%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP296_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 : n001.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 11:33:32 AM UTC 2026
% Result : Theorem 3.38s 1.45s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 13 unt; 0 typ; 6 def)
% Number of atoms : 29 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 9 ~; 3 |; 2 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 51 ( 49 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 33 ( 31 usr; 4 prp; 0-2 aty)
% Number of functors : 448 ( 448 usr; 49 con; 0-3 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'ZF_ZF_ZF_prod_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'ZF_set$': $tType ).
tff(type_def_8,type,
'ZF_ZF_prod_zet$': $tType ).
tff(type_def_9,type,
'ZF_set_ZF_zet_fun$': $tType ).
tff(type_def_10,type,
'ZF_ZF_prod_set$': $tType ).
tff(type_def_11,type,
'Int_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_12,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_13,type,
'ZF_set_set$': $tType ).
tff(type_def_14,type,
'ZF_set_ZF_set_fun$': $tType ).
tff(type_def_15,type,
'ZF_ZF_prod_ZF_ZF_prod_fun$': $tType ).
tff(type_def_16,type,
'ZF_ZF_set_fun$': $tType ).
tff(type_def_17,type,
'ZF_ZF_prod_ZF_fun$': $tType ).
tff(type_def_18,type,
'ZF_set_zet$': $tType ).
tff(type_def_19,type,
'ZF_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_20,type,
'ZF_ZF_prod_ZF_set_fun$': $tType ).
tff(type_def_21,type,
'Int_set$': $tType ).
tff(type_def_22,type,
'Int_int_fun$': $tType ).
tff(type_def_23,type,
'ZF_ZF_prod$': $tType ).
tff(type_def_24,type,
'ZF_set_set_bool_fun$': $tType ).
tff(type_def_25,type,
'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_26,type,
'Nat_nat_fun$': $tType ).
tff(type_def_27,type,
'ZF_set_int_fun$': $tType ).
tff(type_def_28,type,
'Nat$': $tType ).
tff(type_def_29,type,
'Nat_ZF_ZF_prod_fun$': $tType ).
tff(type_def_30,type,
'ZF_ZF_fun$': $tType ).
tff(type_def_31,type,
'ZF_ZF_prod_bool_fun$': $tType ).
tff(type_def_32,type,
'ZF_zet$': $tType ).
tff(type_def_33,type,
'Nat_ZF_set_fun$': $tType ).
tff(type_def_34,type,
'ZF_set_set_ZF_set_fun$': $tType ).
tff(type_def_35,type,
'ZF_zet_bool_fun$': $tType ).
tff(type_def_36,type,
'ZF_ZF_prod_set_ZF_set_fun$': $tType ).
tff(type_def_37,type,
'ZF_set_ZF_fun$': $tType ).
tff(type_def_38,type,
'ZF_zet_ZF_set_fun$': $tType ).
tff(type_def_39,type,
'ZF_bool_fun$': $tType ).
tff(type_def_40,type,
'ZF_nat_fun$': $tType ).
tff(type_def_41,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_42,type,
'ZF_set_bool_fun$': $tType ).
tff(type_def_43,type,
'Nat_bool_fun$': $tType ).
tff(type_def_44,type,
'ZF$': $tType ).
tff(type_def_45,type,
'ZF_set_set_set$': $tType ).
tff(type_def_46,type,
'ZF_int_fun$': $tType ).
tff(type_def_47,type,
'ZF_set_ZF_ZF_prod_fun$': $tType ).
tff(type_def_48,type,
'ZF_set_ZF_ZF_prod_set_fun$': $tType ).
tff(type_def_49,type,
'ZF_ZF_prod_set_bool_fun$': $tType ).
tff(type_def_50,type,
'Nat_set$': $tType ).
tff(type_def_51,type,
'Nat_ZF_fun$': $tType ).
tff(type_def_52,type,
'ZF_ZF_prod_set_int_fun$': $tType ).
tff(type_def_53,type,
'Int_ZF_set_fun$': $tType ).
