%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n004.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 11:33:42 AM UTC 2026
% Result : Theorem 9.15s 2.25s
% Output : Refutation 10.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 28
% Syntax : Number of formulae : 124 ( 3 unt; 0 typ; 21 def)
% Number of atoms : 378 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 420 ( 166 ~; 162 |; 43 &)
% ( 34 <=>; 14 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 248 ( 66 atm; 62 fun; 120 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 : 58 ( 56 usr; 22 prp; 0-3 aty)
% Number of functors : 279 ( 275 usr; 31 con; 0-3 aty)
% Number of variables : 185 ( 136 !; 49 ?; 185 :)
% 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,
sK22: 'Int_int_fun$' > $int ).
tff(func_def_99,type,
sK23: 'Int_int_fun$' > $int ).
tff(func_def_100,type,
sK24: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_101,type,
sK25: ( 'Nat_a_set_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_102,type,
sK26: 'Int_int_fun$' > $int ).
tff(func_def_103,type,
sK27: 'Int_int_fun$' > $int ).
tff(func_def_104,type,
sK28: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_105,type,
sK29: 'Int_int_fun$' > $int ).
tff(func_def_106,type,
sK30: 'Int_int_fun$' > $int ).
tff(func_def_107,type,
sK31: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_108,type,
sK32: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_109,type,
sK33: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_110,type,
sK34: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_111,type,
sK35: 'Bool_bool_bool_fun_fun$' > tlbool ).
tff(func_def_112,type,
sK36: 'Num_int_fun$' > 'Num$' ).
tff(func_def_113,type,
sK37: 'Num_int_fun$' > 'Num$' ).
tff(func_def_114,type,
sK38: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_115,type,
sK39: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_116,type,
sK40: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_117,type,
sK41: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_118,type,
sK42: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_119,type,
sK43: 'Num_a_ltln_set_fun$' > 'Num$' ).
tff(func_def_120,type,
sK44: 'Num_a_ltln_set_fun$' > 'Num$' ).
tff(func_def_121,type,
sK45: 'Nat_a_ltln_set_fun$' > 'Nat$' ).
tff(func_def_122,type,
sK46: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_123,type,
sK47: 'Nat_a_ltln_set_fun$' > 'Nat$' ).
tff(func_def_124,type,
sK48: 'Nat_a_ltln_bool_fun_fun$' > 'Nat$' ).
tff(func_def_125,type,
sK49: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_126,type,
sK50: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_127,type,
sK51: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_128,type,
sK52: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_129,type,
sK53: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_130,type,
sK54: ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_131,type,
sK55: ( 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat_a_set_fun$' ).
tff(func_def_132,type,
sK56: ( 'A_set_list$' * 'Nat$' ) > 'A_set$' ).
tff(func_def_133,type,
sK57: ( 'A_set_list$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_134,type,
sK58: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_135,type,
sK59: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_136,type,
sK60: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_137,type,
sK61: 'Nat$' > 'Nat$' ).
tff(func_def_138,type,
sK62: 'Nat$' ).
tff(func_def_139,type,
sK63: 'Nat$' > 'Nat$' ).
tff(func_def_140,type,
sK64: 'Nat$' ).
tff(func_def_141,type,
sK65: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_142,type,
sK66: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_143,type,
sK67: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_144,type,
sK68: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_145,type,
sK69: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_146,type,
sK70: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_147,type,
sK71: '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_148,type,
sK72: '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_149,type,
sK73: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_150,type,
sK74: 'Num_int_fun$' > 'Num$' ).
tff(func_def_151,type,
sK75: 'Num_int_fun$' > 'Num$' ).
tff(func_def_152,type,
sK76: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_153,type,
sK77: 'Int_int_fun$' > $int ).
tff(func_def_154,type,
sK78: 'Int_int_fun$' > $int ).
tff(func_def_155,type,
sK79: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_156,type,
sK80: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_157,type,
sK81: 'Int_num_fun$' > $int ).
tff(func_def_158,type,
sK82: 'Int_num_fun$' > $int ).
tff(func_def_159,type,
sK83: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_160,type,
sK84: 'Nat$' > 'Nat$' ).
tff(func_def_161,type,
sK85: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_162,type,
sK86: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_163,type,
sK87: 'Num_int_fun$' > 'Num$' ).
tff(func_def_164,type,
sK88: 'Num_int_fun$' > 'Num$' ).
tff(func_def_165,type,
sK89: '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_166,type,
sK90: '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_167,type,
sK91: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_168,type,
sK92: 'Int_num_fun$' > $int ).
tff(func_def_169,type,
sK93: 'Int_num_fun$' > $int ).
tff(func_def_170,type,
sK94: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_171,type,
sK95: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_172,type,
sK96: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_173,type,
sK97: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_174,type,
sK98: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_175,type,
sK99: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_176,type,
sK100: 'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_177,type,
sK101: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_178,type,
sK102: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_179,type,
sK103: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_180,type,
sK104: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_181,type,
sK105: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_182,type,
sK106: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_183,type,
sK107: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_184,type,
sK108: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_185,type,
sK109: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_186,type,
sK110: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_187,type,
sK111: 'Nat$' > 'Nat$' ).
tff(func_def_188,type,
sK112: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_189,type,
sK113: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_190,type,
sK114: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_191,type,
sK115: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_192,type,
sK116: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_193,type,
sK117: ( 'Nat_a_set_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_194,type,
sK118: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_195,type,
sK119: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_196,type,
sK120: 'Nat$' ).
tff(func_def_197,type,
sK121: 'Nat$' > 'Nat$' ).
tff(func_def_198,type,
sK122: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_199,type,
sK123: 'Int_num_fun$' > $int ).
tff(func_def_200,type,
sK124: 'Int_num_fun$' > $int ).
tff(func_def_201,type,
sK125: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_202,type,
sK126: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_203,type,
sK127: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_204,type,
sK128: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_205,type,
sK129: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_206,type,
sK130: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_207,type,
sK131: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_208,type,
sK132: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_209,type,
sK133: '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_210,type,
sK134: '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_211,type,
sK135: ( 'A_ltln_set$' * 'A_ltln_set$' ) > 'A_ltln$' ).
tff(func_def_212,type,
sK136: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_213,type,
sK137: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_214,type,
sK138: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_215,type,
sK139: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_216,type,
sK140: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_217,type,
sK141: 'Int_num_fun$' > $int ).
tff(func_def_218,type,
sK142: 'Int_num_fun$' > $int ).
tff(func_def_219,type,
sK143: 'Nat$' > 'Nat$' ).
tff(func_def_220,type,
sK144: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$' ).
tff(func_def_221,type,
sK145: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_set$' ).
tff(func_def_222,type,
sK146: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_223,type,
sK147: 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln$' ).
tff(func_def_224,type,
sK148: 'Num_num_fun$' > 'Num$' ).
tff(func_def_225,type,
sK149: 'Num_num_fun$' > 'Num$' ).
tff(func_def_226,type,
sK150: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_227,type,
sK151: 'Int_a_ltln_set_fun$' > $int ).
tff(func_def_228,type,
sK152: 'Nat_a_ltln_bool_fun_fun$' > 'Nat$' ).
tff(func_def_229,type,
sK153: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_230,type,
sK154: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_231,type,
sK155: 'Num_num_fun$' > 'Num$' ).
tff(func_def_232,type,
sK156: 'Num_num_fun$' > 'Num$' ).
tff(func_def_233,type,
sK157: 'Nat$' > 'Nat$' ).
tff(func_def_234,type,
sK158: 'Nat$' ).
tff(func_def_235,type,
sK159: 'Nat$' ).
tff(func_def_236,type,
sK160: 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' > 'Nat$' ).
tff(func_def_237,type,
sK161: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_238,type,
sK162: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_239,type,
sK163: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_240,type,
sK164: 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' > $int ).
tff(func_def_241,type,
sK165: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_242,type,
sK166: ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln$' ).
tff(func_def_243,type,
sK167: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_244,type,
sK168: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_245,type,
sK169: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_246,type,
sK170: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_247,type,
sK171: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_248,type,
sK172: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_249,type,
sK173: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_250,type,
sK174: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_251,type,
sK175: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_252,type,
sK176: 'Nat$' > 'Nat$' ).
tff(func_def_253,type,
sK177: 'Nat$' ).
tff(func_def_254,type,
sK178: 'Nat$' > 'Nat$' ).
tff(func_def_255,type,
sK179: 'Nat$' ).
