%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP339_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 : n017.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 3.40s 1.16s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 52
% Syntax : Number of formulae : 97 ( 71 unt; 0 typ; 49 def)
% Number of atoms : 123 ( 70 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 5 ~; 0 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 14 ( 3 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 99 ( 0 atm; 29 fun; 70 num; 0 var)
% Number of types : 50 ( 48 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 41 ( 39 usr; 27 prp; 0-2 aty)
% Number of functors : 294 ( 291 usr; 53 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'A_c_vec_c_vec$': $tType ).
tff(type_def_8,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'Int_int_prod_bool_fun$': $tType ).
tff(type_def_10,type,
'A_iarray_iarray_a_iarray_iarray_prod$': $tType ).
tff(type_def_11,type,
'A_iarray_iarray$': $tType ).
tff(type_def_12,type,
'Int_int_prod$': $tType ).
tff(type_def_13,type,
'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$': $tType ).
tff(type_def_14,type,
'A_c_vec_c_vec_a_b_vec_c_vec_prod$': $tType ).
tff(type_def_15,type,
'Nat_list$': $tType ).
tff(type_def_16,type,
'Nat_nat_prod_bool_fun$': $tType ).
tff(type_def_17,type,
'Nat_a_c_vec_c_vec_prod$': $tType ).
tff(type_def_18,type,
'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$': $tType ).
tff(type_def_19,type,
'Int_int_fun$': $tType ).
tff(type_def_20,type,
'Nat_nat_prod$': $tType ).
tff(type_def_21,type,
'A_b_vec_c_vec$': $tType ).
tff(type_def_22,type,
'Nat_a_iarray_iarray_bool_fun_fun$': $tType ).
tff(type_def_23,type,
'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$': $tType ).
tff(type_def_24,type,
'Nat_nat_fun$': $tType ).
tff(type_def_25,type,
'A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$': $tType ).
tff(type_def_26,type,
'Nat$': $tType ).
tff(type_def_27,type,
'Nat_int_prod_bool_fun$': $tType ).
tff(type_def_28,type,
'A_iarray_iarray_bool_fun$': $tType ).
tff(type_def_29,type,
'Nat_a_b_vec_c_vec_prod_bool_fun$': $tType ).
tff(type_def_30,type,
tlbool: $tType ).
tff(type_def_31,type,
'A_b_vec_c_vec_bool_fun$': $tType ).
tff(type_def_32,type,
'Nat_a_iarray_iarray_prod$': $tType ).
tff(type_def_33,type,
'Nat_int_prod$': $tType ).
tff(type_def_34,type,
'Int_nat_prod$': $tType ).
tff(type_def_35,type,
'Nat_a_b_vec_c_vec_bool_fun_fun$': $tType ).
tff(type_def_36,type,
'A$': $tType ).
tff(type_def_37,type,
'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$': $tType ).
tff(type_def_38,type,
'Nat_a_b_vec_c_vec_prod$': $tType ).
tff(type_def_39,type,
'Nat_a_iarray_iarray_prod_bool_fun$': $tType ).
tff(type_def_40,type,
'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$': $tType ).
tff(type_def_41,type,
'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$': $tType ).
tff(type_def_42,type,
'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$': $tType ).
tff(type_def_43,type,
'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$': $tType ).
tff(type_def_44,type,
'Nat_a_iarray_prod_bool_fun$': $tType ).
tff(type_def_45,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_46,type,
'A_iarray$': $tType ).
tff(type_def_47,type,
'Int_nat_prod_bool_fun$': $tType ).
tff(type_def_48,type,
'Nat_a_iarray_prod$': $tType ).
tff(type_def_49,type,
'Nat_bool_fun$': $tType ).
tff(type_def_50,type,
'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$': $tType ).
tff(type_def_51,type,
'Nat_int_fun$': $tType ).
tff(type_def_52,type,
'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$': $tType ).
tff(func_def_0,type,
'snd$g': 'Int_nat_prod$' > 'Nat$' ).
tff(func_def_1,type,
'foldl$a': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'Nat_list$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_2,type,
'b$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_3,type,
'fun_app$l': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_bool_fun_fun$' * 'A_c_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod_bool_fun$' ).
tff(func_def_4,type,
'gauss_Jordan_in_ij_iarrays_PA$': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'Nat$' * 'Nat$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_5,type,
'pair$b': ( 'Nat$' * 'A_iarray_iarray$' ) > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_6,type,
'fst$f': 'Nat_int_prod$' > 'Nat$' ).
tff(func_def_7,type,
'ncols$a': 'A_c_vec_c_vec$' > 'Nat$' ).
tff(func_def_8,type,
'fun_app$z': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_9,type,
'plus$h': ( 'Int_nat_prod$' * 'Int_nat_prod$' ) > 'Int_nat_prod$' ).
tff(func_def_10,type,
'pair$d': ( 'A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_11,type,
'mat$': 'A$' > 'A_c_vec_c_vec$' ).
tff(func_def_12,type,
'gauss_Jordan_column_k_PA$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' ).
tff(func_def_13,type,
'gauss_Jordan_upt_k_PA$': ( 'A_b_vec_c_vec$' * 'Nat$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).
tff(func_def_14,type,
'fun_app$q': ( 'Nat_a_b_vec_c_vec_bool_fun_fun$' * 'Nat$' ) > 'A_b_vec_c_vec_bool_fun$' ).
tff(func_def_15,type,
'a$a': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_16,type,
'fst$l': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_17,type,
'pair$e': ( 'Nat$' * 'Nat$' ) > 'Nat_nat_prod$' ).
tff(func_def_18,type,
'snd$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_19,type,
'pair$h': ( $int * $int ) > 'Int_int_prod$' ).
tff(func_def_20,type,
'fun_app$o': ( 'A_iarray_iarray_a_iarray_iarray_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_21,type,
'pair$a': ( 'Nat$' * 'A_b_vec_c_vec$' ) > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_22,type,
'snd$h': 'Int_int_prod$' > $int ).
tff(func_def_23,type,
'fst$e': 'Nat_nat_prod$' > 'Nat$' ).
tff(func_def_24,type,
'fst$k': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_25,type,
'fun_app$': ( 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_26,type,
'foldl$': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_list$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_27,type,
'nrows$': 'A_b_vec_c_vec$' > 'Nat$' ).
tff(func_def_28,type,
'pair$f': ( 'Nat$' * $int ) > 'Nat_int_prod$' ).
