TSTP Solution File: ITP338_1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 17:27:15 EDT 2022
% Result : Theorem 2.73s 0.79s
% Output : Refutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 391
% Syntax : Number of formulae : 445 ( 21 unt; 373 typ; 0 def)
% Number of atoms : 252 ( 144 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 282 ( 102 ~; 88 |; 53 &)
% ( 8 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 2 avg)
% Number arithmetic : 83 ( 21 atm; 25 fun; 25 num; 12 var)
% Number of types : 72 ( 70 usr; 1 ari)
% Number of type conns : 425 ( 268 >; 157 *; 0 +; 0 <<)
% Number of predicates : 34 ( 30 usr; 8 prp; 0-2 aty)
% Number of functors : 282 ( 280 usr; 36 con; 0-4 aty)
% Number of variables : 77 ( 72 !; 5 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_nat_a_b_vec_c_vec_prod_prod$': $tType ).
tff(type_def_6,type,
'A_a_iarray_iarray_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'A_c_vec_c_vec$': $tType ).
tff(type_def_8,type,
'A_nat_a_iarray_iarray_prod_prod$': $tType ).
tff(type_def_9,type,
'A_a_prod$': $tType ).
tff(type_def_10,type,
'A_iarray_iarray$': $tType ).
tff(type_def_11,type,
'A_nat_a_b_vec_c_vec_prod_bool_fun_fun$': $tType ).
tff(type_def_12,type,
'A_a_c_vec_b_vec_prod$': $tType ).
tff(type_def_13,type,
'Int_int_prod$': $tType ).
tff(type_def_14,type,
'C_a_b_vec_bool_fun_fun$': $tType ).
tff(type_def_15,type,
'A_c_vec_c_vec_a_b_vec_c_vec_prod$': $tType ).
tff(type_def_16,type,
'A_a_b_vec_b_vec_prod$': $tType ).
tff(type_def_17,type,
'Nat_a_iarray_bool_fun_fun$': $tType ).
tff(type_def_18,type,
'A_a_iarray_iarray_prod$': $tType ).
tff(type_def_19,type,
'Nat_a_c_vec_c_vec_prod$': $tType ).
tff(type_def_20,type,
'A_a_b_vec_c_vec_bool_fun_fun$': $tType ).
tff(type_def_21,type,
'Int_set$': $tType ).
tff(type_def_22,type,
'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$': $tType ).
tff(type_def_23,type,
'Int_int_fun$': $tType ).
tff(type_def_24,type,
'A_b_vec_b_vec$': $tType ).
tff(type_def_25,type,
'B$': $tType ).
tff(type_def_26,type,
'A_b_vec_c_vec$': $tType ).
tff(type_def_27,type,
'Nat_a_iarray_iarray_bool_fun_fun$': $tType ).
tff(type_def_28,type,
'C_a_b_vec_fun$': $tType ).
tff(type_def_29,type,
'A_c_vec_b_vec$': $tType ).
tff(type_def_30,type,
'Nat_nat_fun$': $tType ).
tff(type_def_31,type,
'C$': $tType ).
tff(type_def_32,type,
'Nat$': $tType ).
tff(type_def_33,type,
'A_b_vec$': $tType ).
tff(type_def_34,type,
'A_nat_a_iarray_iarray_prod_bool_fun_fun$': $tType ).
tff(type_def_35,type,
'A_iarray_iarray_bool_fun$': $tType ).
tff(type_def_36,type,
'B_a_fun$': $tType ).
tff(type_def_37,type,
'Nat_a_b_vec_c_vec_prod_bool_fun$': $tType ).
tff(type_def_38,type,
'A_nat_a_b_vec_b_vec_prod_prod$': $tType ).
tff(type_def_39,type,
'A_nat_a_c_vec_b_vec_prod_prod$': $tType ).
tff(type_def_40,type,
tlbool: $tType ).
tff(type_def_41,type,
'A_b_vec_c_vec_bool_fun$': $tType ).
tff(type_def_42,type,
'A_nat_a_c_vec_c_vec_prod_prod$': $tType ).
tff(type_def_43,type,
'A_b_vec_b_vec_a_c_vec_b_vec_prod$': $tType ).
tff(type_def_44,type,
'A_a_b_vec_c_vec_prod$': $tType ).
tff(type_def_45,type,
'A_bool_fun$': $tType ).
tff(type_def_46,type,
'Nat_a_iarray_iarray_prod$': $tType ).
tff(type_def_47,type,
'A_c_vec_c_vec_a_c_vec_c_vec_prod$': $tType ).
tff(type_def_48,type,
'A_int_prod$': $tType ).
tff(type_def_49,type,
'A_set$': $tType ).
tff(type_def_50,type,
'A_iarray_bool_fun$': $tType ).
tff(type_def_51,type,
'A_nat_a_iarray_iarray_prod_prod_bool_fun$': $tType ).
tff(type_def_52,type,
'A_c_vec$': $tType ).
tff(type_def_53,type,
'Nat_a_b_vec_c_vec_bool_fun_fun$': $tType ).
tff(type_def_54,type,
'A$': $tType ).
tff(type_def_55,type,
'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$': $tType ).
tff(type_def_56,type,
'Nat_a_c_vec_b_vec_prod$': $tType ).
tff(type_def_57,type,
'Int_a_prod$': $tType ).
tff(type_def_58,type,
'Nat_a_b_vec_c_vec_prod$': $tType ).
tff(type_def_59,type,
'Nat_a_iarray_iarray_prod_bool_fun$': $tType ).
tff(type_def_60,type,
'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$': $tType ).
tff(type_def_61,type,
'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$': $tType ).
tff(type_def_62,type,
'A_a_c_vec_c_vec_prod$': $tType ).
tff(type_def_63,type,
'A_a_fun$': $tType ).
tff(type_def_64,type,
'Nat_a_b_vec_b_vec_prod$': $tType ).
tff(type_def_65,type,
'Nat_a_iarray_prod_bool_fun$': $tType ).
tff(type_def_66,type,
'A_b_vec_c_vec_c_vec$': $tType ).
tff(type_def_67,type,
'A_iarray$': $tType ).
tff(type_def_68,type,
'A_b_vec_bool_fun$': $tType ).
tff(type_def_69,type,
'Nat_a_iarray_prod$': $tType ).
tff(type_def_70,type,
'Nat_bool_fun$': $tType ).
tff(type_def_71,type,
'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$': $tType ).
tff(type_def_72,type,
'A_b_vec_b_vec_a_b_vec_b_vec_prod$': $tType ).
tff(type_def_73,type,
'Nat_set$': $tType ).
tff(type_def_74,type,
'B_a_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'gauss_Jordan_in_ij_det_P_iarrays$': ( 'A_iarray_iarray$' * 'Nat$' * 'Nat$' ) > 'A_a_iarray_iarray_prod$' ).
tff(func_def_1,type,
'times$a': ( $int * $int ) > $int ).
tff(func_def_2,type,
'snd$t': 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' > 'Nat_a_c_vec_b_vec_prod$' ).
tff(func_def_3,type,
'zero$i': 'Int_a_prod$' ).
tff(func_def_4,type,
'fun_app$r': ( 'Nat_a_iarray_bool_fun_fun$' * 'Nat$' ) > 'A_iarray_bool_fun$' ).
tff(func_def_5,type,
'times$b': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_6,type,
'pair$x': ( 'A_c_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).
tff(func_def_7,type,
'snd$': 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_8,type,
'plus$b': ( 'C$' * 'C$' ) > 'C$' ).
tff(func_def_9,type,
'from_nat$a': 'Nat$' > 'B$' ).
tff(func_def_10,type,
'fst$k': 'A_nat_a_c_vec_b_vec_prod_prod$' > 'A$' ).
tff(func_def_11,type,
'uu$': 'A_a_fun$' ).
tff(func_def_12,type,
'plus$c': ( 'B$' * 'B$' ) > 'B$' ).