tff(func_def_256,type,
sK180: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_257,type,
sK181: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_258,type,
sK182: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_259,type,
sK183: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_260,type,
sK184: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_261,type,
sK185: 'A_ltln_a_ltln_bool_fun_fun_int_fun$' > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_262,type,
sK186: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_263,type,
sK187: 'Num_int_fun$' > 'Num$' ).
tff(func_def_264,type,
sK188: 'Num_int_fun$' > 'Num$' ).
tff(func_def_265,type,
sK189: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_266,type,
sK190: 'A_ltln_set_num_fun$' > 'A_ltln_set$' ).
tff(func_def_267,type,
sK191: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_268,type,
sK192: 'Num_num_fun$' > 'Num$' ).
tff(func_def_269,type,
sK193: 'Num_num_fun$' > 'Num$' ).
tff(func_def_270,type,
sK194: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_271,type,
sK195: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_272,type,
sK196: 'Num_num_fun$' > 'Num$' ).
tff(func_def_273,type,
sK197: 'Num_num_fun$' > 'Num$' ).
tff(func_def_274,type,
sK198: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_275,type,
sK199: ( 'A_ltln$' * 'A_ltln$' ) > 'Nat_a_set_fun$' ).
tff(func_def_276,type,
sK200: 'Nat$' ).
tff(func_def_277,type,
sK201: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_278,type,
sK202: 'A_ltln_set_int_fun$' > 'A_ltln_set$' ).
tff(func_def_279,type,
sK203: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(pred_def_1,type,
'fun_app$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$' * 'Nat$' ) > $o ).
tff(pred_def_16,type,
sP0: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_17,type,
sP1: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_18,type,
sP2: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_19,type,
sP3: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_20,type,
sP4: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_21,type,
sP5: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_22,type,
sP6: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_23,type,
sP7: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_24,type,
sP8: ( $int * $int * $int ) > $o ).
tff(pred_def_25,type,
sP9: ( $int * $int * $int ) > $o ).
tff(pred_def_26,type,
sP10: ( $int * $int * $int ) > $o ).
tff(pred_def_27,type,
sP11: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_28,type,
sP12: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_29,type,
sP13: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_30,type,
sP14: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_31,type,
sP15: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_32,type,
sP16: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_33,type,
sP17: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_34,type,
sP18: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_35,type,
sP19: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_36,type,
sP20: ( tlbool * tlbool * tlbool ) > $o ).
tff(pred_def_37,type,
sP21: ( tlbool * tlbool * tlbool ) > $o ).
tff(f3,conjecture,
( ! [X0: 'Nat$'] :
? [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$',X0),X1))),'true_ltln$')
<=> 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture2) ).
tff(f4,negated_conjecture,
~ ( ! [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$')
<=> 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,axiom,
! [X0: 'A_ltln$'] : 'fun_app$a'('fun_app$b'('eq$',X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom3) ).
tff(f7,axiom,
! [X2: 'A_ltln$',X0: 'A_ltln$',X1: 'A_ltln$'] :
( ( 'fun_app$a'('fun_app$b'('eq$',X1),X2)
& 'fun_app$a'('fun_app$b'('eq$',X0),X1) )
=> 'fun_app$a'('fun_app$b'('eq$',X0),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom5) ).
tff(f48,axiom,
( ! [X0: 'Nat$'] : '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,
( ! [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$','phi$'))) ),
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$'] :
? [X1: 'Nat$'] : '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$')
<=> ! [X0: 'Nat$'] :
? [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$'(0)),'nat$'($difference('fun_app$g'('of_nat$',X1),'fun_app$g'('of_nat$',X0)))))),'true_ltln$') )
& ( $less('fun_app$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$'(0)),'nat$'(0)))),'true_ltln$') ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom54) ).
tff(f670,plain,
( ! [X0: 'Nat$'] :
? [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$') ) ) ),
inference(theory_normalization,[],[f55]) ).
tff(f674,plain,
( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$')
<=> ! [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$'(0)),'nat$'($sum('fun_app$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$',X0))
=> 'fun_app$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$') ) ) ),
inference(theory_normalization,[],[f56]) ).
tff(f874,plain,
( ! [X2: 'Nat$'] :
? [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$'(0)),'nat$'($sum('fun_app$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$',X2))
=> 'fun_app$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$') ) )
<=> ! [X0: 'Nat$'] :
? [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$'(0)),X1))),'true_ltln$') ),
inference(rectify,[],[f670]) ).
tff(f888,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$'('w$',X0),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$'(0)),'nat$'($sum('fun_app$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$',X2))
=> 'fun_app$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$') ) ) ),
inference(rectify,[],[f674]) ).
tff(f1181,plain,
( ! [X1: 'Nat$'] :
? [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$'(0)),X2))),'true_ltln$')
<=> ! [X0: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
inference(rectify,[],[f48]) ).
tff(f1217,plain,
! [X0: 'A_ltln$',X1: 'A_ltln$',X2: 'A_ltln$'] :
( ( 'fun_app$a'('fun_app$b'('eq$',X2),X0)
& 'fun_app$a'('fun_app$b'('eq$',X1),X2) )
=> 'fun_app$a'('fun_app$b'('eq$',X1),X0) ),
inference(rectify,[],[f7]) ).
tff(f1334,plain,
! [X0: 'A_ltln$',X1: 'A_ltln$',X2: 'A_ltln$'] :
( 'fun_app$a'('fun_app$b'('eq$',X1),X0)
| ~ 'fun_app$a'('fun_app$b'('eq$',X2),X0)
| ~ 'fun_app$a'('fun_app$b'('eq$',X1),X2) ),
inference(ennf_transformation,[],[f1217]) ).
tff(f1335,plain,
! [X2: 'A_ltln$',X0: 'A_ltln$',X1: 'A_ltln$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$',X1),X2)
| ~ 'fun_app$a'('fun_app$b'('eq$',X2),X0)
| 'fun_app$a'('fun_app$b'('eq$',X1),X0) ),
inference(flattening,[],[f1334]) ).
tff(f1398,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$') ),
inference(ennf_transformation,[],[f4]) ).
tff(f1403,plain,
( ! [X2: 'Nat$'] :
? [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$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X3),$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$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2)) ) )
<=> ! [X0: 'Nat$'] :
? [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$'(0)),X1))),'true_ltln$') ),
inference(ennf_transformation,[],[f874]) ).
tff(f1720,plain,
( ! [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$'(0)),'nat$'($sum('fun_app$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$',X2))
| 'fun_app$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$') ) )
<=> ! [X0: 'Nat$'] :
? [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,[],[f888]) ).
tff(f1914,plain,
! [X0: 'A_ltln$',X1: 'A_ltln$',X2: 'A_ltln$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$',X2),X0)
| ~ 'fun_app$a'('fun_app$b'('eq$',X0),X1)
| 'fun_app$a'('fun_app$b'('eq$',X2),X1) ),
inference(rectify,[],[f1335]) ).
tff(f1980,plain,
( ( ! [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$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X3),$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$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2)) ) )
| ? [X0: 'Nat$'] :
! [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$'] :
? [X1: 'Nat$'] : '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$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X3),$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$'(X2,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
& $less('fun_app$g'('of_nat$',X3),'fun_app$g'('of_nat$',X2)) ) ) ) ),
inference(nnf_transformation,[],[f1403]) ).
tff(f1981,plain,
( ( ! [X0: 'Nat$'] :
? [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$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X1),$uminus('fun_app$g'('of_nat$',X0))))))),'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$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'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$d'('subsequence$'('suffix$'(X2,'w$'),'nat$'(0)),X3))),'true_ltln$') )
& ( ! [X4: 'Nat$'] :
? [X5: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X4,'w$'),'nat$'(0)),X5))),'true_ltln$')
| ? [X6: 'Nat$'] :
! [X7: 'Nat$'] :
( ( ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',X6))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X6,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',X6))))))),'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$'(X6,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
& $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',X6)) ) ) ) ),
inference(rectify,[],[f1980]) ).
tff(f1982,plain,
( ( ! [X0: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$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$',sK61(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'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$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$g'('of_nat$',X0)) ) )
| ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK62,'w$'),'nat$'(0)),X3))),'true_ltln$') )
& ( ! [X4: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X4,'w$'),'nat$'(0)),sK63(X4)))),'true_ltln$')
| ! [X7: 'Nat$'] :
( ( ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK64))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK64,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK64))))))),'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$'(sK64,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
& $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK64)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64]),skolemize(X1,sK61(X0)),skolemize(X2,sK62),skolemize(X5,sK63(X4)),skolemize(X6,sK64)],[f1981]) ).
tff(f2252,plain,
( ( ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$')
| ~ '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$')
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ) ),
inference(nnf_transformation,[],[f1398]) ).
