%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP359_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 11:39:26 AM UTC 2026
% Result : Theorem 0.88s 0.67s
% Output : Refutation 0.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 140 ( 16 unt; 0 typ; 18 def)
% Number of atoms : 344 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 357 ( 153 ~; 151 |; 8 &)
% ( 31 <=>; 13 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 154 ( 42 atm; 38 fun; 74 num; 0 var)
% Number of types : 43 ( 41 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 45 ( 43 usr; 19 prp; 0-3 aty)
% Number of functors : 279 ( 275 usr; 31 con; 0-3 aty)
% Number of variables : 103 ( 0 sgn 82 !; 21 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_ltln_set_num_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_8,type,
'Num_num_fun$': $tType ).
tff(type_def_9,type,
'A_ltln_set_int_fun$': $tType ).
tff(type_def_10,type,
'Int_int_fun$': $tType ).
tff(type_def_11,type,
'A_set_list_a_set_list_list_fun$': $tType ).
tff(type_def_12,type,
'Nat_a_ltln_set_fun$': $tType ).
tff(type_def_13,type,
'Num_bool_fun$': $tType ).
tff(type_def_14,type,
'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_15,type,
'A_set_list_list$': $tType ).
tff(type_def_16,type,
'Nat$': $tType ).
tff(type_def_17,type,
'Nat_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_18,type,
'A_ltln_a_ltln_bool_fun_fun_int_fun$': $tType ).
tff(type_def_19,type,
'Int_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_20,type,
'Num$': $tType ).
tff(type_def_21,type,
'A_set_list_nat_fun$': $tType ).
tff(type_def_22,type,
tlbool: $tType ).
tff(type_def_23,type,
'Nat_a_set_list_fun$': $tType ).
tff(type_def_24,type,
'Nat_num_fun$': $tType ).
tff(type_def_25,type,
'A_set_a_ltln_fun$': $tType ).
tff(type_def_26,type,
'A_ltln_bool_fun$': $tType ).
tff(type_def_27,type,
'A_set$': $tType ).
tff(type_def_28,type,
'A_ltln_set$': $tType ).
tff(type_def_29,type,
'Int_a_ltln_set_fun$': $tType ).
tff(type_def_30,type,
'A_set_list$': $tType ).
tff(type_def_31,type,
'A_ltln$': $tType ).
tff(type_def_32,type,
'Num_a_ltln_set_fun$': $tType ).
tff(type_def_33,type,
'Bool_bool_fun$': $tType ).
tff(type_def_34,type,
'Nat_a_set_fun$': $tType ).
tff(type_def_35,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_36,type,
'Nat_bool_fun$': $tType ).
tff(type_def_37,type,
'A_ltln_a_set_a_ltln_fun_fun$': $tType ).
tff(type_def_38,type,
'Nat_int_fun$': $tType ).
tff(type_def_39,type,
'Nat_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_40,type,
'Int_num_fun$': $tType ).
tff(type_def_41,type,
'Bool_bool_bool_fun_fun$': $tType ).
tff(type_def_42,type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_43,type,
'A_set_list_a_ltln_fun$': $tType ).
tff(type_def_44,type,
'Num_int_fun$': $tType ).
tff(type_def_45,type,
'Num_num_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'build$a': ( 'A_set$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_1,type,
'w$': 'Nat_a_set_fun$' ).
tff(func_def_2,type,
'fun_app$x': ( 'A_ltln_set_num_fun$' * 'A_ltln_set$' ) > 'Num$' ).
tff(func_def_3,type,
'gen_length$': 'Nat$' > 'A_set_list_nat_fun$' ).
tff(func_def_4,type,
'dbl_inc$': 'Int_int_fun$' ).
tff(func_def_5,type,
'af_letter$': 'A_ltln_a_set_a_ltln_fun_fun$' ).
tff(func_def_6,type,
def_6: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_7,type,
'fun_app$q': ( 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_8,type,
'size$': 'A_set_list_nat_fun$' ).
tff(func_def_9,type,
'f$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_10,type,
'fun_app$l': ( 'Num_num_bool_fun_fun$' * 'Num$' ) > 'Num_bool_fun$' ).
tff(func_def_11,type,
'fun_app$s': ( 'Int_num_fun$' * $int ) > 'Num$' ).
tff(func_def_12,type,
'or_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_13,type,
'size$b': 'A_set_list_list$' > 'Nat$' ).
tff(func_def_14,type,
'drop$': ( 'Nat$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_15,type,
'g_F$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_16,type,
'and_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_17,type,
'take$': ( 'Nat$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_18,type,
'fun_app$ad': ( 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' * 'Nat$' ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_19,type,
'uu$': 'A_ltln_set$' > 'A_ltln_bool_fun$' ).
tff(func_def_20,type,
'false_ltln$': 'A_ltln$' ).
tff(func_def_21,type,
'fun_app$t': ( 'Num_num_fun$' * 'Num$' ) > 'Num$' ).
tff(func_def_22,type,
'nil$': 'A_set_list$' ).
tff(func_def_23,type,
def_8: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_24,type,
def_7: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_25,type,
'fun_app$g': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_26,type,
'fun_app$af': ( 'A_set_list_a_set_list_list_fun$' * 'A_set_list$' ) > 'A_set_list_list$' ).
tff(func_def_27,type,
'suffix$': ( 'Nat$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_28,type,
'build$': ( 'A_set_list$' * 'Nat_a_set_list_fun$' ) > 'Nat_a_set_list_fun$' ).
tff(func_def_29,type,
'cons$a': ( 'A_set_list$' * 'A_set_list_list$' ) > 'A_set_list_list$' ).
tff(func_def_30,type,
'fun_app$r': ( 'Num_int_fun$' * 'Num$' ) > $int ).
tff(func_def_31,type,
'fun_app$aa': ( 'Nat_a_ltln_bool_fun_fun$' * 'Nat$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_32,type,
'nil$a': 'A_set_list_list$' ).
tff(func_def_33,type,
'cons$': ( 'A_set$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_34,type,
'fun_app$ab': ( 'Nat_a_ltln_set_fun$' * 'Nat$' ) > 'A_ltln_set$' ).
