 % (3963798)Time elapsed: 0.005 s
% 2.99/1.41 % (3963798)Peak memory usage: 85 MB
% 2.99/1.41 % (3963798)Instructions burned: 8 (million)
% 2.99/1.41 % (3963803)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=746296026:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.99/1.41 % (3963803)Instruction limit reached!
% 3.64/1.56 % (3963803)------------------------------
% 3.64/1.56 % (3963803)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963803)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963803)Termination reason: Instruction limit
% 3.64/1.56 % (3963803)Termination phase: Preprocessing 1
% 3.64/1.56 % (3963803)Time elapsed: 0.005 s
% 3.64/1.56 % (3963803)Peak memory usage: 86 MB
% 3.64/1.56 % (3963803)Instructions burned: 16 (million)
% 3.64/1.56 % (3963809)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=1963940908:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.64/1.56 % (3963815)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2921427379:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.64/1.56 % (3963810)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1038168898:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.64/1.56 % (3963809)Instruction limit reached!
% 3.64/1.56 % (3963809)------------------------------
% 3.64/1.56 % (3963809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963809)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963809)Termination reason: Instruction limit
% 3.64/1.56 % (3963809)Termination phase: Preprocessing 3
% 3.64/1.56 % (3963809)Time elapsed: 0.017 s
% 3.64/1.56 % (3963809)Peak memory usage: 88 MB
% 3.64/1.56 % (3963809)Instructions burned: 30 (million)
% 3.64/1.56 % (3963811)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=213967744:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.64/1.56 % (3963810)Instruction limit reached!
% 3.64/1.56 % (3963810)------------------------------
% 3.64/1.56 % (3963810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963810)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963810)Termination reason: Instruction limit
% 3.64/1.56 % (3963810)Termination phase: Preprocessing 2
% 3.64/1.56 % (3963810)Time elapsed: 0.010 s
% 3.64/1.56 % (3963810)Peak memory usage: 86 MB
% 3.64/1.56 % (3963810)Instructions burned: 16 (million)
% 3.64/1.56 % (3963811)Instruction limit reached!
% 3.64/1.56 % (3963811)------------------------------
% 3.64/1.56 % (3963811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963811)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963811)Termination reason: Instruction limit
% 3.64/1.56 % (3963811)Termination phase: Preprocessing 2
% 3.64/1.56 % (3963811)Time elapsed: 0.013 s
% 3.64/1.56 % (3963811)Peak memory usage: 87 MB
% 3.64/1.56 % (3963811)Instructions burned: 24 (million)
% 3.64/1.56 % (3963815)Instruction limit reached!
% 3.64/1.56 % (3963815)------------------------------
% 3.64/1.56 % (3963815)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963815)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963815)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963815)Termination reason: Instruction limit
% 3.64/1.56 % (3963815)Termination phase: Saturation
% 3.64/1.56 % (3963815)Time elapsed: 0.024 s
% 3.64/1.56 % (3963815)Peak memory usage: 89 MB
% 3.64/1.56 % (3963815)Instructions burned: 90 (million)
% 3.64/1.56 % (3963797)Instruction limit reached!
% 3.64/1.56 % (3963797)------------------------------
% 3.64/1.56 % (3963797)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.56 % (3963797)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.56 % (3963797)CaDiCaL version: 2.1.3
% 3.64/1.56 % (3963797)Termination reason: Instruction limit
% 3.64/1.56 % (3963797)Termination phase: Saturation
% 3.64/1.56 % (3963797)Time elapsed: 0.159 s
% 3.64/1.56 % (3963797)Peak memory usage: 119 MB
% 3.64/1.56 % (3963797)Instructions burned: 201 (million)
% 3.64/1.56 % (3963814)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=714608974:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.64/1.56 % (3963814)Instruction limit reached!