tff(f2253,plain,
( ( ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X0),X1))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) )
& ( ! [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$')
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ) ),
inference(rectify,[],[f2252]) ).
tff(f2254,plain,
( ( ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK120),X1))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) )
& ( ! [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK121(X2)))),'true_ltln$')
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK120,sK121]),skolemize(X0,sK120),skolemize(X3,sK121(X2))],[f2253]) ).
tff(f2385,plain,
( ( ! [X1: 'Nat$'] :
? [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$'(0)),X2))),'true_ltln$')
| ? [X0: 'Nat$'] : ~ 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) )
& ( ! [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$') ) ),
inference(nnf_transformation,[],[f1181]) ).
tff(f2386,plain,
( ( ! [X0: 'Nat$'] :
? [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$'] : ~ 'fun_app$a'('semantics_ltln$'('suffix$'(X2,'w$')),'until_ltln$'('true_ltln$','phi$')) )
& ( ! [X3: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X3,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ? [X4: 'Nat$'] :
! [X5: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X4,'w$'),'nat$'(0)),X5))),'true_ltln$') ) ),
inference(rectify,[],[f2385]) ).
tff(f2387,plain,
( ( ! [X0: 'Nat$'] : '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)),sK157(X0)))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK158,'w$')),'until_ltln$'('true_ltln$','phi$')) )
& ( ! [X3: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X3,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ! [X5: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK159,'w$'),'nat$'(0)),X5))),'true_ltln$') ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK157,sK158,sK159]),skolemize(X1,sK157(X0)),skolemize(X2,sK158),skolemize(X4,sK159)],[f2386]) ).
tff(f2478,plain,
( ( ! [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$'(0)),'nat$'($sum('fun_app$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$',X2))
| 'fun_app$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$') ) )
| ? [X0: 'Nat$'] :
! [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$',X0),X1))),'true_ltln$') )
& ( ! [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$')
| ? [X2: 'Nat$'] :
! [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$'(0)),'nat$'($sum('fun_app$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$',X2))
& ~ 'fun_app$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$') ) ) ) ),
inference(nnf_transformation,[],[f1720]) ).
tff(f2479,plain,
( ( ! [X0: 'Nat$'] :
? [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$'(0)),'nat$'($sum('fun_app$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$',X0))
| 'fun_app$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$') ) )
| ? [X2: 'Nat$'] :
! [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$',X2),X3))),'true_ltln$') )
& ( ! [X4: 'Nat$'] :
? [X5: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),X5))),'true_ltln$')
| ? [X6: 'Nat$'] :
! [X7: 'Nat$'] :
( ( ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',X6))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X6,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',X6))))))),'true_ltln$') )
| ( $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',X6))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X6,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ) ) ) ),
inference(rectify,[],[f2478]) ).
tff(f2480,plain,
( ( ! [X0: 'Nat$'] :
( ( $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$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$',sK176(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') )
& ( ~ $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$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$') ) )
| ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK177),X3))),'true_ltln$') )
& ( ! [X4: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$')
| ! [X7: 'Nat$'] :
( ( ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$') )
| ( $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
& ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK176,sK177,sK178,sK179]),skolemize(X1,sK176(X0)),skolemize(X2,sK177),skolemize(X5,sK178(X4)),skolemize(X6,sK179)],[f2479]) ).
tff(f2554,plain,
( ( ! [X0: 'Nat$'] : '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$'))) )
& ( 'fun_app$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$')) ) ),
inference(nnf_transformation,[],[f49]) ).
tff(f2555,plain,
( ( ! [X0: 'Nat$'] : '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$'))) )
& ( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
| ? [X1: 'Nat$'] : ~ 'fun_app$a'('semantics_ltln$'('suffix$'(X1,'w$')),'until_ltln$'('true_ltln$','phi$')) ) ),
inference(rectify,[],[f2554]) ).
tff(f2556,plain,
( ( ! [X0: 'Nat$'] : '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$'))) )
& ( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
| ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK200,'w$')),'until_ltln$'('true_ltln$','phi$')) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(X1,sK200)],[f2555]) ).
tff(f2684,plain,
! [X2: 'A_ltln$',X0: 'A_ltln$',X1: 'A_ltln$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$',X2),X0)
| ~ 'fun_app$a'('fun_app$b'('eq$',X0),X1)
| 'fun_app$a'('fun_app$b'('eq$',X2),X1) ),
inference(cnf_transformation,[],[f1914]) ).
tff(f2769,plain,
! [X3: 'Nat$',X0: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$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$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK62,'w$'),'nat$'(0)),X3))),'true_ltln$') ),
inference(cnf_transformation,[],[f1982]) ).
tff(f2770,plain,
! [X3: 'Nat$',X0: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$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$'(sK62,'w$'),'nat$'(0)),X3))),'true_ltln$')
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK61(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ),
inference(cnf_transformation,[],[f1982]) ).
tff(f3094,plain,
! [X0: 'A_ltln$'] : 'fun_app$a'('fun_app$b'('eq$',X0),X0),
inference(cnf_transformation,[],[f5]) ).
tff(f3204,plain,
! [X2: 'Nat$'] :
( 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK121(X2)))),'true_ltln$') ),
inference(cnf_transformation,[],[f2254]) ).
tff(f3205,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$',sK120),X1))),'true_ltln$')
| ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f2254]) ).
tff(f3452,plain,
! [X3: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK159,'w$'),'nat$'(0)),X5))),'true_ltln$')
| 'fun_app$a'('semantics_ltln$'('suffix$'(X3,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
inference(cnf_transformation,[],[f2387]) ).
tff(f3453,plain,
! [X0: 'Nat$'] :
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK158,'w$')),'until_ltln$'('true_ltln$','phi$'))
| '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)),sK157(X0)))),'true_ltln$') ),
inference(cnf_transformation,[],[f2387]) ).
tff(f3611,plain,
! [X7: 'Nat$',X4: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$')
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'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$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$') ),
inference(cnf_transformation,[],[f2480]) ).
tff(f3612,plain,
! [X7: 'Nat$',X4: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$')
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$') ),
inference(cnf_transformation,[],[f2480]) ).
tff(f3613,plain,
! [X7: 'Nat$',X4: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
| 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$') ),
inference(cnf_transformation,[],[f2480]) ).
tff(f3615,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$'('w$',sK177),X3))),'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$'(X0,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f2480]) ).
tff(f3616,plain,
! [X3: 'Nat$',X0: 'Nat$'] :
( 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(X0,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',sK176(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0))
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK177),X3))),'true_ltln$') ),
inference(cnf_transformation,[],[f2480]) ).
tff(f3763,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK200,'w$')),'until_ltln$'('true_ltln$','phi$'))
| 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
inference(cnf_transformation,[],[f2556]) ).
tff(f3764,plain,
! [X0: 'Nat$'] :
( ~ 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$')))
| 'fun_app$a'('semantics_ltln$'('suffix$'(X0,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
inference(cnf_transformation,[],[f2556]) ).
tff(f4149,definition,
( spl204_14
<=> ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK120),X1))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_14])],[avatar_definition]) ).
tff(f4150,plain,
( ! [X1: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK120),X1))),'true_ltln$')
| ~ spl204_14 ),
inference(avatar_component_clause,[],[f4149]) ).
tff(f4152,definition,
( spl204_15
<=> 'fun_app$a'('semantics_ltln$'('w$'),'release_ltln$'('false_ltln$','until_ltln$'('true_ltln$','phi$'))) ),
introduced(definition,[new_symbols(definition,[spl204_15])],[avatar_definition]) ).
tff(f4155,plain,
( spl204_14
| ~ spl204_15 ),
inference(avatar_split_clause,[],[f3205,f4152,f4149]) ).
tff(f4167,definition,
( spl204_18
<=> ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK62,'w$'),'nat$'(0)),X3))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_18])],[avatar_definition]) ).
tff(f4168,plain,
( ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK62,'w$'),'nat$'(0)),X3))),'true_ltln$')
| ~ spl204_18 ),
inference(avatar_component_clause,[],[f4167]) ).
tff(f4170,definition,
( spl204_19
<=> ! [X0: 'Nat$'] :
( $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$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$',sK61(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl204_19])],[avatar_definition]) ).
tff(f4171,plain,
( ! [X0: 'Nat$'] :
( '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$g'('of_nat$',sK61(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$g'('of_nat$',X0)) )
| ~ spl204_19 ),
inference(avatar_component_clause,[],[f4170]) ).
tff(f4172,plain,
( spl204_18
| spl204_19 ),
inference(avatar_split_clause,[],[f2770,f4170,f4167]) ).
