%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP338_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 11:33:38 AM UTC 2026
% Result : Theorem 3.91s 1.16s
% Output : Refutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 187 ( 110 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 227 ( 86 ~; 64 |; 49 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 10 ( 3 avg)
% Number arithmetic : 57 ( 7 atm; 25 fun; 25 num; 0 var)
% Number of types : 72 ( 70 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 33 ( 29 usr; 7 prp; 0-2 aty)
% Number of functors : 282 ( 280 usr; 36 con; 0-4 aty)
% Number of variables : 38 ( 34 !; 4 ?; 38 :)
% 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$' ).
tff(func_def_199,type,
sK2: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_200,type,
sK3: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_201,type,
sK4: ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'C$' ).
tff(func_def_202,type,
sK5: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_203,type,
sK6: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_204,type,
sK7: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$' ).
tff(func_def_205,type,
sK8: 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_206,type,
sK9: 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_207,type,
sK10: 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_208,type,
sK11: 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_209,type,
sK12: ( 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'C$' ).
tff(func_def_210,type,
sK13: ( 'Nat$' * 'A_b_vec_b_vec_nat_a_c_vec_b_vec_prod_prod$' ) > 'B$' ).
tff(func_def_211,type,
sK14: 'C$' ).
tff(func_def_212,type,
sK15: ( 'A_set$' * 'A_set$' * 'A$' ) > 'A$' ).
tff(func_def_213,type,
sK16: ( 'A_set$' * 'A_set$' * 'A$' ) > 'A$' ).
tff(func_def_214,type,
sK17: ( 'A_b_vec_b_vec$' * 'Nat$' ) > 'B$' ).
tff(func_def_215,type,
sK18: ( 'A_b_vec_b_vec$' * 'Nat$' ) > 'B$' ).
tff(func_def_216,type,
sK19: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_217,type,
sK20: ( $int * 'Int_set$' * 'Int_set$' ) > $int ).
tff(func_def_218,type,
sK21: ( 'B_a_bool_fun_fun$' * 'B$' ) > 'A$' ).
tff(func_def_219,type,
sK22: ( 'B_a_bool_fun_fun$' * 'A_b_vec$' ) > 'B$' ).
tff(func_def_220,type,
sK23: 'B_a_bool_fun_fun$' > 'A_b_vec$' ).
tff(func_def_221,type,
sK24: 'B_a_bool_fun_fun$' > 'B$' ).
tff(func_def_222,type,
sK25: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_223,type,
sK26: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_224,type,
sK27: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_225,type,
sK28: ( 'Nat$' * 'A_b_vec_c_vec_c_vec$' ) > 'C$' ).
tff(func_def_226,type,
sK29: ( 'Nat$' * 'A_b_vec_c_vec_c_vec$' ) > 'C$' ).
tff(func_def_227,type,
sK30: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_228,type,
sK31: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_229,type,
sK32: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$' ).
tff(func_def_230,type,
sK33: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_231,type,
sK34: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_232,type,
sK35: 'C_a_b_vec_bool_fun_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_233,type,
sK36: 'C_a_b_vec_bool_fun_fun$' > 'C$' ).
tff(func_def_234,type,
sK37: ( 'C_a_b_vec_bool_fun_fun$' * 'C$' ) > 'A_b_vec$' ).
tff(func_def_235,type,
sK38: ( 'C_a_b_vec_bool_fun_fun$' * 'A_b_vec_c_vec$' ) > 'C$' ).
tff(func_def_236,type,
sK39: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_237,type,
sK40: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_238,type,
sK41: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_239,type,
sK42: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_240,type,
sK43: ( 'Nat$' * 'A_b_vec_b_vec_nat_a_b_vec_b_vec_prod_prod$' ) > 'B$' ).
tff(func_def_241,type,
sK44: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_242,type,
sK45: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_243,type,
sK46: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_244,type,
sK47: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_245,type,
sK48: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_246,type,
sK49: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_247,type,
sK50: ( 'Nat$' * 'A_nat_a_c_vec_b_vec_prod_prod$' ) > 'B$' ).
tff(func_def_248,type,
sK51: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_249,type,
sK52: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_250,type,
sK53: 'A_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_251,type,
sK54: ( 'A_nat_a_b_vec_b_vec_prod_prod$' * 'Nat$' ) > 'B$' ).
tff(func_def_252,type,
sK55: ( 'A_b_vec$' * 'A_b_vec$' ) > 'B$' ).
tff(func_def_253,type,
sK56: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_254,type,
sK57: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_255,type,
sK58: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_256,type,
sK59: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'Nat$' ).
tff(func_def_257,type,
sK60: 'A_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_258,type,
sK61: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat$' ).
tff(func_def_259,type,
sK62: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_260,type,
sK63: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_261,type,
sK64: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_262,type,
sK65: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_263,type,
sK66: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'A$' ).