% 3.64/1.56 % (3963814)------------------------------
% 4.77/1.72 % (3963814)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963814)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963814)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963814)Termination reason: Instruction limit
% 4.77/1.72 % (3963814)Termination phase: Preprocessing 3
% 4.77/1.72 % (3963814)Time elapsed: 0.016 s
% 4.77/1.72 % (3963814)Peak memory usage: 87 MB
% 4.77/1.72 % (3963814)Instructions burned: 27 (million)
% 4.77/1.72 % (3963796)Instruction limit reached!
% 4.77/1.72 % (3963796)------------------------------
% 4.77/1.72 % (3963796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963796)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963796)Termination reason: Instruction limit
% 4.77/1.72 % (3963796)Termination phase: Saturation
% 4.77/1.72 % (3963796)Time elapsed: 0.208 s
% 4.77/1.72 % (3963796)Peak memory usage: 119 MB
% 4.77/1.72 % (3963796)Instructions burned: 307 (million)
% 4.77/1.72 % (3963823)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2135252604:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 4.77/1.72 % (3963823)Instruction limit reached!
% 4.77/1.72 % (3963823)------------------------------
% 4.77/1.72 % (3963823)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963823)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963823)Termination reason: Instruction limit
% 4.77/1.72 % (3963823)Termination phase: Property scanning
% 4.77/1.72 % (3963823)Time elapsed: 0.002 s
% 4.77/1.72 % (3963823)Peak memory usage: 86 MB
% 4.77/1.72 % (3963823)Instructions burned: 6 (million)
% 4.77/1.72 % (3963821)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=3541362988:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 4.77/1.72 % (3963821)Instruction limit reached!
% 4.77/1.72 % (3963821)------------------------------
% 4.77/1.72 % (3963821)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963821)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963821)Termination reason: Instruction limit
% 4.77/1.72 % (3963821)Termination phase: shuffling
% 4.77/1.72 % (3963821)Time elapsed: 0.002 s
% 4.77/1.72 % (3963821)Peak memory usage: 85 MB
% 4.77/1.72 % (3963821)Instructions burned: 2 (million)
% 4.77/1.72 % (3963822)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=1638752589:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 4.77/1.72 % (3963826)lrs+10_1_thi=all:si=on:fd=off:random_seed=77669275:i=53:rtra=on:gtg=all_2996 on theBenchmark for (2996ds/53Mi)
% 4.77/1.72 % (3963824)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=4160180712:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 4.77/1.72 % (3963827)ott+1011_1_to=kbo:plsq=on:drc=off:si=on:plsqr=32,1:sp=const_frequency:sos=all:uwa=one_side_interpreted:sac=on:random_seed=4255810678:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2996 on theBenchmark for (2996ds/8Mi)
% 4.77/1.72 % (3963827)Instruction limit reached!
% 4.77/1.72 % (3963827)------------------------------
% 4.77/1.72 % (3963827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963827)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963827)Termination reason: Instruction limit
% 4.77/1.72 % (3963827)Termination phase: shuffling
% 4.77/1.72 % (3963827)Time elapsed: 0.005 s
% 4.77/1.72 % (3963827)Peak memory usage: 86 MB
% 4.77/1.72 % (3963827)Instructions burned: 9 (million)
% 4.77/1.72 % (3963826)Instruction limit reached!
% 4.77/1.72 % (3963826)------------------------------
% 4.77/1.72 % (3963826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963826)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963826)Termination reason: Instruction limit
% 4.77/1.72 % (3963826)Termination phase: Preprocessing 3
% 4.77/1.72 % (3963826)Time elapsed: 0.029 s
% 4.77/1.72 % (3963826)Peak memory usage: 88 MB
% 4.77/1.72 % (3963826)Instructions burned: 53 (million)
% 4.77/1.72 % (3963824)Instruction limit reached!
% 4.77/1.72 % (3963824)------------------------------
% 4.77/1.72 % (3963824)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963824)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963824)Termination reason: Instruction limit
% 4.77/1.72 % (3963824)Termination phase: Property scanning
% 4.77/1.72 % (3963824)Time elapsed: 0.037 s
% 4.77/1.72 % (3963824)Peak memory usage: 88 MB
% 4.77/1.72 % (3963824)Instructions burned: 68 (million)
% 4.77/1.72 % (3963848)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=2182866693:i=2:doe=on:canc=force:asg=cautious:rtra=on_2995 on theBenchmark for (2995ds/2Mi)
% 4.77/1.72 % (3963848)Instruction limit reached!