tff(f4188,definition,
( spl204_23
<=> ! [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK121(X2)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_23])],[avatar_definition]) ).
tff(f4189,plain,
( ! [X2: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X2),sK121(X2)))),'true_ltln$')
| ~ spl204_23 ),
inference(avatar_component_clause,[],[f4188]) ).
tff(f4190,plain,
( spl204_23
| spl204_15 ),
inference(avatar_split_clause,[],[f3204,f4152,f4188]) ).
tff(f4193,definition,
( spl204_24
<=> ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK177),X3))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_24])],[avatar_definition]) ).
tff(f4194,plain,
( ! [X3: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',sK177),X3))),'true_ltln$')
| ~ spl204_24 ),
inference(avatar_component_clause,[],[f4193]) ).
tff(f4196,definition,
( spl204_25
<=> ! [X0: 'Nat$'] :
( '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$g'('of_nat$',sK176(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0)) ) ),
introduced(definition,[new_symbols(definition,[spl204_25])],[avatar_definition]) ).
tff(f4197,plain,
( ! [X0: 'Nat$'] :
( '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$g'('of_nat$',sK176(X0)),$uminus('fun_app$g'('of_nat$',X0))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0)) )
| ~ spl204_25 ),
inference(avatar_component_clause,[],[f4196]) ).
tff(f4198,plain,
( spl204_24
| spl204_25 ),
inference(avatar_split_clause,[],[f3616,f4196,f4193]) ).
tff(f4200,definition,
( spl204_26
<=> ! [X0: 'Nat$'] : '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)),sK157(X0)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_26])],[avatar_definition]) ).
tff(f4201,plain,
( ! [X0: 'Nat$'] : '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)),sK157(X0)))),'true_ltln$')
| ~ spl204_26 ),
inference(avatar_component_clause,[],[f4200]) ).
tff(f4203,definition,
( spl204_27
<=> 'fun_app$a'('semantics_ltln$'('suffix$'(sK158,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl204_27])],[avatar_definition]) ).
tff(f4205,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK158,'w$')),'until_ltln$'('true_ltln$','phi$'))
| spl204_27 ),
inference(avatar_component_clause,[],[f4203]) ).
tff(f4206,plain,
( spl204_26
| ~ spl204_27 ),
inference(avatar_split_clause,[],[f3453,f4203,f4200]) ).
tff(f4235,definition,
( spl204_33
<=> ! [X0: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$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$') ) ),
introduced(definition,[new_symbols(definition,[spl204_33])],[avatar_definition]) ).
tff(f4236,plain,
( ! [X0: 'Nat$'] :
( '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$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK61(X0)),'fun_app$g'('of_nat$',X0)) )
| ~ spl204_33 ),
inference(avatar_component_clause,[],[f4235]) ).
tff(f4237,plain,
( spl204_33
| spl204_18 ),
inference(avatar_split_clause,[],[f2769,f4167,f4235]) ).
tff(f4239,definition,
( spl204_34
<=> ! [X7: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
| ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl204_34])],[avatar_definition]) ).
tff(f4240,plain,
( ! [X7: 'Nat$'] :
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$')
| $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179)) )
| ~ spl204_34 ),
inference(avatar_component_clause,[],[f4239]) ).
tff(f4242,definition,
( spl204_35
<=> ! [X4: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_35])],[avatar_definition]) ).
tff(f4243,plain,
( ! [X4: 'Nat$'] : 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('w$',X4),sK178(X4)))),'true_ltln$')
| ~ spl204_35 ),
inference(avatar_component_clause,[],[f4242]) ).
tff(f4244,plain,
( spl204_34
| spl204_35 ),
inference(avatar_split_clause,[],[f3612,f4242,f4239]) ).
tff(f4255,definition,
( spl204_38
<=> ! [X3: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X3,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl204_38])],[avatar_definition]) ).
tff(f4256,plain,
( ! [X3: 'Nat$'] : 'fun_app$a'('semantics_ltln$'('suffix$'(X3,'w$')),'until_ltln$'('true_ltln$','phi$'))
| ~ spl204_38 ),
inference(avatar_component_clause,[],[f4255]) ).
tff(f4258,definition,
( spl204_39
<=> ! [X5: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK159,'w$'),'nat$'(0)),X5))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_39])],[avatar_definition]) ).
tff(f4259,plain,
( ! [X5: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK159,'w$'),'nat$'(0)),X5))),'true_ltln$')
| ~ spl204_39 ),
inference(avatar_component_clause,[],[f4258]) ).
tff(f4260,plain,
( spl204_38
| spl204_39 ),
inference(avatar_split_clause,[],[f3452,f4258,f4255]) ).
tff(f4267,definition,
( spl204_41
<=> 'fun_app$a'('semantics_ltln$'('suffix$'(sK200,'w$')),'until_ltln$'('true_ltln$','phi$')) ),
introduced(definition,[new_symbols(definition,[spl204_41])],[avatar_definition]) ).
tff(f4269,plain,
( ~ 'fun_app$a'('semantics_ltln$'('suffix$'(sK200,'w$')),'until_ltln$'('true_ltln$','phi$'))
| spl204_41 ),
inference(avatar_component_clause,[],[f4267]) ).
tff(f4270,plain,
( ~ spl204_41
| spl204_15 ),
inference(avatar_split_clause,[],[f3763,f4152,f4267]) ).
tff(f4272,definition,
( spl204_42
<=> 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_42])],[avatar_definition]) ).
tff(f4274,plain,
( ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'(0)))),'true_ltln$')
| spl204_42 ),
inference(avatar_component_clause,[],[f4272]) ).
tff(f4276,definition,
( spl204_43
<=> ! [X7: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$') ),
introduced(definition,[new_symbols(definition,[spl204_43])],[avatar_definition]) ).
tff(f4277,plain,
( ! [X7: 'Nat$'] : ~ 'fun_app$a'('fun_app$b'('eq$','fun_app$c'('foldl$'('af_letter$','until_ltln$'('true_ltln$','phi$')),'fun_app$d'('subsequence$'('suffix$'(sK179,'w$'),'nat$'(0)),'nat$'($sum('fun_app$g'('of_nat$',X7),$uminus('fun_app$g'('of_nat$',sK179))))))),'true_ltln$')
| ~ spl204_43 ),
inference(avatar_component_clause,[],[f4276]) ).
tff(f4278,plain,
( spl204_35
| ~ spl204_42
| spl204_43 ),
inference(avatar_split_clause,[],[f3611,f4276,f4272,f4242]) ).
tff(f4280,definition,
( spl204_44
<=> ! [X0: 'Nat$'] :
( '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$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0)) ) ),
introduced(definition,[new_symbols(definition,[spl204_44])],[avatar_definition]) ).
tff(f4281,plain,
( ! [X0: 'Nat$'] :
( '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$'(0)))),'true_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK176(X0)),'fun_app$g'('of_nat$',X0)) )
| ~ spl204_44 ),
inference(avatar_component_clause,[],[f4280]) ).
tff(f4282,plain,
( spl204_24
| spl204_44 ),
inference(avatar_split_clause,[],[f3615,f4280,f4193]) ).
tff(f4288,plain,
( spl204_38
| ~ spl204_15 ),
inference(avatar_split_clause,[],[f3764,f4152,f4255]) ).
tff(f4305,definition,
( spl204_49
<=> ! [X7: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179)) ),
introduced(definition,[new_symbols(definition,[spl204_49])],[avatar_definition]) ).
tff(f4306,plain,
( ! [X7: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',X7),'fun_app$g'('of_nat$',sK179))
| ~ spl204_49 ),
inference(avatar_component_clause,[],[f4305]) ).
tff(f4307,plain,
( spl204_35
| spl204_49
| ~ spl204_42 ),
inference(avatar_split_clause,[],[f3613,f4272,f4305,f4242]) ).
tff(f4323,plain,
( $false
| spl204_27
| ~ spl204_38 ),
inference(unit_resulting_resolution,[],[f4256,f4205]) ).
tff(f4326,plain,
( spl204_27
| ~ spl204_38 ),
inference(avatar_contradiction_clause,[],[f4323]) ).
tff(f4347,plain,
( $false
| ~ spl204_38
| spl204_41 ),
inference(resolution,[],[f4269,f4256]) ).
tff(f4349,plain,
( ~ spl204_38
| spl204_41 ),
inference(avatar_contradiction_clause,[],[f4347]) ).
tff(f4623,plain,
( $false
| ~ spl204_23
| ~ spl204_24 ),
inference(unit_resulting_resolution,[],[f4194,f4189]) ).