tff(func_def_35,type,
'mu_LTL$': 'A_ltln_set$' ).
tff(func_def_36,type,
'until_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_37,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_38,type,
'less_eq$a': 'Bool_bool_bool_fun_fun$' ).
tff(func_def_39,type,
def_2: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_40,type,
'butlast$': 'A_set_list$' > 'A_set_list$' ).
tff(func_def_41,type,
'fun_app$b': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_42,type,
'conc$': ( 'A_set_list$' * 'Nat_a_set_fun$' ) > 'Nat_a_set_fun$' ).
tff(func_def_43,type,
'g$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_44,type,
'collect$': 'A_ltln_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_45,type,
tltrue: tlbool ).
tff(func_def_46,type,
'size$a': 'A_ltln$' > 'Nat$' ).
tff(func_def_47,type,
'fun_app$w': ( 'Num_a_ltln_set_fun$' * 'Num$' ) > 'A_ltln_set$' ).
tff(func_def_48,type,
'ltl_prop_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_49,type,
'ltl_const_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_50,type,
'conc$a': ( 'A_set_list_list$' * 'Nat_a_set_list_fun$' ) > 'Nat_a_set_list_fun$' ).
tff(func_def_51,type,
'fun_app$p': ( 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' * $int ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_52,type,
'eq$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_53,type,
'numeral$': 'Num_int_fun$' ).
tff(func_def_54,type,
'fun_app$': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_55,type,
'foldl$': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_list_a_ltln_fun$' ).
tff(func_def_56,type,
'release_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_57,type,
def_1: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_58,type,
'fun_app$n': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_59,type,
'less_eq$d': 'Num_num_bool_fun_fun$' ).
tff(func_def_60,type,
'fun_app$e': ( 'A_set_a_ltln_fun$' * 'A_set$' ) > 'A_ltln$' ).
tff(func_def_61,type,
'ltl_lang_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_62,type,
def_4: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_63,type,
'fun_app$y': ( 'A_set_list_nat_fun$' * 'A_set_list$' ) > 'Nat$' ).
tff(func_def_64,type,
'fun_app$c': ( 'A_set_list_a_ltln_fun$' * 'A_set_list$' ) > 'A_ltln$' ).
tff(func_def_65,type,
'fun_app$d': ( 'Nat_a_set_list_fun$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_66,type,
'true_ltln$': 'A_ltln$' ).
tff(func_def_67,type,
'f_G$': ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'A_ltln_set$' ).
tff(func_def_68,type,
'append$a': ( 'A_set_list_list$' * 'A_set_list_list$' ) > 'A_set_list_list$' ).
tff(func_def_69,type,
'ltl_prop_implies$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_70,type,
'minus$': ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln_set$' ).
tff(func_def_71,type,
'semantics_ltln$': 'Nat_a_set_fun$' > 'A_ltln_bool_fun$' ).
tff(func_def_72,type,
'fun_app$u': ( 'A_ltln_set_int_fun$' * 'A_ltln_set$' ) > $int ).
tff(func_def_73,type,
'n_lists$': 'Nat$' > 'A_set_list_a_set_list_list_fun$' ).
tff(func_def_74,type,
def_5: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_75,type,
tlfalse: tlbool ).
tff(func_def_76,type,
'nat$': $int > 'Nat$' ).
tff(func_def_77,type,
def_3: ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > tlbool ).
tff(func_def_78,type,
'append$': ( 'A_set_list$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_79,type,
'fun_app$ae': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_80,type,
'nu_LTL$': 'A_ltln_set$' ).
tff(func_def_81,type,
'fun_app$f': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_a_ltln_fun$' ).
tff(func_def_82,type,
'rotate1$': 'A_set_list$' > 'A_set_list$' ).
tff(func_def_83,type,
'fun_app$z': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$' ).
tff(func_def_84,type,
'subsequence$': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat_a_set_list_fun$' ).
tff(func_def_85,type,
'fun_app$j': ( 'Bool_bool_bool_fun_fun$' * tlbool ) > 'Bool_bool_fun$' ).
tff(func_def_86,type,
'fun_app$ac': ( 'Nat_num_fun$' * 'Nat$' ) > 'Num$' ).
tff(func_def_87,type,
'uua$': $int > 'Int_int_fun$' ).
tff(func_def_88,type,
'weakUntil_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_89,type,
'fun_app$o': ( 'A_ltln_a_ltln_bool_fun_fun_int_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > $int ).
tff(func_def_90,type,
'fun_app$v': ( 'Int_a_ltln_set_fun$' * $int ) > 'A_ltln_set$' ).
tff(func_def_91,type,
'phi$': 'A_ltln$' ).
tff(func_def_92,type,
'strongRelease_ltln$': ( 'A_ltln$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_98,type,
sK0: 'Nat$' ).
tff(func_def_99,type,
sK1: 'Nat$' > 'Nat$' ).
tff(func_def_100,type,
sK2: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_101,type,
sK3: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_102,type,
sK4: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_103,type,
sK5: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_104,type,
sK6: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_105,type,
sK7: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_106,type,
sK8: 'Nat$' ).
tff(func_def_107,type,
sK9: 'Nat$' ).
tff(func_def_108,type,
sK10: 'Nat$' > 'Nat$' ).
tff(func_def_109,type,
sK11: 'Nat$' ).
tff(func_def_110,type,
sK12: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_111,type,
sK13: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_112,type,
sK14: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_113,type,
sK15: 'Nat$' ).
tff(func_def_114,type,
sK16: 'Nat$' ).
tff(func_def_115,type,
sK17: 'Nat$' > 'Nat$' ).
tff(func_def_116,type,
sK18: 'Nat$' > 'Nat$' ).
tff(func_def_117,type,
sK19: 'Nat$' ).
tff(func_def_118,type,
sK20: 'Nat$' ).
tff(func_def_119,type,
sK21: 'Nat$' > 'Nat$' ).
tff(func_def_120,type,
sK22: 'Nat$' > 'Nat$' ).
tff(func_def_121,type,
sK23: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_122,type,
sK24: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_123,type,
sK25: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_124,type,
sK26: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_125,type,
sK27: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_126,type,
sK28: ( 'A_ltln$' * 'A_ltln$' ) > 'Nat_a_set_fun$' ).