tff(func_def_13,type,
'nrows$c': 'A_b_vec_b_vec$' > 'Nat$' ).
tff(func_def_14,type,
'uua$': 'Int_int_fun$' ).
tff(func_def_15,type,
'pair$r': ( 'A_c_vec_c_vec$' * 'Nat_a_c_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_16,type,
'pair$b': ( 'Nat$' * 'A_iarray$' ) > 'Nat_a_iarray_prod$' ).
tff(func_def_17,type,
'uud$': 'A_a_fun$' ).
tff(func_def_18,type,
'fst$e': 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_19,type,
'gauss_Jordan_column_k_det_P_iarrays$': ( 'A_nat_a_iarray_iarray_prod_prod$' * 'Nat$' ) > 'A_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_20,type,
'snd$c': 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_21,type,
'fun_app$t': ( 'Nat_a_iarray_iarray_bool_fun_fun$' * 'Nat$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_22,type,
'uuf$': 'Int_int_fun$' ).
tff(func_def_23,type,
'fun_app$l': ( 'B_a_bool_fun_fun$' * 'B$' ) > 'A_bool_fun$' ).
tff(func_def_24,type,
'pair$u': ( 'A_b_vec_b_vec$' * 'A_c_vec_b_vec$' ) > 'A_b_vec_b_vec_a_c_vec_b_vec_prod$' ).
tff(func_def_25,type,
'pair$p': ( $int * 'A$' ) > 'Int_a_prod$' ).
tff(func_def_26,type,
'pair$a': ( 'Nat$' * 'A_b_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_27,type,
'fun_app$d': ( 'C_a_b_vec_fun$' * 'C$' ) > 'A_b_vec$' ).
tff(func_def_28,type,
'fst$u': 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_29,type,
'gauss_Jordan_in_ij_det_P$b': ( 'A_c_vec_b_vec$' * 'B$' * 'C$' ) > 'A_a_c_vec_b_vec_prod$' ).
tff(func_def_30,type,
'zero$': 'Nat$' ).
tff(func_def_31,type,
'gauss_Jordan_column_k_det_P$': ( 'A_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_32,type,
'snd$e': 'A_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_33,type,
'zero$j': 'Int_int_prod$' ).
tff(func_def_34,type,
'times$': 'A$' > 'A_a_fun$' ).
tff(func_def_35,type,
'fun_app$v': ( 'A_nat_a_b_vec_c_vec_prod_bool_fun_fun$' * 'A$' ) > 'Nat_a_b_vec_c_vec_prod_bool_fun$' ).
tff(func_def_36,type,
'fst$t': 'A_b_vec_b_vec_a_c_vec_b_vec_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_37,type,
'plus$q': ( 'A_set$' * 'A_set$' ) > 'A_set$' ).
tff(func_def_38,type,
'zero$a': 'A$' ).
tff(func_def_39,type,
'row_add_iterate_PA$': ( 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' * 'Nat$' * 'C$' * 'B$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).
tff(func_def_40,type,
'plus$o': ( 'A_b_vec$' * 'A_b_vec$' ) > 'A_b_vec$' ).
tff(func_def_41,type,
'nrows$': 'A_b_vec_c_vec$' > 'Nat$' ).
tff(func_def_42,type,
'plus$h': ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_43,type,
'plus$l': ( 'Nat_a_iarray_prod$' * 'Nat_a_iarray_prod$' ) > 'Nat_a_iarray_prod$' ).
tff(func_def_44,type,
'fst$g': 'Nat_a_c_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_45,type,
'zero$g': 'A_a_prod$' ).
tff(func_def_46,type,
'plus$p': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_47,type,
'snd$d': 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_48,type,
'plus$n': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).
tff(func_def_49,type,
'vec_nth$f': ( 'A_b_vec_c_vec_c_vec$' * 'C$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_50,type,
'zero$d': 'A_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_51,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_52,type,
'zero$f': 'C$' ).
tff(func_def_53,type,
'gauss_Jordan_in_ij_PA$a': ( 'A_b_vec_b_vec_a_c_vec_b_vec_prod$' * 'B$' * 'C$' ) > 'A_b_vec_b_vec_a_c_vec_b_vec_prod$' ).
tff(func_def_54,type,
'times$f': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).
tff(func_def_55,type,
'upper_triangular_upt_k$a': 'A_b_vec_c_vec_c_vec$' > 'Nat_bool_fun$' ).
tff(func_def_56,type,
'fun_app$n': ( 'C_a_b_vec_bool_fun_fun$' * 'C$' ) > 'A_b_vec_bool_fun$' ).
tff(func_def_57,type,
'pair$h': ( 'Nat$' * 'A_c_vec_c_vec$' ) > 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_58,type,
'times$d': ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_59,type,
'uuc$': 'Nat_nat_fun$' ).
tff(func_def_60,type,
'snd$x': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_61,type,
'zero$b': 'A_a_b_vec_c_vec_prod$' ).
tff(func_def_62,type,
'zero$e': 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_63,type,
'snd$j': 'A_nat_a_c_vec_b_vec_prod_prod$' > 'Nat_a_c_vec_b_vec_prod$' ).
tff(func_def_64,type,
'snd$n': 'Nat_a_b_vec_b_vec_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_65,type,
'i$': 'Nat$' ).
tff(func_def_66,type,
'one$c': 'B$' ).
tff(func_def_67,type,
'fst$f': 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_68,type,
'plus$i': ( 'A_nat_a_b_vec_c_vec_prod_prod$' * 'A_nat_a_b_vec_c_vec_prod_prod$' ) > 'A_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_69,type,
'nrows$b': 'A_c_vec_b_vec$' > 'Nat$' ).
tff(func_def_70,type,
'one$': 'A$' ).
tff(func_def_71,type,
'snd$k': 'Nat_a_c_vec_b_vec_prod$' > 'A_c_vec_b_vec$' ).
tff(func_def_72,type,
'nrows$a': 'A_c_vec_c_vec$' > 'Nat$' ).
tff(func_def_73,type,
'gauss_Jordan_column_k_det_P$a': ( 'A_nat_a_c_vec_b_vec_prod_prod$' * 'Nat$' ) > 'A_nat_a_c_vec_b_vec_prod_prod$' ).
tff(func_def_74,type,
'fst$p': 'Int_int_prod$' > $int ).
tff(func_def_75,type,
'vec_nth$c': ( 'A_c_vec_c_vec$' * 'C$' ) > 'A_c_vec$' ).
tff(func_def_76,type,
'snd$s': 'A_c_vec_c_vec_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_77,type,
'upper_triangular_upt_k$': 'A_b_vec_b_vec$' > 'Nat_bool_fun$' ).
tff(func_def_78,type,
'pair$o': ( 'A$' * $int ) > 'A_int_prod$' ).
tff(func_def_79,type,
'snd$a': 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_80,type,
'snd$i': 'A_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_81,type,
'fst$v': 'A_b_vec_b_vec_a_b_vec_b_vec_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_82,type,
'nrows_iarray$': 'A_iarray_iarray$' > 'Nat$' ).
tff(func_def_83,type,
tltrue: tlbool ).
tff(func_def_84,type,
'gauss_Jordan_column_k_PA$a': ( 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_85,type,
'plus$f': ( 'Nat_a_iarray_iarray_prod$' * 'Nat_a_iarray_iarray_prod$' ) > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_86,type,
'map_matrix$': ( 'A_a_fun$' * 'A_b_vec_c_vec$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_87,type,
'pair$s': ( 'A_c_vec_c_vec$' * 'A_c_vec_c_vec$' ) > 'A_c_vec_c_vec_a_c_vec_c_vec_prod$' ).
tff(func_def_88,type,
'one$b': 'C$' ).
tff(func_def_89,type,
'pair$j': ( 'Nat$' * 'A_c_vec_b_vec$' ) > 'Nat_a_c_vec_b_vec_prod$' ).
tff(func_def_90,type,
'one$a': 'Nat$' ).
