%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP295_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 11:39:16 AM UTC 2026
% Result : Theorem 2.03s 1.00s
% Output : Refutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 61 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 48 ( 21 ~; 19 |; 3 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 36 ( 34 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 63 ( 61 usr; 1 prp; 0-5 aty)
% Number of functors : 342 ( 342 usr; 46 con; 0-4 aty)
% Number of variables : 36 ( 35 !; 1 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'ZF_set$': $tType ).
tff(type_def_6,type,
'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$': $tType ).
tff(type_def_7,type,
'ZF_ZF_prod_set$': $tType ).
tff(type_def_8,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'ZF_ZF_set_fun$': $tType ).
tff(type_def_10,type,
'ZF_ZF_prod_ZF_fun$': $tType ).
tff(type_def_11,type,
'ZF_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_12,type,
'Int_set$': $tType ).
tff(type_def_13,type,
'Int_int_fun$': $tType ).
tff(type_def_14,type,
'ZF_ZF_prod$': $tType ).
tff(type_def_15,type,
'ZF_ZF_prod_ZF_ZF_prod_prod_set$': $tType ).
tff(type_def_16,type,
'Int_ZF_fun$': $tType ).
tff(type_def_17,type,
'ZF_ZF_prod_ZF_ZF_prod_prod$': $tType ).
tff(type_def_18,type,
'Nat_nat_fun$': $tType ).
tff(type_def_19,type,
'ZF_ZF_prod_int_fun$': $tType ).
tff(type_def_20,type,
'Int_nat_fun$': $tType ).
tff(type_def_21,type,
'Nat$': $tType ).
tff(type_def_22,type,
'ZF_ZF_fun$': $tType ).
tff(type_def_23,type,
'ZF_ZF_prod_bool_fun$': $tType ).
tff(type_def_24,type,
'Bool_nat_fun$': $tType ).
tff(type_def_25,type,
'Nat_ZF_set_fun$': $tType ).
tff(type_def_26,type,
tlbool: $tType ).
tff(type_def_27,type,
'Nat_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_28,type,
'Bool_bool_fun$': $tType ).
tff(type_def_29,type,
'ZF_ZF_prod_nat_fun$': $tType ).
tff(type_def_30,type,
'ZF_bool_fun$': $tType ).
tff(type_def_31,type,
'ZF_nat_fun$': $tType ).
tff(type_def_32,type,
'Nat_bool_fun$': $tType ).
tff(type_def_33,type,
'ZF$': $tType ).
tff(type_def_34,type,
'ZF_int_fun$': $tType ).
tff(type_def_35,type,
'Nat_set$': $tType ).
tff(type_def_36,type,
'Nat_ZF_fun$': $tType ).
tff(type_def_37,type,
'Nat_int_fun$': $tType ).
tff(type_def_38,type,
'ZF_ZF_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'ext_ZF_n$': ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'Nat_ZF_fun$' ).
tff(func_def_1,type,
'uve$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_2,type,
'fun$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_3,type,
'case_nat$a': ( tlbool * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_4,type,
'trancl$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set$' ).
tff(func_def_5,type,
'uu$': 'ZF_ZF_fun$' ).
tff(func_def_6,type,
'comp$c': ( 'Int_nat_fun$' * 'Nat_int_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_7,type,
'uvs$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_8,type,
'uuz$': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_9,type,
'uwa$': ( 'ZF_nat_fun$' * 'ZF_nat_fun$' ) > 'ZF_nat_fun$' ).
tff(func_def_10,type,
'ordering_top$': ( 'Nat_nat_bool_fun_fun$' * 'Nat_nat_bool_fun_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_11,type,
'fun_app$w': ( 'Nat_ZF_set_fun$' * 'Nat$' ) > 'ZF_set$' ).
tff(func_def_12,type,
'fun_app$p': ( 'Int_nat_fun$' * $int ) > 'Nat$' ).
tff(func_def_13,type,
'same_fst$': ( 'ZF_bool_fun$' * 'ZF_ZF_ZF_prod_set_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).
tff(func_def_14,type,
'fun_app$d': ( 'Nat_ZF_fun$' * 'Nat$' ) > 'ZF$' ).
tff(func_def_15,type,
'fun_app$v': ( 'Nat_ZF_ZF_prod_set_fun$' * 'Nat$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_16,type,
'field$': 'ZF_ZF_fun$' ).
tff(func_def_17,type,
'fun_app$o': ( 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod$' ) > 'Nat$' ).
tff(func_def_18,type,
'uum$': $int > 'Nat_int_fun$' ).
tff(func_def_19,type,
'uvr$': 'Int_int_fun$' ).
tff(func_def_20,type,
'uvj$': ( 'Bool_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_21,type,
'comp$l': ( 'Nat_nat_fun$' * 'ZF_nat_fun$' ) > 'ZF_nat_fun$' ).
tff(func_def_22,type,
'v$': 'ZF$' ).
tff(func_def_23,type,
'uvd$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_24,type,
'uva$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_25,type,
'uvx$': ( 'ZF_ZF_prod_int_fun$' * 'ZF_ZF_prod_int_fun$' ) > 'ZF_ZF_prod_int_fun$' ).
tff(func_def_26,type,
'zero$': 'Nat$' ).
tff(func_def_27,type,
'fun_app$l': ( 'ZF_int_fun$' * 'ZF$' ) > $int ).
tff(func_def_28,type,
'gbinomial$': $int > 'Nat_int_fun$' ).
tff(func_def_29,type,
'comp$g': ( 'Int_nat_fun$' * 'Int_int_fun$' ) > 'Int_nat_fun$' ).
tff(func_def_30,type,
'relInvImage$a': ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_31,type,
'singleton$': 'ZF_ZF_fun$' ).
tff(func_def_32,type,
'uuc$': 'ZF_set$' > 'ZF_bool_fun$' ).