tff(func_def_127,type,
sK29: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_128,type,
sK30: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_129,type,
sK31: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_130,type,
sK32: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_131,type,
sK33: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_132,type,
sK34: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_133,type,
sK35: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_134,type,
sK36: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_135,type,
sK37: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_136,type,
sK38: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_137,type,
sK39: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_138,type,
sK55: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_139,type,
sK56: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_140,type,
sK57: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_141,type,
sK58: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_142,type,
sK59: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_143,type,
sK60: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_144,type,
sK61: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_145,type,
sK62: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_146,type,
sK63: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_147,type,
sK64: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_148,type,
sK65: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_149,type,
sK66: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_150,type,
sK67: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_151,type,
sK68: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_152,type,
sK69: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_153,type,
sK70: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_154,type,
sK71: 'Int_int_fun$' > $int ).
tff(func_def_155,type,
sK72: 'Int_int_fun$' > $int ).
tff(func_def_156,type,
sK73: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_157,type,
sK74: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_158,type,
sK75: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_159,type,
sK76: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_160,type,
sK77: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_161,type,
sK78: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_162,type,
sK79: 'Num_int_fun$' > 'Num$' ).
tff(func_def_163,type,
sK80: 'Num_int_fun$' > 'Num$' ).
tff(func_def_164,type,
sK81: 'Int_num_fun$' > $int ).
tff(func_def_165,type,
sK82: 'Int_num_fun$' > $int ).
tff(func_def_166,type,
sK83: 'Num_num_fun$' > 'Num$' ).
tff(func_def_167,type,
sK84: 'Num_num_fun$' > 'Num$' ).
tff(func_def_168,type,
sK85: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_169,type,
sK86: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_170,type,
sK87: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_171,type,
sK88: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_172,type,
sK89: 'Num_a_ltln_set_fun$' > 'Num$' ).
tff(func_def_173,type,
sK90: 'Num_a_ltln_set_fun$' > 'Num$' ).
tff(func_def_174,type,
sK91: 'Int_int_fun$' > $int ).
tff(func_def_175,type,
sK92: 'Int_int_fun$' > $int ).
tff(func_def_176,type,
sK93: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_177,type,
sK94: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_178,type,
sK95: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_179,type,
sK96: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_180,type,
sK97: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_181,type,
sK98: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_182,type,
sK99: 'Int_num_fun$' > $int ).
tff(func_def_183,type,
sK100: 'Int_num_fun$' > $int ).
tff(func_def_184,type,
sK101: 'Num_int_fun$' > 'Num$' ).
tff(func_def_185,type,
sK102: 'Num_int_fun$' > 'Num$' ).
tff(func_def_186,type,
sK103: 'Num_num_fun$' > 'Num$' ).
tff(func_def_187,type,
sK104: 'Num_num_fun$' > 'Num$' ).
tff(func_def_188,type,
sK105: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_189,type,
sK106: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_190,type,
sK107: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_191,type,
sK108: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_192,type,
sK109: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_193,type,
sK110: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_194,type,
sK111: 'Int_int_fun$' > $int ).
tff(func_def_195,type,
sK112: 'Int_int_fun$' > $int ).
tff(func_def_196,type,
sK113: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_197,type,
sK114: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_198,type,
sK115: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_199,type,
sK116: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_200,type,
sK117: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_201,type,
sK118: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_202,type,
sK119: 'Int_num_fun$' > $int ).
tff(func_def_203,type,
sK120: 'Int_num_fun$' > $int ).
tff(func_def_204,type,
sK121: 'Num_int_fun$' > 'Num$' ).
tff(func_def_205,type,
sK122: 'Num_int_fun$' > 'Num$' ).
tff(func_def_206,type,
sK123: 'Num_num_fun$' > 'Num$' ).
tff(func_def_207,type,
sK124: 'Num_num_fun$' > 'Num$' ).
tff(func_def_208,type,
sK125: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_209,type,
sK126: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_210,type,
sK127: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_211,type,
sK128: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_212,type,
sK129: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_213,type,
sK130: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_214,type,
sK131: 'Int_int_fun$' > $int ).
tff(func_def_215,type,
sK132: 'Int_int_fun$' > $int ).
tff(func_def_216,type,
sK133: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_217,type,
sK134: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_218,type,
sK135: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_219,type,
sK136: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_220,type,
sK137: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_221,type,
sK138: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_222,type,
sK139: 'Int_num_fun$' > $int ).
tff(func_def_223,type,
sK140: 'Int_num_fun$' > $int ).
tff(func_def_224,type,
sK141: 'Num_int_fun$' > 'Num$' ).
tff(func_def_225,type,
sK142: 'Num_int_fun$' > 'Num$' ).
tff(func_def_226,type,
sK143: 'Num_num_fun$' > 'Num$' ).
tff(func_def_227,type,
sK144: 'Num_num_fun$' > 'Num$' ).
tff(func_def_228,type,
sK145: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_229,type,
sK146: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_230,type,
sK147: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_231,type,
sK148: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_232,type,
sK149: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_233,type,
sK150: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_234,type,
sK151: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_235,type,
sK152: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_236,type,
sK153: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_237,type,
sK154: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_238,type,
sK155: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_239,type,
sK156: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_240,type,
sK157: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_241,type,
sK158: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_242,type,
sK159: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_243,type,
sK160: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_244,type,
sK161: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_245,type,
sK162: ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_246,type,
sK163: ( 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat_a_set_fun$' ).
tff(func_def_247,type,
sK164: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_248,type,
sK165: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_249,type,
sK166: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_250,type,
sK167: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_251,type,
sK168: 'Nat_a_ltln_bool_fun_fun$' > 'Nat$' ).
tff(func_def_252,type,
sK169: 'Nat_a_ltln_set_fun$' > 'Nat$' ).
tff(func_def_253,type,
sK170: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_254,type,
sK171: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_255,type,
sK172: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$' ).
tff(func_def_256,type,
sK173: 'Nat_a_ltln_bool_fun_fun$' > 'Nat$' ).