tff(f4636,plain,
( ~ spl204_23
| ~ spl204_24 ),
inference(avatar_contradiction_clause,[],[f4623]) ).
tff(f4738,plain,
( $false
| ~ spl204_18
| ~ spl204_26 ),
inference(unit_resulting_resolution,[],[f2684,f3094,f4168,f4201]) ).
tff(f4751,plain,
( ~ spl204_18
| ~ spl204_26 ),
inference(avatar_contradiction_clause,[],[f4738]) ).
tff(f4885,plain,
( ~ $less('fun_app$g'('of_nat$',sK61(sK179)),'fun_app$g'('of_nat$',sK179))
| ~ spl204_33
| spl204_42 ),
inference(resolution,[],[f4236,f4274]) ).
tff(f4893,definition,
( spl204_75
<=> $less('fun_app$g'('of_nat$',sK61(sK179)),'fun_app$g'('of_nat$',sK179)) ),
introduced(definition,[new_symbols(definition,[spl204_75])],[avatar_definition]) ).
tff(f4896,plain,
( ~ spl204_75
| ~ spl204_33
| spl204_42 ),
inference(avatar_split_clause,[],[f4885,f4272,f4235,f4893]) ).
tff(f4939,plain,
( $less('fun_app$g'('of_nat$',sK61(sK179)),'fun_app$g'('of_nat$',sK179))
| $less('fun_app$g'('of_nat$',sK61(sK179)),'fun_app$g'('of_nat$',sK179))
| ~ spl204_19
| ~ spl204_34 ),
inference(resolution,[],[f4171,f4240]) ).
tff(f4946,plain,
( $less('fun_app$g'('of_nat$',sK61(sK179)),'fun_app$g'('of_nat$',sK179))
| ~ spl204_19
| ~ spl204_34 ),
inference(duplicate_literal_removal,[],[f4939]) ).
tff(f4948,plain,
( spl204_75
| ~ spl204_19
| ~ spl204_34 ),
inference(avatar_split_clause,[],[f4946,f4239,f4170,f4893]) ).
tff(f5066,plain,
( $false
| ~ spl204_14
| ~ spl204_35 ),
inference(unit_resulting_resolution,[],[f2684,f4150,f3094,f4243]) ).
tff(f5083,plain,
( ~ spl204_14
| ~ spl204_35 ),
inference(avatar_contradiction_clause,[],[f5066]) ).
tff(f5143,plain,
( ~ $less('fun_app$g'('of_nat$',sK176(sK159)),'fun_app$g'('of_nat$',sK159))
| ~ spl204_39
| ~ spl204_44 ),
inference(unit_resulting_resolution,[],[f4281,f4259]) ).
tff(f5156,definition,
( spl204_85
<=> $less('fun_app$g'('of_nat$',sK176(sK159)),'fun_app$g'('of_nat$',sK159)) ),
introduced(definition,[new_symbols(definition,[spl204_85])],[avatar_definition]) ).
tff(f5159,plain,
( ~ spl204_85
| ~ spl204_39
| ~ spl204_44 ),
inference(avatar_split_clause,[],[f5143,f4280,f4258,f5156]) ).
tff(f5384,plain,
( $less('fun_app$g'('of_nat$',sK176(sK159)),'fun_app$g'('of_nat$',sK159))
| ~ spl204_25
| ~ spl204_39 ),
inference(resolution,[],[f4197,f4259]) ).
tff(f5393,plain,
( spl204_85
| ~ spl204_25
| ~ spl204_39 ),
inference(avatar_split_clause,[],[f5384,f4258,f4196,f5156]) ).
tff(f5550,plain,
( $false
| ~ spl204_19
| ~ spl204_43
| ~ spl204_49 ),
inference(unit_resulting_resolution,[],[f4171,f4306,f4277]) ).
tff(f5558,plain,
( ~ spl204_19
| ~ spl204_43
| ~ spl204_49 ),
inference(avatar_contradiction_clause,[],[f5550]) ).
tff(f5564,plain,
$false,
inference(avatar_smt_refutation,[],[f5558,f5393,f5159,f5083,f4948,f4896,f4751,f4636,f4349,f4326,f4307,f4288,f4282,f4278,f4270,f4260,f4244,f4237,f4206,f4198,f4190,f4172,f4155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP359_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 12:55:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 3.44/1.42 % (3492425)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.44/1.42 % (3492434)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4126224202:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.44/1.42 % (3492434)Instruction limit reached!
% 3.44/1.42 % (3492434)------------------------------
% 3.44/1.42 % (3492434)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (3492434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (3492434)CaDiCaL version: 2.1.3
% 3.44/1.42 % (3492434)Termination reason: Instruction limit
% 3.44/1.42 % (3492434)Termination phase: Property scanning
% 3.44/1.42 % (3492434)Time elapsed: 0.002 s
% 3.44/1.42 % (3492434)Peak memory usage: 86 MB
% 3.44/1.42 % (3492434)Instructions burned: 4 (million)
% 3.44/1.42 % (3492431)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1351287449:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.44/1.42 % (3492432)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=701988059:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.44/1.42 % (3492430)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2730436135:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.44/1.42 % (3492433)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=4026786534:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.44/1.42 % (3492435)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1426596242:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.44/1.42 % (3492436)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=730427463:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.44/1.42 % (3492433)Instruction limit reached!
% 3.44/1.42 % (3492433)------------------------------
% 3.44/1.42 % (3492433)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (3492433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (3492433)CaDiCaL version: 2.1.3
% 3.44/1.42 % (3492433)Termination reason: Instruction limit
% 3.44/1.42 % (3492433)Termination phase: Property scanning
% 3.44/1.42 % (3492433)Time elapsed: 0.005 s
% 3.44/1.42 % (3492433)Peak memory usage: 86 MB
% 3.44/1.42 % (3492433)Instructions burned: 9 (million)
% 3.44/1.42 % (3492430)Instruction limit reached!
% 3.44/1.42 % (3492430)------------------------------
% 3.44/1.42 % (3492430)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (3492430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (3492430)CaDiCaL version: 2.1.3
% 3.44/1.42 % (3492430)Termination reason: Instruction limit
% 3.44/1.42 % (3492430)Termination phase: shuffling
% 3.44/1.42 % (3492430)Time elapsed: 0.007 s
% 3.44/1.42 % (3492430)Peak memory usage: 86 MB
% 3.44/1.42 % (3492430)Instructions burned: 13 (million)
% 3.44/1.42 % (3492436)Instruction limit reached!
% 3.44/1.42 % (3492436)------------------------------
% 3.44/1.42 % (3492436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (3492436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (3492436)CaDiCaL version: 2.1.3
% 3.44/1.42 % (3492436)Termination reason: Instruction limit
% 3.44/1.42 % (3492436)Termination phase: Unused predicate definition removal
% 3.44/1.42 % (3492436)Time elapsed: 0.016 s
% 3.44/1.42 % (3492436)Peak memory usage: 87 MB
% 3.44/1.42 % (3492436)Instructions burned: 33 (million)
% 3.44/1.42 % (3492435)Instruction limit reached!
% 3.44/1.42 % (3492435)------------------------------
% 3.44/1.42 % (3492435)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.44/1.42 % (3492435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.44/1.42 % (3492435)CaDiCaL version: 2.1.3
% 3.44/1.42 % (3492435)Termination reason: Instruction limit
% 3.44/1.42 % (3492435)Termination phase: Property scanning
% 3.44/1.42 % (3492435)Time elapsed: 0.026 s
% 3.44/1.42 % (3492435)Peak memory usage: 88 MB
% 3.44/1.42 % (3492435)Instructions burned: 48 (million)
% 3.44/1.42 % (3492438)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=4130248180:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.44/1.42 % (3492438)Instruction limit reached!
% 4.31/1.57 % (3492438)------------------------------
% 4.31/1.57 % (3492438)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492438)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492438)Termination reason: Instruction limit
% 4.31/1.57 % (3492438)Termination phase: SInE selection
% 4.31/1.57 % (3492438)Time elapsed: 0.004 s
% 4.31/1.57 % (3492438)Peak memory usage: 86 MB
% 4.31/1.57 % (3492438)Instructions burned: 15 (million)
% 4.31/1.57 % (3492432)Instruction limit reached!
% 4.31/1.57 % (3492432)------------------------------
% 4.31/1.57 % (3492432)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492432)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492432)Termination reason: Instruction limit
% 4.31/1.57 % (3492432)Termination phase: Saturation
% 4.31/1.57 % (3492432)Time elapsed: 0.134 s
% 4.31/1.57 % (3492432)Peak memory usage: 118 MB
% 4.31/1.57 % (3492432)Instructions burned: 201 (million)
% 4.31/1.57 % (3492445)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=660406313:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 4.31/1.57 % (3492446)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3031779608:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.31/1.57 % (3492446)Instruction limit reached!