tff(func_def_29,type,
'snd$e': 'Nat_nat_prod$' > 'Nat$' ).
tff(func_def_30,type,
'zero$a': 'A_c_vec_c_vec$' ).
tff(func_def_31,type,
'fun_app$r': ( 'Nat_a_iarray_iarray_bool_fun_fun$' * 'Nat$' ) > 'A_iarray_iarray_bool_fun$' ).
tff(func_def_32,type,
'fun_app$m': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_bool_fun_fun$' * 'A_iarray_iarray$' ) > 'Nat_a_iarray_iarray_prod_bool_fun$' ).
tff(func_def_33,type,
'pair$l': ( 'A_c_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' ).
tff(func_def_34,type,
'fun_app$t': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_35,type,
'snd$a': 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_36,type,
'pair$j': ( 'A_c_vec_c_vec$' * 'Nat_a_c_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_37,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_38,type,
'one$': 'A$' ).
tff(func_def_39,type,
'upt$': ( 'Nat$' * 'Nat$' ) > 'Nat_list$' ).
tff(func_def_40,type,
'nrows$a': 'A_c_vec_c_vec$' > 'Nat$' ).
tff(func_def_41,type,
'fst$c': 'A_iarray_iarray_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_42,type,
'fst$a': 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_43,type,
'snd$b': 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_44,type,
'fst$g': 'Int_nat_prod$' > $int ).
tff(func_def_45,type,
'zero$b': 'Int_nat_prod$' ).
tff(func_def_46,type,
'less$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_47,type,
'nrows_iarray$': 'A_iarray_iarray$' > 'Nat$' ).
tff(func_def_48,type,
'pair$i': ( 'Nat$' * 'A_iarray$' ) > 'Nat_a_iarray_prod$' ).
tff(func_def_49,type,
tltrue: tlbool ).
tff(func_def_50,type,
'gauss_Jordan_column_k_PA$a': ( 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' * 'Nat$' ) > 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' ).
tff(func_def_51,type,
'plus$f': ( 'Nat_a_iarray_iarray_prod$' * 'Nat_a_iarray_iarray_prod$' ) > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_52,type,
'plus$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_53,type,
'fun_app$a': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' ).
tff(func_def_54,type,
'snd$f': 'Nat_int_prod$' > $int ).
tff(func_def_55,type,
'pair$c': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_56,type,
'plus$k': ( 'Nat_nat_prod$' * 'Nat_nat_prod$' ) > 'Nat_nat_prod$' ).
tff(func_def_57,type,
'gauss_Jordan_column_k_iarrays_PA$': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' ).
tff(func_def_58,type,
'one$a': 'Nat$' ).
tff(func_def_59,type,
'fst$i': 'Nat_a_iarray_prod$' > 'Nat$' ).
tff(func_def_60,type,
'plus$j': ( 'Nat_int_prod$' * 'Nat_int_prod$' ) > 'Nat_int_prod$' ).
tff(func_def_61,type,
'zero$i': 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_62,type,
'fun_app$v': ( 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' * 'Nat$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_63,type,
'fst$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_64,type,
'fun_app$y': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_65,type,
'fst$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_66,type,
'ncols$': 'A_b_vec_c_vec$' > 'Nat$' ).
tff(func_def_67,type,
'fst$b': 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_68,type,
'fun_app$u': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_69,type,
'vector_all_zero_from_index$': 'Nat_a_iarray_prod_bool_fun$' ).
tff(func_def_70,type,
'plus$l': ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_71,type,
'plus$c': ( 'Nat_a_b_vec_c_vec_prod$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_72,type,
'matrix_to_iarray$a': 'A_b_vec_c_vec$' > 'A_iarray_iarray$' ).
tff(func_def_73,type,
'plus$d': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ).
tff(func_def_74,type,
'zero$h': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_75,type,
'pair$k': ( 'Nat$' * 'A_c_vec_c_vec$' ) > 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_76,type,
'column_iarray$': ( 'Nat$' * 'A_iarray_iarray$' ) > 'A_iarray$' ).
tff(func_def_77,type,
'fun_app$w': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'Nat_a_iarray_iarray_nat_a_iarray_iarray_prod_prod_fun$' ).
tff(func_def_78,type,
'zero$j': 'A_b_vec_c_vec$' ).
tff(func_def_79,type,
'divides_aux$': 'Int_int_prod_bool_fun$' ).
tff(func_def_80,type,
'less_eq$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_81,type,
'snd$i': 'Nat_a_iarray_prod$' > 'A_iarray$' ).
tff(func_def_82,type,
'plus$e': ( 'A_iarray_iarray$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_83,type,
'zero$c': 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_84,type,
'zero$': 'A$' ).
tff(func_def_85,type,
'matrix_to_iarray$': 'A_c_vec_c_vec$' > 'A_iarray_iarray$' ).
tff(func_def_86,type,
'plus$i': ( 'A_b_vec_c_vec$' * 'A_b_vec_c_vec$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_87,type,
'plus$g': ( 'Int_int_prod$' * 'Int_int_prod$' ) > 'Int_int_prod$' ).
tff(func_def_88,type,
tlfalse: tlbool ).
tff(func_def_89,type,
'zero$g': 'Int_int_prod$' ).
tff(func_def_90,type,
'nat$': $int > 'Nat$' ).
tff(func_def_91,type,
'fst$h': 'Int_int_prod$' > $int ).
tff(func_def_92,type,
'zero$e': 'Nat_nat_prod$' ).
tff(func_def_93,type,
'zero$f': 'Nat_int_prod$' ).
tff(func_def_94,type,
'snd$l': 'A_c_vec_c_vec_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_95,type,
'pair$': ( 'A_c_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_96,type,
'gauss_Jordan_upt_k_iarrays_PA$': ( 'A_iarray_iarray$' * 'Nat$' ) > 'A_iarray_iarray_a_iarray_iarray_prod$' ).
tff(func_def_97,type,
'suc$': 'Nat_nat_fun$' ).
tff(func_def_98,type,
'plus$a': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_99,type,
'pair$g': ( $int * 'Nat$' ) > 'Int_nat_prod$' ).
tff(func_def_100,type,
'fun_app$b': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_101,type,
'fst$j': 'Nat_a_c_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_102,type,
'zero$d': 'Nat$' ).
tff(func_def_103,type,
'a$': 'A_b_vec_c_vec$' ).
tff(func_def_104,type,
'ka$': 'Nat$' ).