tff(func_def_257,type,
sK174: 'Nat_a_ltln_set_fun$' > 'Nat$' ).
tff(func_def_258,type,
sK175: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_259,type,
sK176: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_260,type,
sK177: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$' ).
tff(func_def_261,type,
sK178: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_262,type,
sK179: 'Nat$' > 'Nat$' ).
tff(func_def_263,type,
sK180: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_264,type,
sK181: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_265,type,
sK182: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_266,type,
sK183: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_267,type,
sK184: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_268,type,
sK185: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_269,type,
sK186: 'Nat$' > 'Nat$' ).
tff(func_def_270,type,
sK187: 'Nat$' > 'Nat$' ).
tff(func_def_271,type,
sK188: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_272,type,
sK189: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_273,type,
sK190: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_274,type,
sK191: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_275,type,
sK192: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_276,type,
sK193: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_277,type,
sK194: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_278,type,
sK195: ( 'Nat$' * 'A_set_list$' ) > 'A_set$' ).
tff(func_def_279,type,
sK196: ( 'Nat$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(pred_def_1,type,
'fun_app$a': ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_2,type,
'less_eq$c': ( 'A_ltln_set$' * 'A_ltln_set$' ) > $o ).
tff(pred_def_3,type,
'less_eq$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > $o ).
tff(pred_def_4,type,
'equivp$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_5,type,
'member$': ( 'A_ltln$' * 'A_ltln_set$' ) > $o ).
tff(pred_def_6,type,
'af_congruent$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_7,type,
'ltl_equivalence$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_8,type,
'fun_app$k': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_9,type,
'less_eq$b': ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > $o ).
tff(pred_def_10,type,
'fun_app$i': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_11,type,
'fun_app$m': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_12,type,
'af_congruent_axioms$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_13,type,
'fun_app$h': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_16,type,
sP40: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_17,type,
sP41: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_18,type,
sP42: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_19,type,
sP43: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_21,type,
sP45: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_22,type,
sP46: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_23,type,
sP47: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_24,type,
sP48: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_26,type,
sP50: ( $int * $int * $int ) > $o ).
tff(pred_def_27,type,
sP51: ( $int * $int * $int ) > $o ).
tff(pred_def_28,type,
sP52: ( $int * $int * $int ) > $o ).
tff(pred_def_29,type,
sP53: ( $int * $int * $int ) > $o ).
tff(f3,conjecture,
( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture2) ).
tff(f4,negated_conjecture,
~ ( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$') ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f19,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$',X0),'fun_app$d'('subsequence$'(X1,'nat$'(0)),X2))),'true_ltln$')
=> 'fun_app$a'('semantics_ltln$'(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom17) ).
tff(f48,axiom,
( ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$'))
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),X1))),'true_ltln$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom46) ).
tff(f49,axiom,
( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
<=> ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom47) ).
tff(f55,axiom,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),X1))),'true_ltln$')
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($difference('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0)))))),'true_ltln$') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom53) ).
tff(f56,axiom,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($difference('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0)))))),'true_ltln$') ) )
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$') ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
tff(f653,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),X1))),'true_ltln$')
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ) ) ),
inference(theory_normalization,[],[f55]) ).
tff(f654,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ) )
<=> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$') ),
inference(theory_normalization,[],[f56]) ).
tff(f842,plain,
( ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$'))
<=> ! [X1: 'Nat$'] :
? [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X1,'w$'),'nat$'(0)),X2))),'true_ltln$') ),
inference(rectify,[],[f48]) ).
tff(f843,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),X1))),'true_ltln$')
<=> ! [X2: 'Nat$'] :
? [X3: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X3),$uminus('fun_app$g'('of_nat$',X2))))))),'true_ltln$') ) ) ),
inference(rectify,[],[f653]) ).
tff(f844,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0))
=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ) )
<=> ! [X2: 'Nat$'] :
? [X3: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),X3))),'true_ltln$') ),
inference(rectify,[],[f654]) ).
tff(f851,plain,
( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
<~> ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$') ),
inference(ennf_transformation,[],[f4]) ).
tff(f859,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X2: 'Nat$'] :
( 'fun_app$a'('semantics_ltln$'(X1),X0)
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$',X0),'fun_app$d'('subsequence$'(X1,'nat$'(0)),X2))),'true_ltln$') ),
inference(ennf_transformation,[],[f19]) ).
tff(f881,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),X1))),'true_ltln$')
<=> ! [X2: 'Nat$'] :
? [X3: 'Nat$'] :
( ( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2)) )
& ( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X3),$uminus('fun_app$g'('of_nat$',X2))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2)) ) ) ),
inference(ennf_transformation,[],[f843]) ).
tff(f882,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] :
( ( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0)) )
& ( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0)) ) )
<=> ! [X2: 'Nat$'] :
? [X3: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),X3))),'true_ltln$') ),
inference(ennf_transformation,[],[f844]) ).
tff(f1405,plain,
! [X0: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),sK1(X0)))),'true_ltln$')
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f851]) ).
tff(f1406,plain,
! [X1: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK0),X1))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f851]) ).
tff(f1424,plain,
! [X2: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$',X0),'fun_app$d'('subsequence$'(X1,'nat$'(0)),X2))),'true_ltln$')
| 'fun_app$a'('semantics_ltln$'(X1),X0) ),
inference(cnf_transformation,[],[f859]) ).
tff(f1469,plain,
! [X1: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X1,'w$'),'nat$'(0)),sK10(X1)))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK8,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
inference(cnf_transformation,[],[f842]) ).
tff(f1470,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK11,'w$')),'until_ltln$'('true_ltln$','phi$'))
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f49]) ).
tff(f1471,plain,
! [X0: 'Nat$'] :
( 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f49]) ).
tff(f1480,plain,
! [X2: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK15,'w$'),'nat$'(0)),X1))),'true_ltln$') ),
inference(cnf_transformation,[],[f881]) ).
tff(f1484,plain,
! [X2: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK18(X2)),$uminus('fun_app$g'('of_nat$',X2))))))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK15,'w$'),'nat$'(0)),X1))),'true_ltln$') ),
inference(cnf_transformation,[],[f881]) ).