tff(func_def_264,type,
sK67: 'A_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_265,type,
sK68: ( 'Nat$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'C$' ).
tff(func_def_266,type,
sK69: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A$' ).
tff(func_def_267,type,
sK70: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_268,type,
sK71: ( 'Int_set$' * 'Int_set$' * $int ) > $int ).
tff(func_def_269,type,
sK72: ( 'Int_set$' * 'Int_set$' * $int ) > $int ).
tff(func_def_270,type,
sK73: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_271,type,
sK74: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_272,type,
sK75: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_273,type,
sK76: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_274,type,
sK77: ( 'Nat$' * 'A_nat_a_b_vec_c_vec_prod_prod$' ) > 'C$' ).
tff(func_def_275,type,
sK78: 'A_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_276,type,
sK79: 'A_nat_a_iarray_iarray_prod_prod$' > 'A$' ).
tff(func_def_277,type,
sK80: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_278,type,
sK81: ( 'Nat$' * 'Nat_set$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_279,type,
sK82: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_280,type,
sK83: ( 'Nat$' * 'A_nat_a_c_vec_c_vec_prod_prod$' ) > 'C$' ).
tff(func_def_281,type,
sK84: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_282,type,
sK85: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_283,type,
sK86: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_284,type,
sK87: 'A_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A$' ).
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$' * 'A_b_vec$' ) > $o ).
tff(f9,conjecture,
( ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' ) )
| ( 'of_nat$'('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$c'('fun_app$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$')))))) ) )
& ( ( 'fun_app$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$'))) ) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ) ) )
& ( ~ ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' ) )
| ( 'of_nat$'('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$'('a$'))) ) )
=> ( '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$a'('k$')))))))) = '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$')))) )
=> ( 'matrix_to_iarray$'('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$')))))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture8) ).
tff(f10,negated_conjecture,
~ ( ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' ) )
| ( 'of_nat$'('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$c'('fun_app$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$')))))) ) )
& ( ( 'fun_app$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$'))) ) )
=> ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ) ) )
& ( ~ ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' ) )
| ( 'of_nat$'('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$'('a$'))) ) )
=> ( '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$a'('k$')))))))) = '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$')))) )
=> ( 'matrix_to_iarray$'('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$')))))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
tff(f11,axiom,
$lesseq('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom9) ).
tff(f12,axiom,
~ $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom10) ).
tff(f273,axiom,
! [X0: 'Nat$',X1: 'A_b_vec_c_vec$'] : ( 'snd$'('pair$a'(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom271) ).
tff(f275,axiom,
! [X0: 'Nat$',X1: 'A_iarray_iarray$'] : ( 'snd$c'('pair$d'(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom273) ).
tff(f277,axiom,
! [X1: 'Nat_a_b_vec_c_vec_prod$',X0: 'A$'] : ( 'snd$a'('pair$'(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom275) ).
tff(f278,axiom,
! [X1: 'Nat_a_iarray_iarray_prod$',X0: 'A$'] : ( 'snd$d'('pair$c'(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom276) ).
tff(f573,axiom,
! [X0: 'A_b_vec_c_vec$'] : ( 'of_nat$'('nrows$'(X0)) = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom571) ).
tff(f761,plain,
~ $less('of_nat$'('nrows$'('a$')),'of_nat$'('i$')),
inference(theory_normalization,[],[f11]) ).
tff(f948,plain,
! [X1: 'A$',X0: 'Nat_a_iarray_iarray_prod$'] : ( 'snd$d'('pair$c'(X1,X0)) = X0 ),
inference(rectify,[],[f278]) ).
tff(f1078,plain,
~ ( ( ( ! [X0: 'C$'] :
( 'less_eq$'('from_nat$'('i$'),X0)
=> ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' ) )
| ( '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'('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$','k$')))))) ) )
& ( ( '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$'('a$'))) ) )
=> ( '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$'('nrows$'('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$'))) ) )
=> ( 'matrix_to_iarray$'('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$')))))))) = 'snd$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$'('a$')))) )
=> ( '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$a'('k$')))))))) = 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) ) ) ) ),
inference(rectify,[],[f10]) ).
tff(f1131,plain,
! [X0: 'Nat_a_b_vec_c_vec_prod$',X1: 'A$'] : ( 'snd$a'('pair$'(X1,X0)) = X0 ),
inference(rectify,[],[f277]) ).
tff(f1540,plain,
( ( ( ( ( '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$')))) )
| ( ( 'fun_app$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$'))) ) )
& ( 'matrix_to_iarray$'('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$'('a$')) )
| ! [X0: 'C$'] :
( ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' )
| ~ 'less_eq$'('from_nat$'('i$'),X0) ) ) )
| ( ( ( ( '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$')))))))) )
& ~ 'fun_app$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$')))) )
& ( 'snd$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$'('a$')) )
& ? [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) ) ) ),
inference(ennf_transformation,[],[f1078]) ).