tff(func_def_105,type,
'snd$j': 'Nat_a_c_vec_c_vec_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_106,type,
'plus$b': ( 'A_c_vec_c_vec$' * 'A_c_vec_c_vec$' ) > 'A_c_vec_c_vec$' ).
tff(func_def_107,type,
'mat_iarray$': ( 'A$' * 'Nat$' ) > 'A_iarray_iarray$' ).
tff(func_def_108,type,
'k$': 'Nat$' ).
tff(func_def_109,type,
'snd$d': 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_110,type,
'snd$': 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_111,type,
'snd$k': 'A_c_vec_c_vec_nat_a_c_vec_c_vec_prod_prod$' > 'Nat_a_c_vec_c_vec_prod$' ).
tff(func_def_115,type,
sK0: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_116,type,
sK1: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_117,type,
sK2: ( 'A_iarray_iarray$' * 'A_iarray_iarray_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).
tff(func_def_118,type,
sK3: 'Int_int_fun$' > $int ).
tff(func_def_119,type,
sK4: 'Int_int_fun$' > $int ).
tff(func_def_120,type,
sK5: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_121,type,
sK6: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_122,type,
sK7: 'Nat_nat_prod_bool_fun$' > 'Nat$' ).
tff(func_def_123,type,
sK8: 'Nat_nat_prod_bool_fun$' > 'Nat$' ).
tff(func_def_124,type,
sK9: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_125,type,
sK10: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_126,type,
sK11: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_127,type,
sK12: 'Nat$' > 'Nat$' ).
tff(func_def_128,type,
sK13: ( 'Nat_bool_fun$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_129,type,
sK14: ( 'A_iarray_iarray_a_iarray_iarray_prod$' * 'A_iarray_iarray$' ) > 'A_iarray_iarray$' ).
tff(func_def_130,type,
sK15: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_131,type,
sK16: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_132,type,
sK17: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_133,type,
sK18: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_134,type,
sK19: ( 'Nat_bool_fun$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_135,type,
sK20: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_136,type,
sK21: ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'A_c_vec_c_vec$' ).
tff(func_def_137,type,
sK22: ( 'A_b_vec_c_vec$' * 'Nat_a_b_vec_c_vec_prod$' ) > 'Nat$' ).
tff(func_def_138,type,
sK23: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_139,type,
sK24: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$' ).
tff(func_def_140,type,
sK25: ( 'A_c_vec_c_vec$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_141,type,
sK26: 'Int_int_prod_bool_fun$' > $int ).
tff(func_def_142,type,
sK27: 'Int_int_prod_bool_fun$' > $int ).
tff(func_def_143,type,
sK28: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_144,type,
sK29: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_145,type,
sK30: 'Nat_int_prod_bool_fun$' > $int ).
tff(func_def_146,type,
sK31: 'Nat_int_prod_bool_fun$' > 'Nat$' ).
tff(func_def_147,type,
sK32: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_148,type,
sK33: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_149,type,
sK34: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_150,type,
sK35: 'Int_int_fun$' > $int ).
tff(func_def_151,type,
sK36: 'Int_int_fun$' > $int ).
tff(func_def_152,type,
sK37: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_153,type,
sK38: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_154,type,
sK39: ( 'A_iarray_iarray$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_155,type,
sK40: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat$' ).
tff(func_def_156,type,
sK41: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_157,type,
sK42: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_158,type,
sK43: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_159,type,
sK44: 'Nat_a_iarray_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_160,type,
sK45: 'Nat$' > 'Nat$' ).
tff(func_def_161,type,
sK46: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_162,type,
sK47: 'Nat_a_b_vec_c_vec_prod_bool_fun$' > 'Nat$' ).
tff(func_def_163,type,
sK48: 'Int_int_fun$' > $int ).
tff(func_def_164,type,
sK49: 'Int_int_fun$' > $int ).
tff(func_def_165,type,
sK50: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_166,type,
sK51: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_167,type,
sK52: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' > 'A_c_vec_c_vec$' ).
tff(func_def_168,type,
sK53: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_169,type,
sK54: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_170,type,
sK55: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_171,type,
sK56: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat_a_iarray_iarray_prod$' ).
tff(func_def_172,type,
sK57: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_173,type,
sK58: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_174,type,
sK59: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_175,type,
sK60: ( 'Nat_a_b_vec_c_vec_prod$' * 'Nat$' ) > 'A_b_vec_c_vec$' ).
tff(func_def_176,type,
sK61: 'Int_int_fun$' > $int ).
tff(func_def_177,type,
sK62: 'Int_int_fun$' > $int ).
tff(func_def_178,type,
sK63: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_179,type,
sK64: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'A_iarray_iarray$' ).
tff(func_def_180,type,
sK65: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_181,type,
sK66: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_182,type,
sK67: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_183,type,
sK68: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_184,type,
sK69: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_185,type,
sK70: $int > $int ).
tff(func_def_186,type,
sK71: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_187,type,
sK72: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_188,type,
sK73: ( 'Nat_a_iarray_iarray_prod$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > 'A_iarray_iarray$' ).
tff(func_def_189,type,
sK74: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_190,type,
sK75: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_191,type,
sK76: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_192,type,
sK77: 'Int_int_fun$' > $int ).
tff(func_def_193,type,
sK78: 'Int_int_fun$' > $int ).
tff(func_def_194,type,
sK79: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_195,type,
sK80: $int > $int ).
tff(func_def_196,type,
sK81: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_197,type,
sK82: 'Nat$' > 'Nat$' ).
tff(func_def_198,type,
sK83: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_199,type,
sK84: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_200,type,
sK85: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_201,type,
sK86: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_202,type,
sK87: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_203,type,
sK88: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_204,type,
sK89: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_205,type,
sK90: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_206,type,
sK91: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_207,type,
sK92: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_208,type,
sK93: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'Nat$' ).
tff(func_def_209,type,
sK94: 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' > 'A_iarray_iarray$' ).
tff(func_def_210,type,
sK95: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_211,type,
sK96: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_212,type,
sK97: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_213,type,
sK98: ( 'Nat$' * 'Nat_a_iarray_iarray_prod$' ) > 'A_iarray_iarray$' ).
tff(func_def_214,type,
sK99: 'Int_int_fun$' > $int ).
tff(func_def_215,type,
sK100: 'Int_int_fun$' > $int ).
tff(func_def_216,type,
sK101: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_217,type,
sK102: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_218,type,
sK103: 'Int_int_prod$' > $int ).