tff(func_def_33,type,
'seqSum$': 'Nat_ZF_fun$' > 'ZF$' ).
tff(func_def_34,type,
'uus$': 'Int_int_fun$' ).
tff(func_def_35,type,
'sum$': 'ZF_ZF_fun$' ).
tff(func_def_36,type,
def_5: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_37,type,
'comp$t': ( 'ZF_nat_fun$' * 'Nat_ZF_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_38,type,
'uua$': 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' ).
tff(func_def_39,type,
'nat2nat$': 'ZF_nat_fun$' ).
tff(func_def_40,type,
'comp$f': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_41,type,
'pred$': 'Nat_nat_fun$' ).
tff(func_def_42,type,
'natInterval$': 'Nat$' > 'Nat_ZF_fun$' ).
tff(func_def_43,type,
'image2$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_44,type,
'fun_app$s': ( 'Int_ZF_fun$' * $int ) > 'ZF$' ).
tff(func_def_45,type,
'u$': 'ZF$' ).
tff(func_def_46,type,
'of_nat$a': 'Nat_nat_fun$' ).
tff(func_def_47,type,
'opair$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_48,type,
'nat$': 'Int_nat_fun$' ).
tff(func_def_49,type,
'empty$': 'ZF$' ).
tff(func_def_50,type,
'uvi$': ( 'Bool_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_51,type,
'uuf$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_52,type,
'times$a': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_53,type,
'sum$c': ( 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod_set$' ) > 'Nat$' ).
tff(func_def_54,type,
'repl$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_55,type,
'fun_app$r': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_56,type,
'comp$a': ( 'Nat_int_fun$' * 'Int_nat_fun$' ) > 'Int_int_fun$' ).
tff(func_def_57,type,
'fun_app$u': ( 'ZF_ZF_set_fun$' * 'ZF$' ) > 'ZF_set$' ).
tff(func_def_58,type,
'uvb$': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).
tff(func_def_59,type,
'uvq$': ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_60,type,
'comp$q': ( 'ZF_int_fun$' * 'Int_ZF_fun$' ) > 'Int_int_fun$' ).
tff(func_def_61,type,
'uvn$': ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_62,type,
'sum$a': ( 'ZF_ZF_prod_int_fun$' * 'ZF_ZF_prod_set$' ) > $int ).
tff(func_def_63,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_64,type,
'uvw$': 'Nat_nat_fun$' ).
tff(func_def_65,type,
'cartProd$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_66,type,
'relImage$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_67,type,
'times$': $int > 'Int_int_fun$' ).
tff(func_def_68,type,
'universe$': 'ZF_bool_fun$' ).
tff(func_def_69,type,
def_10: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_70,type,
'pair$a': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod$' ).
tff(func_def_71,type,
'sum$f': ( 'Int_nat_fun$' * 'Int_set$' ) > 'Nat$' ).
tff(func_def_72,type,
def_1: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_73,type,
'comp$b': ( 'Int_ZF_fun$' * 'Int_int_fun$' ) > 'Int_ZF_fun$' ).
tff(func_def_74,type,
'uuv$': 'Nat_nat_fun$' ).
tff(func_def_75,type,
'fun_app$g': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_76,type,
'fun_app$j': ( 'ZF_ZF_bool_fun_fun$' * 'ZF$' ) > 'ZF_bool_fun$' ).
tff(func_def_77,type,
'comp$h': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).
tff(func_def_78,type,
'uuk$': 'ZF_bool_fun$' ).
tff(func_def_79,type,
tltrue: tlbool ).
tff(func_def_80,type,
'uux$': 'ZF_ZF_prod_set$' > 'ZF_ZF_bool_fun_fun$' ).
tff(func_def_81,type,
def_8: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_82,type,
'plus$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_83,type,
'pFun$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_84,type,
'uvf$': ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF_bool_fun$' ).
tff(func_def_85,type,
'ext_ZF$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).
tff(func_def_86,type,
'is_Elem_of$': 'ZF_ZF_prod_set$' ).
tff(func_def_87,type,
'gr$': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_88,type,
'uub$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_89,type,
'uuo$': 'Nat$' > 'Int_nat_fun$' ).
tff(func_def_90,type,
'union$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_91,type,
'one$': 'Nat$' ).
tff(func_def_92,type,
'comp$n': ( 'Nat_ZF_fun$' * 'Int_nat_fun$' ) > 'Int_ZF_fun$' ).
tff(func_def_93,type,
'comp$': ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_fun$' ).
tff(func_def_94,type,
'comp$r': ( 'Int_ZF_fun$' * 'Nat_int_fun$' ) > 'Nat_ZF_fun$' ).
tff(func_def_95,type,
'u$a': 'ZF$' ).
tff(func_def_96,type,
'sum$d': ( 'ZF_nat_fun$' * 'ZF_set$' ) > 'Nat$' ).
tff(func_def_97,type,
'the$': 'ZF_bool_fun$' > 'ZF$' ).
tff(func_def_98,type,
'uuh$': ( 'ZF$' * 'ZF$' ) > 'ZF_bool_fun$' ).
tff(func_def_99,type,
'comp$m': ( 'Nat_ZF_fun$' * 'Nat_nat_fun$' ) > 'Nat_ZF_fun$' ).
tff(func_def_100,type,
'uvg$': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_101,type,
'uvm$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_102,type,
'ext_ZF_hull$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).
tff(func_def_103,type,
'implode$': 'ZF_set$' > 'ZF$' ).
tff(func_def_104,type,
'ext$': 'ZF_ZF_prod_set$' > 'ZF_ZF_set_fun$' ).
tff(func_def_105,type,
'comp$i': ( 'ZF_ZF_fun$' * 'Nat_ZF_fun$' ) > 'Nat_ZF_fun$' ).
tff(func_def_106,type,
'nat2Nat$': 'Nat_ZF_fun$' ).