% 4.31/1.57 % (3492446)------------------------------
% 4.31/1.57 % (3492446)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492446)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492446)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492446)Termination reason: Instruction limit
% 4.31/1.57 % (3492446)Termination phase: Preprocessing 1
% 4.31/1.57 % (3492446)Time elapsed: 0.010 s
% 4.31/1.57 % (3492446)Peak memory usage: 86 MB
% 4.31/1.57 % (3492446)Instructions burned: 17 (million)
% 4.31/1.57 % (3492445)Instruction limit reached!
% 4.31/1.57 % (3492445)------------------------------
% 4.31/1.57 % (3492445)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492445)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492445)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492445)Termination reason: Instruction limit
% 4.31/1.57 % (3492445)Termination phase: Preprocessing 1
% 4.31/1.57 % (3492445)Time elapsed: 0.015 s
% 4.31/1.57 % (3492445)Peak memory usage: 86 MB
% 4.31/1.57 % (3492445)Instructions burned: 30 (million)
% 4.31/1.57 % (3492447)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=54713962:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.31/1.57 % (3492448)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=3335666973:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 4.31/1.57 % (3492447)Instruction limit reached!
% 4.31/1.57 % (3492447)------------------------------
% 4.31/1.57 % (3492447)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492447)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492447)Termination reason: Instruction limit
% 4.31/1.57 % (3492447)Termination phase: Property scanning
% 4.31/1.57 % (3492447)Time elapsed: 0.013 s
% 4.31/1.57 % (3492447)Peak memory usage: 86 MB
% 4.31/1.57 % (3492447)Instructions burned: 26 (million)
% 4.31/1.57 % (3492448)Instruction limit reached!
% 4.31/1.57 % (3492448)------------------------------
% 4.31/1.57 % (3492448)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.31/1.57 % (3492448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.31/1.57 % (3492448)CaDiCaL version: 2.1.3
% 4.31/1.57 % (3492448)Termination reason: Instruction limit
% 4.31/1.57 % (3492448)Termination phase: Preprocessing 1
% 4.31/1.57 % (3492448)Time elapsed: 0.014 s
% 4.31/1.57 % (3492448)Peak memory usage: 86 MB
% 4.31/1.57 % (3492448)Instructions burned: 28 (million)
% 4.31/1.57 % (3492450)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1361149944:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 4.31/1.57 % (3492431)Instruction limit reached!
% 5.43/1.72 % (3492431)------------------------------
% 5.43/1.72 % (3492431)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492431)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492431)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492431)Termination reason: Instruction limit
% 5.43/1.72 % (3492431)Termination phase: Saturation
% 5.43/1.72 % (3492431)Time elapsed: 0.202 s
% 5.43/1.72 % (3492431)Peak memory usage: 119 MB
% 5.43/1.72 % (3492431)Instructions burned: 308 (million)
% 5.43/1.72 % (3492450)Instruction limit reached!
% 5.43/1.72 % (3492450)------------------------------
% 5.43/1.72 % (3492450)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492450)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492450)Termination reason: Instruction limit
% 5.43/1.72 % (3492450)Termination phase: Property scanning
% 5.43/1.72 % (3492450)Time elapsed: 0.023 s
% 5.43/1.72 % (3492450)Peak memory usage: 88 MB
% 5.43/1.72 % (3492450)Instructions burned: 87 (million)
% 5.43/1.72 % (3492451)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=72999426:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 5.43/1.72 % (3492451)Instruction limit reached!
% 5.43/1.72 % (3492451)------------------------------
% 5.43/1.72 % (3492451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492451)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492451)Termination reason: Instruction limit
% 5.43/1.72 % (3492451)Termination phase: shuffling
% 5.43/1.72 % (3492451)Time elapsed: 0.003 s
% 5.43/1.72 % (3492451)Peak memory usage: 85 MB
% 5.43/1.72 % (3492451)Instructions burned: 4 (million)
% 5.43/1.72 % (3492454)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=3879315115:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 5.43/1.72 % (3492457)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=3768857982:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 5.43/1.72 % (3492457)Instruction limit reached!
% 5.43/1.72 % (3492457)------------------------------
% 5.43/1.72 % (3492457)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492457)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492457)Termination reason: Instruction limit
% 5.43/1.72 % (3492457)Termination phase: Property scanning
% 5.43/1.72 % (3492457)Time elapsed: 0.004 s
% 5.43/1.72 % (3492457)Peak memory usage: 86 MB
% 5.43/1.72 % (3492457)Instructions burned: 6 (million)
% 5.43/1.72 % (3492462)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=4244529100:st=3:i=2:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/2Mi)
% 5.43/1.72 % (3492462)Instruction limit reached!
% 5.43/1.72 % (3492462)------------------------------
% 5.43/1.72 % (3492462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492462)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492462)Termination reason: Instruction limit
% 5.43/1.72 % (3492462)Termination phase: Property scanning
% 5.43/1.72 % (3492462)Time elapsed: 0.002 s
% 5.43/1.72 % (3492462)Peak memory usage: 86 MB
% 5.43/1.72 % (3492462)Instructions burned: 5 (million)
% 5.43/1.72 % (3492459)lrs+10_1_thi=all:si=on:fd=off:random_seed=1671719628:i=53:rtra=on:gtg=all_2995 on theBenchmark for (2995ds/53Mi)
% 5.43/1.72 % (3492458)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=1187677117:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2995 on theBenchmark for (2995ds/66Mi)
% 5.43/1.72 % (3492459)Instruction limit reached!
% 5.43/1.72 % (3492459)------------------------------
% 5.43/1.72 % (3492459)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.43/1.72 % (3492459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.43/1.72 % (3492459)CaDiCaL version: 2.1.3
% 5.43/1.72 % (3492459)Termination reason: Instruction limit
% 5.43/1.72 % (3492459)Termination phase: Preprocessing 1
% 5.43/1.72 % (3492459)Time elapsed: 0.025 s
% 5.43/1.72 % (3492459)Peak memory usage: 86 MB
% 5.43/1.72 % (3492459)Instructions burned: 54 (million)
% 5.43/1.72 % (3492458)Instruction limit reached!
% 5.94/1.86 % (3492458)------------------------------
% 5.94/1.86 % (3492458)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492458)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492458)Termination reason: Instruction limit
% 5.94/1.86 % (3492458)Termination phase: Property scanning
% 5.94/1.86 % (3492458)Time elapsed: 0.036 s
% 5.94/1.86 % (3492458)Peak memory usage: 88 MB
% 5.94/1.86 % (3492458)Instructions burned: 69 (million)
% 5.94/1.86 % (3492461)ott+1011_1_to=kbo:plsq=on:drc=off:si=on:plsqr=32,1:sp=const_frequency:sos=all:uwa=one_side_interpreted:sac=on:random_seed=518443465:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2995 on theBenchmark for (2995ds/8Mi)
% 5.94/1.86 % (3492461)Instruction limit reached!
% 5.94/1.86 % (3492461)------------------------------
% 5.94/1.86 % (3492461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492461)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492461)Termination reason: Instruction limit
% 5.94/1.86 % (3492461)Termination phase: Property scanning
% 5.94/1.86 % (3492461)Time elapsed: 0.005 s
% 5.94/1.86 % (3492461)Peak memory usage: 85 MB
% 5.94/1.86 % (3492461)Instructions burned: 10 (million)
% 5.94/1.86 % (3492471)dis+10_1_si=on:random_seed=1616591073:i=10:ep=R:rtra=on_2994 on theBenchmark for (2994ds/10Mi)
% 5.94/1.86 % (3492471)Instruction limit reached!
% 5.94/1.86 % (3492471)------------------------------
% 5.94/1.86 % (3492471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492471)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492471)Termination reason: Instruction limit
% 5.94/1.86 % (3492471)Termination phase: Including theory axioms
% 5.94/1.86 % (3492471)Time elapsed: 0.004 s
% 5.94/1.86 % (3492471)Peak memory usage: 86 MB
% 5.94/1.86 % (3492471)Instructions burned: 15 (million)
% 5.94/1.86 % (3492454)Instruction limit reached!