tff(func_def_219,type,
sK104: 'Int_int_prod$' > $int ).
tff(func_def_220,type,
sK105: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_221,type,
sK106: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_222,type,
sK107: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_223,type,
sK108: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_224,type,
sK109: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_225,type,
sK110: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_226,type,
sK111: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_227,type,
sK112: 'Int_int_fun$' > $int ).
tff(func_def_228,type,
sK113: 'Int_int_fun$' > $int ).
tff(func_def_229,type,
sK114: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_230,type,
sK115: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_231,type,
sK116: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_232,type,
sK117: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_233,type,
sK118: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_234,type,
sK119: 'Int_int_fun$' > $int ).
tff(func_def_235,type,
sK120: 'Int_int_fun$' > $int ).
tff(func_def_236,type,
sK121: 'Nat$' > 'Nat$' ).
tff(func_def_237,type,
sK122: 'Int_int_fun$' > $int ).
tff(func_def_238,type,
sK123: 'Int_int_fun$' > $int ).
tff(func_def_239,type,
sK124: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_240,type,
sK125: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_241,type,
sK126: 'Nat_a_iarray_prod_bool_fun$' > 'Nat$' ).
tff(func_def_242,type,
sK127: 'Nat_a_iarray_prod_bool_fun$' > 'A_iarray$' ).
tff(func_def_243,type,
sK128: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_244,type,
sK129: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_245,type,
sK130: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_246,type,
sK131: 'Int_int_fun$' > $int ).
tff(func_def_247,type,
sK132: 'Int_int_fun$' > $int ).
tff(func_def_248,type,
sK133: 'Nat_a_b_vec_c_vec_prod$' > 'Nat$' ).
tff(func_def_249,type,
sK134: 'Nat_a_b_vec_c_vec_prod$' > 'A_b_vec_c_vec$' ).
tff(func_def_250,type,
sK135: 'Nat_a_iarray_iarray_prod$' > 'A_iarray_iarray$' ).
tff(func_def_251,type,
sK136: 'Nat_a_iarray_iarray_prod$' > 'Nat$' ).
tff(func_def_252,type,
sK137: ( 'A_iarray_iarray$' * 'Nat_a_iarray_iarray_prod$' ) > 'Nat$' ).
tff(func_def_253,type,
sK138: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_254,type,
sK139: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_255,type,
sK140: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_256,type,
sK141: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_257,type,
sK142: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_258,type,
sK143: 'Int_int_fun$' > $int ).
tff(func_def_259,type,
sK144: 'Int_int_fun$' > $int ).
tff(func_def_260,type,
sK145: 'Int_int_fun$' > $int ).
tff(func_def_261,type,
sK146: 'Int_int_fun$' > $int ).
tff(func_def_262,type,
sK147: 'Int_nat_prod_bool_fun$' > 'Nat$' ).
tff(func_def_263,type,
sK148: 'Int_nat_prod_bool_fun$' > $int ).
tff(func_def_264,type,
sK149: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_265,type,
sK150: 'Nat$' > 'Nat$' ).
tff(func_def_266,type,
sK151: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_c_vec_c_vec$' ).
tff(func_def_267,type,
sK152: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'A_b_vec_c_vec$' ).
tff(func_def_268,type,
sK153: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' > 'Nat$' ).
tff(func_def_269,type,
sK154: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_270,type,
sK155: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_271,type,
sF156: 'A_c_vec_c_vec$' ).
tff(func_def_272,type,
sF157: 'Nat$' ).
tff(func_def_273,type,
sF158: 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_274,type,
sF159: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_275,type,
sF160: $int ).
tff(func_def_276,type,
sF161: $int ).
tff(func_def_277,type,
sF162: 'Nat$' ).
tff(func_def_278,type,
sF163: 'Nat_list$' ).
tff(func_def_279,type,
sF164: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_280,type,
sF165: 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' ).
tff(func_def_281,type,
sF166: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_282,type,
sF167: 'A_c_vec_c_vec$' ).
tff(func_def_283,type,
sF168: 'A_iarray_iarray$' ).
tff(func_def_284,type,
sF169: 'A_c_vec_c_vec$' ).
tff(func_def_285,type,
sF170: 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_286,type,
sF171: 'Nat$' ).
tff(func_def_287,type,
sF172: 'A_b_vec_c_vec$' ).
tff(func_def_288,type,
sF173: 'Nat_a_b_vec_c_vec_prod$' ).
tff(func_def_289,type,
sF174: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_290,type,
sF175: 'Nat_a_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_fun$' ).
tff(func_def_291,type,
sF176: 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ).
tff(func_def_292,type,
sF177: 'A_c_vec_c_vec$' ).
tff(func_def_293,type,
sF178: 'A_iarray_iarray$' ).
tff(pred_def_1,type,
'fun_app$n': ( 'A_iarray_iarray_bool_fun$' * 'A_iarray_iarray$' ) > $o ).
tff(pred_def_2,type,
'fun_app$f': ( 'Int_nat_prod_bool_fun$' * 'Int_nat_prod$' ) > $o ).
tff(pred_def_3,type,
'fun_app$p': ( 'A_b_vec_c_vec_bool_fun$' * 'A_b_vec_c_vec$' ) > $o ).
tff(pred_def_4,type,
'fun_app$g': ( 'Int_int_prod_bool_fun$' * 'Int_int_prod$' ) > $o ).
tff(pred_def_5,type,
'fun_app$j': ( 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod_bool_fun$' * 'A_iarray_iarray_nat_a_iarray_iarray_prod_prod$' ) > $o ).
tff(pred_def_6,type,
'fun_app$d': ( 'Nat_nat_prod_bool_fun$' * 'Nat_nat_prod$' ) > $o ).
tff(pred_def_7,type,
'fun_app$e': ( 'Nat_int_prod_bool_fun$' * 'Nat_int_prod$' ) > $o ).
tff(pred_def_8,type,
'fun_app$i': ( 'Nat_a_b_vec_c_vec_prod_bool_fun$' * 'Nat_a_b_vec_c_vec_prod$' ) > $o ).
tff(pred_def_9,type,
'fun_app$k': ( 'Nat_a_iarray_iarray_prod_bool_fun$' * 'Nat_a_iarray_iarray_prod$' ) > $o ).
tff(pred_def_10,type,
'fun_app$x': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_11,type,
'fun_app$h': ( 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod_bool_fun$' * 'A_c_vec_c_vec_nat_a_b_vec_c_vec_prod_prod$' ) > $o ).