tff(func_def_107,type,
'collect$b': 'ZF_bool_fun$' > 'ZF_set$' ).
tff(func_def_108,type,
'fun_app$': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_109,type,
def_9: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_110,type,
'comp$p': ( 'ZF_ZF_fun$' * 'Int_ZF_fun$' ) > 'Int_ZF_fun$' ).
tff(func_def_111,type,
'of_nat_aux$a': ( 'Int_int_fun$' * 'Nat$' ) > 'Int_int_fun$' ).
tff(func_def_112,type,
'relInvImage$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).
tff(func_def_113,type,
'uvp$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' ).
tff(func_def_114,type,
'fun_app$n': ( 'Bool_nat_fun$' * tlbool ) > 'Nat$' ).
tff(func_def_115,type,
'uvu$': 'Int_int_fun$' ).
tff(func_def_116,type,
'uvz$': ( 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod_nat_fun$' ) > 'ZF_ZF_prod_nat_fun$' ).
tff(func_def_117,type,
'sum$g': ( 'Int_int_fun$' * 'Int_set$' ) > $int ).
tff(func_def_118,type,
'sucNat$': 'ZF_ZF_fun$' ).
tff(func_def_119,type,
'uvt$': 'Int_int_fun$' ).
tff(func_def_120,type,
'uui$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_121,type,
'isFun$': 'ZF_bool_fun$' ).
tff(func_def_122,type,
'fun_app$h': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_123,type,
'of_nat_aux$': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat_nat_fun$' ).
tff(func_def_124,type,
'fun_app$b': ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_125,type,
'less_eq$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_126,type,
'app$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_127,type,
'comp$d': ( 'Int_int_fun$' * 'Nat_int_fun$' ) > 'Nat_int_fun$' ).
tff(func_def_128,type,
'uuy$': 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_129,type,
'range$': 'ZF_ZF_fun$' ).
tff(func_def_130,type,
'case_nat$': ( 'Nat$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_131,type,
'lambda$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_132,type,
def_4: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_133,type,
'uug$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_134,type,
'collect$': 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' > 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ).
tff(func_def_135,type,
'comp$j': ( 'Nat_nat_fun$' * 'Int_nat_fun$' ) > 'Int_nat_fun$' ).
tff(func_def_136,type,
tlfalse: tlbool ).
tff(func_def_137,type,
'sum$b': ( 'ZF_int_fun$' * 'ZF_set$' ) > $int ).
tff(func_def_138,type,
'uvv$': 'Int_int_fun$' ).
tff(func_def_139,type,
'uvo$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_140,type,
'sum$e': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_141,type,
'uuu$': ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF_bool_fun$' ).
tff(func_def_142,type,
'elem$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_143,type,
'inf$': 'ZF$' ).
tff(func_def_144,type,
'comp$k': ( 'ZF_nat_fun$' * 'ZF_ZF_fun$' ) > 'ZF_nat_fun$' ).
tff(func_def_145,type,
'uut$': 'Nat_nat_fun$' ).
tff(func_def_146,type,
def_2: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_147,type,
def_6: ( 'Bool_bool_fun$' * tlbool ) > tlbool ).
tff(func_def_148,type,
'comp$e': ( 'Int_int_fun$' * 'Int_int_fun$' ) > 'Int_int_fun$' ).
tff(func_def_149,type,
'abs$': 'Int_int_fun$' ).
tff(func_def_150,type,
'comp$s': ( 'Nat_int_fun$' * 'Nat_nat_fun$' ) > 'Nat_int_fun$' ).
tff(func_def_151,type,
'power$': 'ZF_ZF_fun$' ).
tff(func_def_152,type,
'sep$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_153,type,
'uue$': 'ZF_ZF_fun$' > 'ZF_ZF_fun$' ).
tff(func_def_154,type,
'uun$': 'ZF$' > 'Int_ZF_fun$' ).
tff(func_def_155,type,
'uul$': ( tlbool * 'ZF$' * 'ZF$' ) > 'ZF_bool_fun$' ).
tff(func_def_156,type,
'uud$': ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_fun$' ).
tff(func_def_157,type,
'fun_app$t': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_158,type,
'fun_app$a': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_159,type,
'domain$': 'ZF_ZF_fun$' ).
tff(func_def_160,type,
'comp$o': ( 'ZF_nat_fun$' * 'Int_ZF_fun$' ) > 'Int_nat_fun$' ).
tff(func_def_161,type,
'upair$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_162,type,
'uvl$': 'Nat_bool_fun$' ).
tff(func_def_163,type,
'suc$': 'Nat_nat_fun$' ).
tff(func_def_164,type,
'uvc$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_165,type,
'binomial$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_166,type,
'uvh$': ( 'Nat_bool_fun$' * 'Nat_nat_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_167,type,
'pair$': ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_prod$' ).
tff(func_def_168,type,
'uvy$': ( 'ZF_int_fun$' * 'ZF_int_fun$' ) > 'ZF_int_fun$' ).
tff(func_def_169,type,
'nat$a': 'ZF$' ).
tff(func_def_170,type,
'image2$a': ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_171,type,
'uur$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_172,type,
def_3: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_173,type,
def_7: ( tlbool * 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_174,type,
'explode$': 'ZF_ZF_set_fun$' ).
tff(func_def_175,type,
'uuj$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_176,type,
'uup$': $int > 'Int_int_fun$' ).
tff(func_def_177,type,
'uvk$': 'Nat_bool_fun$' ).
tff(func_def_178,type,
'fun_app$q': ( 'ZF_nat_fun$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_179,type,
'uuq$': 'ZF$' > 'Nat_ZF_fun$' ).
tff(func_def_180,type,
'subset$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_181,type,
'uuw$': 'Int_int_fun$' ).
tff(func_def_182,type,
'collect$a': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_183,type,
'fun_app$k': ( 'ZF_ZF_prod_int_fun$' * 'ZF_ZF_prod$' ) > $int ).
