%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP375_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 11:33:44 AM UTC 2026
% Result : Theorem 10.73s 2.73s
% Output : Refutation 12.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 17
% Syntax : Number of formulae : 85 ( 7 unt; 0 typ; 8 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 304 ( 144 ~; 107 |; 19 &)
% ( 17 <=>; 16 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number arithmetic : 61 ( 31 atm; 0 fun; 30 num; 0 var)
% Number of types : 38 ( 36 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 9 prp; 0-3 aty)
% Number of functors : 115 ( 114 usr; 22 con; 0-4 aty)
% Number of variables : 215 ( 169 !; 46 ?; 215 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'A_set_list_bool_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'A_set_list_a_set_list_fun$': $tType ).
tff(type_def_8,type,
'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$': $tType ).
tff(type_def_9,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_10,type,
'A_ltln_a_ltln_fun$': $tType ).
tff(type_def_11,type,
'Int_int_fun$': $tType ).
tff(type_def_12,type,
'A_set_list_a_set_list_list_fun$': $tType ).
tff(type_def_13,type,
'A_ltln_a_ltln_bool_fun_fun_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_14,type,
'Nat_nat_fun$': $tType ).
tff(type_def_15,type,
'A_set_list_list$': $tType ).
tff(type_def_16,type,
'Nat$': $tType ).
tff(type_def_17,type,
'Nat_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_18,type,
'A_ltln_a_ltln_bool_fun_fun_int_fun$': $tType ).
tff(type_def_19,type,
'Int_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_20,type,
'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$': $tType ).
tff(type_def_21,type,
'A_set_list_a_set_list_bool_fun_fun$': $tType ).
tff(type_def_22,type,
tlbool: $tType ).
tff(type_def_23,type,
'Nat_a_set_list_fun$': $tType ).
tff(type_def_24,type,
'A_set_a_ltln_fun$': $tType ).
tff(type_def_25,type,
'A_ltln_bool_fun$': $tType ).
tff(type_def_26,type,
'A_set$': $tType ).
tff(type_def_27,type,
'A_ltln_set$': $tType ).
tff(type_def_28,type,
'A_set_list$': $tType ).
tff(type_def_29,type,
'A_ltln$': $tType ).
tff(type_def_30,type,
'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_31,type,
'A_ltln_bool_fun_int_fun$': $tType ).
tff(type_def_32,type,
'Nat_a_set_fun$': $tType ).
tff(type_def_33,type,
'A_ltln_bool_fun_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_34,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_35,type,
'Int_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_36,type,
'Nat_bool_fun$': $tType ).
tff(type_def_37,type,
'A_ltln_a_set_a_ltln_fun_fun$': $tType ).
tff(type_def_38,type,
'Nat_int_fun$': $tType ).
tff(type_def_39,type,
'A_ltln_a_ltln_bool_fun_fun$': $tType ).
tff(type_def_40,type,
'A_set_list_a_ltln_fun$': $tType ).
tff(func_def_0,type,
'uua$': 'Int_int_bool_fun_fun$' ).
tff(func_def_1,type,
'w$': 'Nat_a_set_fun$' ).
tff(func_def_2,type,
'af_letter$': 'A_ltln_a_set_a_ltln_fun_fun$' ).
tff(func_def_3,type,
'fun_app$m': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_4,type,
'uu$': 'A_ltln_set$' > 'A_ltln_bool_fun$' ).
tff(func_def_5,type,
'false_ltln$': 'A_ltln$' ).
tff(func_def_6,type,
'fun_app$p': ( 'A_ltln_bool_fun_int_fun$' * 'A_ltln_bool_fun$' ) > $int ).
tff(func_def_7,type,
'nil$': 'A_set_list$' ).
tff(func_def_8,type,
'append$': 'A_set_list$' > 'A_set_list_a_set_list_fun$' ).
tff(func_def_9,type,
'fun_app$g': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_10,type,
'cons$a': ( 'A_set_list$' * 'A_set_list_list$' ) > 'A_set_list_list$' ).
tff(func_def_11,type,
'fun_app$f': ( 'Nat_a_set_list_fun$' * 'Nat$' ) > 'A_set_list$' ).
tff(func_def_12,type,
'fun_app$h': ( 'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$' * 'A_ltln$' ) > 'A_ltln_a_set_a_ltln_fun_fun$' ).
tff(func_def_13,type,
'nil$a': 'A_set_list_list$' ).
tff(func_def_14,type,
'cons$': ( 'A_set$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_15,type,
'mu_LTL$': 'A_ltln_set$' ).
tff(func_def_16,type,
'fun_app$d': ( 'A_set_list_a_ltln_fun$' * 'A_set_list$' ) > 'A_ltln$' ).
tff(func_def_17,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_18,type,
'fun_app$a': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_19,type,
'product_lists$': 'A_set_list_list$' > 'A_set_list_list$' ).
tff(func_def_20,type,
'collect$': 'A_ltln_bool_fun$' > 'A_ltln_set$' ).
tff(func_def_21,type,
'fun_app$x': ( 'A_set_list_a_set_list_bool_fun_fun$' * 'A_set_list$' ) > 'A_set_list_bool_fun$' ).
tff(func_def_22,type,
'fun_app$c': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_23,type,
'fun_app$s': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_24,type,
tltrue: tlbool ).
tff(func_def_25,type,
'af_letter_F$': 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$' ).
tff(func_def_26,type,
'ltl_prop_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_27,type,
'ltl_const_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_28,type,
'fun_app$y': ( 'A_set_list_a_set_list_list_fun$' * 'A_set_list$' ) > 'A_set_list_list$' ).
tff(func_def_29,type,
'eq$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_30,type,
'until_ltln$': 'A_ltln$' > 'A_ltln_a_ltln_fun$' ).
tff(func_def_31,type,
'fun_app$j': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_a_ltln_fun$' ).
tff(func_def_32,type,
'foldl$': ( 'A_ltln_a_set_a_ltln_fun_fun$' * 'A_ltln$' ) > 'A_set_list_a_ltln_fun$' ).
tff(func_def_33,type,
'ltl_lang_equiv$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_34,type,
'fun_app$u': ( 'A_ltln_a_ltln_bool_fun_fun_int_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > $int ).
tff(func_def_35,type,
'fun_app$k': ( 'A_set_list_a_set_list_fun$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_36,type,
'fun_app$e': ( 'A_ltln_a_ltln_fun$' * 'A_ltln$' ) > 'A_ltln$' ).
tff(func_def_37,type,
'true_ltln$': 'A_ltln$' ).
tff(func_def_38,type,
'fun_app$o': ( 'A_ltln_a_ltln_bool_fun_fun_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_39,type,
'ltl_prop_implies$': 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_40,type,
'semantics_ltln$': 'Nat_a_set_fun$' > 'A_ltln_bool_fun$' ).
tff(func_def_41,type,
'n_lists$': 'Nat$' > 'A_set_list_a_set_list_list_fun$' ).
tff(func_def_42,type,
tlfalse: tlbool ).
tff(func_def_43,type,
'fun_app$ab': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_44,type,
'fun_app$v': ( '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$' ).