tff(func_def_91,type,
'to_nat$a': 'B$' > 'Nat$' ).
tff(func_def_92,type,
'plus$j': ( 'Nat_a_b_vec_c_vec_prod$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_93,type,
'gauss_Jordan_column_k_PA$b': ( 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' * 'Nat$' ) > 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' ).
tff(func_def_94,type,
'gauss_Jordan_in_ij_PA$': ( 'A_c_vec_c_vec_a_c_vec_c_vec_prod$' * 'C$' * 'C$' ) > 'A_c_vec_c_vec_a_c_vec_c_vec_prod$' ).
tff(func_def_95,type,
'snd$g': 'A_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_96,type,
'fst$b': 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_97,type,
'ncols$': 'A_b_vec_c_vec$' > 'Nat$' ).
tff(func_def_98,type,
'fst$c': 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_99,type,
'fun_app$': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_100,type,
'fst$j': 'Nat_a_c_vec_b_vec_prod$' > 'Nat$' ).
tff(func_def_101,type,
'gauss_Jordan_in_ij_det_P$': ( 'A_b_vec_c_vec$' * 'C$' * 'B$' ) > 'A_a_b_vec_c_vec_prod$' ).
tff(func_def_102,type,
'pair$n': ( 'A$' * 'A$' ) > 'A_a_prod$' ).
tff(func_def_103,type,
'less$': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_104,type,
'gauss_Jordan_column_k_PA$': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_105,type,
'fst$m': 'Nat_a_b_vec_b_vec_prod$' > 'Nat$' ).
tff(func_def_106,type,
'fun_app$c': ( 'B_a_fun$' * 'B$' ) > 'A$' ).
tff(func_def_107,type,
'gauss_Jordan_column_k_det_P$c': ( 'A_nat_a_b_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_108,type,
'gauss_Jordan_column_k_PA$c': ( 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' * 'Nat$' ) > 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' ).
tff(func_def_109,type,
'to_nat$': 'C$' > 'Nat$' ).
tff(func_def_110,type,
'vector_all_zero_from_index$': 'Nat_a_iarray_prod_bool_fun$' ).
tff(func_def_111,type,
'vec_nth$b': ( 'A_c_vec$' * 'C$' ) > 'A$' ).
tff(func_def_112,type,
'snd$o': 'A_a_b_vec_b_vec_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_113,type,
'snd$q': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_114,type,
'snd$v': 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' > 'Nat_a_b_vec_b_vec_prod$' ).
tff(func_def_115,type,
'fst$h': 'A_nat_a_c_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_116,type,
'fun_app$x': ( 'A_a_iarray_iarray_bool_fun_fun$' * 'A$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_117,type,
'one$e': 'A_b_vec_c_vec$' ).
tff(func_def_118,type,
'fst$l': 'A_a_c_vec_b_vec_prod$' > 'A$' ).
tff(func_def_119,type,
'times$g': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_120,type,
'snd$r': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_121,type,
'gauss_Jordan_in_ij_det_P$a': ( 'A_c_vec_c_vec$' * 'C$' * 'C$' ) > 'A_a_c_vec_c_vec_prod$' ).
tff(func_def_122,type,
'zero$h': 'A_int_prod$' ).
tff(func_def_123,type,
'fun_app$u': ( 'A_a_b_vec_c_vec_bool_fun_fun$' * 'A$' ) > 'A_b_vec_c_vec_bool_fun$' ).
tff(func_def_124,type,
'pair$t': ( 'A_b_vec_b_vec$' * 'Nat_a_c_vec_b_vec_prod$' ) > 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' ).
tff(func_def_125,type,
'column_iarray$': ( 'Nat$' * 'A_iarray_iarray$' ) > 'A_iarray$' ).
tff(func_def_126,type,
'gauss_Jordan_in_ij_PA$b': ( 'A_b_vec_b_vec_a_b_vec_b_vec_prod$' * 'B$' * 'B$' ) > 'A_b_vec_b_vec_a_b_vec_b_vec_prod$' ).
tff(func_def_127,type,
'fst$q': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_128,type,
'zero$c': 'A_b_vec_c_vec$' ).
tff(func_def_129,type,
'fst$w': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_130,type,
'fst$': 'A_a_b_vec_c_vec_prod$' > 'A$' ).
tff(func_def_131,type,
'plus$a': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_132,type,
'fst$r': 'A_c_vec_c_vec_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_133,type,
'one$d': 'A_b_vec$' ).
tff(func_def_134,type,
'vec_nth$a': 'A_b_vec_c_vec$' > 'C_a_b_vec_fun$' ).
tff(func_def_135,type,
'snd$u': 'A_b_vec_b_vec_a_c_vec_b_vec_prod$' > 'A_c_vec_b_vec$' ).
tff(func_def_136,type,
'fun_app$p': ( 'Nat_a_b_vec_c_vec_bool_fun_fun$' * 'Nat$' ) > 'A_b_vec_c_vec_bool_fun$' ).
tff(func_def_137,type,
'snd$p': 'Int_int_prod$' > $int ).
tff(func_def_138,type,
'pair$k': ( 'A$' * 'Nat_a_b_vec_b_vec_prod$' ) > 'A_nat_a_b_vec_b_vec_prod_prod$' ).
tff(func_def_139,type,
'pair$': ( 'A$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_140,type,
'plus$m': ( 'A_iarray$' * 'A_iarray$' ) > 'A_iarray$' ).
tff(func_def_141,type,
'fst$s': 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_142,type,
'plus$': 'A$' > 'A_a_fun$' ).
tff(func_def_143,type,
'snd$w': 'A_b_vec_b_vec_a_b_vec_b_vec_prod$' > 'A_b_vec_b_vec$' ).
tff(func_def_144,type,
'plus$d': ( 'A_a_b_vec_c_vec_prod$' * 'A_a_b_vec_c_vec_prod$' ) > 'A_a_b_vec_c_vec_prod$' ).
tff(func_def_145,type,
'pair$d': ( 'Nat$' * 'A_iarray_iarray$' ) > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_146,type,
'less_eq$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_147,type,
tlfalse: tlbool ).
tff(func_def_148,type,
'pair$i': ( 'A$' * 'Nat_a_c_vec_b_vec_prod$' ) > 'A_nat_a_c_vec_b_vec_prod_prod$' ).
tff(func_def_149,type,
'nat$': $int > 'Nat$' ).
tff(func_def_150,type,
'fst$a': 'A_a_iarray_iarray_prod$' > 'A$' ).
tff(func_def_151,type,
'plus$g': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_152,type,
'pair$q': ( 'A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_153,type,
'snd$f': 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_154,type,
'zero$k': 'B$' ).
tff(func_def_155,type,
'pair$f': ( 'A$' * 'A_iarray_iarray$' ) > 'A_a_iarray_iarray_prod$' ).
tff(func_def_156,type,
'uug$': 'Nat_nat_fun$' ).
tff(func_def_157,type,
'matrix_to_iarray$': 'A_b_vec_c_vec$' > 'A_iarray_iarray$' ).
tff(func_def_158,type,
'plus$e': ( 'A_a_iarray_iarray_prod$' * 'A_a_iarray_iarray_prod$' ) > 'A_a_iarray_iarray_prod$' ).
tff(func_def_159,type,
'vec_nth$': 'A_b_vec$' > 'B_a_fun$' ).
tff(func_def_160,type,
'uue$': 'Int_int_fun$' ).
tff(func_def_161,type,
'fst$o': 'A_a_b_vec_b_vec_prod$' > 'A$' ).
tff(func_def_162,type,
'snd$h': 'Nat_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_163,type,
'times$c': ( 'A_b_vec$' * 'A_b_vec$' ) > 'A_b_vec$' ).
tff(func_def_164,type,
'fun_app$w': ( 'A_nat_a_iarray_iarray_prod_bool_fun_fun$' * 'A$' ) > 'Nat_a_iarray_iarray_prod_bool_fun$' ).