tff(f1485,plain,
! [X3: 'Nat$',X0: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK20),X3))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ),
inference(cnf_transformation,[],[f882]) ).
tff(f1486,plain,
! [X2: 'Nat$',X1: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK22(X2)))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19)) ),
inference(cnf_transformation,[],[f882]) ).
tff(f1487,plain,
! [X2: 'Nat$',X1: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK22(X2)))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ),
inference(cnf_transformation,[],[f882]) ).
tff(f1488,plain,
! [X2: 'Nat$',X1: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK22(X2)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19))
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ),
inference(cnf_transformation,[],[f882]) ).
tff(f1489,plain,
! [X3: 'Nat$',X0: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK20),X3))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK21(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ),
inference(cnf_transformation,[],[f882]) ).
tff(f2839,definition,
( spl197_22
<=> ! [X0: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl197_22])],[avatar_definition]) ).
tff(f2840,plain,
( ! [X0: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') )
| ~ spl197_22 ),
inference(avatar_component_clause,[],[f2839]) ).
tff(f2842,definition,
( spl197_23
<=> ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK20),X3))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_23])],[avatar_definition]) ).
tff(f2843,plain,
( ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK20),X3))),'true_ltln$')
| ~ spl197_23 ),
inference(avatar_component_clause,[],[f2842]) ).
tff(f2844,plain,
( spl197_22
| spl197_23 ),
inference(avatar_split_clause,[],[f1485,f2842,f2839]) ).
tff(f2846,definition,
( spl197_24
<=> ! [X1: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19)) ) ),
introduced(definition,[new_symbols(definition,[spl197_24])],[avatar_definition]) ).
tff(f2847,plain,
( ! [X1: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19)) )
| ~ spl197_24 ),
inference(avatar_component_clause,[],[f2846]) ).
tff(f2849,definition,
( spl197_25
<=> ! [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK22(X2)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_25])],[avatar_definition]) ).
tff(f2850,plain,
( ! [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK22(X2)))),'true_ltln$')
| ~ spl197_25 ),
inference(avatar_component_clause,[],[f2849]) ).
tff(f2851,plain,
( spl197_24
| spl197_25 ),
inference(avatar_split_clause,[],[f1486,f2849,f2846]) ).
tff(f2853,definition,
( spl197_26
<=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_26])],[avatar_definition]) ).
tff(f2855,plain,
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| spl197_26 ),
inference(avatar_component_clause,[],[f2853]) ).
tff(f2857,definition,
( spl197_27
<=> ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_27])],[avatar_definition]) ).
tff(f2858,plain,
( ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK19,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',sK19))))))),'true_ltln$')
| ~ spl197_27 ),
inference(avatar_component_clause,[],[f2857]) ).
tff(f2859,plain,
( ~ spl197_26
| spl197_27
| spl197_25 ),
inference(avatar_split_clause,[],[f1487,f2849,f2857,f2853]) ).
tff(f2861,definition,
( spl197_28
<=> ! [X1: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19)) ),
introduced(definition,[new_symbols(definition,[spl197_28])],[avatar_definition]) ).
tff(f2862,plain,
( ! [X1: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',sK19))
| ~ spl197_28 ),
inference(avatar_component_clause,[],[f2861]) ).
tff(f2863,plain,
( ~ spl197_26
| spl197_28
| spl197_25 ),
inference(avatar_split_clause,[],[f1488,f2849,f2861,f2853]) ).
tff(f2865,definition,
( spl197_29
<=> ! [X0: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK21(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl197_29])],[avatar_definition]) ).
tff(f2866,plain,
( ! [X0: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK21(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK21(X0)),'fun_app$g'('of_nat$',X0)) )
| ~ spl197_29 ),
inference(avatar_component_clause,[],[f2865]) ).
tff(f2867,plain,
( spl197_29
| spl197_23 ),
inference(avatar_split_clause,[],[f1489,f2842,f2865]) ).
tff(f2869,definition,
( spl197_30
<=> ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK15,'w$'),'nat$'(0)),X1))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_30])],[avatar_definition]) ).
tff(f2870,plain,
( ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK15,'w$'),'nat$'(0)),X1))),'true_ltln$')
| ~ spl197_30 ),
inference(avatar_component_clause,[],[f2869]) ).
tff(f2872,definition,
( spl197_31
<=> ! [X2: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl197_31])],[avatar_definition]) ).
tff(f2873,plain,
( ! [X2: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2)) )
| ~ spl197_31 ),
inference(avatar_component_clause,[],[f2872]) ).
tff(f2874,plain,
( spl197_30
| spl197_31 ),
inference(avatar_split_clause,[],[f1480,f2872,f2869]) ).
tff(f2895,definition,
( spl197_37
<=> ! [X2: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK18(X2)),$uminus('fun_app$g'('of_nat$',X2))))))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl197_37])],[avatar_definition]) ).
tff(f2896,plain,
( ! [X2: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK18(X2)),$uminus('fun_app$g'('of_nat$',X2))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK18(X2)),'fun_app$g'('of_nat$',X2)) )
| ~ spl197_37 ),
inference(avatar_component_clause,[],[f2895]) ).
tff(f2897,plain,
( spl197_30
| spl197_37 ),
inference(avatar_split_clause,[],[f1484,f2895,f2869]) ).
tff(f2899,definition,
( spl197_38
<=> 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
introduced(definition,[new_symbols(definition,[spl197_38])],[avatar_definition]) ).
tff(f2903,definition,
( spl197_39
<=> 'fun_app$a'('semantics_ltln$'('suffix$'(sK11,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl197_39])],[avatar_definition]) ).
tff(f2905,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK11,'w$')),'until_ltln$'('true_ltln$','phi$'))
| spl197_39 ),
inference(avatar_component_clause,[],[f2903]) ).
tff(f2906,plain,
( spl197_38
| ~ spl197_39 ),
inference(avatar_split_clause,[],[f1470,f2903,f2899]) ).
tff(f2908,definition,
( spl197_40
<=> ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl197_40])],[avatar_definition]) ).
tff(f2909,plain,
( ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ~ spl197_40 ),
inference(avatar_component_clause,[],[f2908]) ).