tff(func_def_45,type,
'nat$': $int > 'Nat$' ).
tff(func_def_46,type,
'fun_app$q': ( 'A_ltln_bool_fun_a_ltln_a_ltln_bool_fun_fun_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_47,type,
'fun_app$aa': ( 'Nat_a_ltln_a_ltln_bool_fun_fun_fun$' * 'Nat$' ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_48,type,
'nu_LTL$': 'A_ltln_set$' ).
tff(func_def_49,type,
'fun_app$n': ( 'Int_a_ltln_bool_fun_fun$' * $int ) > 'A_ltln_bool_fun$' ).
tff(func_def_50,type,
'fun_app$z': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$' ).
tff(func_def_51,type,
'fun_app$r': ( 'A_ltln_bool_fun_a_ltln_bool_fun_fun$' * 'A_ltln_bool_fun$' ) > 'A_ltln_bool_fun$' ).
tff(func_def_52,type,
'subsequence$': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat_a_set_list_fun$' ).
tff(func_def_53,type,
'fun_app$t': ( 'Int_a_ltln_a_ltln_bool_fun_fun_fun$' * $int ) > 'A_ltln_a_ltln_bool_fun_fun$' ).
tff(func_def_54,type,
'af_letter_G$': 'A_ltln_a_ltln_bool_fun_fun$' > 'A_ltln_a_ltln_a_set_a_ltln_fun_fun_fun$' ).
tff(func_def_55,type,
'fun_app$i': ( 'A_set_a_ltln_fun$' * 'A_set$' ) > 'A_ltln$' ).
tff(func_def_56,type,
'release_ltln$': 'A_ltln$' > 'A_ltln_a_ltln_fun$' ).
tff(func_def_57,type,
'phi$': 'A_ltln$' ).
tff(func_def_61,type,
sK3: 'Nat$' > 'Nat$' ).
tff(func_def_62,type,
sK4: 'Nat$' ).
tff(func_def_63,type,
sK5: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_64,type,
sK6: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_65,type,
sK7: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_66,type,
sK8: 'A_set_list$' > 'A_set_list$' ).
tff(func_def_67,type,
sK9: 'A_set_list$' > 'A_set$' ).
tff(func_def_68,type,
sK10: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_69,type,
sK11: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_70,type,
sK12: ( 'A_ltln$' * 'A_set_list$' * 'A_ltln$' ) > 'A_set_list$' ).
tff(func_def_71,type,
sK13: ( 'A_ltln$' * 'A_set_list$' * 'A_ltln$' ) > 'A_set_list$' ).
tff(func_def_72,type,
sK14: 'Nat$' > 'Nat$' ).
tff(func_def_73,type,
sK15: 'Nat$' > 'Nat$' ).
tff(func_def_74,type,
sK16: 'Nat$' ).
tff(func_def_75,type,
sK17: 'Nat$' ).
tff(func_def_76,type,
sK18: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_77,type,
sK19: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'Nat$' ).
tff(func_def_78,type,
sK20: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_79,type,
sK21: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_80,type,
sK22: ( 'A_set_list$' * 'A_set_list$' * 'A_set_list$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_81,type,
sK23: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_82,type,
sK24: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_83,type,
sK25: 'A_set_list$' > 'A_set$' ).
tff(func_def_84,type,
sK26: 'A_set_list$' > 'A_set$' ).
tff(func_def_85,type,
sK27: 'A_set_list$' > 'A_set_list$' ).
tff(func_def_86,type,
sK28: 'A_set_list$' > 'A_set$' ).
tff(func_def_87,type,
sK29: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_88,type,
sK30: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_89,type,
sK31: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_90,type,
sK32: ( 'A_set_list$' * 'A_ltln$' ) > 'A_set_list$' ).
tff(func_def_91,type,
sK33: ( 'A_set_list$' * 'A_ltln$' ) > 'A_set_list$' ).
tff(func_def_92,type,
sK34: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_93,type,
sK35: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_94,type,
sK36: ( 'A_ltln$' * 'A_ltln$' ) > 'Nat_a_set_fun$' ).
tff(func_def_95,type,
sK37: 'A_set_list$' > 'A_set$' ).
tff(func_def_96,type,
sK38: 'A_set_list$' > 'A_set_list$' ).
tff(func_def_97,type,
sK39: 'A_set_list$' > 'A_set$' ).
tff(func_def_98,type,
sK40: 'A_set_list$' > 'A_set_list$' ).
tff(func_def_99,type,
sK41: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_100,type,
sK42: ( 'Nat_a_set_fun$' * 'A_ltln$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_101,type,
sK43: 'A_set_list$' > 'A_set_list$' ).
tff(func_def_102,type,
sK44: 'A_set_list$' > 'A_set$' ).
tff(func_def_103,type,
sK45: ( 'A_set_list$' * 'A_set_list$' * 'A_set_list$' * 'A_set$' ) > 'A_set_list$' ).
tff(func_def_104,type,
sK46: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_105,type,
sK47: $int > $int ).
tff(func_def_106,type,
sK48: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_107,type,
sK49: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_108,type,
sK50: $int > $int ).
tff(func_def_109,type,
sK51: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_110,type,
sK52: ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'A_ltln$' ).
tff(func_def_111,type,
sK53: ( 'A_ltln$' * 'Nat_a_set_fun$' ) > 'Nat$' ).
tff(func_def_112,type,
sK54: ( 'A_ltln$' * 'A_ltln$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_113,type,
sK55: ( 'A_ltln$' * 'A_ltln$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(func_def_114,type,
sK56: ( 'A_ltln$' * 'Nat_a_set_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > 'Nat$' ).
tff(func_def_115,type,
sK57: ( 'Nat_a_set_fun$' * 'A_ltln$' ) > 'Nat$' ).
tff(func_def_116,type,
sK58: ( 'A_set$' * 'A_set_list$' * 'A_set_list$' * 'A_set_list$' ) > 'A_set_list$' ).
tff(pred_def_1,type,
'less_eq$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > $o ).
tff(pred_def_2,type,
'less$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_bool_fun_fun$' ) > $o ).
tff(pred_def_3,type,
'less$a': ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > $o ).
tff(pred_def_4,type,
'equivp$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_5,type,
'fun_app$': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_6,type,
'member$': ( 'A_ltln$' * 'A_ltln_set$' ) > $o ).
tff(pred_def_7,type,
'af_congruent$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_8,type,
'ltl_equivalence$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_9,type,
'fun_app$b': ( 'A_ltln_bool_fun$' * 'A_ltln$' ) > $o ).
tff(pred_def_10,type,
'transition_functions$': ( 'A_ltln_a_ltln_bool_fun_fun$' * 'A_ltln_a_ltln_fun$' ) > $o ).
tff(pred_def_11,type,
'af_congruent_axioms$': 'A_ltln_a_ltln_bool_fun_fun$' > $o ).
tff(pred_def_12,type,
'fun_app$l': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_13,type,
'fun_app$w': ( 'A_set_list_bool_fun$' * 'A_set_list$' ) > $o ).
tff(pred_def_14,type,
'less_eq$a': ( 'A_ltln_bool_fun$' * 'A_ltln_bool_fun$' ) > $o ).