tff(func_def_165,type,
'gauss_Jordan_column_k_det_P$b': ( 'A_nat_a_b_vec_b_vec_prod_prod$' * 'Nat$' ) > 'A_nat_a_b_vec_b_vec_prod_prod$' ).
tff(func_def_166,type,
'pair$c': ( 'A$' * 'Nat_a_iarray_iarray_prod$' ) > 'A_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_167,type,
'fun_app$b': ( 'A_a_fun$' * 'A$' ) > 'A$' ).
tff(func_def_168,type,
'gauss_Jordan_in_ij_det_P$c': ( 'A_b_vec_b_vec$' * 'B$' * 'B$' ) > 'A_a_b_vec_b_vec_prod$' ).
tff(func_def_169,type,
'times$e': ( 'A_set$' * 'A_set$' ) > 'A_set$' ).
tff(func_def_170,type,
'fun_app$a': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_171,type,
'vec_nth$e': ( 'A_b_vec_b_vec$' * 'B$' ) > 'A_b_vec$' ).
tff(func_def_172,type,
'fst$i': 'A_a_c_vec_c_vec_prod$' > 'A$' ).
tff(func_def_173,type,
'from_nat$': 'Nat$' > 'C$' ).
tff(func_def_174,type,
'fst$d': 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_175,type,
'plus$k': ( 'A_nat_a_iarray_iarray_prod_prod$' * 'A_nat_a_iarray_iarray_prod_prod$' ) > 'A_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_176,type,
'fst$n': 'A_nat_a_b_vec_b_vec_prod_prod$' > 'A$' ).
tff(func_def_177,type,
'pair$m': ( $int * $int ) > 'Int_int_prod$' ).
tff(func_def_178,type,
'n$': 'A$' ).
tff(func_def_179,type,
'fst$x': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_180,type,
'a$': 'A_b_vec_c_vec$' ).
tff(func_def_181,type,
'zero$l': 'A_b_vec$' ).
tff(func_def_182,type,
'gauss_Jordan_in_ij_PA$c': ( 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' * 'C$' * 'B$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).
tff(func_def_183,type,
'pair$l': ( 'Nat$' * 'A_b_vec_b_vec$' ) > 'Nat_a_b_vec_b_vec_prod$' ).
tff(func_def_184,type,
'snd$l': 'A_a_c_vec_b_vec_prod$' > 'A_c_vec_b_vec$' ).
tff(func_def_185,type,
'pair$e': ( 'A$' * 'A_b_vec_c_vec$' ) > 'A_a_b_vec_c_vec_prod$' ).
tff(func_def_186,type,
'snd$m': 'A_nat_a_b_vec_b_vec_prod_prod$' > 'Nat_a_b_vec_b_vec_prod$' ).
tff(func_def_187,type,
'pair$g': ( 'A$' * 'Nat_a_c_vec_c_vec_prod$' ) > 'A_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_188,type,
'vec_nth$d': ( 'A_c_vec_b_vec$' * 'B$' ) > 'A_c_vec$' ).
tff(func_def_189,type,
'snd$b': 'A_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_190,type,
'pair$w': ( 'A_b_vec_b_vec$' * 'A_b_vec_b_vec$' ) > 'A_b_vec_b_vec_a_b_vec_b_vec_prod$' ).
tff(func_def_191,type,
'k$': 'Nat$' ).
tff(func_def_192,type,
'uub$': 'Int_int_fun$' ).
tff(func_def_193,type,
'pair$v': ( 'A_b_vec_b_vec$' * 'Nat_a_b_vec_b_vec_prod$' ) > 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' ).
tff(func_def_199,type,
sK2: 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_200,type,
sK3: 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_201,type,
sK4: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_202,type,
sK5: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_203,type,
sK6: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_204,type,
sK7: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_205,type,
sK8: ( 'C_a_b_vec_bool_fun_fun$' * 'C$' ) > 'A_b_vec$' ).
tff(func_def_206,type,
sK9: ( 'C_a_b_vec_bool_fun_fun$' * 'A_b_vec_c_vec$' ) > 'C$' ).
tff(func_def_207,type,
sK10: 'C_a_b_vec_bool_fun_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_208,type,
sK11: 'C_a_b_vec_bool_fun_fun$' > 'C$' ).
tff(func_def_209,type,
sK12: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_210,type,
sK13: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_211,type,
sK14: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_212,type,
sK15: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_213,type,
sK16: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_214,type,
sK17: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_215,type,
sK18: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_216,type,
sK19: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$' ).
tff(func_def_217,type,
sK20: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_218,type,
sK21: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$' ).
tff(func_def_219,type,
sK22: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_220,type,
sK23: ( 'A_b_vec$' * 'A_b_vec$' ) > 'B$' ).
tff(func_def_221,type,
sK24: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_222,type,
sK25: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_223,type,
sK26: ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'C$' ).
tff(func_def_224,type,
sK27: ( 'A_nat_a_b_vec_b_vec_prod_prod$' * 'Nat$' ) > 'B$' ).
tff(func_def_225,type,
sK28: ( 'B_a_bool_fun_fun$' * 'B$' ) > 'A$' ).
tff(func_def_226,type,
sK29: ( 'B_a_bool_fun_fun$' * 'A_b_vec$' ) > 'B$' ).
tff(func_def_227,type,
sK30: 'B_a_bool_fun_fun$' > 'A_b_vec$' ).
tff(func_def_228,type,
sK31: 'B_a_bool_fun_fun$' > 'B$' ).
tff(func_def_229,type,
sK32: ( 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'C$' ).
tff(func_def_230,type,
sK33: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_231,type,
sK34: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_232,type,
sK35: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_233,type,
sK36: ( 'Nat$' * 'A_nat_a_c_vec_b_vec_prod_prod$' ) > 'B$' ).
tff(func_def_234,type,
sK37: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_235,type,
sK38: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_236,type,
sK39: 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_237,type,
sK40: 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_238,type,
sK41: 'A_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_239,type,
sK42: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat$' ).
tff(func_def_240,type,
sK43: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_241,type,
sK44: ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat$' ) > 'C$' ).
tff(func_def_242,type,
sK45: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_243,type,
sK46: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_244,type,
sK47: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_245,type,
sK48: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_246,type,
sK49: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_247,type,
sK50: ( 'A_set$' * 'A$' * 'A_set$' ) > 'A$' ).
tff(func_def_248,type,
sK51: ( 'A_set$' * 'A$' * 'A_set$' ) > 'A$' ).
tff(func_def_249,type,
sK52: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_250,type,
sK53: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_251,type,
sK54: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_252,type,
sK55: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_253,type,
sK56: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_254,type,
sK57: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_255,type,
sK58: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_256,type,
sK59: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_257,type,
sK60: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_258,type,
sK61: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_259,type,
sK62: ( 'A_nat_a_b_vec_c_vec_prod_prod$' * 'Nat$' ) > 'C$' ).
tff(func_def_260,type,
sK63: ( 'Nat$' * 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' ) > 'B$' ).
tff(func_def_261,type,
sK64: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_262,type,
sK65: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_263,type,
sK66: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_264,type,
sK67: ( 'A_b_vec_c_vec_c_vec$' * 'Nat$' ) > 'C$' ).
tff(func_def_265,type,
sK68: ( 'A_b_vec_c_vec_c_vec$' * 'Nat$' ) > 'C$' ).
tff(func_def_266,type,
sK69: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_267,type,
sK70: ( 'A_b_vec_b_vec$' * 'Nat$' ) > 'B$' ).
tff(func_def_268,type,
sK71: ( 'A_b_vec_b_vec$' * 'Nat$' ) > 'B$' ).
tff(func_def_269,type,
sK72: ( 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' * 'Nat$' ) > 'B$' ).
tff(func_def_270,type,
sK73: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_271,type,
sK74: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_272,type,
sK75: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'Nat$' ).
tff(func_def_273,type,
sK76: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_274,type,
sK77: ( 'A_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'C$' ).