tff(func_def_0,type,
'ext_ZF_n$': ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'Nat_ZF_fun$' ).
tff(func_def_1,type,
'fun_app$l': ( 'ZF_set_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_2,type,
'fun$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_3,type,
'type_definition$a': ( 'ZF_ZF_set_fun$' * 'ZF_set_ZF_fun$' ) > 'ZF_set_set_bool_fun$' ).
tff(func_def_4,type,
'inv_into$d': ( 'Nat_set$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_5,type,
'fun_app$aj': ( 'ZF_int_fun$' * 'ZF$' ) > $int ).
tff(func_def_6,type,
'top$e': 'Nat_bool_fun$' ).
tff(func_def_7,type,
'y$': 'ZF$' ).
tff(func_def_8,type,
'rep_zet$a': 'ZF_set_zet$' > 'ZF_set_set$' ).
tff(func_def_9,type,
'field$': 'ZF_ZF_fun$' ).
tff(func_def_10,type,
'inv_into$k': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod_ZF_ZF_prod_fun$' ).
tff(func_def_11,type,
'fun_app$p': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod$' ) > 'ZF_set$' ).
tff(func_def_12,type,
'fun_app$w': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat$' ) > 'ZF_ZF_prod$' ).
tff(func_def_13,type,
'top$': 'ZF_set$' ).
tff(func_def_14,type,
'image$a': 'ZF_ZF_fun$' > 'ZF_set_ZF_set_fun$' ).
tff(func_def_15,type,
'sup$b': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' ).
tff(func_def_16,type,
'zempty$': 'ZF_zet$' ).
tff(func_def_17,type,
'inv_into$i': ( 'ZF_set$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod_ZF_fun$' ).
tff(func_def_18,type,
'inv_into$g': ( 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set_ZF_set_fun$' ).
tff(func_def_19,type,
'top$b': 'ZF_ZF_prod_set$' ).
tff(func_def_20,type,
'collect$a': 'Nat_bool_fun$' > 'Nat_set$' ).
tff(func_def_21,type,
'fun_app$ad': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_22,type,
'image$f': 'ZF_ZF_prod_ZF_fun$' > 'ZF_ZF_prod_set_ZF_set_fun$' ).
tff(func_def_23,type,
'fun_app$e': ( 'ZF_set_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_24,type,
'zimage$a': ( 'ZF_ZF_fun$' * 'ZF_zet$' ) > 'ZF_zet$' ).
tff(func_def_25,type,
'comp$b': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).
tff(func_def_26,type,
'less_eq$c': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_27,type,
'singleton$': 'ZF_ZF_fun$' ).
tff(func_def_28,type,
'image$c': 'ZF_set_ZF_fun$' > 'ZF_set_set_ZF_set_fun$' ).
tff(func_def_29,type,
'seqSum$': 'Nat_ZF_fun$' > 'ZF$' ).
tff(func_def_30,type,
'fun_app$ai': ( 'ZF_ZF_ZF_prod_set_fun$' * 'ZF$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_31,type,
'sum$': 'ZF_ZF_fun$' ).
tff(func_def_32,type,
'nat2nat$': 'ZF_nat_fun$' ).
tff(func_def_33,type,
'less_eq$b': 'ZF_set_set$' > 'ZF_set_set_bool_fun$' ).
tff(func_def_34,type,
'type_definition$c': ( 'ZF_set_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_set_bool_fun$' ).
tff(func_def_35,type,
'opair$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_36,type,
'zin$': 'ZF$' > 'ZF_zet_bool_fun$' ).
tff(func_def_37,type,
'fun_app$v': ( 'Nat_ZF_set_fun$' * 'Nat$' ) > 'ZF_set$' ).
tff(func_def_38,type,
'empty$': 'ZF$' ).
tff(func_def_39,type,
'sup$d': $int > 'Int_int_fun$' ).