tff(pred_def_12,type,
'fun_app$c': ( 'Nat_a_iarray_prod_bool_fun$' * 'Nat_a_iarray_prod$' ) > $o ).
tff(pred_def_13,type,
'fun_app$s': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(f1,conjecture,
'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture0) ).
tff(f2,negated_conjecture,
( ( ~ 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) ) = 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f4,axiom,
'a$a' = 'foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
tff(f5,axiom,
'a$a' = 'pair$'('fst$'('a$a'),'pair$a'('fst$a'('snd$'('a$a')),'snd$a'('snd$'('a$a')))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
tff(f803,plain,
'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
inference(flattening,[],[f2]) ).
tff(f3202,plain,
'a$a' = 'pair$'('fst$'('a$a'),'pair$a'('fst$a'('snd$'('a$a')),'snd$a'('snd$'('a$a')))),
inference(cnf_transformation,[],[f5]) ).
tff(f3283,plain,
'foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))) = 'a$a',
inference(cnf_transformation,[],[f4]) ).
tff(f3290,plain,
'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))) != 'matrix_to_iarray$'('fst$'('fun_app$'('fun_app$a'('gauss_Jordan_column_k_PA$','pair$'('fst$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),'pair$a'('fst$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))))),'snd$a'('snd$'('foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))))))),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1))))),
inference(cnf_transformation,[],[f803]) ).
tff(f3543,definition,
sF156 = 'mat$'('one$'),
introduced(definition,[new_symbols(definition,[sF156])],[function_definition]) ).
tff(f3544,plain,
'mat$'('one$') = sF156,
inference(reorient_equations,[],[f3543]) ).
tff(f3545,definition,
sF157 = 'nat$'(0),
introduced(definition,[new_symbols(definition,[sF157])],[function_definition]) ).
tff(f3546,plain,
'nat$'(0) = sF157,
inference(reorient_equations,[],[f3545]) ).
tff(f3547,definition,
sF158 = 'pair$a'(sF157,'a$'),
introduced(definition,[new_symbols(definition,[sF158])],[function_definition]) ).
tff(f3548,plain,
'pair$a'(sF157,'a$') = sF158,
inference(reorient_equations,[],[f3547]) ).
tff(f3549,definition,
sF159 = 'pair$'(sF156,sF158),
introduced(definition,[new_symbols(definition,[sF159])],[function_definition]) ).
tff(f3550,plain,
'pair$'(sF156,sF158) = sF159,
inference(reorient_equations,[],[f3549]) ).
tff(f3551,definition,
sF160 = 'fun_app$b'('of_nat$','ka$'),
introduced(definition,[new_symbols(definition,[sF160])],[function_definition]) ).
tff(f3552,plain,
'fun_app$b'('of_nat$','ka$') = sF160,
inference(reorient_equations,[],[f3551]) ).
tff(f3553,definition,
sF161 = $sum(sF160,1),
introduced(definition,[new_symbols(definition,[sF161])],[function_definition]) ).
tff(f3554,definition,
sF162 = 'nat$'(sF161),
introduced(definition,[new_symbols(definition,[sF162])],[function_definition]) ).
tff(f3555,definition,
sF163 = 'upt$'(sF157,sF162),
introduced(definition,[new_symbols(definition,[sF163])],[function_definition]) ).
tff(f3556,plain,
'upt$'(sF157,sF162) = sF163,
inference(reorient_equations,[],[f3555]) ).
tff(f3557,definition,
sF164 = 'foldl$'('gauss_Jordan_column_k_PA$',sF159,sF163),
introduced(definition,[new_symbols(definition,[sF164])],[function_definition]) ).
tff(f3558,definition,
sF165 = 'fun_app$a'('gauss_Jordan_column_k_PA$',sF164),
introduced(definition,[new_symbols(definition,[sF165])],[function_definition]) ).
tff(f3559,definition,
sF166 = 'fun_app$'(sF165,sF162),
introduced(definition,[new_symbols(definition,[sF166])],[function_definition]) ).
tff(f3560,definition,
sF167 = 'fst$'(sF166),
introduced(definition,[new_symbols(definition,[sF167])],[function_definition]) ).
tff(f3561,definition,
sF168 = 'matrix_to_iarray$'(sF167),
introduced(definition,[new_symbols(definition,[sF168])],[function_definition]) ).
tff(f3562,plain,
'matrix_to_iarray$'(sF167) = sF168,
inference(reorient_equations,[],[f3561]) ).
tff(f3563,definition,
sF169 = 'fst$'(sF164),
introduced(definition,[new_symbols(definition,[sF169])],[function_definition]) ).
tff(f3564,definition,
sF170 = 'snd$'(sF164),
introduced(definition,[new_symbols(definition,[sF170])],[function_definition]) ).
tff(f3565,definition,
sF171 = 'fst$a'(sF170),
introduced(definition,[new_symbols(definition,[sF171])],[function_definition]) ).
tff(f3566,definition,
sF172 = 'snd$a'(sF170),
introduced(definition,[new_symbols(definition,[sF172])],[function_definition]) ).
tff(f3567,plain,
'snd$a'(sF170) = sF172,
inference(reorient_equations,[],[f3566]) ).
tff(f3568,definition,
sF173 = 'pair$a'(sF171,sF172),
introduced(definition,[new_symbols(definition,[sF173])],[function_definition]) ).
tff(f3569,plain,
'pair$a'(sF171,sF172) = sF173,
inference(reorient_equations,[],[f3568]) ).
tff(f3570,definition,
sF174 = 'pair$'(sF169,sF173),
introduced(definition,[new_symbols(definition,[sF174])],[function_definition]) ).
tff(f3571,plain,
'pair$'(sF169,sF173) = sF174,
inference(reorient_equations,[],[f3570]) ).
tff(f3572,definition,
sF175 = 'fun_app$a'('gauss_Jordan_column_k_PA$',sF174),
introduced(definition,[new_symbols(definition,[sF175])],[function_definition]) ).
tff(f3573,plain,
'fun_app$a'('gauss_Jordan_column_k_PA$',sF174) = sF175,
inference(reorient_equations,[],[f3572]) ).
tff(f3574,definition,
sF176 = 'fun_app$'(sF175,sF162),
introduced(definition,[new_symbols(definition,[sF176])],[function_definition]) ).
tff(f3575,plain,
'fun_app$'(sF175,sF162) = sF176,
inference(reorient_equations,[],[f3574]) ).