tff(func_def_190,type,
sK0: 'ZF$' > 'Nat$' ).
tff(func_def_191,type,
sK1: 'ZF_ZF_prod$' > 'ZF$' ).
tff(func_def_192,type,
sK2: 'ZF_ZF_prod$' > 'ZF$' ).
tff(func_def_193,type,
sK3: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_194,type,
sK4: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_195,type,
sK5: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_196,type,
sK9: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).
tff(func_def_197,type,
sK10: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_198,type,
sK11: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > 'ZF_ZF_prod$' ).
tff(func_def_199,type,
sK12: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > 'ZF_ZF_prod$' ).
tff(func_def_200,type,
sK13: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_201,type,
sK14: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_202,type,
sK15: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_203,type,
sK16: ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_fun$' ).
tff(func_def_204,type,
sK17: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_205,type,
sK18: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_206,type,
sK19: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_207,type,
sK20: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_208,type,
sK21: 'ZF$' > 'ZF$' ).
tff(func_def_209,type,
sK22: 'ZF$' > 'ZF$' ).
tff(func_def_210,type,
sK23: 'ZF$' > 'ZF$' ).
tff(func_def_211,type,
sK24: 'ZF$' > 'ZF$' ).
tff(func_def_212,type,
sK25: 'ZF$' > 'ZF$' ).
tff(func_def_213,type,
sK29: 'ZF$' > 'ZF$' ).
tff(func_def_214,type,
sK30: 'ZF$' > 'ZF$' ).
tff(func_def_215,type,
sK31: 'ZF$' > 'ZF$' ).
tff(func_def_216,type,
sK32: 'ZF$' > 'ZF$' ).
tff(func_def_217,type,
sK33: 'ZF$' > 'ZF$' ).
tff(func_def_218,type,
sK37: 'ZF$' > 'ZF$' ).
tff(func_def_219,type,
sK38: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_220,type,
sK39: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_221,type,
sK40: ( 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_prod$' ).
tff(func_def_222,type,
sK41: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_223,type,
sK42: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_224,type,
sK43: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_225,type,
sK44: 'ZF_bool_fun$' > 'ZF$' ).
tff(func_def_226,type,
sK45: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_227,type,
sK46: ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_228,type,
sK47: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_229,type,
sK48: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_230,type,
sK49: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_231,type,
sK50: 'ZF$' > 'ZF$' ).
tff(func_def_232,type,
sK51: 'ZF$' > 'ZF$' ).
tff(func_def_233,type,
sK52: 'ZF$' > 'ZF$' ).
tff(func_def_234,type,
sK53: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_235,type,
sK54: 'ZF$' > 'ZF$' ).
tff(func_def_236,type,
sK55: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_237,type,
sK56: ( 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_238,type,
sK57: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_239,type,
sK58: ( 'ZF$' * 'Nat_ZF_fun$' ) > 'Nat$' ).
tff(func_def_240,type,
sK59: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_241,type,
sK60: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_242,type,
sK61: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_243,type,
sK62: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_244,type,
sK63: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_245,type,
sK64: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_246,type,
sK65: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_247,type,
sK66: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_248,type,
sK67: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_249,type,
sK70: 'Nat$' > 'Nat$' ).
tff(func_def_250,type,
sK72: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_251,type,
sK73: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_252,type,
sK74: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_253,type,
sK75: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_254,type,
sK76: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_255,type,
sK77: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_256,type,
sK78: 'Nat$' > 'Nat$' ).
tff(func_def_257,type,
sK79: ( 'ZF_ZF_prod_set$' * 'ZF$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_258,type,
sK82: 'ZF_ZF_prod_set$' > 'ZF$' ).
tff(func_def_259,type,
sK83: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_260,type,
sK84: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_261,type,
sK85: ( 'ZF$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_262,type,
sK86: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_263,type,
sK87: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_264,type,
sK88: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_265,type,
sK89: 'Nat_ZF_ZF_prod_set_fun$' > 'Nat$' ).
tff(func_def_266,type,
sK90: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_267,type,
sK91: 'Nat_ZF_set_fun$' > 'Nat$' ).
tff(func_def_268,type,
sK92: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_269,type,
sK93: 'Nat_ZF_ZF_prod_set_fun$' > 'Nat$' ).
tff(func_def_270,type,
sK94: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_271,type,
sK95: 'Nat_ZF_set_fun$' > 'Nat$' ).
tff(func_def_272,type,
sK96: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_273,type,
sK97: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_274,type,
sK98: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_275,type,
sK99: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_276,type,
sK100: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_277,type,
sK101: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_278,type,
sK102: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_279,type,
sK103: 'Nat$' > 'Nat$' ).
tff(func_def_280,type,
sK106: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_281,type,
sK107: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_282,type,
sK115: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_283,type,
sK125: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_284,type,
sK126: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_285,type,
sK128: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_286,type,
sK131: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_287,type,
sK133: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_288,type,
sK134: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_289,type,
sK136: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_290,type,
sK137: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_291,type,
sK138: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_292,type,
sK139: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_293,type,
sK140: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_294,type,
sK141: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_295,type,
sK142: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_296,type,
sK143: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_297,type,
sK145: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_298,type,
sK146: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_299,type,
sK149: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_300,type,
sK150: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_301,type,
sK151: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_302,type,
sK152: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_303,type,
sK153: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_304,type,
sK155: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_305,type,
sK156: 'Nat$' > 'Nat$' ).
tff(func_def_306,type,
sK157: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_307,type,
sK159: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_308,type,
sK160: 'Nat$' > 'Nat$' ).