tff(pred_def_17,type,
sP0: ( $int * $int * $int ) > $o ).
tff(pred_def_18,type,
sP1: ( $int * $int * $int ) > $o ).
tff(pred_def_19,type,
sP2: ( $int * $int * $int ) > $o ).
tff(f3,conjecture,
( ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')
<=> ? [X0: 'Nat$'] :
! [X1: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture2) ).
tff(f4,negated_conjecture,
~ ( ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')
<=> ? [X0: 'Nat$'] :
! [X1: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X0),'fun_app$g'('of_nat$',X1))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X1))),'false_ltln$') ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f11,axiom,
'member$'('phi$','nu_LTL$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
tff(f14,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') )
=> ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
tff(f15,axiom,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')
=> ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
tff(f98,axiom,
'ltl_equivalence$'('eq$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
tff(f130,axiom,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ( 'ltl_equivalence$'(X0)
& 'member$'(X1,'nu_LTL$') )
=> ( ? [X3: 'Nat$'] :
! [X4: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$')
<=> 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom128) ).
tff(f136,axiom,
! [X1: 'Nat_a_set_fun$',X0: 'A_ltln$'] :
( 'member$'(X0,'nu_LTL$')
=> ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0)))
<=> ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
tff(f480,axiom,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$',X1: 'A_ltln$'] :
( ( 'fun_app$b'('fun_app$c'(X0,X1),X2)
& 'ltl_equivalence$'(X0) )
=> 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
tff(f481,axiom,
'ltl_equivalence$'('ltl_lang_equiv$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
tff(f772,plain,
~ ( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$') )
<=> ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') ),
inference(rectify,[],[f4]) ).
tff(f868,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') )
=> ? [X4: 'Nat$'] :
! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$') ),
inference(rectify,[],[f14]) ).
tff(f872,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')
=> ? [X4: 'Nat$'] :
! [X5: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))
=> ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') ) ),
inference(rectify,[],[f15]) ).
tff(f954,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'Nat_a_set_fun$',X2: 'A_ltln$'] :
( ( 'ltl_equivalence$'(X0)
& 'member$'(X2,'nu_LTL$') )
=> ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X2)))
<=> ? [X3: 'Nat$'] :
! [X4: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X2)),'fun_app$f'('subsequence$'(X1,X3),X4))),'false_ltln$') ) ),
inference(rectify,[],[f130]) ).
tff(f980,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$',X1: 'A_ltln$'] :
( ( 'ltl_equivalence$'(X0)
& 'fun_app$b'('fun_app$c'(X0,X2),X1) )
=> 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X2),X1) ),
inference(rectify,[],[f480]) ).
tff(f1023,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X4: 'Nat$'] :
! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$')
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
& 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X3))),'false_ltln$') ) ),
inference(ennf_transformation,[],[f868]) ).
tff(f1054,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'member$'(X0,'nu_LTL$')
| ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0)))
<=> ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') ) ),
inference(ennf_transformation,[],[f136]) ).
tff(f1074,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'Nat_a_set_fun$',X2: 'A_ltln$'] :
( ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X2)))
<=> ? [X3: 'Nat$'] :
! [X4: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X2)),'fun_app$f'('subsequence$'(X1,X3),X4))),'false_ltln$') )
| ~ 'ltl_equivalence$'(X0)
| ~ 'member$'(X2,'nu_LTL$') ),
inference(ennf_transformation,[],[f954]) ).
tff(f1075,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'ltl_equivalence$'(X0)
| ~ 'member$'(X2,'nu_LTL$')
| ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X2)))
<=> ? [X3: 'Nat$'] :
! [X4: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X2)),'fun_app$f'('subsequence$'(X1,X3),X4))),'false_ltln$') ) ),
inference(flattening,[],[f1074]) ).
tff(f1152,plain,
! [X1: 'Nat_a_set_fun$',X0: 'A_ltln$'] :
( ? [X4: 'Nat$'] :
! [X5: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') )
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') ),
inference(ennf_transformation,[],[f872]) ).
tff(f1169,plain,
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) )
<~> ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$') ),
inference(ennf_transformation,[],[f772]) ).
tff(f1176,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$',X1: 'A_ltln$'] :
( 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X2),X1)
| ~ 'ltl_equivalence$'(X0)
| ~ 'fun_app$b'('fun_app$c'(X0,X2),X1) ),
inference(ennf_transformation,[],[f980]) ).
tff(f1177,plain,
! [X2: 'A_ltln$',X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln$'] :
( ~ 'ltl_equivalence$'(X0)
| 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X2),X1)
| ~ 'fun_app$b'('fun_app$c'(X0,X2),X1) ),
inference(flattening,[],[f1176]) ).
tff(f1255,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')
| ! [X4: 'Nat$'] :
? [X5: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',X5))
& 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),X5))),'false_ltln$') ) ),
inference(rectify,[],[f1023]) ).
tff(f1256,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK5(X0,X1)),X3))),'false_ltln$')
| ! [X4: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',sK6(X0,X1,X4)))
& 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),sK6(X0,X1,X4)))),'false_ltln$') ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X2,sK5(X0,X1)),skolemize(X5,sK6(X0,X1,X4))],[f1255]) ).
tff(f1327,plain,
( ( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] :
( 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$')
& $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) ) )
& ( ? [X0: 'Nat$'] :
! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')
| ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) ) ) ),
inference(nnf_transformation,[],[f1169]) ).
tff(f1328,plain,
( ( ! [X0: 'Nat$'] :
? [X1: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),X1))),'false_ltln$')
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] :
( 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X3))),'false_ltln$')
& $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3)) ) )
& ( ? [X4: 'Nat$'] :
! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X4),X5))),'false_ltln$')
| ? [X6: 'Nat$'] :
! [X7: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X7))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',X6),'fun_app$g'('of_nat$',X7)) ) ) ),
inference(rectify,[],[f1327]) ).
tff(f1329,plain,
( ( ! [X0: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK14(X0)))),'false_ltln$')
| ! [X2: 'Nat$'] :
( 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(X2)))),'false_ltln$')
& $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',sK15(X2))) ) )
& ( ! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK16),X5))),'false_ltln$')
| ! [X7: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X7))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',X7)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17]),skolemize(X1,sK14(X0)),skolemize(X3,sK15(X2)),skolemize(X4,sK16),skolemize(X6,sK17)],[f1328]) ).
tff(f1336,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'ltl_equivalence$'(X0)
| ~ 'member$'(X2,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X2)))
| ! [X3: 'Nat$'] :
? [X4: 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X2)),'fun_app$f'('subsequence$'(X1,X3),X4))),'false_ltln$') )
& ( ? [X3: 'Nat$'] :
! [X4: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X2)),'fun_app$f'('subsequence$'(X1,X3),X4))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X2))) ) ) ),
inference(nnf_transformation,[],[f1075]) ).
tff(f1337,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln$',X2: 'Nat_a_set_fun$'] :
( ~ 'ltl_equivalence$'(X0)
| ~ 'member$'(X1,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1)))
| ! [X3: 'Nat$'] :
? [X4: 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),X4))),'false_ltln$') )
& ( ? [X5: 'Nat$'] :
! [X6: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X5),X6))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) ) ) ),
inference(rectify,[],[f1336]) ).