tff(func_def_40,type,
'fun_app$f': ( 'ZF_ZF_set_fun$' * 'ZF$' ) > 'ZF_set$' ).
tff(func_def_41,type,
'repl$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_42,type,
'inv_into$j': ( 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod_ZF_set_fun$' ).
tff(func_def_43,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_44,type,
'top$c': 'Nat_set$' ).
tff(func_def_45,type,
'fun_app$z': ( 'ZF_ZF_prod_set_int_fun$' * 'ZF_ZF_prod_set$' ) > $int ).
tff(func_def_46,type,
'image$h': 'ZF_ZF_prod_ZF_ZF_prod_fun$' > 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' ).
tff(func_def_47,type,
'pair$': 'ZF$' > 'ZF_ZF_ZF_prod_fun$' ).
tff(func_def_48,type,
'type_definition$b': ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF_set_bool_fun$' ).
tff(func_def_49,type,
'zimage$': ( 'ZF_ZF_set_fun$' * 'ZF_zet$' ) > 'ZF_set_zet$' ).
tff(func_def_50,type,
'inv_into$': ( 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set_ZF_fun$' ).
tff(func_def_51,type,
'cartProd$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_52,type,
'fun_app$n': ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_53,type,
'image$j': ( 'Nat_ZF_fun$' * 'Nat_set$' ) > 'ZF_set$' ).
tff(func_def_54,type,
'universe$': 'ZF_bool_fun$' ).
tff(func_def_55,type,
'abs_zet$a': 'ZF_set_ZF_zet_fun$' ).
tff(func_def_56,type,
'zimplode$': 'ZF_zet$' > 'ZF$' ).
tff(func_def_57,type,
'rep_zet$b': 'ZF_ZF_prod_zet$' > 'ZF_ZF_prod_set$' ).
tff(func_def_58,type,
'abs_zet$': 'ZF_set_set$' > 'ZF_set_zet$' ).
tff(func_def_59,type,
'fun_app$k': ( 'ZF_set_ZF_ZF_prod_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_60,type,
'pFun$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_61,type,
'fun_app$ab': ( 'Int_ZF_ZF_prod_set_fun$' * $int ) > 'ZF_ZF_prod_set$' ).
tff(func_def_62,type,
'ext_ZF$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).
tff(func_def_63,type,
'is_Elem_of$': 'ZF_ZF_prod_set$' ).
tff(func_def_64,type,
'inv_into$e': ( 'ZF_set_set$' * 'ZF_set_ZF_fun$' ) > 'ZF_ZF_set_fun$' ).
tff(func_def_65,type,
'member$a': 'ZF$' > 'ZF_set_bool_fun$' ).
tff(func_def_66,type,
'uub$': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_67,type,
'union$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_68,type,
'image$l': ( 'Nat_ZF_set_fun$' * 'Nat_set$' ) > 'ZF_set_set$' ).
tff(func_def_69,type,
'comp$a': ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat_nat_fun$' ).
tff(func_def_70,type,
'comp$': ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'ZF_ZF_fun$' ).
tff(func_def_71,type,
'inv_into$h': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_set_ZF_ZF_prod_fun$' ).
tff(func_def_72,type,
'ext_ZF_hull$': 'ZF_ZF_prod_set$' > 'ZF_ZF_fun$' ).
tff(func_def_73,type,
'fun_app$i': ( 'ZF_set_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_74,type,
'ext$': 'ZF_ZF_prod_set$' > 'ZF_ZF_set_fun$' ).
tff(func_def_75,type,
'set_like$': 'ZF_ZF_prod_set_bool_fun$' ).
tff(func_def_76,type,
'nat2Nat$': 'Nat_ZF_fun$' ).
tff(func_def_77,type,
'inv_into$a': ( 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF_ZF_fun$' ).
tff(func_def_78,type,
'image$e': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_79,type,
'nat$a': $int > 'Nat$' ).
tff(func_def_80,type,
'top$a': 'ZF_set_set$' ).