% 5.94/1.86 % (3492454)------------------------------
% 5.94/1.86 % (3492454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492454)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492454)Termination reason: Instruction limit
% 5.94/1.86 % (3492454)Termination phase: Saturation
% 5.94/1.86 % (3492454)Time elapsed: 0.123 s
% 5.94/1.86 % (3492454)Peak memory usage: 92 MB
% 5.94/1.86 % (3492454)Instructions burned: 181 (million)
% 5.94/1.86 % (3492464)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=1826401916:i=2:doe=on:canc=force:asg=cautious:rtra=on_2995 on theBenchmark for (2995ds/2Mi)
% 5.94/1.86 % (3492464)Instruction limit reached!
% 5.94/1.86 % (3492464)------------------------------
% 5.94/1.86 % (3492464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492464)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492464)Termination reason: Instruction limit
% 5.94/1.86 % (3492464)Termination phase: Property scanning
% 5.94/1.86 % (3492464)Time elapsed: 0.003 s
% 5.94/1.86 % (3492464)Peak memory usage: 86 MB
% 5.94/1.86 % (3492464)Instructions burned: 4 (million)
% 5.94/1.86 % (3492467)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=2926749023:i=127:doe=on:rtra=on_2994 on theBenchmark for (2994ds/127Mi)
% 5.94/1.86 % (3492474)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=3241678281:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2994 on theBenchmark for (2994ds/35Mi)
% 5.94/1.86 % (3492472)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=4195343589:i=26:canc=cautious:av=off:rtra=on_2994 on theBenchmark for (2994ds/26Mi)
% 5.94/1.86 % (3492472)Instruction limit reached!
% 5.94/1.86 % (3492472)------------------------------
% 5.94/1.86 % (3492472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.94/1.86 % (3492472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.94/1.86 % (3492472)CaDiCaL version: 2.1.3
% 5.94/1.86 % (3492472)Termination reason: Instruction limit
% 5.94/1.86 % (3492472)Termination phase: Preprocessing 1
% 9.15/2.19 % (3492472)Time elapsed: 0.013 s
% 9.15/2.19 % (3492472)Peak memory usage: 86 MB
% 9.15/2.19 % (3492472)Instructions burned: 27 (million)
% 9.15/2.19 % (3492474)Instruction limit reached!
% 9.15/2.19 % (3492474)------------------------------
% 9.15/2.19 % (3492474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.19 % (3492474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.19 % (3492474)CaDiCaL version: 2.1.3
% 9.15/2.19 % (3492474)Termination reason: Instruction limit
% 9.15/2.19 % (3492474)Termination phase: shuffling
% 9.15/2.19 % (3492474)Time elapsed: 0.019 s
% 9.15/2.19 % (3492474)Peak memory usage: 86 MB
% 9.15/2.19 % (3492474)Instructions burned: 35 (million)
% 9.15/2.19 % (3492475)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=2128369219:i=2:fsr=off:rtra=on:inst=on_2994 on theBenchmark for (2994ds/2Mi)
% 9.15/2.19 % (3492475)Instruction limit reached!
% 9.15/2.19 % (3492475)------------------------------
% 9.15/2.19 % (3492475)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.19 % (3492475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.19 % (3492475)CaDiCaL version: 2.1.3
% 9.15/2.19 % (3492475)Termination reason: Instruction limit
% 9.15/2.19 % (3492475)Termination phase: Property scanning
% 9.15/2.19 % (3492475)Time elapsed: 0.003 s
% 9.15/2.19 % (3492475)Peak memory usage: 86 MB
% 9.15/2.19 % (3492475)Instructions burned: 4 (million)
% 9.15/2.19 % (3492478)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=3138570756:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2993 on theBenchmark for (2993ds/8Mi)
% 9.15/2.19 % (3492478)Instruction limit reached!
% 9.15/2.19 % (3492478)------------------------------
% 9.15/2.19 % (3492478)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.19 % (3492478)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.19 % (3492478)CaDiCaL version: 2.1.3
% 9.15/2.19 % (3492478)Termination reason: Instruction limit
% 9.15/2.19 % (3492478)Termination phase: Property scanning
% 9.15/2.19 % (3492478)Time elapsed: 0.003 s
% 9.15/2.19 % (3492478)Peak memory usage: 86 MB
% 9.15/2.19 % (3492478)Instructions burned: 10 (million)
% 9.15/2.19 % (3492467)Instruction limit reached!
% 9.15/2.19 % (3492467)------------------------------
% 9.15/2.19 % (3492467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.19 % (3492467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.19 % (3492467)CaDiCaL version: 2.1.3
% 9.15/2.19 % (3492467)Termination reason: Instruction limit
% 9.15/2.19 % (3492467)Termination phase: Saturation
% 9.15/2.19 % (3492467)Time elapsed: 0.087 s
% 9.15/2.19 % (3492467)Peak memory usage: 115 MB
% 9.15/2.19 % (3492467)Instructions burned: 129 (million)
% 9.15/2.19 % (3492479)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=3695912797:i=370:ep=RS:fsr=off:rtra=on_2993 on theBenchmark for (2993ds/370Mi)
% 9.15/2.19 % (3492480)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=1652513247:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2993 on theBenchmark for (2993ds/13Mi)
% 9.15/2.19 % (3492480)Instruction limit reached!
% 9.15/2.19 % (3492480)------------------------------
% 9.15/2.19 % (3492480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.19 % (3492480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.19 % (3492480)CaDiCaL version: 2.1.3
% 9.15/2.19 % (3492480)Termination reason: Instruction limit
% 9.15/2.19 % (3492480)Termination phase: Property scanning
% 9.15/2.19 % (3492480)Time elapsed: 0.007 s
% 9.15/2.19 % (3492480)Peak memory usage: 85 MB
% 9.15/2.19 % (3492480)Instructions burned: 15 (million)
% 9.15/2.19 % (3492486)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=1392400025:i=10:rtra=on_2992 on theBenchmark for (2992ds/10Mi)
% 9.15/2.19 % (3492484)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=2870890114:i=226:rtra=on:gtg=position:ss=axioms_2992 on theBenchmark for (2992ds/226Mi)
% 9.15/2.19 % (3492487)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=3689799285:i=71:rtra=on:gtg=exists_top_2992 on theBenchmark for (2992ds/71Mi)
% 9.15/2.19 % (3492486)Instruction limit reached!
% 9.15/2.19 % (3492486)------------------------------
% 9.15/2.19 % (3492486)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492486)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492486)Termination reason: Instruction limit
% 9.15/2.25 % (3492486)Termination phase: Property scanning
% 9.15/2.25 % (3492486)Time elapsed: 0.006 s
% 9.15/2.25 % (3492486)Peak memory usage: 86 MB
% 9.15/2.25 % (3492486)Instructions burned: 12 (million)
% 9.15/2.25 % (3492490)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=1582991406:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2992 on theBenchmark for (2992ds/294Mi)
% 9.15/2.25 % (3492489)lrs+1010_1_to=lpo:prlc=on:sil=128000:prc=on:drc=off:si=on:sp=const_max:thsqr=8,1:tha=some:nwc=5:random_seed=1306563382:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2992 on theBenchmark for (2992ds/75Mi)
% 9.15/2.25 % (3492487)Instruction limit reached!
% 9.15/2.25 % (3492487)------------------------------
% 9.15/2.25 % (3492487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492487)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492487)Termination reason: Instruction limit
% 9.15/2.25 % (3492487)Termination phase: shuffling
% 9.15/2.25 % (3492487)Time elapsed: 0.037 s
% 9.15/2.25 % (3492487)Peak memory usage: 88 MB
% 9.15/2.25 % (3492487)Instructions burned: 72 (million)
% 9.15/2.25 % (3492489)Instruction limit reached!
% 9.15/2.25 % (3492489)------------------------------
% 9.15/2.25 % (3492489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492489)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492489)Termination reason: Instruction limit
% 9.15/2.25 % (3492489)Termination phase: Property scanning
% 9.15/2.25 % (3492489)Time elapsed: 0.038 s
% 9.15/2.25 % (3492489)Peak memory usage: 89 MB
% 9.15/2.25 % (3492489)Instructions burned: 76 (million)
% 9.15/2.25 % (3492493)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=2693433464:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2991 on theBenchmark for (2991ds/130Mi)
% 9.15/2.25 % (3492490)Instruction limit reached!
% 9.15/2.25 % (3492490)------------------------------
% 9.15/2.25 % (3492490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492490)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492490)Termination reason: Instruction limit
% 9.15/2.25 % (3492490)Termination phase: Saturation
% 9.15/2.25 % (3492490)Time elapsed: 0.098 s
% 9.15/2.25 % (3492490)Peak memory usage: 93 MB
% 9.15/2.25 % (3492490)Instructions burned: 295 (million)
% 9.15/2.25 % (3492479)Instruction limit reached!