tff(f2910,plain,
( ~ spl197_38
| spl197_40 ),
inference(avatar_split_clause,[],[f1471,f2908,f2899]) ).
tff(f2916,definition,
( spl197_42
<=> 'fun_app$a'('semantics_ltln$'('suffix$'(sK8,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl197_42])],[avatar_definition]) ).
tff(f2918,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK8,'w$')),'until_ltln$'('true_ltln$','phi$'))
| spl197_42 ),
inference(avatar_component_clause,[],[f2916]) ).
tff(f2920,definition,
( spl197_43
<=> ! [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X1,'w$'),'nat$'(0)),sK10(X1)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_43])],[avatar_definition]) ).
tff(f2921,plain,
( ! [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X1,'w$'),'nat$'(0)),sK10(X1)))),'true_ltln$')
| ~ spl197_43 ),
inference(avatar_component_clause,[],[f2920]) ).
tff(f2922,plain,
( ~ spl197_42
| spl197_43 ),
inference(avatar_split_clause,[],[f1469,f2920,f2916]) ).
tff(f2947,definition,
( spl197_50
<=> ! [X0: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),sK1(X0)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_50])],[avatar_definition]) ).
tff(f2948,plain,
( ! [X0: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),sK1(X0)))),'true_ltln$')
| ~ spl197_50 ),
inference(avatar_component_clause,[],[f2947]) ).
tff(f2949,plain,
( spl197_38
| spl197_50 ),
inference(avatar_split_clause,[],[f1405,f2947,f2899]) ).
tff(f2951,definition,
( spl197_51
<=> ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK0),X1))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl197_51])],[avatar_definition]) ).
tff(f2952,plain,
( ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK0),X1))),'true_ltln$')
| ~ spl197_51 ),
inference(avatar_component_clause,[],[f2951]) ).
tff(f2953,plain,
( ~ spl197_38
| spl197_51 ),
inference(avatar_split_clause,[],[f1406,f2951,f2899]) ).
tff(f2981,plain,
( $false
| ~ spl197_25
| ~ spl197_51 ),
inference(resolution,[],[f2850,f2952]) ).
tff(f2982,plain,
( $false
| ~ spl197_23
| ~ spl197_25 ),
inference(resolution,[],[f2850,f2843]) ).
tff(f2988,plain,
( ~ spl197_23
| ~ spl197_25 ),
inference(avatar_contradiction_clause,[],[f2982]) ).
tff(f2989,plain,
( ~ spl197_25
| ~ spl197_51 ),
inference(avatar_contradiction_clause,[],[f2981]) ).
tff(f3006,plain,
( $false
| ~ spl197_30
| ~ spl197_43 ),
inference(resolution,[],[f2921,f2870]) ).
tff(f3013,plain,
( ~ spl197_30
| ~ spl197_43 ),
inference(avatar_contradiction_clause,[],[f3006]) ).
tff(f3015,plain,
( $false
| ~ spl197_40
| spl197_42 ),
inference(forward_subsumption_resolution,[],[f2918,f2909]) ).
tff(f3016,plain,
( ~ spl197_40
| spl197_42 ),
inference(avatar_contradiction_clause,[],[f3015]) ).
tff(f3018,plain,
( $false
| ~ spl197_23
| ~ spl197_50 ),
inference(resolution,[],[f2948,f2843]) ).
tff(f3025,plain,
( ~ spl197_23
| ~ spl197_50 ),
inference(avatar_contradiction_clause,[],[f3018]) ).
tff(f3062,plain,
( ! [X0: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK18(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) )
| ~ spl197_31 ),
inference(resolution,[],[f2873,f1424]) ).
tff(f3206,plain,
( $less('fun_app$g'('of_nat$',sK18(sK19)),'fun_app$g'('of_nat$',sK19))
| ~ spl197_27
| ~ spl197_37 ),
inference(resolution,[],[f2896,f2858]) ).
tff(f3208,plain,
( ! [X0: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK18(X0)),'fun_app$g'('of_nat$',X0))
| 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) )
| ~ spl197_37 ),
inference(resolution,[],[f2896,f1424]) ).
tff(f3221,plain,
( $false
| ~ spl197_27
| ~ spl197_28
| ~ spl197_37 ),
inference(forward_subsumption_resolution,[],[f3206,f2862]) ).
tff(f3222,plain,
( ~ spl197_27
| ~ spl197_28
| ~ spl197_37 ),
inference(avatar_contradiction_clause,[],[f3221]) ).
tff(f3223,plain,
( ~ $less('fun_app$g'('of_nat$',sK18(sK19)),'fun_app$g'('of_nat$',sK19))
| spl197_26
| ~ spl197_31 ),
inference(resolution,[],[f2855,f2873]) ).
tff(f3229,plain,
( $less('fun_app$g'('of_nat$',sK18(sK19)),'fun_app$g'('of_nat$',sK19))
| $less('fun_app$g'('of_nat$',sK18(sK19)),'fun_app$g'('of_nat$',sK19))
| ~ spl197_24
| ~ spl197_37 ),
inference(resolution,[],[f2847,f2896]) ).
tff(f3230,plain,
( $less('fun_app$g'('of_nat$',sK18(sK19)),'fun_app$g'('of_nat$',sK19))
| ~ spl197_24
| ~ spl197_37 ),
inference(duplicate_literal_removal,[],[f3229]) ).
tff(f3231,plain,
( $false
| ~ spl197_24
| spl197_26
| ~ spl197_31
| ~ spl197_37 ),
inference(forward_subsumption_resolution,[],[f3230,f3223]) ).
tff(f3232,plain,
( ~ spl197_24
| spl197_26
| ~ spl197_31
| ~ spl197_37 ),
inference(avatar_contradiction_clause,[],[f3231]) ).
tff(f3303,plain,
( $less('fun_app$g'('of_nat$',sK21(sK15)),'fun_app$g'('of_nat$',sK15))
| ~ spl197_29
| ~ spl197_30 ),
inference(resolution,[],[f2866,f2870]) ).
tff(f3375,plain,
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK15,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ spl197_22
| ~ spl197_29
| ~ spl197_30 ),
inference(resolution,[],[f3303,f2840]) ).