tff(f1541,plain,
( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) )
| ! [X0: 'C$'] :
( ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' )
| ~ 'less_eq$'('from_nat$'('i$'),X0) ) )
& ( ( ( 'fun_app$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$'))) ) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ~ 'fun_app$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$'))) )
& ( 'matrix_to_iarray$'('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$'('a$')))) )
& ( '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$a'('k$')))))))) ) )
| ( ( '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) ) ) ),
inference(flattening,[],[f1540]) ).
tff(f1647,definition,
( ( ( ( '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$c'('n$','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$a'('k$')))))))) ) )
| ( ( '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$')))) )
| ~ sP0 ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f1648,definition,
( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) )
| ! [X0: 'C$'] :
( ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' )
| ~ 'less_eq$'('from_nat$'('i$'),X0) ) )
& ( ( ( '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$'('a$'))) ) )
& ( '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$'('a$'))))) ) )
| ( ~ '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$'('a$'))) )
& ( '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$')))))) ) ) ) )
| ~ sP1 ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f1649,plain,
( sP1
| ( sP0
& ( 'of_nat$'('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) ) ) ),
inference(definition_folding,[],[f1541,f1648,f1647]) ).
tff(f1730,plain,
( ( ( ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) )
| ! [X0: 'C$'] :
( ( 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) = 'zero$a' )
| ~ 'less_eq$'('from_nat$'('i$'),X0) ) )
& ( ( ( 'fun_app$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$'))) ) )
& ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('snd$d'('pair$c'('n$','pair$d'('i$','matrix_to_iarray$'('a$'))))) ) )
| ( ~ 'fun_app$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$'))) )
& ( 'matrix_to_iarray$'('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$','k$')))))) ) ) ) )
| ~ sP1 ),
inference(nnf_transformation,[],[f1648]) ).
tff(f1732,plain,
( sP1
| ( sP0
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& ? [X0: 'C$'] :
( ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),X0)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),X0) ) ) ),
inference(rectify,[],[f1649]) ).
tff(f1733,plain,
( sP1
| ( sP0
& ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
& ( 'zero$a' != 'fun_app$c'('vec_nth$'('fun_app$d'('vec_nth$a'('a$'),sK14)),'from_nat$a'('k$')) )
& 'less_eq$'('from_nat$'('i$'),sK14) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f1732]) ).
tff(f2200,plain,
! [X0: 'A$',X1: 'Nat_a_iarray_iarray_prod$'] : ( 'snd$d'('pair$c'(X0,X1)) = X1 ),
inference(rectify,[],[f948]) ).
tff(f2313,plain,
! [X0: 'Nat$',X1: 'A_b_vec_c_vec$'] : ( 'snd$'('pair$a'(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f273]) ).
tff(f2386,plain,
( ( 'of_nat$'('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$'))))) )
| ~ sP1 ),
inference(cnf_transformation,[],[f1730]) ).
tff(f2400,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
| sP1 ),
inference(cnf_transformation,[],[f1733]) ).
tff(f2436,plain,
~ $less('of_nat$'('nrows$'('a$')),'of_nat$'('i$')),
inference(cnf_transformation,[],[f761]) ).
tff(f2737,plain,
! [X0: 'A_b_vec_c_vec$'] : ( 'of_nat$'('nrows$'(X0)) = 'of_nat$'('nrows_iarray$'('matrix_to_iarray$'(X0))) ),
inference(cnf_transformation,[],[f573]) ).
tff(f3047,plain,
! [X0: 'Nat$',X1: 'A_iarray_iarray$'] : ( 'snd$c'('pair$d'(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f275]) ).
tff(f3058,plain,
~ $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))),
inference(cnf_transformation,[],[f12]) ).
tff(f3149,plain,
! [X0: 'A$',X1: 'Nat_a_iarray_iarray_prod$'] : ( 'snd$d'('pair$c'(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f2200]) ).
tff(f3164,plain,
! [X0: 'Nat_a_b_vec_c_vec_prod$',X1: 'A$'] : ( 'snd$a'('pair$'(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f1131]) ).
tff(f3316,definition,
( spl88_3
<=> sP1 ),
introduced(definition,[new_symbols(definition,[spl88_3])],[avatar_definition]) ).
tff(f3356,definition,
( spl88_10
<=> $less('of_nat$'('i$'),'of_nat$'('nrows$'('a$'))) ),
introduced(definition,[new_symbols(definition,[spl88_10])],[avatar_definition]) ).
tff(f3359,plain,
~ spl88_10,
inference(avatar_split_clause,[],[f3058,f3356]) ).
tff(f3441,definition,
( spl88_25
<=> ( 'of_nat$'('i$') = 'of_nat$'('nrows$'('a$')) ) ),
introduced(definition,[new_symbols(definition,[spl88_25])],[avatar_definition]) ).