tff(f1338,plain,
! [X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln$',X2: 'Nat_a_set_fun$'] :
( ~ 'ltl_equivalence$'(X0)
| ~ 'member$'(X1,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1)))
| ! [X3: 'Nat$'] : 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),sK20(X0,X1,X2,X3)))),'false_ltln$') )
& ( ! [X6: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,sK21(X0,X1,X2)),X6))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20,sK21]),skolemize(X4,sK20(X0,X1,X2,X3)),skolemize(X5,sK21(X0,X1,X2))],[f1337]) ).
tff(f1349,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',X3))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X1),'fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,'nat$'(0)),X3))),'false_ltln$') )
| ! [X4: 'Nat$'] :
? [X5: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,X4),X5))),'false_ltln$') ),
inference(rectify,[],[f1152]) ).
tff(f1350,plain,
! [X0: 'Nat_a_set_fun$',X1: 'A_ltln$'] :
( ! [X3: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK23(X0,X1)),'fun_app$g'('of_nat$',X3))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X1),'fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,'nat$'(0)),X3))),'false_ltln$') )
| ! [X4: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,X4),sK24(X0,X1,X4)))),'false_ltln$') ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23,sK24]),skolemize(X2,sK23(X0,X1)),skolemize(X5,sK24(X0,X1,X4))],[f1349]) ).
tff(f1375,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'member$'(X0,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0)))
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') )
& ( ? [X2: 'Nat$'] :
! [X3: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) ) ) ),
inference(nnf_transformation,[],[f1054]) ).
tff(f1376,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'member$'(X0,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0)))
| ! [X2: 'Nat$'] :
? [X3: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),X3))),'false_ltln$') )
& ( ? [X4: 'Nat$'] :
! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X4),X5))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) ) ) ),
inference(rectify,[],[f1375]) ).
tff(f1377,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$'] :
( ~ 'member$'(X0,'nu_LTL$')
| ( ( 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0)))
| ! [X2: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,X2),sK29(X0,X1,X2)))),'false_ltln$') )
& ( ! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK30(X0,X1)),X5))),'false_ltln$')
| ~ 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29,sK30]),skolemize(X3,sK29(X0,X1,X2)),skolemize(X4,sK30(X0,X1))],[f1376]) ).
tff(f1533,plain,
! [X0: 'A_ltln$',X1: 'A_ltln_a_ltln_bool_fun_fun$',X2: 'A_ltln$'] :
( ~ 'ltl_equivalence$'(X1)
| 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2)
| ~ 'fun_app$b'('fun_app$c'(X1,X0),X2) ),
inference(rectify,[],[f1177]) ).
tff(f1590,plain,
! [X3: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X4: 'Nat$'] :
( 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X0),'fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,'nat$'(0)),sK6(X0,X1,X4)))),'false_ltln$')
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK5(X0,X1)),X3))),'false_ltln$') ),
inference(cnf_transformation,[],[f1256]) ).
tff(f1591,plain,
! [X3: 'Nat$',X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X4: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK5(X0,X1)),X3))),'false_ltln$')
| $less('fun_app$g'('of_nat$',X4),'fun_app$g'('of_nat$',sK6(X0,X1,X4))) ),
inference(cnf_transformation,[],[f1256]) ).
tff(f1661,plain,
'ltl_equivalence$'('ltl_lang_equiv$'),
inference(cnf_transformation,[],[f481]) ).
tff(f1694,plain,
! [X7: 'Nat$',X5: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',X7))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X7))),'false_ltln$')
| ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK16),X5))),'false_ltln$') ),
inference(cnf_transformation,[],[f1329]) ).
tff(f1695,plain,
! [X2: 'Nat$',X0: 'Nat$'] :
( $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',sK15(X2)))
| 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK14(X0)))),'false_ltln$') ),
inference(cnf_transformation,[],[f1329]) ).
tff(f1696,plain,
! [X2: 'Nat$',X0: 'Nat$'] :
( 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(X2)))),'false_ltln$')
| 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK14(X0)))),'false_ltln$') ),
inference(cnf_transformation,[],[f1329]) ).
tff(f1703,plain,
! [X2: 'Nat_a_set_fun$',X3: 'Nat$',X0: 'A_ltln_a_ltln_bool_fun_fun$',X1: 'A_ltln$'] :
( 'fun_app$b'('fun_app$c'(X0,'fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X2,X3),sK20(X0,X1,X2,X3)))),'false_ltln$')
| ~ 'ltl_equivalence$'(X0)
| 'fun_app$b'('semantics_ltln$'(X2),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X1)))
| ~ 'member$'(X1,'nu_LTL$') ),
inference(cnf_transformation,[],[f1338]) ).
tff(f1720,plain,
! [X3: 'Nat$',X0: 'Nat_a_set_fun$',X1: 'A_ltln$',X4: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),X1),'fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,'nat$'(0)),X3))),'false_ltln$')
| 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X1)),'fun_app$f'('subsequence$'(X0,X4),sK24(X0,X1,X4)))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK23(X0,X1)),'fun_app$g'('of_nat$',X3)) ),
inference(cnf_transformation,[],[f1350]) ).
tff(f1758,plain,
! [X0: 'A_ltln$',X1: 'Nat_a_set_fun$',X5: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),X0)),'fun_app$f'('subsequence$'(X1,sK30(X0,X1)),X5))),'false_ltln$')
| ~ 'member$'(X0,'nu_LTL$')
| ~ 'fun_app$b'('semantics_ltln$'(X1),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),X0))) ),
inference(cnf_transformation,[],[f1377]) ).
tff(f1815,plain,
'member$'('phi$','nu_LTL$'),
inference(cnf_transformation,[],[f11]) ).
tff(f1958,plain,
'ltl_equivalence$'('eq$'),
inference(cnf_transformation,[],[f98]) ).
tff(f1976,plain,
! [X2: 'A_ltln$',X0: 'A_ltln$',X1: 'A_ltln_a_ltln_bool_fun_fun$'] :
( 'fun_app$b'('fun_app$c'('ltl_lang_equiv$',X0),X2)
| ~ 'fun_app$b'('fun_app$c'(X1,X0),X2)
| ~ 'ltl_equivalence$'(X1) ),
inference(cnf_transformation,[],[f1533]) ).
tff(f2120,definition,
( spl59_1
<=> ! [X7: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',X7))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X7))),'false_ltln$') ) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
tff(f2121,plain,
( ! [X7: 'Nat$'] :
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),X7))),'false_ltln$')
| ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',X7)) )
| ~ spl59_1 ),
inference(avatar_component_clause,[],[f2120]) ).
tff(f2123,definition,
( spl59_2
<=> ! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK16),X5))),'false_ltln$') ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
tff(f2124,plain,
( ! [X5: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK16),X5))),'false_ltln$')
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f2123]) ).
tff(f2125,plain,
( spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f1694,f2123,f2120]) ).