tff(func_def_309,type,
sK161: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_310,type,
sK162: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_311,type,
sK163: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_312,type,
sK164: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_313,type,
sK165: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_314,type,
sK166: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_315,type,
sK167: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_316,type,
sK168: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_317,type,
sK169: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_318,type,
sK170: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_319,type,
sK174: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_320,type,
sK177: ( 'Nat_bool_fun$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_321,type,
sK181: ( 'Nat_bool_fun$' * 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_322,type,
sK183: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_323,type,
sK188: ( $int * $int ) > 'Nat$' ).
tff(func_def_324,type,
sK189: ( 'Nat$' * 'Nat_int_fun$' ) > 'Nat$' ).
tff(func_def_325,type,
sK190: ( 'Nat$' * 'Nat_int_fun$' * $int ) > 'Nat$' ).
tff(func_def_326,type,
sK192: ( 'Nat$' * 'Nat$' * 'Nat_int_fun$' ) > 'Nat$' ).
tff(func_def_327,type,
sK193: ( 'Nat$' * 'Nat$' * 'Nat_int_fun$' * $int ) > 'Nat$' ).
tff(func_def_328,type,
sK195: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_329,type,
sK196: ( 'ZF_set$' * 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_330,type,
sK197: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_331,type,
sK198: ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_332,type,
sK199: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_int_fun$' * $int * $int ) > 'ZF_ZF_prod$' ).
tff(func_def_333,type,
sK200: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_int_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_334,type,
sK201: ( 'ZF_set$' * 'ZF_int_fun$' * $int * $int ) > 'ZF$' ).
tff(func_def_335,type,
sK202: ( 'ZF_set$' * 'ZF_int_fun$' ) > 'ZF$' ).
tff(func_def_336,type,
sK203: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod_nat_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_337,type,
sK204: ( 'ZF_set$' * 'ZF_nat_fun$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_338,type,
sK205: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_int_fun$' * 'ZF_ZF_prod_int_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_339,type,
sK206: ( 'ZF_set$' * 'ZF_int_fun$' * 'ZF_int_fun$' ) > 'ZF$' ).
tff(func_def_340,type,
sK207: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod_nat_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_341,type,
sK208: ( 'ZF_set$' * 'ZF_nat_fun$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_342,type,
sK209: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_343,type,
sK210: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_344,type,
sK211: 'Int_nat_fun$' > $int ).
tff(func_def_345,type,
sK212: 'Int_nat_fun$' > $int ).
tff(func_def_346,type,
sK213: ( 'ZF_ZF_prod_nat_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_347,type,
sK214: ( 'ZF_nat_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(pred_def_1,type,
'fun_app$c': ( 'ZF_bool_fun$' * 'ZF$' ) > $o ).
tff(pred_def_2,type,
'wfzf$': 'ZF_ZF_prod_set$' > $o ).
tff(pred_def_3,type,
'fun_app$e': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' ) > $o ).
tff(pred_def_4,type,
'less_eq$a': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$m': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_6,type,
'set_like$': 'ZF_ZF_prod_set$' > $o ).
tff(pred_def_7,type,
'less_eq$c': ( 'ZF_ZF_bool_fun_fun$' * 'ZF_ZF_bool_fun_fun$' ) > $o ).
tff(pred_def_8,type,
'member$b': ( 'ZF$' * 'ZF_set$' ) > $o ).
tff(pred_def_9,type,
'member$a': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' ) > $o ).
tff(pred_def_10,type,
'less_eq$b': ( 'ZF_set$' * 'ZF_set$' ) > $o ).
tff(pred_def_11,type,
'is_measure$': 'Int_nat_fun$' > $o ).
tff(pred_def_12,type,
'fun_app$i': ( 'ZF_ZF_prod_ZF_ZF_prod_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_prod$' ) > $o ).
tff(pred_def_13,type,
'member$': ( 'ZF_ZF_prod_ZF_ZF_prod_prod$' * 'ZF_ZF_prod_ZF_ZF_prod_prod_set$' ) > $o ).
tff(pred_def_14,type,
'less_eq$d': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > $o ).
tff(pred_def_15,type,
'less_eq$e': ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > $o ).
tff(pred_def_16,type,
'regular$': 'ZF_ZF_prod_set$' > $o ).
tff(pred_def_17,type,
'fun_app$f': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_20,type,
sP6: ( 'ZF$' * 'ZF$' * tlbool ) > $o ).
tff(pred_def_23,type,
sP26: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_24,type,
sP27: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_25,type,
sP28: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_26,type,
sP34: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_27,type,
sP35: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_28,type,
sP36: ( 'ZF$' * 'ZF$' ) > $o ).
tff(pred_def_32,type,
sP80: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_33,type,
sP81: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_37,type,
sP109: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_38,type,
sP110: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_39,type,
sP111: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_40,type,
sP112: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_41,type,
sP113: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_42,type,
sP114: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_43,type,
sP116: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_44,type,
sP117: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_45,type,
sP118: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_46,type,
sP119: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_47,type,
sP120: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_48,type,
sP121: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_49,type,
sP122: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_50,type,
sP123: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_51,type,
sP124: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_55,type,
sP132: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_56,type,
sP135: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_57,type,
sP144: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_60,type,
sP154: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_61,type,
sP158: ( 'Nat$' * 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_62,type,
sP171: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_63,type,
sP172: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_64,type,
sP173: ( 'Nat$' * 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_65,type,
sP175: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_66,type,
sP176: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_67,type,
sP178: ( 'Nat$' * 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_68,type,
sP179: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_69,type,
sP180: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_70,type,
sP182: ( 'Nat$' * 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_71,type,
sP184: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_72,type,
sP185: ( 'Nat$' * tlbool * 'Bool_bool_fun$' ) > $o ).
tff(pred_def_73,type,
sP186: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_74,type,
sP187: ( 'Nat$' * tlbool * 'Bool_bool_fun$' ) > $o ).
tff(pred_def_75,type,
sP191: ( 'Nat$' * 'Nat_int_fun$' ) > $o ).