tff(func_def_275,type,
sK78: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_276,type,
sK79: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_277,type,
sK80: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_278,type,
sK81: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_279,type,
sK82: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_280,type,
sK83: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_281,type,
sK84: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_282,type,
sK85: 'C$' ).
tff(func_def_283,type,
sK86: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_284,type,
sK87: 'Nat_nat_fun$' > 'Nat$' ).
tff(pred_def_1,type,
'upper_triangular$': 'A_b_vec_b_vec$' > $o ).
tff(pred_def_2,type,
'less_eq$c': ( 'A_set$' * 'A_set$' ) > $o ).
tff(pred_def_3,type,
'fun_app$i': ( 'Nat_a_iarray_iarray_prod_bool_fun$' * 'Nat_a_iarray_iarray_prod$' ) > $o ).
tff(pred_def_4,type,
'divides_aux$': 'Int_int_prod$' > $o ).
tff(pred_def_5,type,
'less_eq$b': ( 'B$' * 'B$' ) > $o ).
tff(pred_def_6,type,
'fun_app$k': ( 'A_bool_fun$' * 'A$' ) > $o ).
tff(pred_def_7,type,
'fun_app$g': ( 'Nat_a_b_vec_c_vec_prod_bool_fun$' * 'Nat_a_b_vec_c_vec_prod$' ) > $o ).
tff(pred_def_8,type,
'fun_app$o': ( 'A_b_vec_c_vec_bool_fun$' * 'A_b_vec_c_vec$' ) > $o ).
tff(pred_def_9,type,
'fun_app$s': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > $o ).
tff(pred_def_10,type,
'fun_app$f': ( 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' * 'A_nat_a_b_vec_c_vec_prod_prod$' ) > $o ).
tff(pred_def_11,type,
'fun_app$h': ( 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' * 'A_nat_a_iarray_iarray_prod_prod$' ) > $o ).
tff(pred_def_12,type,
'upper_triangular$a': 'A_b_vec_c_vec_c_vec$' > $o ).
tff(pred_def_13,type,
'less$a': ( 'C$' * 'C$' ) > $o ).
tff(pred_def_14,type,
'fun_app$e': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$' ) > $o ).
tff(pred_def_15,type,
'member$b': ( 'Nat$' * 'Nat_set$' ) > $o ).
tff(pred_def_16,type,
'fun_app$j': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_17,type,
'less$b': ( 'B$' * 'B$' ) > $o ).
tff(pred_def_18,type,
'fun_app$q': ( 'A_iarray_bool_fun$' * 'A_iarray$' ) > $o ).
tff(pred_def_19,type,
'member$a': ( 'A$' * 'A_set$' ) > $o ).
tff(pred_def_20,type,
'less_eq$d': ( 'Int_set$' * 'Int_set$' ) > $o ).
tff(pred_def_21,type,
'member$': ( $int * 'Int_set$' ) > $o ).
tff(pred_def_22,type,
'less_eq$': ( 'C$' * 'C$' ) > $o ).
tff(pred_def_23,type,
'fun_app$m': ( 'A_b_vec_bool_fun$' * 'A_b_vec$' ) > $o ).
tff(f4306,plain,
$false,
inference(avatar_sat_refutation,[],[f3546,f3563,f4288,f4294,f4303,f4304]) ).
tff(f4304,plain,
~ spl88_18,
inference(avatar_split_clause,[],[f3139,f4284]) ).
tff(f4284,plain,
( spl88_18
<=> $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_18])]) ).
tff(f3139,plain,
~ $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
inference(cnf_transformation,[],[f12]) ).
tff(f12,axiom,
~ $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
tff(f4303,plain,
( spl88_2
| ~ spl88_10 ),
inference(avatar_contradiction_clause,[],[f4302]) ).
tff(f4302,plain,
( $false
| spl88_2
| ~ spl88_10 ),
inference(trivial_inequality_removal,[],[f4301]) ).
tff(f4301,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('i$') )
| spl88_2
| ~ spl88_10 ),
inference(forward_demodulation,[],[f4300,f3522]) ).
tff(f3522,plain,
( ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) )
| ~ spl88_10 ),
inference(avatar_component_clause,[],[f3520]) ).
tff(f3520,plain,
( spl88_10
<=> ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_10])]) ).
tff(f4300,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
| spl88_2 ),
inference(forward_demodulation,[],[f3472,f4115]) ).
tff(f4115,plain,
! [X6: 'A_b_vec_c_vec$'] : ( 'nrows_iarray$'('matrix_to_iarray$'(X6)) = 'nrows$'(X6) ),
inference(forward_demodulation,[],[f4103,f2883]) ).
tff(f2883,plain,
! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
inference(cnf_transformation,[],[f633]) ).
tff(f633,axiom,
! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).
tff(f4103,plain,
! [X6: 'A_b_vec_c_vec$'] : ( 'nat$'('of_nat$'('nrows$'(X6))) = 'nrows_iarray$'('matrix_to_iarray$'(X6)) ),
inference(superposition,[],[f2883,f3188]) ).
tff(f3188,plain,
! [X0: 'A_b_vec_c_vec$'] : ( 'of_nat$'('nrows$'(X0)) = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'(X0))) ),
inference(cnf_transformation,[],[f573]) ).
tff(f573,axiom,
! [X0: 'A_b_vec_c_vec$'] : ( 'of_nat$'('nrows$'(X0)) = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
tff(f3472,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| spl88_2 ),
inference(avatar_component_clause,[],[f3471]) ).
tff(f3471,plain,
( spl88_2
<=> ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_2])]) ).
tff(f4294,plain,
spl88_11,
inference(avatar_contradiction_clause,[],[f4293]) ).
tff(f4293,plain,
( $false
| spl88_11 ),
inference(trivial_inequality_removal,[],[f4292]) ).
tff(f4292,plain,
( ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('a$') )
| spl88_11 ),
inference(forward_demodulation,[],[f3545,f3360]) ).
tff(f3360,plain,
! [X0: 'Nat$',X1: 'A_b_vec_c_vec$'] : ( 'snd$'('pair$a'(X0,X1)) = X1 ),
inference(equality_resolution,[],[f2710]) ).
tff(f2710,plain,
! [X2: 'A_b_vec_c_vec$',X0: 'Nat$',X1: 'A_b_vec_c_vec$'] :
( ( 'snd$'('pair$a'(X0,X1)) != X2 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f1899,plain,
! [X0: 'Nat$',X1: 'A_b_vec_c_vec$',X2: 'A_b_vec_c_vec$'] :
( ( 'snd$'('pair$a'(X0,X1)) != X2 )
| ( X1 = X2 ) ),
inference(rectify,[],[f1438]) ).
tff(f1438,plain,
! [X1: 'Nat$',X0: 'A_b_vec_c_vec$',X2: 'A_b_vec_c_vec$'] :
( ( 'snd$'('pair$a'(X1,X0)) != X2 )
| ( X0 = X2 ) ),
inference(ennf_transformation,[],[f1143]) ).
tff(f1143,plain,
! [X0: 'A_b_vec_c_vec$',X1: 'Nat$',X2: 'A_b_vec_c_vec$'] :
( ( 'snd$'('pair$a'(X1,X0)) = X2 )
=> ( X0 = X2 ) ),
inference(rectify,[],[f280]) ).
tff(f280,axiom,
! [X1: 'A_b_vec_c_vec$',X0: 'Nat$',X2: 'A_b_vec_c_vec$'] :
( ( 'snd$'('pair$a'(X0,X1)) = X2 )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
tff(f3545,plain,
( ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('snd$'('pair$a'('i$','a$'))) )
| spl88_11 ),
inference(avatar_component_clause,[],[f3543]) ).
tff(f3543,plain,
( spl88_11
<=> ( 'matrix_to_iarray$'('a$') = 'matrix_to_iarray$'('snd$'('pair$a'('i$','a$'))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl88_11])]) ).