tff(f3457,plain,
( ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
| ( '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$'('a$'))))) )
| ~ sP1 ),
inference(forward_demodulation,[],[f2386,f2737]) ).
tff(f3459,definition,
( spl88_28
<=> $less('of_nat$'('nrows$'('a$')),'of_nat$'('i$')) ),
introduced(definition,[new_symbols(definition,[spl88_28])],[avatar_definition]) ).
tff(f3462,plain,
~ spl88_28,
inference(avatar_split_clause,[],[f2436,f3459]) ).
tff(f3463,plain,
( spl88_3
| ~ spl88_25 ),
inference(avatar_split_clause,[],[f2400,f3441,f3316]) ).
tff(f3508,plain,
( ~ sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
| ( 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) != 'snd$c'('pair$d'('i$','matrix_to_iarray$'('a$'))) ) ),
inference(forward_demodulation,[],[f3457,f3149]) ).
tff(f3520,plain,
( ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('snd$'('snd$a'('pair$'('n$','pair$a'('i$','a$'))))) )
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) )
| ~ sP1 ),
inference(forward_demodulation,[],[f3508,f3047]) ).
tff(f3530,plain,
( ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('snd$'('pair$a'('i$','a$'))) )
| ~ sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) ) ),
inference(forward_demodulation,[],[f3520,f3164]) ).
tff(f3546,plain,
( ~ sP1
| ( 'matrix_to_iarray$'('a$') != 'matrix_to_iarray$'('a$') )
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) ) ),
inference(forward_demodulation,[],[f3530,f2313]) ).
tff(f3547,plain,
( ~ sP1
| ( 'of_nat$'('i$') != 'of_nat$'('nrows$'('a$')) ) ),
inference(trivial_inequality_removal,[],[f3546]) ).
tff(f3561,plain,
( ~ spl88_3
| ~ spl88_25 ),
inference(avatar_split_clause,[],[f3547,f3441,f3316]) ).
tff(f3571,plain,
$false,
inference(avatar_smt_refutation,[],[f3561,f3463,f3462,f3359]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ITP338_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 27 12:54:34 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.69/0.87 % (2365198)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.69/0.87 % (2365203)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=535304420:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.69/0.87 % (2365205)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1376136157:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.69/0.87 % (2365206)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=156005470:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.69/0.87 % (2365207)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2255762127:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.69/0.87 % (2365208)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3105842054:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.69/0.87 % (2365209)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2287330745:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.69/0.87 % (2365204)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1542441843:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.69/0.87 % (2365207)Instruction limit reached!
% 1.69/0.87 % (2365207)------------------------------
% 1.69/0.87 % (2365207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.87 % (2365207)CaDiCaL version: 2.1.3
% 1.69/0.87 % (2365207)Termination reason: Instruction limit
% 1.69/0.87 % (2365207)Termination phase: Property scanning
% 1.69/0.87 % (2365207)Time elapsed: 0.002 s
% 1.69/0.87 % (2365207)Peak memory usage: 85 MB
% 1.69/0.87 % (2365207)Instructions burned: 5 (million)
% 1.69/0.87 % (2365206)Instruction limit reached!
% 1.69/0.87 % (2365206)------------------------------
% 1.69/0.87 % (2365206)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.87 % (2365206)CaDiCaL version: 2.1.3
% 1.69/0.87 % (2365206)Termination reason: Instruction limit
% 1.69/0.87 % (2365206)Termination phase: Property scanning
% 1.69/0.87 % (2365206)Time elapsed: 0.003 s
% 1.69/0.87 % (2365206)Peak memory usage: 86 MB
% 1.69/0.87 % (2365206)Instructions burned: 10 (million)
% 1.69/0.87 % (2365203)Instruction limit reached!
% 1.69/0.87 % (2365203)------------------------------
% 1.69/0.87 % (2365203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.87 % (2365203)CaDiCaL version: 2.1.3
% 1.69/0.87 % (2365203)Termination reason: Instruction limit
% 1.69/0.87 % (2365203)Termination phase: Property scanning
% 1.69/0.87 % (2365203)Time elapsed: 0.004 s
% 1.69/0.87 % (2365203)Peak memory usage: 86 MB
% 1.69/0.87 % (2365203)Instructions burned: 16 (million)
% 1.69/0.87 % (2365209)Instruction limit reached!
% 1.69/0.87 % (2365209)------------------------------
% 1.69/0.87 % (2365209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.87 % (2365209)CaDiCaL version: 2.1.3
% 1.69/0.87 % (2365209)Termination reason: Instruction limit
% 1.69/0.87 % (2365209)Termination phase: Property scanning
% 1.69/0.87 % (2365209)Time elapsed: 0.011 s
% 1.69/0.87 % (2365209)Peak memory usage: 88 MB
% 1.69/0.87 % (2365209)Instructions burned: 34 (million)
% 1.69/0.87 % (2365208)Instruction limit reached!