tff(pred_def_76,type,
sP194: ( 'Nat$' * $int * 'Nat_int_fun$' * 'Nat$' * 'Nat$' ) > $o ).
tff(f6,axiom,
! [X0: 'ZF$'] : ( 'fun_app$b'('uu$',X0) = 'fun_app$b'('singleton$','fun_app$b'('opair$'(X0),'v$')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f55,conjecture,
'fun_app$c'('elem$'('lambda$'('u$','uu$')),'fun_app$b'('fun$'('u$'),'u$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture54) ).
tff(f56,negated_conjecture,
~ 'fun_app$c'('elem$'('lambda$'('u$','uu$')),'fun_app$b'('fun$'('u$'),'u$a')),
inference(negated_conjecture,[status(cth)],[f55]) ).
tff(f57,axiom,
'fun_app$c'('elem$'('u$'),'u$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis55) ).
tff(f58,axiom,
'fun_app$c'('elem$'('v$'),'u$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hypothesis56) ).
tff(f60,axiom,
! [X0: 'ZF$',X1: 'ZF$'] :
( ( 'fun_app$c'('elem$'(X0),'u$a')
& 'fun_app$c'('elem$'(X1),X0) )
=> 'fun_app$c'('elem$'(X1),'u$a') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
tff(f61,axiom,
! [X0: 'ZF$',X1: 'ZF$'] :
( ( 'fun_app$c'('elem$'(X0),'u$a')
& 'fun_app$c'('elem$'(X1),'u$a') )
=> 'fun_app$c'('elem$'('fun_app$b'('opair$'(X0),X1)),'u$a') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom59) ).
tff(f62,axiom,
! [X0: 'ZF$'] :
( 'fun_app$c'('elem$'(X0),'u$a')
=> 'fun_app$c'('elem$'('fun_app$b'('singleton$',X0)),'u$a') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom60) ).
tff(f67,axiom,
! [X0: 'ZF$',X1: 'ZF_ZF_fun$',X2: 'ZF$'] :
( ! [X3: 'ZF$'] :
( 'fun_app$c'('elem$'(X3),X0)
=> 'fun_app$c'('elem$'('fun_app$b'(X1,X3)),X2) )
=> 'fun_app$c'('elem$'('lambda$'(X0,X1)),'fun_app$b'('fun$'(X0),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
tff(f879,plain,
~ 'fun_app$c'('elem$'('lambda$'('u$','uu$')),'fun_app$b'('fun$'('u$'),'u$a')),
inference(flattening,[],[f56]) ).
tff(f904,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( 'fun_app$c'('elem$'(X1),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| ~ 'fun_app$c'('elem$'(X1),X0) ),
inference(ennf_transformation,[],[f60]) ).
tff(f905,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( 'fun_app$c'('elem$'(X1),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| ~ 'fun_app$c'('elem$'(X1),X0) ),
inference(flattening,[],[f904]) ).
tff(f906,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( 'fun_app$c'('elem$'('fun_app$b'('opair$'(X0),X1)),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| ~ 'fun_app$c'('elem$'(X1),'u$a') ),
inference(ennf_transformation,[],[f61]) ).
tff(f907,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( 'fun_app$c'('elem$'('fun_app$b'('opair$'(X0),X1)),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| ~ 'fun_app$c'('elem$'(X1),'u$a') ),
inference(flattening,[],[f906]) ).
tff(f908,plain,
! [X0: 'ZF$'] :
( 'fun_app$c'('elem$'('fun_app$b'('singleton$',X0)),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a') ),
inference(ennf_transformation,[],[f62]) ).
tff(f914,plain,
! [X0: 'ZF$',X1: 'ZF_ZF_fun$',X2: 'ZF$'] :
( 'fun_app$c'('elem$'('lambda$'(X0,X1)),'fun_app$b'('fun$'(X0),X2))
| ? [X3: 'ZF$'] :
( ~ 'fun_app$c'('elem$'('fun_app$b'(X1,X3)),X2)
& 'fun_app$c'('elem$'(X3),X0) ) ),
inference(ennf_transformation,[],[f67]) ).
tff(f1387,plain,
! [X0: 'ZF$'] : ( 'fun_app$b'('uu$',X0) = 'fun_app$b'('singleton$','fun_app$b'('opair$'(X0),'v$')) ),
inference(cnf_transformation,[],[f6]) ).
tff(f1492,plain,
~ 'fun_app$c'('elem$'('lambda$'('u$','uu$')),'fun_app$b'('fun$'('u$'),'u$a')),
inference(cnf_transformation,[],[f879]) ).
tff(f1493,plain,
'fun_app$c'('elem$'('u$'),'u$a'),
inference(cnf_transformation,[],[f57]) ).
tff(f1494,plain,
'fun_app$c'('elem$'('v$'),'u$a'),
inference(cnf_transformation,[],[f58]) ).
tff(f1496,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( ~ 'fun_app$c'('elem$'(X1),X0)
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| 'fun_app$c'('elem$'(X1),'u$a') ),
inference(cnf_transformation,[],[f905]) ).
tff(f1497,plain,
! [X0: 'ZF$',X1: 'ZF$'] :
( ~ 'fun_app$c'('elem$'(X1),'u$a')
| ~ 'fun_app$c'('elem$'(X0),'u$a')
| 'fun_app$c'('elem$'('fun_app$b'('opair$'(X0),X1)),'u$a') ),
inference(cnf_transformation,[],[f907]) ).
tff(f1498,plain,
! [X0: 'ZF$'] :
( ~ 'fun_app$c'('elem$'(X0),'u$a')
| 'fun_app$c'('elem$'('fun_app$b'('singleton$',X0)),'u$a') ),
inference(cnf_transformation,[],[f908]) ).