% 4.77/1.72 % (3963848)------------------------------
% 4.77/1.72 % (3963848)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963848)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963848)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963848)Termination reason: Instruction limit
% 4.77/1.72 % (3963848)Termination phase: Property scanning
% 4.77/1.72 % (3963848)Time elapsed: 0.002 s
% 4.77/1.72 % (3963848)Peak memory usage: 86 MB
% 4.77/1.72 % (3963848)Instructions burned: 5 (million)
% 4.77/1.72 % (3963833)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=620501032:st=3:i=2:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/2Mi)
% 4.77/1.72 % (3963833)Instruction limit reached!
% 4.77/1.72 % (3963833)------------------------------
% 4.77/1.72 % (3963833)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963833)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963833)Termination reason: Instruction limit
% 4.77/1.72 % (3963833)Termination phase: shuffling
% 4.77/1.72 % (3963833)Time elapsed: 0.002 s
% 4.77/1.72 % (3963833)Peak memory usage: 85 MB
% 4.77/1.72 % (3963833)Instructions burned: 2 (million)
% 4.77/1.72 % (3963822)First to succeed.
% 4.77/1.72 % (3963822)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3963756"
% 4.77/1.72 % (3963861)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=2070271047:i=127:doe=on:rtra=on_2995 on theBenchmark for (2995ds/127Mi)
% 4.77/1.72 % (3963895)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=4065554794:i=2:fsr=off:rtra=on:inst=on_2994 on theBenchmark for (2994ds/2Mi)
% 4.77/1.72 % (3963895)Instruction limit reached!
% 4.77/1.72 % (3963895)------------------------------
% 4.77/1.72 % (3963895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963895)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963895)Termination reason: Instruction limit
% 4.77/1.72 % (3963895)Termination phase: Property scanning
% 4.77/1.72 % (3963895)Time elapsed: 0.002 s
% 4.77/1.72 % (3963895)Peak memory usage: 85 MB
% 4.77/1.72 % (3963895)Instructions burned: 5 (million)
% 4.77/1.72 % (3963882)dis+10_1_si=on:random_seed=152670536:i=10:ep=R:rtra=on_2995 on theBenchmark for (2995ds/10Mi)
% 4.77/1.72 % (3963882)Instruction limit reached!
% 4.77/1.72 % (3963882)------------------------------
% 4.77/1.72 % (3963882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963882)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963882)Termination reason: Instruction limit
% 4.77/1.72 % (3963882)Termination phase: Property scanning
% 4.77/1.72 % (3963882)Time elapsed: 0.006 s
% 4.77/1.72 % (3963882)Peak memory usage: 86 MB
% 4.77/1.72 % (3963882)Instructions burned: 10 (million)
% 4.77/1.72 % (3963883)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3855768119:i=26:canc=cautious:av=off:rtra=on_2995 on theBenchmark for (2995ds/26Mi)
% 4.77/1.72 % (3963888)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=3206455052:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2994 on theBenchmark for (2994ds/35Mi)
% 4.77/1.72 % (3963898)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=2663342043:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2994 on theBenchmark for (2994ds/8Mi)
% 4.77/1.72 % (3963883)Instruction limit reached!
% 4.77/1.72 % (3963883)------------------------------
% 4.77/1.72 % (3963883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963883)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963883)Termination reason: Instruction limit
% 4.77/1.72 % (3963883)Termination phase: Preprocessing 3
% 4.77/1.72 % (3963883)Time elapsed: 0.015 s
% 4.77/1.72 % (3963883)Peak memory usage: 87 MB
% 4.77/1.72 % (3963883)Instructions burned: 26 (million)
% 4.77/1.72 % (3963898)Instruction limit reached!