tff(f3376,plain,
( $false
| ~ spl197_22
| ~ spl197_29
| ~ spl197_30 ),
inference(forward_subsumption_resolution,[],[f3375,f2870]) ).
tff(f3377,plain,
( ~ spl197_22
| ~ spl197_29
| ~ spl197_30 ),
inference(avatar_contradiction_clause,[],[f3376]) ).
tff(f3489,plain,
( ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ~ spl197_31
| ~ spl197_37 ),
inference(forward_subsumption_resolution,[],[f3208,f3062]) ).
tff(f3490,plain,
( $false
| ~ spl197_31
| ~ spl197_37
| spl197_39 ),
inference(resolution,[],[f3489,f2905]) ).
tff(f3493,plain,
( ~ spl197_31
| ~ spl197_37
| spl197_39 ),
inference(avatar_contradiction_clause,[],[f3490]) ).
cnf(s17,plain,
( spl197_22
| spl197_23 ),
inference(sat_conversion,[],[f2844]) ).
cnf(s18,plain,
( spl197_24
| spl197_25 ),
inference(sat_conversion,[],[f2851]) ).
cnf(s19,plain,
( spl197_25
| ~ spl197_26
| spl197_27 ),
inference(sat_conversion,[],[f2859]) ).
cnf(s20,plain,
( spl197_25
| ~ spl197_26
| spl197_28 ),
inference(sat_conversion,[],[f2863]) ).
cnf(s21,plain,
( spl197_23
| spl197_29 ),
inference(sat_conversion,[],[f2867]) ).
cnf(s22,plain,
( spl197_30
| spl197_31 ),
inference(sat_conversion,[],[f2874]) ).
cnf(s26,plain,
( spl197_30
| spl197_37 ),
inference(sat_conversion,[],[f2897]) ).
cnf(s27,plain,
( spl197_38
| ~ spl197_39 ),
inference(sat_conversion,[],[f2906]) ).
cnf(s28,plain,
( ~ spl197_38
| spl197_40 ),
inference(sat_conversion,[],[f2910]) ).
cnf(s30,plain,
( ~ spl197_42
| spl197_43 ),
inference(sat_conversion,[],[f2922]) ).
cnf(s36,plain,
( spl197_38
| spl197_50 ),
inference(sat_conversion,[],[f2949]) ).
cnf(s37,plain,
( ~ spl197_38
| spl197_51 ),
inference(sat_conversion,[],[f2953]) ).
cnf(s41,plain,
( ~ spl197_23
| ~ spl197_25 ),
inference(sat_conversion,[],[f2988]) ).
cnf(s42,plain,
( ~ spl197_25
| ~ spl197_51 ),
inference(sat_conversion,[],[f2989]) ).
cnf(s44,plain,
( ~ spl197_30
| ~ spl197_43 ),
inference(sat_conversion,[],[f3013]) ).
cnf(s45,plain,
( ~ spl197_40
| spl197_42 ),
inference(sat_conversion,[],[f3016]) ).
cnf(s46,plain,
( ~ spl197_23
| ~ spl197_50 ),
inference(sat_conversion,[],[f3025]) ).
cnf(s56,plain,
( ~ spl197_27
| ~ spl197_28
| ~ spl197_37 ),
inference(sat_conversion,[],[f3222]) ).
cnf(s57,plain,
( ~ spl197_24
| spl197_26
| ~ spl197_31
| ~ spl197_37 ),
inference(sat_conversion,[],[f3232]) ).
cnf(s63,plain,
( ~ spl197_22
| ~ spl197_29
| ~ spl197_30 ),
inference(sat_conversion,[],[f3377]) ).
cnf(s68,plain,
( ~ spl197_31
| ~ spl197_37
| spl197_39 ),
inference(sat_conversion,[],[f3493]) ).
cnf(s84,plain,
~ spl197_23,
inference(rat,[],[s56,s19,s20,s57,s22,s26,s44,s30,s45,s28,s18,s36,s41,s46]) ).
cnf(s85,plain,
spl197_29,
inference(rat,[],[s21,s84]) ).
cnf(s86,plain,
spl197_22,
inference(rat,[],[s17,s84]) ).
cnf(s87,plain,
~ spl197_30,
inference(rat,[],[s63,s85,s86]) ).
cnf(s88,plain,
spl197_37,
inference(rat,[],[s26,s87]) ).
cnf(s89,plain,
spl197_31,
inference(rat,[],[s22,s87]) ).
cnf(s90,plain,
spl197_39,
inference(rat,[],[s68,s88,s89]) ).
cnf(s92,plain,
spl197_38,
inference(rat,[],[s27,s90]) ).
cnf(s94,plain,
spl197_51,
inference(rat,[],[s37,s92]) ).
cnf(s100,plain,
~ spl197_25,
inference(rat,[],[s42,s94]) ).
cnf(s101,plain,
spl197_24,
inference(rat,[],[s18,s100]) ).
cnf(s102,plain,
spl197_26,
inference(rat,[],[s57,s88,s89,s101]) ).
cnf(s103,plain,
spl197_28,
inference(rat,[],[s20,s100,s102]) ).
cnf(s104,plain,
spl197_27,
inference(rat,[],[s19,s100,s102]) ).
cnf(s105,plain,
$false,
inference(rat,[],[s56,s88,s103,s104]) ).
tff(f3494,plain,
$false,
inference(avatar_sat_refutation,[],[s105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP359_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n020.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
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 12:56:34 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.88/0.67 % (3360574)Will run a generic schedule for satisfiability detection.
% 0.88/0.67 % (3360618)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2653455011:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.88/0.67 % (3360613)% WARNING: option uhcvi not known.
% 0.88/0.67 % (3360613)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2673276616:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.88/0.67 % (3360612)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=155569489_2999 on theBenchmark for (2999ds/0Mi)
% 0.88/0.67 % (3360616)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3220539426:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.88/0.67 % (3360614)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3131697060:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.88/0.67 % (3360615)dis+10_1_sil=32000:sp=arity:random_seed=2049466750:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.88/0.67 % (3360619)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3205480449:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.88/0.67 % (3360618)Instruction limit reached!