% 1.69/0.87 % (2365208)------------------------------
% 1.69/0.87 % (2365208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.69/0.87 % (2365208)CaDiCaL version: 2.1.3
% 1.69/0.87 % (2365208)Termination reason: Instruction limit
% 1.69/0.87 % (2365208)Termination phase: Property scanning
% 1.69/0.87 % (2365208)Time elapsed: 0.014 s
% 1.69/0.87 % (2365208)Peak memory usage: 88 MB
% 1.69/0.87 % (2365208)Instructions burned: 48 (million)
% 1.69/0.87 % (2365205)Instruction limit reached!
% 1.69/0.87 % (2365205)------------------------------
% 1.69/0.87 % (2365205)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.69/0.87 % (2365205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365205)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365205)Termination reason: Instruction limit
% 2.22/0.98 % (2365205)Termination phase: Saturation
% 2.22/0.98 % (2365205)Time elapsed: 0.082 s
% 2.22/0.98 % (2365205)Peak memory usage: 119 MB
% 2.22/0.98 % (2365205)Instructions burned: 203 (million)
% 2.22/0.98 % (2365219)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1532930938:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 2.22/0.98 % (2365217)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=978009004:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.22/0.98 % (2365218)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=3347859396:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 2.22/0.98 % (2365219)Instruction limit reached!
% 2.22/0.98 % (2365219)------------------------------
% 2.22/0.98 % (2365219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365219)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365219)Termination reason: Instruction limit
% 2.22/0.98 % (2365219)Termination phase: Preprocessing 3
% 2.22/0.98 % (2365219)Time elapsed: 0.006 s
% 2.22/0.98 % (2365219)Peak memory usage: 87 MB
% 2.22/0.98 % (2365219)Instructions burned: 18 (million)
% 2.22/0.98 % (2365217)Instruction limit reached!
% 2.22/0.98 % (2365217)------------------------------
% 2.22/0.98 % (2365217)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365217)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365217)Termination reason: Instruction limit
% 2.22/0.98 % (2365217)Termination phase: Preprocessing 1
% 2.22/0.98 % (2365217)Time elapsed: 0.005 s
% 2.22/0.98 % (2365217)Peak memory usage: 86 MB
% 2.22/0.98 % (2365217)Instructions burned: 16 (million)
% 2.22/0.98 % (2365218)Instruction limit reached!
% 2.22/0.98 % (2365218)------------------------------
% 2.22/0.98 % (2365218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365218)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365218)Termination reason: Instruction limit
% 2.22/0.98 % (2365218)Termination phase: Preprocessing 3
% 2.22/0.98 % (2365218)Time elapsed: 0.011 s
% 2.22/0.98 % (2365218)Peak memory usage: 88 MB
% 2.22/0.98 % (2365218)Instructions burned: 31 (million)
% 2.22/0.98 % (2365221)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=1890721760:i=27:canc=cautious:fsr=off:rtra=on_2998 on theBenchmark for (2998ds/27Mi)
% 2.22/0.98 % (2365220)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2988817501:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 2.22/0.98 % (2365204)Instruction limit reached!
% 2.22/0.98 % (2365204)------------------------------
% 2.22/0.98 % (2365204)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365204)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365204)Termination reason: Instruction limit
% 2.22/0.98 % (2365204)Termination phase: Saturation
% 2.22/0.98 % (2365204)Time elapsed: 0.113 s
% 2.22/0.98 % (2365204)Peak memory usage: 119 MB
% 2.22/0.98 % (2365204)Instructions burned: 308 (million)
% 2.22/0.98 % (2365220)Instruction limit reached!
% 2.22/0.98 % (2365220)------------------------------
% 2.22/0.98 % (2365220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.22/0.98 % (2365220)CaDiCaL version: 2.1.3
% 2.22/0.98 % (2365220)Termination reason: Instruction limit
% 2.22/0.98 % (2365220)Termination phase: Preprocessing 3
% 2.22/0.98 % (2365220)Time elapsed: 0.008 s
% 2.22/0.98 % (2365220)Peak memory usage: 87 MB
% 2.22/0.98 % (2365220)Instructions burned: 26 (million)
% 2.22/0.98 % (2365221)Instruction limit reached!
% 2.22/0.98 % (2365221)------------------------------
% 2.22/0.98 % (2365221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.22/0.98 % (2365221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365221)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365221)Termination reason: Instruction limit
% 3.47/1.09 % (2365221)Termination phase: Preprocessing 3
% 3.47/1.09 % (2365221)Time elapsed: 0.009 s
% 3.47/1.09 % (2365221)Peak memory usage: 88 MB
% 3.47/1.09 % (2365221)Instructions burned: 29 (million)
% 3.47/1.09 % (2365226)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=741683310:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2997 on theBenchmark for (2997ds/2Mi)
% 3.47/1.09 % (2365226)Instruction limit reached!