tff(f4288,plain,
( spl88_10
| spl88_18 ),
inference(avatar_split_clause,[],[f4259,f4284,f3520]) ).
tff(f4259,plain,
( $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$')))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ),
inference(resolution,[],[f2671,f2651]) ).
tff(f2651,plain,
~ $less('of_nat$'('nrows$'('a$')),'of_nat$'('i$')),
inference(cnf_transformation,[],[f771]) ).
tff(f771,plain,
~ $less('of_nat$'('nrows$'('a$')),'of_nat$'('i$')),
inference(theory_normalization,[],[f11]) ).
tff(f11,axiom,
$lesseq('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
tff(f2671,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f1873,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| ( ( ( X0 = X1 )
| $less(X1,X0) )
& ( ~ $less(X1,X0)
| ( X0 != X1 ) ) ) ),
inference(rectify,[],[f1872]) ).
tff(f1872,plain,
! [X1: $int,X0: $int] :
( $less(X1,X0)
| ( ( ( X0 = X1 )
| $less(X0,X1) )
& ( ~ $less(X0,X1)
| ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[],[f1467]) ).
tff(f1467,plain,
! [X1: $int,X0: $int] :
( $less(X1,X0)
| ( ( X0 = X1 )
<=> ~ $less(X0,X1) ) ),
inference(ennf_transformation,[],[f660]) ).
tff(f660,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
=> ( ( X0 = X1 )
<=> ~ $less(X0,X1) ) ),
inference(theory_normalization,[],[f631]) ).
tff(f631,axiom,
! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> ( $lesseq(X1,X0)
<=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).
tff(f3563,plain,
( ~ spl88_10
| spl88_1 ),
inference(avatar_split_clause,[],[f3263,f3467,f3520]) ).
tff(f3467,plain,
( spl88_1
<=> sP1 ),
introduced(avatar_definition,[new_symbols(naming,[spl88_1])]) ).
tff(f3263,plain,
( sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) ) ),
inference(cnf_transformation,[],[f2268]) ).
tff(f2268,plain,
( ( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),sK85)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),sK85)
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& sP0 )
| sP1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f2266,f2267]) ).
tff(f2267,plain,
( ? [X0: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X0) )
=> ( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),sK85)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),sK85) ) ),
introduced(choice_axiom,[]) ).
tff(f2266,plain,
( ( ? [X0: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X0) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& sP0 )
| sP1 ),
inference(rectify,[],[f1620]) ).
tff(f1620,plain,
( ( ? [X1: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X1)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X1) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& sP0 )
| sP1 ),
inference(definition_folding,[],[f1276,f1619,f1618]) ).
tff(f1618,plain,
( ( ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
& ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) )
| ( ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) ) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f1619,plain,
( ( ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
& ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) )
& ( ! [X0: 'C$'] :
( ~ 'less_eq$'('from_nat$'('i$'),X0)
| ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ) )
| ~ sP1 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1276,plain,
( ( ? [X1: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X1)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X1) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& ( ( ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
& ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) )
| ( ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) ) ) ) )
| ( ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
& ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) )
& ( ! [X0: 'C$'] :
( ~ 'less_eq$'('from_nat$'('i$'),X0)
| ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ) ) ),
inference(flattening,[],[f1275]) ).
tff(f1275,plain,
( ( ( ( ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) ) )
| ( ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
& ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) ) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& ? [X1: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X1)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X1) ) )
| ( ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) )
& ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
& ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) ) )
& ( ! [X0: 'C$'] :
( ~ 'less_eq$'('from_nat$'('i$'),X0)
| ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ) ) ),
inference(ennf_transformation,[],[f854]) ).
tff(f854,plain,
~ ( ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) )
| ! [X1: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X1)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X1)),'from_nat$a'('k$')) ) ) )
=> ( ( ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) )
=> ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) ) ) )
& ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) )
=> ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) ) ) ),
inference(rectify,[],[f10]) ).
tff(f10,negated_conjecture,
~ ( ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) )
=> ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) ) )
& ( ~ ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) )
=> ( ( ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) )
=> ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) ) ) ) ),
inference(negated_conjecture,[],[f9]) ).
tff(f9,conjecture,
( ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) )
=> ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) ) )
& ( ~ ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) )
=> ( ( ( 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
| ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) )
=> ( 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) )
& ( ~ ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
=> ( 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) = 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('fun_app$b'('times$'('fst$'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))),'n$'),'pair$a'('nat$'($sum('of_nat$'('i$'),1)),'snd$b'('gauss_Jordan_in_ij_det_P$'('a$','from_nat$'('i$'),'from_nat$a'('k$')))))))) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture8) ).
tff(f3546,plain,
( ~ spl88_1
| ~ spl88_2
| ~ spl88_11 ),
inference(avatar_split_clause,[],[f3541,f3543,f3471,f3467]) ).
tff(f3541,plain,
( ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('snd$'('pair$a'('i$','a$'))) )
| ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| ~ sP1 ),
inference(forward_demodulation,[],[f3540,f3441]) ).
tff(f3441,plain,
! [X2: 'Nat_a_b_vec_c_vec_prod$',X0: 'A$'] : ( 'snd$a'('pair$'(X0,X2)) = X2 ),
inference(equality_resolution,[],[f3220]) ).
tff(f3220,plain,
! [X2: 'Nat_a_b_vec_c_vec_prod$',X0: 'A$',X1: 'Nat_a_b_vec_c_vec_prod$'] :
( ( 'snd$a'('pair$'(X0,X2)) != X1 )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f2240]) ).
tff(f2240,plain,
! [X0: 'A$',X1: 'Nat_a_b_vec_c_vec_prod$',X2: 'Nat_a_b_vec_c_vec_prod$'] :
( ( 'snd$a'('pair$'(X0,X2)) != X1 )
| ( X1 = X2 ) ),
inference(rectify,[],[f1415]) ).
tff(f1415,plain,
! [X1: 'A$',X0: 'Nat_a_b_vec_c_vec_prod$',X2: 'Nat_a_b_vec_c_vec_prod$'] :
( ( 'snd$a'('pair$'(X1,X2)) != X0 )
| ( X0 = X2 ) ),
inference(ennf_transformation,[],[f890]) ).
tff(f890,plain,
! [X1: 'A$',X0: 'Nat_a_b_vec_c_vec_prod$',X2: 'Nat_a_b_vec_c_vec_prod$'] :
( ( 'snd$a'('pair$'(X1,X2)) = X0 )
=> ( X0 = X2 ) ),
inference(rectify,[],[f284]) ).
tff(f284,axiom,
! [X2: 'Nat_a_b_vec_c_vec_prod$',X0: 'A$',X1: 'Nat_a_b_vec_c_vec_prod$'] :
( ( 'snd$a'('pair$'(X0,X1)) = X2 )
=> ( X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
tff(f3540,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) )
| ~ sP1 ),
inference(forward_demodulation,[],[f3539,f3130]) ).
tff(f3130,plain,
! [X0: 'A_iarray_iarray$',X1: 'Nat$'] : ( 'snd$c'('pair$d'(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2179]) ).
tff(f2179,plain,
! [X0: 'A_iarray_iarray$',X1: 'Nat$'] : ( 'snd$c'('pair$d'(X1,X0)) = X0 ),
inference(rectify,[],[f275]) ).
tff(f275,axiom,
! [X1: 'A_iarray_iarray$',X0: 'Nat$'] : ( 'snd$c'('pair$d'(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
tff(f3539,plain,
( ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('pair$d'('i$','matrix_to_iarray$'('a$'))) )
| ~ sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) ) ),
inference(forward_demodulation,[],[f3252,f2692]) ).
tff(f2692,plain,
! [X0: 'A$',X1: 'Nat_a_iarray_iarray_prod$'] : ( 'snd$d'('pair$c'(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,axiom,
! [X0: 'A$',X1: 'Nat_a_iarray_iarray_prod$'] : ( 'snd$d'('pair$c'(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
tff(f3252,plain,
( ~ sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ),
inference(cnf_transformation,[],[f2264]) ).
tff(f2264,plain,
( ( ( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
| 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$')))) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ( 'of_nat$'('i$') != 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'('a$'))) )
& ~ 'fun_app$e'('vector_all_zero_from_index$','pair$b'('i$','column_iarray$'('k$','matrix_to_iarray$'('a$'))))
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('fun_app$b'('times$'('fst$a'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$'))),'n$'),'pair$d'('nat$'($sum('of_nat$'('i$'),1)),'snd$e'('gauss_Jordan_in_ij_det_P_iarrays$'('matrix_to_iarray$'('a$'),'i$','k$')))))) ) ) )
& ( ! [X0: 'C$'] :
( ~ 'less_eq$'('from_nat$'('i$'),X0)
| ( 'zero$a' = 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) ) )
| ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f1619]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ITP001_1 : TPTP v8.1.0. Released v8.1.0.