tff(f2127,definition,
( spl59_3
<=> ! [X0: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK14(X0)))),'false_ltln$') ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
tff(f2128,plain,
( ! [X0: 'Nat$'] : 'fun_app$b'('fun_app$c'('ltl_lang_equiv$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',X0),sK14(X0)))),'false_ltln$')
| ~ spl59_3 ),
inference(avatar_component_clause,[],[f2127]) ).
tff(f2130,definition,
( spl59_4
<=> ! [X2: 'Nat$'] : $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',sK15(X2))) ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
tff(f2131,plain,
( ! [X2: 'Nat$'] : $less('fun_app$g'('of_nat$',X2),'fun_app$g'('of_nat$',sK15(X2)))
| ~ spl59_4 ),
inference(avatar_component_clause,[],[f2130]) ).
tff(f2132,plain,
( spl59_3
| spl59_4 ),
inference(avatar_split_clause,[],[f1695,f2130,f2127]) ).
tff(f2134,definition,
( spl59_5
<=> ! [X2: 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(X2)))),'false_ltln$') ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
tff(f2135,plain,
( ! [X2: 'Nat$'] : 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(X2)))),'false_ltln$')
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f2134]) ).
tff(f2136,plain,
( spl59_5
| spl59_3 ),
inference(avatar_split_clause,[],[f1696,f2127,f2134]) ).
tff(f3250,plain,
( ~ 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))
| ~ spl59_3 ),
inference(unit_resulting_resolution,[],[f1758,f1815,f2128]) ).
tff(f3339,definition,
( spl59_8
<=> 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$'))) ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
tff(f3342,plain,
( ~ spl59_8
| ~ spl59_3 ),
inference(avatar_split_clause,[],[f3250,f2127,f3339]) ).
tff(f3365,plain,
( ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',sK6('phi$','w$',X0)))
| ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK5('phi$','w$')),X1))),'false_ltln$') )
| ~ spl59_1 ),
inference(resolution,[],[f2121,f1590]) ).
tff(f3384,definition,
( spl59_11
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',sK6('phi$','w$',X0))) ),
introduced(definition,[new_symbols(definition,[spl59_11])],[avatar_definition]) ).
tff(f3385,plain,
( ! [X0: 'Nat$'] : ~ $less('fun_app$g'('of_nat$',sK17),'fun_app$g'('of_nat$',sK6('phi$','w$',X0)))
| ~ spl59_11 ),
inference(avatar_component_clause,[],[f3384]) ).
tff(f3387,definition,
( spl59_12
<=> ! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK5('phi$','w$')),X1))),'false_ltln$') ),
introduced(definition,[new_symbols(definition,[spl59_12])],[avatar_definition]) ).
tff(f3388,plain,
( ! [X1: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK5('phi$','w$')),X1))),'false_ltln$')
| ~ spl59_12 ),
inference(avatar_component_clause,[],[f3387]) ).
tff(f3389,plain,
( spl59_11
| spl59_12
| ~ spl59_1 ),
inference(avatar_split_clause,[],[f3365,f2120,f3387,f3384]) ).
tff(f3554,plain,
( ~ 'ltl_equivalence$'('ltl_lang_equiv$')
| ~ spl59_2
| ~ spl59_3 ),
inference(unit_resulting_resolution,[],[f1976,f2128,f2124]) ).
tff(f3649,plain,
( $false
| ~ spl59_2
| ~ spl59_3 ),
inference(forward_subsumption_resolution,[],[f3554,f1661]) ).
tff(f3650,plain,
( ~ spl59_2
| ~ spl59_3 ),
inference(avatar_contradiction_clause,[],[f3649]) ).
tff(f3980,plain,
( ! [X0: 'Nat$'] : ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('af_letter$','fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$',sK5('phi$','w$')),X0))),'false_ltln$')
| ~ spl59_11 ),
inference(unit_resulting_resolution,[],[f1591,f3385]) ).
tff(f4900,plain,
( spl59_12
| ~ spl59_11 ),
inference(avatar_split_clause,[],[f3980,f3384,f3387]) ).
tff(f5175,plain,
( 'fun_app$b'('semantics_ltln$'('w$'),'fun_app$e'('until_ltln$'('true_ltln$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')))
| ~ spl59_12 ),
inference(unit_resulting_resolution,[],[f1703,f1958,f1815,f3388]) ).
tff(f5251,plain,
( spl59_8
| ~ spl59_12 ),
inference(avatar_split_clause,[],[f5175,f3387,f3339]) ).
tff(f5776,plain,
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(sK17)))),'false_ltln$')
| ~ spl59_1
| ~ spl59_4 ),
inference(unit_resulting_resolution,[],[f2121,f2131]) ).
tff(f6757,plain,
( $false
| ~ spl59_1
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f5776,f2135]) ).
tff(f6758,plain,
( ~ spl59_1
| ~ spl59_4
| ~ spl59_5 ),
inference(avatar_contradiction_clause,[],[f6757]) ).
tff(f7586,plain,
( ~ 'fun_app$b'('fun_app$c'('eq$','fun_app$d'('foldl$'('fun_app$h'('af_letter_G$'('eq$'),'phi$'),'fun_app$e'('release_ltln$'('false_ltln$'),'phi$')),'fun_app$f'('subsequence$'('w$','nat$'(0)),sK15(sK23('w$','phi$'))))),'false_ltln$')
| ~ spl59_2
| ~ spl59_4 ),
inference(unit_resulting_resolution,[],[f1720,f2131,f2124]) ).
tff(f7651,plain,
( $false
| ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(forward_subsumption_resolution,[],[f7586,f2135]) ).
tff(f7652,plain,
( ~ spl59_2
| ~ spl59_4
| ~ spl59_5 ),
inference(avatar_contradiction_clause,[],[f7651]) ).
tff(f7653,plain,
$false,
inference(avatar_smt_refutation,[],[f7652,f6758,f5251,f4900,f3650,f3389,f3342,f2136,f2132,f2125]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP375_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 % Computer : n009.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sun Sep 27 12:56:15 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.47 Running first-order theorem proving
% 0.15/0.47 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.17/2.01 % (2009869)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 5.17/2.01 % (2009878)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2326899063:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 5.17/2.01 % (2009878)Instruction limit reached!
% 5.17/2.01 % (2009878)------------------------------
% 5.17/2.01 % (2009878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/2.01 % (2009878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/2.01 % (2009878)CaDiCaL version: 2.1.3
% 5.17/2.01 % (2009878)Termination reason: Instruction limit
% 5.17/2.01 % (2009878)Termination phase: Property scanning
% 5.17/2.01 % (2009878)Time elapsed: 0.003 s
% 5.17/2.01 % (2009878)Peak memory usage: 85 MB
% 5.17/2.01 % (2009878)Instructions burned: 5 (million)
% 5.17/2.01 % (2009874)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3582970951:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 5.17/2.01 % (2009874)Instruction limit reached!