% 3.47/1.09 % (2365226)------------------------------
% 3.47/1.09 % (2365226)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.09 % (2365226)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365226)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365226)Termination reason: Instruction limit
% 3.47/1.09 % (2365226)Termination phase: Property scanning
% 3.47/1.09 % (2365226)Time elapsed: 0.002 s
% 3.47/1.09 % (2365226)Peak memory usage: 86 MB
% 3.47/1.09 % (2365226)Instructions burned: 6 (million)
% 3.47/1.09 % (2365223)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2308139226:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.47/1.09 % (2365227)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2861797547:i=181:rtra=on:ss=axioms:ev=cautious_2997 on theBenchmark for (2997ds/181Mi)
% 3.47/1.09 % (2365230)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=627772788:i=4:ep=RST:ins=2:rtra=on_2997 on theBenchmark for (2997ds/4Mi)
% 3.47/1.09 % (2365230)Instruction limit reached!
% 3.47/1.09 % (2365230)------------------------------
% 3.47/1.09 % (2365230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.09 % (2365230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365230)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365230)Termination reason: Instruction limit
% 3.47/1.09 % (2365230)Termination phase: Property scanning
% 3.47/1.09 % (2365230)Time elapsed: 0.002 s
% 3.47/1.09 % (2365230)Peak memory usage: 86 MB
% 3.47/1.09 % (2365230)Instructions burned: 5 (million)
% 3.47/1.09 % (2365223)Instruction limit reached!
% 3.47/1.09 % (2365223)------------------------------
% 3.47/1.09 % (2365223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.09 % (2365223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365223)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365223)Termination reason: Instruction limit
% 3.47/1.09 % (2365223)Termination phase: Saturation
% 3.47/1.09 % (2365223)Time elapsed: 0.026 s
% 3.47/1.09 % (2365223)Peak memory usage: 90 MB
% 3.47/1.09 % (2365223)Instructions burned: 85 (million)
% 3.47/1.09 % (2365232)lrs+10_1_thi=all:si=on:fd=off:random_seed=829056654:i=53:rtra=on:gtg=all_2997 on theBenchmark for (2997ds/53Mi)
% 3.47/1.09 % (2365231)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=152452849:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2997 on theBenchmark for (2997ds/66Mi)
% 3.47/1.09 % (2365233)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=2280446882:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2997 on theBenchmark for (2997ds/8Mi)
% 3.47/1.09 % (2365233)Instruction limit reached!
% 3.47/1.09 % (2365233)------------------------------
% 3.47/1.09 % (2365233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.09 % (2365233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365233)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365233)Termination reason: Instruction limit
% 3.47/1.09 % (2365233)Termination phase: shuffling
% 3.47/1.09 % (2365233)Time elapsed: 0.003 s
% 3.47/1.09 % (2365233)Peak memory usage: 86 MB
% 3.47/1.09 % (2365233)Instructions burned: 10 (million)
% 3.47/1.09 % (2365232)Instruction limit reached!
% 3.47/1.09 % (2365232)------------------------------
% 3.47/1.09 % (2365232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.09 % (2365232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.09 % (2365232)CaDiCaL version: 2.1.3
% 3.47/1.09 % (2365232)Termination reason: Instruction limit
% 3.47/1.09 % (2365232)Termination phase: Property scanning
% 3.47/1.09 % (2365232)Time elapsed: 0.016 s
% 3.47/1.09 % (2365232)Peak memory usage: 88 MB
% 3.47/1.09 % (2365232)Instructions burned: 55 (million)
% 3.91/1.16 % (2365231)Instruction limit reached!
% 3.91/1.16 % (2365231)------------------------------
% 3.91/1.16 % (2365231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365231)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365231)Termination reason: Instruction limit
% 3.91/1.16 % (2365231)Termination phase: Saturation
% 3.91/1.16 % (2365231)Time elapsed: 0.041 s
% 3.91/1.16 % (2365231)Peak memory usage: 125 MB
% 3.91/1.16 % (2365231)Instructions burned: 66 (million)
% 3.91/1.16 % (2365236)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=1378119104:st=3:i=2:rtra=on:ss=axioms_2996 on theBenchmark for (2996ds/2Mi)
% 3.91/1.16 % (2365236)Instruction limit reached!
% 3.91/1.16 % (2365236)------------------------------
% 3.91/1.16 % (2365236)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365236)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365236)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365236)Termination reason: Instruction limit
% 3.91/1.16 % (2365236)Termination phase: Property scanning
% 3.91/1.16 % (2365236)Time elapsed: 0.002 s
% 3.91/1.16 % (2365236)Peak memory usage: 86 MB
% 3.91/1.16 % (2365236)Instructions burned: 5 (million)
% 3.91/1.16 % (2365227)Instruction limit reached!