% 9.15/2.25 % (3492479)------------------------------
% 9.15/2.25 % (3492479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492479)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492479)Termination reason: Instruction limit
% 9.15/2.25 % (3492479)Termination phase: Saturation
% 9.15/2.25 % (3492479)Time elapsed: 0.213 s
% 9.15/2.25 % (3492479)Peak memory usage: 94 MB
% 9.15/2.25 % (3492479)Instructions burned: 370 (million)
% 9.15/2.25 % (3492493)Instruction limit reached!
% 9.15/2.25 % (3492493)------------------------------
% 9.15/2.25 % (3492493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492493)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492493)Termination reason: Instruction limit
% 9.15/2.25 % (3492493)Termination phase: Property scanning
% 9.15/2.25 % (3492493)Time elapsed: 0.058 s
% 9.15/2.25 % (3492493)Peak memory usage: 89 MB
% 9.15/2.25 % (3492493)Instructions burned: 132 (million)
% 9.15/2.25 % (3492484)Instruction limit reached!
% 9.15/2.25 % (3492484)------------------------------
% 9.15/2.25 % (3492484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492484)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492484)Termination reason: Instruction limit
% 9.15/2.25 % (3492484)Termination phase: Saturation
% 9.15/2.25 % (3492484)Time elapsed: 0.147 s
% 9.15/2.25 % (3492484)Peak memory usage: 118 MB
% 9.15/2.25 % (3492484)Instructions burned: 226 (million)
% 9.15/2.25 % (3492497)lrs+21_1_to=kbo:sil=64000:thi=all:sas=z3:si=on:spb=goal_then_units:tha=off:nwc=3:random_seed=1325990359:i=131:rtra=on_2991 on theBenchmark for (2991ds/131Mi)
% 9.15/2.25 % (3492500)dis+1010_16_to=lpo:sil=64000:thi=strong:sas=z3:si=on:nwc=5:random_seed=3878004549:i=40:gtgl=2:rtra=on:gtg=exists_sym:ev=force_2990 on theBenchmark for (2990ds/40Mi)
% 9.15/2.25 % (3492500)Instruction limit reached!
% 9.15/2.25 % (3492500)------------------------------
% 9.15/2.25 % (3492500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492500)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492500)Termination reason: Instruction limit
% 9.15/2.25 % (3492500)Termination phase: Property scanning
% 9.15/2.25 % (3492500)Time elapsed: 0.020 s
% 9.15/2.25 % (3492500)Peak memory usage: 86 MB
% 9.15/2.25 % (3492500)Instructions burned: 40 (million)
% 9.15/2.25 % (3492501)lrs+10_1_to=lpo:sil=64000:si=on:sos=on:urr=on:random_seed=3986536007:i=307:rtra=on:gtg=exists_top_2990 on theBenchmark for (2990ds/307Mi)
% 9.15/2.25 % (3492503)ott+1010_3:1_to=kbo:sil=128000:thi=overlap:sas=z3:si=on:urr=on:tha=off:s2agt=32:random_seed=1774830542:s2a=on:i=598:doe=on:bs=on:canc=cautious:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/598Mi)
% 9.15/2.25 % (3492504)lrs+1011_5:1_to=kbo:sil=64000:thi=all:si=on:uwa=ground:br=off:random_seed=3260394806:i=131:canc=cautious:fsr=off:rtra=on_2989 on theBenchmark for (2989ds/131Mi)
% 9.15/2.25 % (3492497)Instruction limit reached!
% 9.15/2.25 % (3492497)------------------------------
% 9.15/2.25 % (3492497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492497)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492497)Termination reason: Instruction limit
% 9.15/2.25 % (3492497)Termination phase: Saturation
% 9.15/2.25 % (3492497)Time elapsed: 0.117 s
% 9.15/2.25 % (3492497)Peak memory usage: 132 MB
% 9.15/2.25 % (3492497)Instructions burned: 132 (million)
% 9.15/2.25 % (3492505)dis+11_1_to=lpo:pum=on:sas=z3:si=on:sp=reverse_arity:sos=theory:thsqr=2,1:tha=some:s2agt=20:random_seed=3693885386:s2pl=no:i=259:sd=10:thsqd=64:thsqc=64:rtra=on:ss=axioms:thsq=on_2989 on theBenchmark for (2989ds/259Mi)
% 9.15/2.25 % (3492507)dis+10_1_si=on:random_seed=2297952717:s2a=on:i=1000:rtra=on:gtg=exists_all_2989 on theBenchmark for (2989ds/1000Mi)
% 9.15/2.25 % (3492504)Instruction limit reached!
% 9.15/2.25 % (3492504)------------------------------
% 9.15/2.25 % (3492504)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492504)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492504)Termination reason: Instruction limit
% 9.15/2.25 % (3492504)Termination phase: Saturation
% 9.15/2.25 % (3492504)Time elapsed: 0.090 s
% 9.15/2.25 % (3492504)Peak memory usage: 115 MB
% 9.15/2.25 % (3492504)Instructions burned: 132 (million)
% 9.15/2.25 % (3492509)dis+1010_1_to=lpo:sil=128000:tgt=full:si=on:sp=const_frequency:uwa=off:tha=off:nwc=1:random_seed=770504810:i=383:fsr=off:rtra=on:ev=force_2989 on theBenchmark for (2989ds/383Mi)
% 9.15/2.25 % (3492503)First to succeed.
% 9.15/2.25 % (3492503)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3492425"
% 9.15/2.25 % (3492501)Instruction limit reached!
% 9.15/2.25 % (3492501)------------------------------
% 9.15/2.25 % (3492501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492501)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492501)Termination reason: Instruction limit
% 9.15/2.25 % (3492501)Termination phase: Saturation
% 9.15/2.25 % (3492501)Time elapsed: 0.166 s
% 9.15/2.25 % (3492501)Peak memory usage: 94 MB
% 9.15/2.25 % (3492501)Instructions burned: 307 (million)
% 9.15/2.25 % (3492513)lrs+10_1_to=kbo:sil=64000:si=on:norm_ineq=on:sp=unary_frequency:random_seed=2047417827:i=141:doe=on:rtra=on_2988 on theBenchmark for (2988ds/141Mi)
% 9.15/2.25 % (3492505)Instruction limit reached!
% 9.15/2.25 % (3492505)------------------------------
% 9.15/2.25 % (3492505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492505)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492505)Termination reason: Instruction limit
% 9.15/2.25 % (3492505)Termination phase: Saturation
% 9.15/2.25 % (3492505)Time elapsed: 0.186 s
% 9.15/2.25 % (3492505)Peak memory usage: 118 MB
% 9.15/2.25 % (3492505)Instructions burned: 260 (million)
% 9.15/2.25 % (3492513)Instruction limit reached!
% 9.15/2.25 % (3492513)------------------------------
% 9.15/2.25 % (3492513)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.15/2.25 % (3492513)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.15/2.25 % (3492513)CaDiCaL version: 2.1.3
% 9.15/2.25 % (3492513)Termination reason: Instruction limit
% 9.15/2.25 % (3492513)Termination phase: Saturation
% 9.15/2.25 % (3492513)Time elapsed: 0.076 s
% 9.15/2.25 % (3492513)Peak memory usage: 91 MB
% 9.15/2.25 % (3492513)Instructions burned: 141 (million)
% 9.15/2.25 % (3492517)lrs+10_1024_to=kbo:sil=128000:fde=unused:sas=z3:si=on:norm_ineq=on:sos=on:tha=off:random_seed=1399068641:i=65:nm=16:rtra=on_2987 on theBenchmark for (2987ds/65Mi)
% 9.15/2.25 % (3492503)Refutation found. Thanks to Tanya!
% 9.15/2.25 % SZS status Theorem for theBenchmark
% 9.15/2.25 % SZS output start Proof for theBenchmark
% See solution above
% 10.13/2.35 % (3492503)------------------------------
% 10.13/2.35 % (3492503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.13/2.35 % (3492503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.13/2.35 % (3492503)CaDiCaL version: 2.1.3
% 10.13/2.35 % (3492503)Termination reason: Refutation
% 10.13/2.35 % (3492503)Time elapsed: 0.149 s
% 10.13/2.35 % (3492503)Peak memory usage: 138 MB
% 10.13/2.35 % (3492503)Instructions burned: 356 (million)
% 10.13/2.35 % (3492503)------------------------------
% 10.13/2.35 % (3492503)------------------------------
% 10.13/2.35 % (3492425)Success in time 1.401 s
% 10.13/2.35 % Vampire exiting
%------------------------------------------------------------------------------