% 5.17/2.01 % (2009874)------------------------------
% 5.17/2.01 % (2009874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/2.01 % (2009874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/2.01 % (2009874)CaDiCaL version: 2.1.3
% 5.17/2.01 % (2009874)Termination reason: Instruction limit
% 5.17/2.01 % (2009874)Termination phase: Property scanning
% 5.17/2.01 % (2009874)Time elapsed: 0.007 s
% 5.17/2.01 % (2009874)Peak memory usage: 86 MB
% 5.17/2.01 % (2009874)Instructions burned: 12 (million)
% 5.17/2.01 % (2009880)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=145606530:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 5.17/2.01 % (2009876)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1159293486:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 5.17/2.01 % (2009875)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=313963358:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 5.17/2.01 % (2009879)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=298415656:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 5.17/2.01 % (2009877)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3773305347:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 5.17/2.01 % (2009877)Instruction limit reached!
% 5.17/2.01 % (2009877)------------------------------
% 5.17/2.01 % (2009877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/2.01 % (2009877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/2.01 % (2009877)CaDiCaL version: 2.1.3
% 5.17/2.01 % (2009877)Termination reason: Instruction limit
% 5.17/2.01 % (2009877)Termination phase: Property scanning
% 5.17/2.01 % (2009877)Time elapsed: 0.008 s
% 5.17/2.01 % (2009877)Peak memory usage: 85 MB
% 5.17/2.01 % (2009877)Instructions burned: 8 (million)
% 5.17/2.01 % (2009880)Instruction limit reached!
% 5.17/2.01 % (2009880)------------------------------
% 5.17/2.01 % (2009880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/2.01 % (2009880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/2.01 % (2009880)CaDiCaL version: 2.1.3
% 5.17/2.01 % (2009880)Termination reason: Instruction limit
% 5.17/2.01 % (2009880)Termination phase: Preprocessing 3
% 5.17/2.01 % (2009880)Time elapsed: 0.033 s
% 5.17/2.01 % (2009880)Peak memory usage: 88 MB
% 5.17/2.01 % (2009880)Instructions burned: 34 (million)
% 5.17/2.01 % (2009879)Instruction limit reached!
% 5.17/2.01 % (2009879)------------------------------
% 5.17/2.01 % (2009879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.17/2.01 % (2009879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.17/2.01 % (2009879)CaDiCaL version: 2.1.3
% 5.17/2.01 % (2009879)Termination reason: Instruction limit
% 5.17/2.01 % (2009879)Termination phase: Property scanning
% 5.17/2.01 % (2009879)Time elapsed: 0.045 s
% 5.17/2.01 % (2009879)Peak memory usage: 88 MB
% 5.17/2.01 % (2009879)Instructions burned: 46 (million)
% 5.17/2.01 % (2009882)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=497680950:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2997 on theBenchmark for (2997ds/14Mi)
% 5.17/2.01 % (2009882)Instruction limit reached!
% 5.17/2.01 % (2009882)------------------------------
% 7.31/2.25 % (2009882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009882)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009882)Termination reason: Instruction limit
% 7.31/2.25 % (2009882)Termination phase: SInE selection
% 7.31/2.25 % (2009882)Time elapsed: 0.008 s
% 7.31/2.25 % (2009882)Peak memory usage: 86 MB
% 7.31/2.25 % (2009882)Instructions burned: 14 (million)
% 7.31/2.25 % (2009885)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=2778839453:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2996 on theBenchmark for (2996ds/29Mi)
% 7.31/2.25 % (2009885)Instruction limit reached!
% 7.31/2.25 % (2009885)------------------------------
% 7.31/2.25 % (2009885)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009885)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009885)Termination reason: Instruction limit
% 7.31/2.25 % (2009885)Termination phase: Preprocessing 3
% 7.31/2.25 % (2009885)Time elapsed: 0.014 s
% 7.31/2.25 % (2009885)Peak memory usage: 88 MB
% 7.31/2.25 % (2009885)Instructions burned: 29 (million)
% 7.31/2.25 % (2009893)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1504961569:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 7.31/2.25 % (2009876)Instruction limit reached!
% 7.31/2.25 % (2009876)------------------------------
% 7.31/2.25 % (2009876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009876)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009876)Termination reason: Instruction limit
% 7.31/2.25 % (2009876)Termination phase: Saturation
% 7.31/2.25 % (2009876)Time elapsed: 0.228 s
% 7.31/2.25 % (2009876)Peak memory usage: 118 MB
% 7.31/2.25 % (2009876)Instructions burned: 202 (million)
% 7.31/2.25 % (2009893)Instruction limit reached!
% 7.31/2.25 % (2009893)------------------------------
% 7.31/2.25 % (2009893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009893)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009893)Termination reason: Instruction limit
% 7.31/2.25 % (2009893)Termination phase: shuffling
% 7.31/2.25 % (2009893)Time elapsed: 0.024 s
% 7.31/2.25 % (2009893)Peak memory usage: 86 MB
% 7.31/2.25 % (2009893)Instructions burned: 25 (million)
% 7.31/2.25 % (2009892)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2684979650:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 7.31/2.25 % (2009892)Instruction limit reached!
% 7.31/2.25 % (2009892)------------------------------
% 7.31/2.25 % (2009892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009892)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009892)Termination reason: Instruction limit
% 7.31/2.25 % (2009892)Termination phase: shuffling
% 7.31/2.25 % (2009892)Time elapsed: 0.016 s
% 7.31/2.25 % (2009892)Peak memory usage: 86 MB
% 7.31/2.25 % (2009892)Instructions burned: 16 (million)
% 7.31/2.25 % (2009894)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=3577651922:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 7.31/2.25 % (2009875)Instruction limit reached!
% 7.31/2.25 % (2009875)------------------------------
% 7.31/2.25 % (2009875)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009875)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.31/2.25 % (2009875)CaDiCaL version: 2.1.3
% 7.31/2.25 % (2009875)Termination reason: Instruction limit
% 7.31/2.25 % (2009875)Termination phase: Saturation
% 7.31/2.25 % (2009875)Time elapsed: 0.359 s
% 7.31/2.25 % (2009875)Peak memory usage: 118 MB
% 7.31/2.25 % (2009875)Instructions burned: 307 (million)
% 7.31/2.25 % (2009894)Instruction limit reached!
% 7.31/2.25 % (2009894)------------------------------
% 7.31/2.25 % (2009894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.31/2.25 % (2009894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009894)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009894)Termination reason: Instruction limit
% 8.83/2.53 % (2009894)Termination phase: shuffling
% 8.83/2.53 % (2009894)Time elapsed: 0.027 s
% 8.83/2.53 % (2009894)Peak memory usage: 87 MB
% 8.83/2.53 % (2009894)Instructions burned: 27 (million)
% 8.83/2.53 % (2009897)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=1011752263:i=85:gtgl=4:rtra=on:gtg=exists_sym_2995 on theBenchmark for (2995ds/85Mi)
% 8.83/2.53 % (2009900)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=1258126507:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 8.83/2.53 % (2009898)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=1151439999:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2994 on theBenchmark for (2994ds/2Mi)
% 8.83/2.53 % (2009898)Instruction limit reached!
% 8.83/2.53 % (2009898)------------------------------
% 8.83/2.53 % (2009898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.53 % (2009898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009898)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009898)Termination reason: Instruction limit
% 8.83/2.53 % (2009898)Termination phase: Property scanning
% 8.83/2.53 % (2009898)Time elapsed: 0.004 s
% 8.83/2.53 % (2009898)Peak memory usage: 85 MB
% 8.83/2.53 % (2009898)Instructions burned: 3 (million)
% 8.83/2.53 % (2009897)Instruction limit reached!