% 0.88/0.67 % (3360618)------------------------------
% 0.88/0.67 % (3360618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360618)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360618)Termination reason: Instruction limit
% 0.88/0.67 % (3360618)Termination phase: Saturation
% 0.88/0.67 % (3360618)Time elapsed: 0.036 s
% 0.88/0.67 % (3360618)Peak memory usage: 14 MB
% 0.88/0.67 % (3360618)Instructions burned: 131 (million)
% 0.88/0.67 % (3360633)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1897200765:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 0.88/0.67 % (3360615)Instruction limit reached!
% 0.88/0.67 % (3360615)------------------------------
% 0.88/0.67 % (3360615)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360615)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360615)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360615)Termination reason: Instruction limit
% 0.88/0.67 % (3360615)Termination phase: Saturation
% 0.88/0.67 % (3360615)Time elapsed: 0.047 s
% 0.88/0.67 % (3360615)Peak memory usage: 13 MB
% 0.88/0.67 % (3360615)Instructions burned: 104 (million)
% 0.88/0.67 % (3360612)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.88/0.67 % (3360612)Terminated due to inappropriate strategy.
% 0.88/0.67 % (3360612)------------------------------
% 0.88/0.67 % (3360612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360612)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360612)Termination reason: Inappropriate
% 0.88/0.67 % (3360612)Time elapsed: 0.049 s
% 0.88/0.67 % (3360612)Peak memory usage: 12 MB
% 0.88/0.67 % (3360612)Instructions burned: 109 (million)
% 0.88/0.67 % (3360612)------------------------------
% 0.88/0.67 % (3360612)------------------------------
% 0.88/0.67 % (3360616)Instruction limit reached!
% 0.88/0.67 % (3360616)------------------------------
% 0.88/0.67 % (3360616)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360616)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360616)Termination reason: Instruction limit
% 0.88/0.67 % (3360616)Termination phase: Saturation
% 0.88/0.67 % (3360616)Time elapsed: 0.054 s
% 0.88/0.67 % (3360616)Peak memory usage: 13 MB
% 0.88/0.67 % (3360616)Instructions burned: 117 (million)
% 0.88/0.67 % (3360633)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.88/0.67 % (3360633)Terminated due to inappropriate strategy.
% 0.88/0.67 % (3360633)------------------------------
% 0.88/0.67 % (3360633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360633)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360633)Termination reason: Inappropriate
% 0.88/0.67 % (3360633)Time elapsed: 0.021 s
% 0.88/0.67 % (3360633)Peak memory usage: 12 MB
% 0.88/0.67 % (3360633)Instructions burned: 88 (million)
% 0.88/0.67 % (3360633)------------------------------
% 0.88/0.67 % (3360633)------------------------------
% 0.88/0.67 % (3360635)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1435711902:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 0.88/0.67 % (3360636)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=779552930:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 0.88/0.67 % (3360637)ott-21_1_sil=16000:fs=off:random_seed=2717721322:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.88/0.67 % (3360638)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2453336394:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.88/0.67 % (3360619)Instruction limit reached!
% 0.88/0.67 % (3360619)------------------------------
% 0.88/0.67 % (3360619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360619)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360619)Termination reason: Instruction limit
% 0.88/0.67 % (3360619)Termination phase: Saturation
% 0.88/0.67 % (3360619)Time elapsed: 0.082 s
% 0.88/0.67 % (3360619)Peak memory usage: 14 MB
% 0.88/0.67 % (3360619)Instructions burned: 160 (million)
% 0.88/0.67 % (3360643)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2972228963:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.88/0.67 % (3360635)Instruction limit reached!
% 0.88/0.67 % (3360635)------------------------------
% 0.88/0.67 % (3360635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360635)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360635)Termination reason: Instruction limit
% 0.88/0.67 % (3360635)Termination phase: Saturation
% 0.88/0.67 % (3360635)Time elapsed: 0.058 s
% 0.88/0.67 % (3360635)Peak memory usage: 13 MB
% 0.88/0.67 % (3360635)Instructions burned: 131 (million)
% 0.88/0.67 % (3360643)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.88/0.67 % (3360643)Terminated due to inappropriate strategy.
% 0.88/0.67 % (3360643)------------------------------
% 0.88/0.67 % (3360643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360643)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360643)Termination reason: Inappropriate
% 0.88/0.67 % (3360643)Time elapsed: 0.031 s
% 0.88/0.67 % (3360643)Peak memory usage: 12 MB
% 0.88/0.67 % (3360643)Instructions burned: 69 (million)
% 0.88/0.67 % (3360643)------------------------------
% 0.88/0.67 % (3360643)------------------------------
% 0.88/0.67 % (3360645)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3189916889:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 0.88/0.67 % (3360646)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1327128331:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 0.88/0.67 % (3360636) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3360574-3360636"...
% 0.88/0.67 % (3360637)Instruction limit reached!
% 0.88/0.67 % (3360637)------------------------------
% 0.88/0.67 % (3360637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360637)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360637)Termination reason: Instruction limit
% 0.88/0.67 % (3360637)Termination phase: Saturation
% 0.88/0.67 % (3360637)Time elapsed: 0.084 s
% 0.88/0.67 % (3360637)Peak memory usage: 13 MB
% 0.88/0.67 % (3360637)Instructions burned: 181 (million)
% 0.88/0.67 % (3360636)...printing done.
% 0.88/0.67 % (3360636)Refutation found. Thanks to Tanya!
% 0.88/0.67 % SZS status Theorem for theBenchmark
% 0.88/0.67 % SZS output start Proof for theBenchmark
% See solution above
% 0.88/0.67 % (3360636)------------------------------
% 0.88/0.67 % (3360636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.88/0.67 % (3360636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.88/0.67 % (3360636)CaDiCaL version: 2.1.3
% 0.88/0.67 % (3360636)Termination reason: Refutation
% 0.88/0.67 % (3360636)Time elapsed: 0.091 s
% 0.88/0.67 % (3360636)Peak memory usage: 15 MB
% 0.88/0.67 % (3360636)Instructions burned: 175 (million)
% 0.88/0.67 % (3360574)Success in time 0.241 s
% 0.88/0.67 % Vampire exiting
%------------------------------------------------------------------------------