tff(f1503,plain,
! [X2: 'ZF$',X0: 'ZF$',X1: 'ZF_ZF_fun$'] :
( 'fun_app$c'('elem$'('lambda$'(X0,X1)),'fun_app$b'('fun$'(X0),X2))
| 'fun_app$c'('elem$'(sK15(X0,X1,X2)),X0) ),
inference(cnf_transformation,[],[f914]) ).
tff(f1504,plain,
! [X2: 'ZF$',X0: 'ZF$',X1: 'ZF_ZF_fun$'] :
( ~ 'fun_app$c'('elem$'('fun_app$b'(X1,sK15(X0,X1,X2))),X2)
| 'fun_app$c'('elem$'('lambda$'(X0,X1)),'fun_app$b'('fun$'(X0),X2)) ),
inference(cnf_transformation,[],[f914]) ).
tff(f4215,plain,
! [X0: 'ZF$'] :
( ~ 'fun_app$c'('elem$'(X0),'u$a')
| 'fun_app$c'('elem$'('fun_app$b'('opair$'(X0),'v$')),'u$a') ),
inference(resolution,[],[f1497,f1494]) ).
tff(f4246,plain,
'fun_app$c'('elem$'(sK15('u$','uu$','u$a')),'u$'),
inference(resolution,[],[f1503,f1492]) ).
tff(f4259,plain,
( ~ 'fun_app$c'('elem$'('u$'),'u$a')
| 'fun_app$c'('elem$'(sK15('u$','uu$','u$a')),'u$a') ),
inference(resolution,[],[f4246,f1496]) ).
tff(f4261,plain,
'fun_app$c'('elem$'(sK15('u$','uu$','u$a')),'u$a'),
inference(forward_subsumption_resolution,[],[f4259,f1493]) ).
tff(f7823,plain,
'fun_app$c'('elem$'('fun_app$b'('opair$'(sK15('u$','uu$','u$a')),'v$')),'u$a'),
inference(resolution,[],[f4215,f4261]) ).
tff(f7905,plain,
'fun_app$c'('elem$'('fun_app$b'('singleton$','fun_app$b'('opair$'(sK15('u$','uu$','u$a')),'v$'))),'u$a'),
inference(resolution,[],[f7823,f1498]) ).
tff(f7918,plain,
'fun_app$c'('elem$'('fun_app$b'('uu$',sK15('u$','uu$','u$a'))),'u$a'),
inference(forward_demodulation,[],[f7905,f1387]) ).
tff(f7933,plain,
'fun_app$c'('elem$'('lambda$'('u$','uu$')),'fun_app$b'('fun$'('u$'),'u$a')),
inference(resolution,[],[f7918,f1504]) ).
tff(f7934,plain,
$false,
inference(forward_subsumption_resolution,[],[f7933,f1492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP295_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n004.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 12:53:22 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.03/1.00 % (3488448)Will run a generic schedule for satisfiability detection.
% 2.03/1.00 % (3488458)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2095963045:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 2.03/1.00 % (3488454)% WARNING: option uhcvi not known.
% 2.03/1.00 % (3488453)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4157153110_2999 on theBenchmark for (2999ds/0Mi)
% 2.03/1.00 % (3488454)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3183274845:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 2.03/1.00 % (3488455)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=420756761:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 2.03/1.00 % (3488456)dis+10_1_sil=32000:sp=arity:random_seed=2819610166:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 2.03/1.00 % (3488457)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1903744199:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 2.03/1.00 % (3488459)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1233536934:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 2.03/1.00 % (3488458)Instruction limit reached!
% 2.03/1.00 % (3488458)------------------------------
% 2.03/1.00 % (3488458)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488458)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488458)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488458)Termination reason: Instruction limit
% 2.03/1.00 % (3488458)Termination phase: Property scanning
% 2.03/1.00 % (3488458)Time elapsed: 0.030 s
% 2.03/1.00 % (3488458)Peak memory usage: 12 MB
% 2.03/1.00 % (3488458)Instructions burned: 131 (million)
% 2.03/1.00 % (3488467)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2638746417:i=714:nm=2_2998 on theBenchmark for (2998ds/714Mi)
% 2.03/1.00 % (3488456)Instruction limit reached!
% 2.03/1.00 % (3488456)------------------------------
% 2.03/1.00 % (3488456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488456)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488456)Termination reason: Instruction limit
% 2.03/1.00 % (3488456)Termination phase: Property scanning
% 2.03/1.00 % (3488456)Time elapsed: 0.046 s
% 2.03/1.00 % (3488456)Peak memory usage: 13 MB
% 2.03/1.00 % (3488456)Instructions burned: 103 (million)
% 2.03/1.00 % (3488457)Instruction limit reached!
% 2.03/1.00 % (3488457)------------------------------
% 2.03/1.00 % (3488457)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488457)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488457)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488457)Termination reason: Instruction limit
% 2.03/1.00 % (3488457)Termination phase: Property scanning
% 2.03/1.00 % (3488457)Time elapsed: 0.052 s
% 2.03/1.00 % (3488457)Peak memory usage: 13 MB
% 2.03/1.00 % (3488457)Instructions burned: 119 (million)
% 2.03/1.00 % (3488453)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.03/1.00 % (3488453)Terminated due to inappropriate strategy.
% 2.03/1.00 % (3488453)------------------------------
% 2.03/1.00 % (3488453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488453)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488453)Termination reason: Inappropriate
% 2.03/1.00 % (3488453)Time elapsed: 0.064 s
% 2.03/1.00 % (3488453)Peak memory usage: 13 MB
% 2.03/1.00 % (3488453)Instructions burned: 143 (million)
% 2.03/1.00 % (3488467)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.03/1.00 % (3488467)Terminated due to inappropriate strategy.