% 8.83/2.53 % (2009897)------------------------------
% 8.83/2.53 % (2009897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.53 % (2009897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009897)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009897)Termination reason: Instruction limit
% 8.83/2.53 % (2009897)Termination phase: Saturation
% 8.83/2.53 % (2009897)Time elapsed: 0.079 s
% 8.83/2.53 % (2009897)Peak memory usage: 90 MB
% 8.83/2.53 % (2009897)Instructions burned: 86 (million)
% 8.83/2.53 % (2009901)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=2907633140:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 8.83/2.53 % (2009901)Instruction limit reached!
% 8.83/2.53 % (2009901)------------------------------
% 8.83/2.53 % (2009901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.53 % (2009901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009901)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009901)Termination reason: Instruction limit
% 8.83/2.53 % (2009901)Termination phase: Property scanning
% 8.83/2.53 % (2009901)Time elapsed: 0.005 s
% 8.83/2.53 % (2009901)Peak memory usage: 85 MB
% 8.83/2.53 % (2009901)Instructions burned: 5 (million)
% 8.83/2.53 % (2009900)Instruction limit reached!
% 8.83/2.53 % (2009900)------------------------------
% 8.83/2.53 % (2009900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.53 % (2009900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009900)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009900)Termination reason: Instruction limit
% 8.83/2.53 % (2009900)Termination phase: Saturation
% 8.83/2.53 % (2009900)Time elapsed: 0.098 s
% 8.83/2.53 % (2009900)Peak memory usage: 92 MB
% 8.83/2.53 % (2009900)Instructions burned: 181 (million)
% 8.83/2.53 % (2009903)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=2377699915:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2993 on theBenchmark for (2993ds/66Mi)
% 8.83/2.53 % (2009905)lrs+10_1_thi=all:si=on:fd=off:random_seed=1187802790:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 8.83/2.53 % (2009905)Instruction limit reached!
% 8.83/2.53 % (2009905)------------------------------
% 8.83/2.53 % (2009905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.83/2.53 % (2009905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.83/2.53 % (2009905)CaDiCaL version: 2.1.3
% 8.83/2.53 % (2009905)Termination reason: Instruction limit
% 8.83/2.53 % (2009905)Termination phase: Preprocessing 3
% 8.83/2.53 % (2009905)Time elapsed: 0.050 s
% 8.83/2.53 % (2009905)Peak memory usage: 87 MB
% 8.83/2.53 % (2009905)Instructions burned: 53 (million)
% 8.83/2.53 % (2009906)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=2469891092:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/8Mi)
% 10.73/2.73 % (2009903)Instruction limit reached!
% 10.73/2.73 % (2009903)------------------------------
% 10.73/2.73 % (2009903)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009903)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009903)Termination reason: Instruction limit
% 10.73/2.73 % (2009903)Termination phase: Saturation
% 10.73/2.73 % (2009903)Time elapsed: 0.062 s
% 10.73/2.73 % (2009903)Peak memory usage: 88 MB
% 10.73/2.73 % (2009903)Instructions burned: 67 (million)
% 10.73/2.73 % (2009906)Instruction limit reached!
% 10.73/2.73 % (2009906)------------------------------
% 10.73/2.73 % (2009906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009906)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009906)Termination reason: Instruction limit
% 10.73/2.73 % (2009906)Termination phase: shuffling
% 10.73/2.73 % (2009906)Time elapsed: 0.011 s
% 10.73/2.73 % (2009906)Peak memory usage: 86 MB
% 10.73/2.73 % (2009906)Instructions burned: 11 (million)
% 10.73/2.73 % (2009911)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=1777892867:i=2:doe=on:canc=force:asg=cautious:rtra=on_2992 on theBenchmark for (2992ds/2Mi)
% 10.73/2.73 % (2009911)Instruction limit reached!
% 10.73/2.73 % (2009911)------------------------------
% 10.73/2.73 % (2009911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009911)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009911)Termination reason: Instruction limit
% 10.73/2.73 % (2009911)Termination phase: shuffling
% 10.73/2.73 % (2009911)Time elapsed: 0.004 s
% 10.73/2.73 % (2009911)Peak memory usage: 85 MB
% 10.73/2.73 % (2009911)Instructions burned: 2 (million)
% 10.73/2.73 % (2009910)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=3812083941:st=3:i=2:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/2Mi)
% 10.73/2.73 % (2009910)Instruction limit reached!
% 10.73/2.73 % (2009910)------------------------------
% 10.73/2.73 % (2009910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009910)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009910)Termination reason: Instruction limit
% 10.73/2.73 % (2009910)Termination phase: shuffling
% 10.73/2.73 % (2009910)Time elapsed: 0.003 s
% 10.73/2.73 % (2009910)Peak memory usage: 85 MB
% 10.73/2.73 % (2009910)Instructions burned: 2 (million)
% 10.73/2.73 % (2009913)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=2843282036:i=127:doe=on:rtra=on_2991 on theBenchmark for (2991ds/127Mi)
% 10.73/2.73 % (2009914)dis+10_1_si=on:random_seed=2737536947:i=10:ep=R:rtra=on_2991 on theBenchmark for (2991ds/10Mi)
% 10.73/2.73 % (2009913)Instruction limit reached!
% 10.73/2.73 % (2009913)------------------------------
% 10.73/2.73 % (2009913)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009913)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009913)Termination reason: Instruction limit
% 10.73/2.73 % (2009913)Termination phase: Saturation
% 10.73/2.73 % (2009913)Time elapsed: 0.086 s
% 10.73/2.73 % (2009913)Peak memory usage: 118 MB
% 10.73/2.73 % (2009913)Instructions burned: 128 (million)
% 10.73/2.73 % (2009914)Instruction limit reached!
% 10.73/2.73 % (2009914)------------------------------
% 10.73/2.73 % (2009914)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009914)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009914)Termination reason: Instruction limit
% 10.73/2.73 % (2009914)Termination phase: Property scanning
% 10.73/2.73 % (2009914)Time elapsed: 0.011 s
% 10.73/2.73 % (2009914)Peak memory usage: 85 MB
% 10.73/2.73 % (2009914)Instructions burned: 11 (million)
% 10.73/2.73 % (2009919)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=1309820007: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_2990 on theBenchmark for (2990ds/35Mi)
% 10.73/2.73 % (2009919)Instruction limit reached!
% 10.73/2.73 % (2009919)------------------------------
% 10.73/2.73 % (2009919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009919)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009919)Termination reason: Instruction limit
% 10.73/2.73 % (2009919)Termination phase: Preprocessing 3
% 10.73/2.73 % (2009919)Time elapsed: 0.036 s
% 10.73/2.73 % (2009919)Peak memory usage: 88 MB
% 10.73/2.73 % (2009919)Instructions burned: 35 (million)
% 10.73/2.73 % (2009917)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3289508437:i=26:canc=cautious:av=off:rtra=on_2990 on theBenchmark for (2990ds/26Mi)
% 10.73/2.73 % (2009921)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=780543339:i=2:fsr=off:rtra=on:inst=on_2990 on theBenchmark for (2990ds/2Mi)
% 10.73/2.73 % (2009921)Instruction limit reached!