tff(f3576,definition,
sF177 = 'fst$'(sF176),
introduced(definition,[new_symbols(definition,[sF177])],[function_definition]) ).
tff(f3577,definition,
sF178 = 'matrix_to_iarray$'(sF177),
introduced(definition,[new_symbols(definition,[sF178])],[function_definition]) ).
tff(f3578,plain,
sF178 != sF168,
inference(definition_folding,[],[f3290,f3577,f3576,f3575,f3554,f3553,f3552,f3573,f3571,f3569,f3567,f3564,f3557,f3556,f3554,f3553,f3552,f3546,f3550,f3548,f3546,f3544,f3565,f3564,f3557,f3556,f3554,f3553,f3552,f3546,f3550,f3548,f3546,f3544,f3563,f3557,f3556,f3554,f3553,f3552,f3546,f3550,f3548,f3546,f3544,f3562,f3560,f3559,f3554,f3553,f3552,f3558,f3557,f3556,f3554,f3553,f3552,f3546,f3550,f3548,f3546,f3544]) ).
tff(f3673,definition,
( spl179_2
<=> ( 'pair$'(sF169,sF173) = sF174 ) ),
introduced(definition,[new_symbols(definition,[spl179_2])],[avatar_definition]) ).
tff(f3676,plain,
spl179_2,
inference(avatar_split_clause,[],[f3571,f3673]) ).
tff(f3683,definition,
( spl179_4
<=> ( sF167 = 'fst$'(sF166) ) ),
introduced(definition,[new_symbols(definition,[spl179_4])],[avatar_definition]) ).
tff(f3686,plain,
spl179_4,
inference(avatar_split_clause,[],[f3560,f3683]) ).
tff(f3688,definition,
( spl179_5
<=> ( 'nat$'(0) = sF157 ) ),
introduced(definition,[new_symbols(definition,[spl179_5])],[avatar_definition]) ).
tff(f3691,plain,
spl179_5,
inference(avatar_split_clause,[],[f3546,f3688]) ).
tff(f3698,definition,
( spl179_7
<=> ( sF165 = 'fun_app$a'('gauss_Jordan_column_k_PA$',sF164) ) ),
introduced(definition,[new_symbols(definition,[spl179_7])],[avatar_definition]) ).
tff(f3701,plain,
spl179_7,
inference(avatar_split_clause,[],[f3558,f3698]) ).
tff(f3718,definition,
( spl179_11
<=> ( 'snd$a'(sF170) = sF172 ) ),
introduced(definition,[new_symbols(definition,[spl179_11])],[avatar_definition]) ).
tff(f3721,plain,
spl179_11,
inference(avatar_split_clause,[],[f3567,f3718]) ).
tff(f3741,definition,
( spl179_16
<=> ( 'pair$a'(sF171,sF172) = sF173 ) ),
introduced(definition,[new_symbols(definition,[spl179_16])],[avatar_definition]) ).
tff(f3744,plain,
spl179_16,
inference(avatar_split_clause,[],[f3569,f3741]) ).
tff(f3746,definition,
( spl179_17
<=> ( 'fun_app$a'('gauss_Jordan_column_k_PA$',sF174) = sF175 ) ),
introduced(definition,[new_symbols(definition,[spl179_17])],[avatar_definition]) ).
tff(f3749,plain,
spl179_17,
inference(avatar_split_clause,[],[f3573,f3746]) ).
tff(f3761,definition,
( spl179_20
<=> ( 'a$a' = 'pair$'('fst$'('a$a'),'pair$a'('fst$a'('snd$'('a$a')),'snd$a'('snd$'('a$a')))) ) ),
introduced(definition,[new_symbols(definition,[spl179_20])],[avatar_definition]) ).
tff(f3764,plain,
spl179_20,
inference(avatar_split_clause,[],[f3202,f3761]) ).
tff(f3778,definition,
( spl179_24
<=> ( sF166 = 'fun_app$'(sF165,sF162) ) ),
introduced(definition,[new_symbols(definition,[spl179_24])],[avatar_definition]) ).
tff(f3781,plain,
spl179_24,
inference(avatar_split_clause,[],[f3559,f3778]) ).
tff(f3783,definition,
( spl179_25
<=> ( 'mat$'('one$') = sF156 ) ),
introduced(definition,[new_symbols(definition,[spl179_25])],[avatar_definition]) ).
tff(f3786,plain,
spl179_25,
inference(avatar_split_clause,[],[f3544,f3783]) ).
tff(f3835,definition,
( spl179_35
<=> ( 'upt$'(sF157,sF162) = sF163 ) ),
introduced(definition,[new_symbols(definition,[spl179_35])],[avatar_definition]) ).
tff(f3838,plain,
spl179_35,
inference(avatar_split_clause,[],[f3556,f3835]) ).
tff(f3840,definition,
( spl179_36
<=> ( sF169 = 'fst$'(sF164) ) ),
introduced(definition,[new_symbols(definition,[spl179_36])],[avatar_definition]) ).
tff(f3843,plain,
spl179_36,
inference(avatar_split_clause,[],[f3563,f3840]) ).
tff(f3845,definition,
( spl179_37
<=> ( sF164 = 'foldl$'('gauss_Jordan_column_k_PA$',sF159,sF163) ) ),
introduced(definition,[new_symbols(definition,[spl179_37])],[avatar_definition]) ).
tff(f3848,plain,
spl179_37,
inference(avatar_split_clause,[],[f3557,f3845]) ).
tff(f3868,definition,
( spl179_42
<=> ( sF177 = 'fst$'(sF176) ) ),
introduced(definition,[new_symbols(definition,[spl179_42])],[avatar_definition]) ).
tff(f3871,plain,
spl179_42,
inference(avatar_split_clause,[],[f3576,f3868]) ).
tff(f3901,definition,
( spl179_48
<=> ( 'fun_app$b'('of_nat$','ka$') = sF160 ) ),
introduced(definition,[new_symbols(definition,[spl179_48])],[avatar_definition]) ).
tff(f3904,plain,
spl179_48,
inference(avatar_split_clause,[],[f3552,f3901]) ).
tff(f3906,definition,
( spl179_49
<=> ( 'fun_app$'(sF175,sF162) = sF176 ) ),
introduced(definition,[new_symbols(definition,[spl179_49])],[avatar_definition]) ).
tff(f3909,plain,
spl179_49,
inference(avatar_split_clause,[],[f3575,f3906]) ).