% 2.03/1.00 % (3488467)------------------------------
% 2.03/1.00 % (3488467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488467)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488467)Termination reason: Inappropriate
% 2.03/1.00 % (3488467)Time elapsed: 0.030 s
% 2.03/1.00 % (3488467)Peak memory usage: 13 MB
% 2.03/1.00 % (3488467)Instructions burned: 127 (million)
% 2.03/1.00 % (3488453)------------------------------
% 2.03/1.00 % (3488453)------------------------------
% 2.03/1.00 % (3488467)------------------------------
% 2.03/1.00 % (3488467)------------------------------
% 2.03/1.00 % (3488469)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1518876545:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 2.03/1.00 % (3488459)Instruction limit reached!
% 2.03/1.00 % (3488459)------------------------------
% 2.03/1.00 % (3488459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488459)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488459)Termination reason: Instruction limit
% 2.03/1.00 % (3488459)Termination phase: Saturation
% 2.03/1.00 % (3488459)Time elapsed: 0.071 s
% 2.03/1.00 % (3488459)Peak memory usage: 14 MB
% 2.03/1.00 % (3488459)Instructions burned: 159 (million)
% 2.03/1.00 % (3488470)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4048371437:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 2.03/1.00 % (3488472)ott-21_1_sil=16000:fs=off:random_seed=1619227847:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 2.03/1.00 % (3488473)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2991617237:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 2.03/1.00 % (3488475)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1743587169:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 2.03/1.00 % (3488472)Instruction limit reached!
% 2.03/1.00 % (3488472)------------------------------
% 2.03/1.00 % (3488472)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488472)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488472)Termination reason: Instruction limit
% 2.03/1.00 % (3488472)Termination phase: Saturation
% 2.03/1.00 % (3488472)Time elapsed: 0.043 s
% 2.03/1.00 % (3488472)Peak memory usage: 14 MB
% 2.03/1.00 % (3488472)Instructions burned: 182 (million)
% 2.03/1.00 % (3488469)Instruction limit reached!
% 2.03/1.00 % (3488469)------------------------------
% 2.03/1.00 % (3488469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488469)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488469)Termination reason: Instruction limit
% 2.03/1.00 % (3488469)Termination phase: Property scanning
% 2.03/1.00 % (3488469)Time elapsed: 0.057 s
% 2.03/1.00 % (3488469)Peak memory usage: 12 MB
% 2.03/1.00 % (3488469)Instructions burned: 132 (million)
% 2.03/1.00 % (3488479)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=420369782:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 2.03/1.00 % (3488480)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=1524056089:i=889:ins=1_2997 on theBenchmark for (2997ds/889Mi)
% 2.03/1.00 % (3488475)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.03/1.00 % (3488475)Terminated due to inappropriate strategy.
% 2.03/1.00 % (3488475)------------------------------
% 2.03/1.00 % (3488475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488475)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488475)Termination reason: Inappropriate
% 2.03/1.00 % (3488475)Time elapsed: 0.056 s
% 2.03/1.00 % (3488475)Peak memory usage: 12 MB
% 2.03/1.00 % (3488475)Instructions burned: 132 (million)
% 2.03/1.00 % (3488475)------------------------------
% 2.03/1.00 % (3488475)------------------------------
% 2.03/1.00 % (3488483)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=939824535:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 2.03/1.00 % (3488480)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.03/1.00 % (3488480)Terminated due to inappropriate strategy.
% 2.03/1.00 % (3488480)------------------------------
% 2.03/1.00 % (3488480)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488480)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488480)Termination reason: Inappropriate
% 2.03/1.00 % (3488480)Time elapsed: 0.057 s
% 2.03/1.00 % (3488480)Peak memory usage: 12 MB
% 2.03/1.00 % (3488480)Instructions burned: 134 (million)
% 2.03/1.00 % (3488480)------------------------------
% 2.03/1.00 % (3488480)------------------------------
% 2.03/1.00 % (3488485)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3136872729:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 2.03/1.00 % (3488473)Instruction limit reached!
% 2.03/1.00 % (3488473)------------------------------
% 2.03/1.00 % (3488473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488473)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488473)Termination reason: Instruction limit
% 2.03/1.00 % (3488473)Termination phase: Saturation
% 2.03/1.00 % (3488473)Time elapsed: 0.293 s
% 2.03/1.00 % (3488473)Peak memory usage: 15 MB
% 2.03/1.00 % (3488473)Instructions burned: 478 (million)
% 2.03/1.00 % (3488487)fmb+10_1_sil=64000:random_seed=774492208:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 2.03/1.00 % (3488487)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 2.03/1.00 % (3488487)Terminated due to inappropriate strategy.
% 2.03/1.00 % (3488487)------------------------------
% 2.03/1.00 % (3488487)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488487)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488487)Termination reason: Inappropriate
% 2.03/1.00 % (3488487)Time elapsed: 0.060 s
% 2.03/1.00 % (3488487)Peak memory usage: 13 MB
% 2.03/1.00 % (3488487)Instructions burned: 135 (million)
% 2.03/1.00 % (3488487)------------------------------
% 2.03/1.00 % (3488487)------------------------------
% 2.03/1.00 % (3488483) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3488448-3488483"...
% 2.03/1.00 % (3488483)...printing done.
% 2.03/1.00 % (3488483)Refutation found. Thanks to Tanya!
% 2.03/1.00 % SZS status Theorem for theBenchmark
% 2.03/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 2.03/1.00 % (3488483)------------------------------
% 2.03/1.00 % (3488483)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.03/1.00 % (3488483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.03/1.00 % (3488483)CaDiCaL version: 2.1.3
% 2.03/1.00 % (3488483)Termination reason: Refutation
% 2.03/1.00 % (3488483)Time elapsed: 0.307 s
% 2.03/1.00 % (3488483)Peak memory usage: 19 MB
% 2.03/1.00 % (3488483)Instructions burned: 523 (million)
% 2.03/1.00 % (3488448)Success in time 0.564 s
% 2.03/1.00 % Vampire exiting
%------------------------------------------------------------------------------