% 3.91/1.16 % (2365227)------------------------------
% 3.91/1.16 % (2365227)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365227)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365227)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365227)Termination reason: Instruction limit
% 3.91/1.16 % (2365227)Termination phase: Saturation
% 3.91/1.16 % (2365227)Time elapsed: 0.073 s
% 3.91/1.16 % (2365227)Peak memory usage: 92 MB
% 3.91/1.16 % (2365227)Instructions burned: 182 (million)
% 3.91/1.16 % (2365239)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=887500427:i=2:doe=on:canc=force:asg=cautious:rtra=on_2996 on theBenchmark for (2996ds/2Mi)
% 3.91/1.16 % (2365240)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=3241657208:i=127:doe=on:rtra=on_2996 on theBenchmark for (2996ds/127Mi)
% 3.91/1.16 % (2365239)Instruction limit reached!
% 3.91/1.16 % (2365239)------------------------------
% 3.91/1.16 % (2365239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365239)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365239)Termination reason: Instruction limit
% 3.91/1.16 % (2365239)Termination phase: Property scanning
% 3.91/1.16 % (2365239)Time elapsed: 0.002 s
% 3.91/1.16 % (2365239)Peak memory usage: 86 MB
% 3.91/1.16 % (2365239)Instructions burned: 5 (million)
% 3.91/1.16 % (2365244)dis+10_1_si=on:random_seed=4170120440:i=10:ep=R:rtra=on_2996 on theBenchmark for (2996ds/10Mi)
% 3.91/1.16 % (2365244)Instruction limit reached!
% 3.91/1.16 % (2365244)------------------------------
% 3.91/1.16 % (2365244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365244)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365244)Termination reason: Instruction limit
% 3.91/1.16 % (2365244)Termination phase: Including theory axioms
% 3.91/1.16 % (2365244)Time elapsed: 0.003 s
% 3.91/1.16 % (2365244)Peak memory usage: 86 MB
% 3.91/1.16 % (2365244)Instructions burned: 10 (million)
% 3.91/1.16 % (2365245)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3859523518:i=26:canc=cautious:av=off:rtra=on_2996 on theBenchmark for (2996ds/26Mi)
% 3.91/1.16 % (2365245)Instruction limit reached!
% 3.91/1.16 % (2365245)------------------------------
% 3.91/1.16 % (2365245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365245)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365245)Termination reason: Instruction limit
% 3.91/1.16 % (2365245)Termination phase: Preprocessing 3
% 3.91/1.16 % (2365245)Time elapsed: 0.008 s
% 3.91/1.16 % (2365245)Peak memory usage: 87 MB
% 3.91/1.16 % (2365245)Instructions burned: 26 (million)
% 3.91/1.16 % (2365246)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=4210421930: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_2996 on theBenchmark for (2996ds/35Mi)
% 3.91/1.16 % (2365240)First to succeed.
% 3.91/1.16 % (2365240)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2365198"
% 3.91/1.16 % (2365246)Instruction limit reached!
% 3.91/1.16 % (2365246)------------------------------
% 3.91/1.16 % (2365246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365246)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365246)Termination reason: Instruction limit
% 3.91/1.16 % (2365246)Termination phase: Preprocessing 3
% 3.91/1.16 % (2365246)Time elapsed: 0.012 s
% 3.91/1.16 % (2365246)Peak memory usage: 88 MB
% 3.91/1.16 % (2365246)Instructions burned: 35 (million)
% 3.91/1.16 % (2365249)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=2981874638:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2996 on theBenchmark for (2996ds/8Mi)
% 3.91/1.16 % (2365248)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=3954571941:i=2:fsr=off:rtra=on:inst=on_2996 on theBenchmark for (2996ds/2Mi)
% 3.91/1.16 % (2365249)Instruction limit reached!
% 3.91/1.16 % (2365249)------------------------------
% 3.91/1.16 % (2365249)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365249)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365249)Termination reason: Instruction limit
% 3.91/1.16 % (2365249)Termination phase: Property scanning
% 3.91/1.16 % (2365249)Time elapsed: 0.003 s
% 3.91/1.16 % (2365249)Peak memory usage: 86 MB
% 3.91/1.16 % (2365249)Instructions burned: 12 (million)
% 3.91/1.16 % (2365248)Instruction limit reached!
% 3.91/1.16 % (2365248)------------------------------
% 3.91/1.16 % (2365248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365248)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365248)Termination reason: Instruction limit
% 3.91/1.16 % (2365248)Termination phase: Property scanning
% 3.91/1.16 % (2365248)Time elapsed: 0.003 s
% 3.91/1.16 % (2365248)Peak memory usage: 86 MB
% 3.91/1.16 % (2365248)Instructions burned: 9 (million)
% 3.91/1.16 % (2365252)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=891318278:i=370:ep=RS:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/370Mi)
% 3.91/1.16 % (2365254)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=3252848159:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2995 on theBenchmark for (2995ds/13Mi)
% 3.91/1.16 % (2365254)Instruction limit reached!