tff(f3922,definition,
( spl179_52
<=> ( 'foldl$'('gauss_Jordan_column_k_PA$','pair$'('mat$'('one$'),'pair$a'('nat$'(0),'a$')),'upt$'('nat$'(0),'nat$'($sum('fun_app$b'('of_nat$','ka$'),1)))) = 'a$a' ) ),
introduced(definition,[new_symbols(definition,[spl179_52])],[avatar_definition]) ).
tff(f3925,plain,
spl179_52,
inference(avatar_split_clause,[],[f3283,f3922]) ).
tff(f3927,definition,
( spl179_53
<=> ( 'pair$'(sF156,sF158) = sF159 ) ),
introduced(definition,[new_symbols(definition,[spl179_53])],[avatar_definition]) ).
tff(f3930,plain,
spl179_53,
inference(avatar_split_clause,[],[f3550,f3927]) ).
tff(f3932,definition,
( spl179_54
<=> ( sF161 = $sum(sF160,1) ) ),
introduced(definition,[new_symbols(definition,[spl179_54])],[avatar_definition]) ).
tff(f3935,plain,
spl179_54,
inference(avatar_split_clause,[],[f3553,f3932]) ).
tff(f3941,definition,
( spl179_56
<=> ( sF171 = 'fst$a'(sF170) ) ),
introduced(definition,[new_symbols(definition,[spl179_56])],[avatar_definition]) ).
tff(f3944,plain,
spl179_56,
inference(avatar_split_clause,[],[f3565,f3941]) ).
tff(f3946,definition,
( spl179_57
<=> ( sF162 = 'nat$'(sF161) ) ),
introduced(definition,[new_symbols(definition,[spl179_57])],[avatar_definition]) ).
tff(f3949,plain,
spl179_57,
inference(avatar_split_clause,[],[f3554,f3946]) ).
tff(f3969,definition,
( spl179_61
<=> ( sF178 = sF168 ) ),
introduced(definition,[new_symbols(definition,[spl179_61])],[avatar_definition]) ).
tff(f3972,plain,
~ spl179_61,
inference(avatar_split_clause,[],[f3578,f3969]) ).
tff(f3974,definition,
( spl179_62
<=> ( 'pair$a'(sF157,'a$') = sF158 ) ),
introduced(definition,[new_symbols(definition,[spl179_62])],[avatar_definition]) ).
tff(f3977,plain,
spl179_62,
inference(avatar_split_clause,[],[f3548,f3974]) ).
tff(f3994,definition,
( spl179_66
<=> ( sF178 = 'matrix_to_iarray$'(sF177) ) ),
introduced(definition,[new_symbols(definition,[spl179_66])],[avatar_definition]) ).
tff(f3997,plain,
spl179_66,
inference(avatar_split_clause,[],[f3577,f3994]) ).
tff(f3999,definition,
( spl179_67
<=> ( sF170 = 'snd$'(sF164) ) ),
introduced(definition,[new_symbols(definition,[spl179_67])],[avatar_definition]) ).
tff(f4002,plain,
spl179_67,
inference(avatar_split_clause,[],[f3564,f3999]) ).
tff(f4004,definition,
( spl179_68
<=> ( 'matrix_to_iarray$'(sF167) = sF168 ) ),
introduced(definition,[new_symbols(definition,[spl179_68])],[avatar_definition]) ).
tff(f4007,plain,
spl179_68,
inference(avatar_split_clause,[],[f3562,f4004]) ).
tff(f4022,plain,
$false,
inference(avatar_smt_refutation,[],[f4007,f4002,f3997,f3977,f3972,f3949,f3944,f3935,f3930,f3925,f3909,f3904,f3871,f3848,f3843,f3838,f3786,f3781,f3764,f3749,f3744,f3721,f3701,f3691,f3686,f3676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP339_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 12:50:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.43 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
% 3.40/1.16 % (2521021)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.40/1.16 % (2521031)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=611830156:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.40/1.16 % (2521026)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2363485571:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.40/1.16 % (2521030)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=645053394:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.40/1.16 % (2521028)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=809428022:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.40/1.16 % (2521029)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2022947480:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.40/1.16 % (2521027)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4120187296:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.40/1.16 % (2521032)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=38155295:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.40/1.16 % (2521030)Instruction limit reached!
% 3.40/1.16 % (2521030)------------------------------
% 3.40/1.16 % (2521030)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521030)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521030)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521030)Termination reason: Instruction limit
% 3.40/1.16 % (2521030)Termination phase: Property scanning
% 3.40/1.16 % (2521030)Time elapsed: 0.003 s
% 3.40/1.16 % (2521030)Peak memory usage: 85 MB
% 3.40/1.16 % (2521030)Instructions burned: 5 (million)
% 3.40/1.16 % (2521029)Instruction limit reached!
% 3.40/1.16 % (2521029)------------------------------
% 3.40/1.16 % (2521029)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521029)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521029)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521029)Termination reason: Instruction limit
% 3.40/1.16 % (2521029)Termination phase: Property scanning
% 3.40/1.16 % (2521029)Time elapsed: 0.004 s
% 3.40/1.16 % (2521029)Peak memory usage: 85 MB
% 3.40/1.16 % (2521029)Instructions burned: 8 (million)
% 3.40/1.16 % (2521026)Instruction limit reached!
% 3.40/1.16 % (2521026)------------------------------
% 3.40/1.16 % (2521026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521026)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521026)Termination reason: Instruction limit
% 3.40/1.16 % (2521026)Termination phase: Property scanning
% 3.40/1.16 % (2521026)Time elapsed: 0.006 s
% 3.40/1.16 % (2521026)Peak memory usage: 85 MB
% 3.40/1.16 % (2521026)Instructions burned: 12 (million)
% 3.40/1.16 % (2521032)Instruction limit reached!
% 3.40/1.16 % (2521032)------------------------------
% 3.40/1.16 % (2521032)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521032)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521032)Termination reason: Instruction limit
% 3.40/1.16 % (2521032)Termination phase: Preprocessing 3
% 3.40/1.16 % (2521032)Time elapsed: 0.019 s
% 3.40/1.16 % (2521032)Peak memory usage: 87 MB
% 3.40/1.16 % (2521032)Instructions burned: 33 (million)
% 3.40/1.16 % (2521031)Instruction limit reached!