% 0.03/0.12 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.32 % Computer : n022.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Aug 30 00:18:56 EDT 2022
% 0.13/0.32 % CPUTime :
% 0.18/0.54 % (16691)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.54 % (16688)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.18/0.55 % (16696)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.18/0.55 % (16690)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.18/0.55 % (16698)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.18/0.56 % (16685)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.18/0.56 % (16706)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.18/0.56 % (16707)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.18/0.56 % (16689)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.32/0.56 % (16697)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 1.32/0.56 % (16694)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.32/0.57 % (16699)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.32/0.57 % (16709)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.32/0.57 % (16714)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.32/0.57 % (16713)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.32/0.57 % (16701)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.54/0.58 % (16705)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.54/0.58 % (16708)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.54/0.58 % (16700)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.54/0.58 % (16686)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.54/0.58 % (16693)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.54/0.58 % (16693)Instruction limit reached!
% 1.54/0.58 % (16693)------------------------------
% 1.54/0.58 % (16693)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.58 % (16693)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.58 % (16693)Termination reason: Unknown
% 1.54/0.58 % (16693)Termination phase: shuffling
% 1.54/0.58
% 1.54/0.58 % (16693)Memory used [KB]: 1535
% 1.54/0.58 % (16693)Time elapsed: 0.003 s
% 1.54/0.58 % (16693)Instructions burned: 2 (million)
% 1.54/0.58 % (16693)------------------------------
% 1.54/0.58 % (16693)------------------------------
% 1.54/0.58 % (16712)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.54/0.58 % (16710)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.54/0.59 % (16704)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.54/0.59 % (16695)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.54/0.59 % (16692)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.54/0.59 % (16702)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.54/0.60 % (16692)Instruction limit reached!
% 1.54/0.60 % (16692)------------------------------
% 1.54/0.60 % (16692)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.61 % (16692)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.61 % (16692)Termination reason: Unknown
% 1.54/0.61 % (16692)Termination phase: Property scanning
% 1.54/0.61
% 1.54/0.61 % (16692)Memory used [KB]: 1663
% 1.54/0.61 % (16692)Time elapsed: 0.011 s
% 1.54/0.61 % (16692)Instructions burned: 7 (million)
% 1.54/0.61 % (16692)------------------------------
% 1.54/0.61 % (16692)------------------------------
% 1.54/0.61 % (16687)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.54/0.63 % (16691)Instruction limit reached!
% 1.54/0.63 % (16691)------------------------------
% 1.54/0.63 % (16691)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.63 % (16711)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.54/0.64 % (16703)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.54/0.64 % (16688)Instruction limit reached!
% 1.54/0.64 % (16688)------------------------------
% 1.54/0.64 % (16688)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.54/0.64 % (16688)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.64 % (16688)Termination reason: Unknown
% 1.54/0.64 % (16688)Termination phase: Property scanning
% 1.54/0.64
% 1.54/0.64 % (16688)Memory used [KB]: 2814
% 1.54/0.64 % (16688)Time elapsed: 0.025 s
% 1.54/0.64 % (16688)Instructions burned: 51 (million)
% 1.54/0.64 % (16688)------------------------------
% 1.54/0.64 % (16688)------------------------------
% 1.54/0.64 % (16691)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.54/0.64 % (16691)Termination reason: Unknown
% 1.54/0.64 % (16691)Termination phase: Property scanning
% 1.54/0.64
% 1.54/0.64 % (16691)Memory used [KB]: 2942
% 1.54/0.64 % (16691)Time elapsed: 0.037 s
% 1.54/0.64 % (16691)Instructions burned: 53 (million)
% 1.54/0.64 % (16691)------------------------------
% 1.54/0.64 % (16691)------------------------------
% 2.10/0.65 % (16694)Instruction limit reached!
% 2.10/0.65 % (16694)------------------------------
% 2.10/0.65 % (16694)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.10/0.65 % (16694)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.10/0.65 % (16694)Termination reason: Unknown
% 2.10/0.65 % (16694)Termination phase: Property scanning
% 2.10/0.65
% 2.10/0.65 % (16694)Memory used [KB]: 2942
% 2.10/0.65 % (16694)Time elapsed: 0.036 s
% 2.10/0.65 % (16694)Instructions burned: 51 (million)
% 2.10/0.65 % (16694)------------------------------
% 2.10/0.65 % (16694)------------------------------
% 2.10/0.65 % (16690)Instruction limit reached!
% 2.10/0.65 % (16690)------------------------------
% 2.10/0.65 % (16690)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.10/0.65 % (16690)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.10/0.65 % (16690)Termination reason: Unknown
% 2.10/0.65 % (16690)Termination phase: Property scanning
% 2.10/0.65
% 2.10/0.65 % (16690)Memory used [KB]: 2942
% 2.10/0.65 % (16690)Time elapsed: 0.035 s
% 2.10/0.65 % (16690)Instructions burned: 48 (million)
% 2.10/0.65 % (16690)------------------------------
% 2.10/0.65 % (16690)------------------------------
% 2.10/0.65 % (16689)Instruction limit reached!
% 2.10/0.65 % (16689)------------------------------
% 2.10/0.65 % (16689)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.10/0.65 % (16689)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.10/0.65 % (16689)Termination reason: Unknown
% 2.10/0.65 % (16689)Termination phase: Property scanning
% 2.10/0.65
% 2.10/0.65 % (16689)Memory used [KB]: 2942
% 2.10/0.65 % (16689)Time elapsed: 0.026 s
% 2.10/0.65 % (16689)Instructions burned: 52 (million)
% 2.10/0.65 % (16689)------------------------------
% 2.10/0.65 % (16689)------------------------------
% 2.10/0.66 % (16686)Instruction limit reached!
% 2.10/0.66 % (16686)------------------------------
% 2.10/0.66 % (16686)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.10/0.66 % (16686)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.10/0.66 % (16686)Termination reason: Unknown
% 2.10/0.66 % (16686)Termination phase: Property scanning
% 2.10/0.66
% 2.10/0.66 % (16686)Memory used [KB]: 2942
% 2.10/0.66 % (16686)Time elapsed: 0.036 s
% 2.10/0.66 % (16686)Instructions burned: 51 (million)
% 2.10/0.66 % (16686)------------------------------
% 2.10/0.66 % (16686)------------------------------
% 2.31/0.67 % (16699)Instruction limit reached!
% 2.31/0.67 % (16699)------------------------------
% 2.31/0.67 % (16699)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.67 % (16699)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.67 % (16699)Termination reason: Unknown
% 2.31/0.67 % (16699)Termination phase: Property scanning
% 2.31/0.67
% 2.31/0.67 % (16699)Memory used [KB]: 3326
% 2.31/0.67 % (16699)Time elapsed: 0.062 s
% 2.31/0.67 % (16699)Instructions burned: 68 (million)
% 2.31/0.67 % (16699)------------------------------
% 2.31/0.67 % (16699)------------------------------
% 2.31/0.68 % (16702)Instruction limit reached!