% 3.91/1.16 % (2365254)------------------------------
% 3.91/1.16 % (2365254)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365254)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365254)Termination reason: Instruction limit
% 3.91/1.16 % (2365254)Termination phase: shuffling
% 3.91/1.16 % (2365254)Time elapsed: 0.004 s
% 3.91/1.16 % (2365254)Peak memory usage: 86 MB
% 3.91/1.16 % (2365254)Instructions burned: 17 (million)
% 3.91/1.16 % (2365256)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=1335427280:i=226:rtra=on:gtg=position:ss=axioms_2995 on theBenchmark for (2995ds/226Mi)
% 3.91/1.16 % (2365259)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=186298055:i=10:rtra=on_2995 on theBenchmark for (2995ds/10Mi)
% 3.91/1.16 % (2365259)Instruction limit reached!
% 3.91/1.16 % (2365259)------------------------------
% 3.91/1.16 % (2365259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365259)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365259)Termination reason: Instruction limit
% 3.91/1.16 % (2365259)Termination phase: Preprocessing 1
% 3.91/1.16 % (2365259)Time elapsed: 0.004 s
% 3.91/1.16 % (2365259)Peak memory usage: 86 MB
% 3.91/1.16 % (2365259)Instructions burned: 12 (million)
% 3.91/1.16 % (2365262)lrs+1010_1_to=lpo:prlc=on:sil=128000:prc=on:drc=off:si=on:sp=const_max:thsqr=8,1:tha=some:nwc=5:random_seed=3129884122:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2995 on theBenchmark for (2995ds/75Mi)
% 3.91/1.16 % (2365256)Refutation not found, incomplete strategy
% 3.91/1.16 % (2365256)------------------------------
% 3.91/1.16 % (2365256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365256)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365256)Termination reason: Refutation not found, incomplete strategy
% 3.91/1.16 % (2365256)Time elapsed: 0.040 s
% 3.91/1.16 % (2365256)Peak memory usage: 117 MB
% 3.91/1.16 % (2365256)Instructions burned: 77 (million)
% 3.91/1.16 % (2365261)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=2154059475:i=71:rtra=on:gtg=exists_top_2995 on theBenchmark for (2995ds/71Mi)
% 3.91/1.16 % (2365262)Instruction limit reached!
% 3.91/1.16 % (2365262)------------------------------
% 3.91/1.16 % (2365262)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365262)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365262)Termination reason: Instruction limit
% 3.91/1.16 % (2365262)Termination phase: Saturation
% 3.91/1.16 % (2365262)Time elapsed: 0.022 s
% 3.91/1.16 % (2365262)Peak memory usage: 90 MB
% 3.91/1.16 % (2365262)Instructions burned: 76 (million)
% 3.91/1.16 % (2365265)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=1684137542:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2994 on theBenchmark for (2994ds/294Mi)
% 3.91/1.16 % (2365261)Instruction limit reached!
% 3.91/1.16 % (2365261)------------------------------
% 3.91/1.16 % (2365261)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365261)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365261)Termination reason: Instruction limit
% 3.91/1.16 % (2365261)Termination phase: Saturation
% 3.91/1.16 % (2365261)Time elapsed: 0.047 s
% 3.91/1.16 % (2365261)Peak memory usage: 130 MB
% 3.91/1.16 % (2365261)Instructions burned: 73 (million)
% 3.91/1.16 % (2365252)Instruction limit reached!
% 3.91/1.16 % (2365252)------------------------------
% 3.91/1.16 % (2365252)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.16 % (2365252)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.16 % (2365252)CaDiCaL version: 2.1.3
% 3.91/1.16 % (2365252)Termination reason: Instruction limit
% 3.91/1.16 % (2365252)Termination phase: Saturation
% 3.91/1.16 % (2365252)Time elapsed: 0.123 s
% 3.91/1.16 % (2365252)Peak memory usage: 94 MB
% 3.91/1.16 % (2365252)Instructions burned: 371 (million)
% 3.91/1.16 % (2365240)Refutation found. Thanks to Tanya!
% 3.91/1.16 % SZS status Theorem for theBenchmark
% 3.91/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 4.55/1.25 % (2365240)------------------------------
% 4.55/1.25 % (2365240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.55/1.25 % (2365240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.55/1.25 % (2365240)CaDiCaL version: 2.1.3
% 4.55/1.25 % (2365240)Termination reason: Refutation
% 4.55/1.25 % (2365240)Time elapsed: 0.056 s
% 4.55/1.25 % (2365240)Peak memory usage: 119 MB
% 4.55/1.25 % (2365240)Instructions burned: 117 (million)
% 4.55/1.25 % (2365240)------------------------------
% 4.55/1.25 % (2365240)------------------------------
% 4.55/1.25 % (2365198)Success in time 0.637 s
% 4.55/1.25 % Vampire exiting
%------------------------------------------------------------------------------