% 3.40/1.16 % (2521031)------------------------------
% 3.40/1.16 % (2521031)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521031)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521031)Termination reason: Instruction limit
% 3.40/1.16 % (2521031)Termination phase: Property scanning
% 3.40/1.16 % (2521031)Time elapsed: 0.025 s
% 3.40/1.16 % (2521031)Peak memory usage: 88 MB
% 3.40/1.16 % (2521031)Instructions burned: 47 (million)
% 3.40/1.16 % (2521027)First to succeed.
% 3.40/1.16 % (2521027)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2521021"
% 3.40/1.16 % (2521041)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=2216452725:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.40/1.16 % (2521041)Instruction limit reached!
% 3.40/1.16 % (2521041)------------------------------
% 3.40/1.16 % (2521041)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521041)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521041)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521041)Termination reason: Instruction limit
% 3.40/1.16 % (2521041)Termination phase: Preprocessing 3
% 3.40/1.16 % (2521041)Time elapsed: 0.009 s
% 3.40/1.16 % (2521041)Peak memory usage: 88 MB
% 3.40/1.16 % (2521041)Instructions burned: 29 (million)
% 3.40/1.16 % (2521028)Instruction limit reached!
% 3.40/1.16 % (2521028)------------------------------
% 3.40/1.16 % (2521028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521028)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521028)Termination reason: Instruction limit
% 3.40/1.16 % (2521028)Termination phase: Saturation
% 3.40/1.16 % (2521028)Time elapsed: 0.130 s
% 3.40/1.16 % (2521028)Peak memory usage: 118 MB
% 3.40/1.16 % (2521028)Instructions burned: 201 (million)
% 3.40/1.16 % (2521040)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3151989293:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.40/1.16 % (2521042)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=992664079:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.40/1.16 % (2521040)Instruction limit reached!
% 3.40/1.16 % (2521040)------------------------------
% 3.40/1.16 % (2521040)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521040)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521040)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521040)Termination reason: Instruction limit
% 3.40/1.16 % (2521040)Termination phase: SInE selection
% 3.40/1.16 % (2521040)Time elapsed: 0.008 s
% 3.40/1.16 % (2521040)Peak memory usage: 85 MB
% 3.40/1.16 % (2521040)Instructions burned: 15 (million)
% 3.40/1.16 % (2521042)Instruction limit reached!
% 3.40/1.16 % (2521042)------------------------------
% 3.40/1.16 % (2521042)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521042)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521042)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521042)Termination reason: Instruction limit
% 3.40/1.16 % (2521042)Termination phase: Preprocessing 2
% 3.40/1.16 % (2521042)Time elapsed: 0.010 s
% 3.40/1.16 % (2521042)Peak memory usage: 86 MB
% 3.40/1.16 % (2521042)Instructions burned: 16 (million)
% 3.40/1.16 % (2521043)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1206268829:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.40/1.16 % (2521044)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=1667938658:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.40/1.16 % (2521043)Instruction limit reached!
% 3.40/1.16 % (2521043)------------------------------
% 3.40/1.16 % (2521043)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521043)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521043)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521043)Termination reason: Instruction limit
% 3.40/1.16 % (2521043)Termination phase: Preprocessing 3
% 3.40/1.16 % (2521043)Time elapsed: 0.014 s
% 3.40/1.16 % (2521043)Peak memory usage: 87 MB
% 3.40/1.16 % (2521043)Instructions burned: 26 (million)
% 3.40/1.16 % (2521044)Instruction limit reached!
% 3.40/1.16 % (2521044)------------------------------
% 3.40/1.16 % (2521044)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521044)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521044)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521044)Termination reason: Instruction limit
% 3.40/1.16 % (2521044)Termination phase: Preprocessing 3
% 3.40/1.16 % (2521044)Time elapsed: 0.020 s
% 3.40/1.16 % (2521044)Peak memory usage: 87 MB
% 3.40/1.16 % (2521044)Instructions burned: 27 (million)
% 3.40/1.16 % (2521046)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1816416885:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 3.40/1.16 % (2521046)Instruction limit reached!
% 3.40/1.16 % (2521046)------------------------------
% 3.40/1.16 % (2521046)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521046)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521046)Termination reason: Instruction limit
% 3.40/1.16 % (2521046)Termination phase: Saturation
% 3.40/1.16 % (2521046)Time elapsed: 0.024 s
% 3.40/1.16 % (2521046)Peak memory usage: 90 MB
% 3.40/1.16 % (2521046)Instructions burned: 88 (million)
% 3.40/1.16 % (2521047)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=1236059127:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 3.40/1.16 % (2521047)Instruction limit reached!
% 3.40/1.16 % (2521047)------------------------------
% 3.40/1.16 % (2521047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521047)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521047)Termination reason: Instruction limit
% 3.40/1.16 % (2521047)Termination phase: shuffling
% 3.40/1.16 % (2521047)Time elapsed: 0.002 s
% 3.40/1.16 % (2521047)Peak memory usage: 85 MB
% 3.40/1.16 % (2521047)Instructions burned: 2 (million)
% 3.40/1.16 % (2521051)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=1082623789:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 3.40/1.16 % (2521050)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=960414745:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 3.40/1.16 % (2521051)Instruction limit reached!
% 3.40/1.16 % (2521051)------------------------------
% 3.40/1.16 % (2521051)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.16 % (2521051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.16 % (2521051)CaDiCaL version: 2.1.3
% 3.40/1.16 % (2521051)Termination reason: Instruction limit
% 3.40/1.16 % (2521051)Termination phase: Property scanning
% 3.40/1.16 % (2521051)Time elapsed: 0.003 s
% 3.40/1.16 % (2521051)Peak memory usage: 85 MB
% 3.40/1.16 % (2521051)Instructions burned: 5 (million)
% 3.40/1.16 % (2521027)Refutation found. Thanks to Tanya!
% 3.40/1.16 % SZS status Theorem for theBenchmark
% 3.40/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.36 % (2521027)------------------------------
% 4.03/1.36 % (2521027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.36 % (2521027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.36 % (2521027)CaDiCaL version: 2.1.3
% 4.03/1.36 % (2521027)Termination reason: Refutation
% 4.03/1.36 % (2521027)Time elapsed: 0.084 s
% 4.03/1.36 % (2521027)Peak memory usage: 118 MB
% 4.03/1.36 % (2521027)Instructions burned: 101 (million)
% 4.03/1.36 % (2521027)------------------------------
% 4.03/1.36 % (2521027)------------------------------
% 4.03/1.36 % (2521021)Success in time 0.527 s
% 4.03/1.36 % Vampire exiting
%------------------------------------------------------------------------------