% 4.77/1.72 % (3963898)------------------------------
% 4.77/1.72 % (3963898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963898)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963898)Termination reason: Instruction limit
% 4.77/1.72 % (3963898)Termination phase: Property scanning
% 4.77/1.72 % (3963898)Time elapsed: 0.005 s
% 4.77/1.72 % (3963898)Peak memory usage: 86 MB
% 4.77/1.72 % (3963898)Instructions burned: 9 (million)
% 4.77/1.72 % (3963888)Instruction limit reached!
% 4.77/1.72 % (3963888)------------------------------
% 4.77/1.72 % (3963888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963888)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963888)Termination reason: Instruction limit
% 4.77/1.72 % (3963888)Termination phase: Preprocessing 3
% 4.77/1.72 % (3963888)Time elapsed: 0.022 s
% 4.77/1.72 % (3963888)Peak memory usage: 88 MB
% 4.77/1.72 % (3963888)Instructions burned: 36 (million)
% 4.77/1.72 % (3963861)Instruction limit reached!
% 4.77/1.72 % (3963861)------------------------------
% 4.77/1.72 % (3963861)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963861)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963861)Termination reason: Instruction limit
% 4.77/1.72 % (3963861)Termination phase: Saturation
% 4.77/1.72 % (3963861)Time elapsed: 0.099 s
% 4.77/1.72 % (3963861)Peak memory usage: 116 MB
% 4.77/1.72 % (3963861)Instructions burned: 127 (million)
% 4.77/1.72 % (3963932)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=1443407834:i=370:ep=RS:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/370Mi)
% 4.77/1.72 % (3963939)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=1076089091:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2993 on theBenchmark for (2993ds/13Mi)
% 4.77/1.72 % (3963939)Instruction limit reached!
% 4.77/1.72 % (3963939)------------------------------
% 4.77/1.72 % (3963939)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963939)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963939)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963939)Termination reason: Instruction limit
% 4.77/1.72 % (3963939)Termination phase: Property scanning
% 4.77/1.72 % (3963939)Time elapsed: 0.007 s
% 4.77/1.72 % (3963939)Peak memory usage: 85 MB
% 4.77/1.72 % (3963939)Instructions burned: 14 (million)
% 4.77/1.72 % (3963949)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=2445122471:i=226:rtra=on:gtg=position:ss=axioms_2993 on theBenchmark for (2993ds/226Mi)
% 4.77/1.72 % (3963950)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=1531523649:i=10:rtra=on_2993 on theBenchmark for (2993ds/10Mi)
% 4.77/1.72 % (3963950)Instruction limit reached!
% 4.77/1.72 % (3963950)------------------------------
% 4.77/1.72 % (3963950)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.77/1.72 % (3963950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.77/1.72 % (3963950)CaDiCaL version: 2.1.3
% 4.77/1.72 % (3963950)Termination reason: Instruction limit
% 4.77/1.72 % (3963950)Termination phase: Preprocessing 1
% 4.77/1.72 % (3963950)Time elapsed: 0.006 s
% 4.77/1.72 % (3963950)Peak memory usage: 86 MB
% 4.77/1.72 % (3963950)Instructions burned: 11 (million)
% 4.77/1.72 % (3963956)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=509455000:i=71:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/71Mi)
% 4.77/1.72 % (3963822)Refutation found. Thanks to Tanya!
% 4.77/1.72 % SZS status Theorem for theBenchmark
% 4.77/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/1.91 % (3963822)------------------------------
% 0.18/1.91 % (3963822)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/1.91 % (3963822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/1.91 % (3963822)CaDiCaL version: 2.1.3
% 0.18/1.91 % (3963822)Termination reason: Refutation
% 0.18/1.91 % (3963822)Time elapsed: 0.087 s
% 0.18/1.91 % (3963822)Peak memory usage: 92 MB
% 0.18/1.91 % (3963822)Instructions burned: 131 (million)
% 0.18/1.91 % (3963822)------------------------------
% 0.18/1.91 % (3963822)------------------------------
% 0.18/1.91 % (3963756)Success in time 0.8 s
% 0.18/1.91 % Vampire exiting
%------------------------------------------------------------------------------