% 2.31/0.68 % (16702)------------------------------
% 2.31/0.68 % (16702)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.68 % (16702)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.68 % (16702)Termination reason: Unknown
% 2.31/0.68 % (16702)Termination phase: Function definition elimination
% 2.31/0.68
% 2.31/0.68 % (16702)Memory used [KB]: 2942
% 2.31/0.68 % (16702)Time elapsed: 0.040 s
% 2.31/0.68 % (16702)Instructions burned: 59 (million)
% 2.31/0.68 % (16702)------------------------------
% 2.31/0.68 % (16702)------------------------------
% 2.31/0.70 % (16698)Instruction limit reached!
% 2.31/0.70 % (16698)------------------------------
% 2.31/0.70 % (16698)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.70 % (16687)Instruction limit reached!
% 2.31/0.70 % (16687)------------------------------
% 2.31/0.70 % (16687)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.70 % (16687)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.70 % (16687)Termination reason: Unknown
% 2.31/0.70 % (16687)Termination phase: shuffling
% 2.31/0.70
% 2.31/0.70 % (16687)Memory used [KB]: 1918
% 2.31/0.70 % (16687)Time elapsed: 0.027 s
% 2.31/0.70 % (16687)Instructions burned: 37 (million)
% 2.31/0.70 % (16687)------------------------------
% 2.31/0.70 % (16687)------------------------------
% 2.31/0.70 % (16685)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.31/0.70 % (16685)Terminated due to inappropriate strategy.
% 2.31/0.70 % (16685)------------------------------
% 2.31/0.70 % (16685)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.70 % (16685)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.70 % (16685)Termination reason: Inappropriate
% 2.31/0.70
% 2.31/0.70 % (16685)Memory used [KB]: 3198
% 2.31/0.70 % (16685)Time elapsed: 0.041 s
% 2.31/0.70 % (16685)Instructions burned: 94 (million)
% 2.31/0.70 % (16685)------------------------------
% 2.31/0.70 % (16685)------------------------------
% 2.31/0.70 % (16698)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.70 % (16698)Termination reason: Unknown
% 2.31/0.70 % (16698)Termination phase: Saturation
% 2.31/0.70
% 2.31/0.70 % (16698)Memory used [KB]: 7675
% 2.31/0.70 % (16698)Time elapsed: 0.065 s
% 2.31/0.70 % (16698)Instructions burned: 99 (million)
% 2.31/0.70 % (16698)------------------------------
% 2.31/0.70 % (16698)------------------------------
% 2.31/0.72 % (16701)Instruction limit reached!
% 2.31/0.72 % (16701)------------------------------
% 2.31/0.72 % (16701)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.31/0.72 % (16701)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.31/0.72 % (16701)Termination reason: Unknown
% 2.31/0.72 % (16701)Termination phase: Saturation
% 2.31/0.72
% 2.31/0.72 % (16701)Memory used [KB]: 7803
% 2.31/0.72 % (16701)Time elapsed: 0.300 s
% 2.31/0.72 % (16701)Instructions burned: 99 (million)
% 2.31/0.72 % (16701)------------------------------
% 2.31/0.72 % (16701)------------------------------
% 2.57/0.73 % (16700)Instruction limit reached!
% 2.57/0.73 % (16700)------------------------------
% 2.57/0.73 % (16700)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.73 % (16700)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.73 % (16700)Termination reason: Unknown
% 2.57/0.73 % (16700)Termination phase: Saturation
% 2.57/0.73
% 2.57/0.73 % (16700)Memory used [KB]: 3070
% 2.57/0.73 % (16700)Time elapsed: 0.072 s
% 2.57/0.73 % (16700)Instructions burned: 76 (million)
% 2.57/0.73 % (16700)------------------------------
% 2.57/0.73 % (16700)------------------------------
% 2.57/0.73 % (16695)Instruction limit reached!
% 2.57/0.73 % (16695)------------------------------
% 2.57/0.73 % (16695)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.73 % (16695)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.73 % (16695)Termination reason: Unknown
% 2.57/0.73 % (16695)Termination phase: Property scanning
% 2.57/0.73
% 2.57/0.73 % (16695)Memory used [KB]: 2942
% 2.57/0.73 % (16695)Time elapsed: 0.038 s
% 2.57/0.73 % (16695)Instructions burned: 51 (million)
% 2.57/0.73 % (16695)------------------------------
% 2.57/0.73 % (16695)------------------------------
% 2.57/0.73 % (16696)Instruction limit reached!
% 2.57/0.73 % (16696)------------------------------
% 2.57/0.73 % (16696)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.73 % (16696)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.73 % (16696)Termination reason: Unknown
% 2.57/0.73 % (16696)Termination phase: Saturation
% 2.57/0.73
% 2.57/0.73 % (16696)Memory used [KB]: 7803
% 2.57/0.73 % (16696)Time elapsed: 0.048 s
% 2.57/0.73 % (16696)Instructions burned: 101 (million)
% 2.57/0.73 % (16696)------------------------------
% 2.57/0.73 % (16696)------------------------------
% 2.57/0.73 % (16697)Instruction limit reached!
% 2.57/0.73 % (16697)------------------------------
% 2.57/0.73 % (16697)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.57/0.73 % (16697)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.57/0.73 % (16697)Termination reason: Unknown
% 2.57/0.73 % (16697)Termination phase: Saturation
% 2.57/0.73
% 2.57/0.73 % (16697)Memory used [KB]: 7803
% 2.57/0.73 % (16697)Time elapsed: 0.048 s
% 2.57/0.73 % (16697)Instructions burned: 102 (million)
% 2.57/0.73 % (16697)------------------------------
% 2.57/0.73 % (16697)------------------------------
% 2.73/0.75 % (16728)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/388Mi)
% 2.73/0.76 % (16704)Instruction limit reached!
% 2.73/0.76 % (16704)------------------------------
% 2.73/0.76 % (16704)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.73/0.76 % (16704)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.73/0.76 % (16704)Termination reason: Unknown
% 2.73/0.76 % (16704)Termination phase: Saturation
% 2.73/0.76
% 2.73/0.76 % (16704)Memory used [KB]: 3198
% 2.73/0.76 % (16704)Time elapsed: 0.047 s
% 2.73/0.76 % (16704)Instructions burned: 100 (million)
% 2.73/0.76 % (16704)------------------------------
% 2.73/0.76 % (16704)------------------------------
% 2.73/0.76 % (16711)Instruction limit reached!
% 2.73/0.76 % (16711)------------------------------
% 2.73/0.76 % (16711)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.73/0.76 % (16711)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.73/0.76 % (16711)Termination reason: Unknown
% 2.73/0.76 % (16711)Termination phase: Property scanning
% 2.73/0.76
% 2.73/0.76 % (16711)Memory used [KB]: 3326
% 2.73/0.76 % (16711)Time elapsed: 0.045 s
% 2.73/0.76 % (16711)Instructions burned: 68 (million)
% 2.73/0.76 % (16711)------------------------------
% 2.73/0.76 % (16711)------------------------------
% 2.73/0.78 % (16714)First to succeed.
% 2.73/0.79 % (16714)Refutation found. Thanks to Tanya!
% 2.73/0.79 % SZS status Theorem for theBenchmark
% 2.73/0.79 % SZS output start Proof for theBenchmark
% See solution above
% 2.73/0.79 % (16714)------------------------------
% 2.73/0.79 % (16714)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.73/0.79 % (16714)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.73/0.79 % (16714)Termination reason: Refutation
% 2.73/0.79
% 2.73/0.79 % (16714)Memory used [KB]: 8443
% 2.73/0.79 % (16714)Time elapsed: 0.347 s
% 2.73/0.79 % (16714)Instructions burned: 142 (million)
% 2.73/0.79 % (16714)------------------------------
% 2.73/0.79 % (16714)------------------------------
% 2.73/0.79 % (16676)Success in time 0.463 s
%------------------------------------------------------------------------------