% 10.73/2.73 % (2009921)------------------------------
% 10.73/2.73 % (2009921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009921)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009921)Termination reason: Instruction limit
% 10.73/2.73 % (2009921)Termination phase: shuffling
% 10.73/2.73 % (2009921)Time elapsed: 0.003 s
% 10.73/2.73 % (2009921)Peak memory usage: 85 MB
% 10.73/2.73 % (2009921)Instructions burned: 2 (million)
% 10.73/2.73 % (2009917)Instruction limit reached!
% 10.73/2.73 % (2009917)------------------------------
% 10.73/2.73 % (2009917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009917)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009917)Termination reason: Instruction limit
% 10.73/2.73 % (2009917)Termination phase: shuffling
% 10.73/2.73 % (2009917)Time elapsed: 0.026 s
% 10.73/2.73 % (2009917)Peak memory usage: 87 MB
% 10.73/2.73 % (2009917)Instructions burned: 26 (million)
% 10.73/2.73 % (2009924)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=683860920:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2990 on theBenchmark for (2990ds/8Mi)
% 10.73/2.73 % (2009925)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=3426689185:i=370:ep=RS:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/370Mi)
% 10.73/2.73 % (2009924)Instruction limit reached!
% 10.73/2.73 % (2009924)------------------------------
% 10.73/2.73 % (2009924)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009924)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009924)Termination reason: Instruction limit
% 10.73/2.73 % (2009924)Termination phase: Property scanning
% 10.73/2.73 % (2009924)Time elapsed: 0.009 s
% 10.73/2.73 % (2009924)Peak memory usage: 85 MB
% 10.73/2.73 % (2009924)Instructions burned: 8 (million)
% 10.73/2.73 % (2009930)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=2169987454:i=226:rtra=on:gtg=position:ss=axioms_2988 on theBenchmark for (2988ds/226Mi)
% 10.73/2.73 % (2009929)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=157937408:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2988 on theBenchmark for (2988ds/13Mi)
% 10.73/2.73 % (2009929)Instruction limit reached!
% 10.73/2.73 % (2009929)------------------------------
% 10.73/2.73 % (2009929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009929)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009929)Termination reason: Instruction limit
% 10.73/2.73 % (2009929)Termination phase: Property scanning
% 10.73/2.73 % (2009929)Time elapsed: 0.008 s
% 10.73/2.73 % (2009929)Peak memory usage: 85 MB
% 10.73/2.73 % (2009929)Instructions burned: 15 (million)
% 10.73/2.73 % (2009930)First to succeed.
% 10.73/2.73 % (2009930)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2009869"
% 10.73/2.73 % (2009932)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=959888989:i=10:rtra=on_2988 on theBenchmark for (2988ds/10Mi)
% 10.73/2.73 % (2009932)Instruction limit reached!
% 10.73/2.73 % (2009932)------------------------------
% 10.73/2.73 % (2009932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009932)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009932)Termination reason: Instruction limit
% 10.73/2.73 % (2009932)Termination phase: Property scanning
% 10.73/2.73 % (2009932)Time elapsed: 0.010 s
% 10.73/2.73 % (2009932)Peak memory usage: 86 MB
% 10.73/2.73 % (2009932)Instructions burned: 10 (million)
% 10.73/2.73 % (2009935)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=464352950:i=71:rtra=on:gtg=exists_top_2987 on theBenchmark for (2987ds/71Mi)
% 10.73/2.73 % (2009942)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=1893027451:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2986 on theBenchmark for (2986ds/130Mi)
% 10.73/2.73 % (2009936)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=1892391778:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2987 on theBenchmark for (2987ds/75Mi)
% 10.73/2.73 % (2009939)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=565496780:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2987 on theBenchmark for (2987ds/294Mi)
% 10.73/2.73 % (2009935)Instruction limit reached!
% 10.73/2.73 % (2009935)------------------------------
% 10.73/2.73 % (2009935)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009935)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009935)Termination reason: Instruction limit
% 10.73/2.73 % (2009935)Termination phase: Saturation
% 10.73/2.73 % (2009935)Time elapsed: 0.091 s
% 10.73/2.73 % (2009935)Peak memory usage: 107 MB
% 10.73/2.73 % (2009935)Instructions burned: 71 (million)
% 10.73/2.73 % (2009936)Instruction limit reached!
% 10.73/2.73 % (2009936)------------------------------
% 10.73/2.73 % (2009936)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009936)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009936)Termination reason: Instruction limit
% 10.73/2.73 % (2009936)Termination phase: Saturation
% 10.73/2.73 % (2009936)Time elapsed: 0.071 s
% 10.73/2.73 % (2009936)Peak memory usage: 90 MB
% 10.73/2.73 % (2009936)Instructions burned: 75 (million)
% 10.73/2.73 % (2009925)Instruction limit reached!
% 10.73/2.73 % (2009925)------------------------------
% 10.73/2.73 % (2009925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009925)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009925)Termination reason: Instruction limit
% 10.73/2.73 % (2009925)Termination phase: Saturation
% 10.73/2.73 % (2009925)Time elapsed: 0.347 s
% 10.73/2.73 % (2009925)Peak memory usage: 94 MB
% 10.73/2.73 % (2009925)Instructions burned: 370 (million)
% 10.73/2.73 % (2009942)Instruction limit reached!
% 10.73/2.73 % (2009942)------------------------------
% 10.73/2.73 % (2009942)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.73/2.73 % (2009942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.73/2.73 % (2009942)CaDiCaL version: 2.1.3
% 10.73/2.73 % (2009942)Termination reason: Instruction limit
% 10.73/2.73 % (2009942)Termination phase: Saturation
% 10.73/2.73 % (2009942)Time elapsed: 0.132 s
% 10.73/2.73 % (2009942)Peak memory usage: 118 MB
% 10.73/2.73 % (2009942)Instructions burned: 130 (million)
% 10.73/2.73 % (2009930)Refutation found. Thanks to Tanya!
% 10.73/2.73 % SZS status Theorem for theBenchmark
% 10.73/2.73 % SZS output start Proof for theBenchmark
% See solution above
% 12.09/2.89 % (2009930)------------------------------
% 12.09/2.89 % (2009930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.09/2.89 % (2009930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.09/2.89 % (2009930)CaDiCaL version: 2.1.3
% 12.09/2.89 % (2009930)Termination reason: Refutation
% 12.09/2.89 % (2009930)Time elapsed: 0.119 s
% 12.09/2.89 % (2009930)Peak memory usage: 119 MB
% 12.09/2.89 % (2009930)Instructions burned: 214 (million)
% 12.09/2.89 % (2009930)------------------------------
% 12.09/2.89 % (2009930)------------------------------
% 12.09/2.89 % (2009869)Success in time 1.648 s
% 12.09/2.89 % Vampire exiting
%------------------------------------------------------------------------------