tff(func_def_81,type,
'sup$': 'ZF_set$' > 'ZF_set_ZF_set_fun$' ).
tff(func_def_82,type,
'uu$': 'ZF_set$' > 'ZF_bool_fun$' ).
tff(func_def_83,type,
'fun_app$af': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_84,type,
'fun_app$ag': ( 'ZF_set_ZF_zet_fun$' * 'ZF_set$' ) > 'ZF_zet$' ).
tff(func_def_85,type,
'fun_app$u': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_86,type,
'image$b': 'ZF_ZF_ZF_prod_fun$' > 'ZF_set_ZF_ZF_prod_set_fun$' ).
tff(func_def_87,type,
'collect$b': 'ZF_set_bool_fun$' > 'ZF_set_set$' ).
tff(func_def_88,type,
'member$': 'ZF_ZF_prod$' > 'ZF_ZF_prod_set_bool_fun$' ).
tff(func_def_89,type,
'sup$c': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_90,type,
'member$b': 'ZF_set$' > 'ZF_set_set_bool_fun$' ).
tff(func_def_91,type,
'fun_app$ac': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_92,type,
'sucNat$': 'ZF_ZF_fun$' ).
tff(func_def_93,type,
'id$': 'ZF_ZF_fun$' ).
tff(func_def_94,type,
'f$': 'ZF_ZF_set_fun$' ).
tff(func_def_95,type,
'fun_app$g': ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_96,type,
'type_definition$': ( 'ZF_zet_ZF_set_fun$' * 'ZF_set_ZF_zet_fun$' ) > 'ZF_set_set_bool_fun$' ).
tff(func_def_97,type,
'isFun$': 'ZF_bool_fun$' ).
tff(func_def_98,type,
'collect$': 'ZF_bool_fun$' > 'ZF_set$' ).
tff(func_def_99,type,
'fun_app$r': ( 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_100,type,
'inv_into$b': ( 'ZF_set$' * 'ZF_nat_fun$' ) > 'Nat_ZF_fun$' ).
tff(func_def_101,type,
'regular$': 'ZF_ZF_prod_set_bool_fun$' ).
tff(func_def_102,type,
'less_eq$': 'ZF_set$' > 'ZF_set_bool_fun$' ).
tff(func_def_103,type,
'fun_app$q': ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' ) > 'ZF_ZF_prod$' ).
tff(func_def_104,type,
'inv_into$f': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_ZF_prod_fun$' ).
tff(func_def_105,type,
'uua$': 'ZF_set_set$' > 'ZF_set_bool_fun$' ).
tff(func_def_106,type,
'top$d': 'ZF_bool_fun$' ).
tff(func_def_107,type,
'app$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_108,type,
'range$': 'ZF_ZF_fun$' ).
tff(func_def_109,type,
'lambda$': ( 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_110,type,
'image$i': ( 'ZF_nat_fun$' * 'ZF_set$' ) > 'Nat_set$' ).
tff(func_def_111,type,
'fun_app$h': ( 'ZF_zet_ZF_set_fun$' * 'ZF_zet$' ) > 'ZF_set$' ).
tff(func_def_112,type,
'fun_app$j': ( 'ZF_ZF_ZF_prod_fun$' * 'ZF$' ) > 'ZF_ZF_prod$' ).
tff(func_def_113,type,
'fun_app$s': ( 'ZF_nat_fun$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_114,type,
'zexplode$': 'ZF$' > 'ZF_zet$' ).
tff(func_def_115,type,
'wfzf$': 'ZF_ZF_prod_set_bool_fun$' ).
tff(func_def_116,type,
'zet$': 'ZF_set_set$' ).
tff(func_def_117,type,
'top$f': 'ZF_set_bool_fun$' ).
tff(func_def_118,type,
'fun_app$t': ( 'Nat_ZF_fun$' * 'Nat$' ) > 'ZF$' ).
tff(func_def_119,type,
'less_eq$a': 'ZF_ZF_prod_set$' > 'ZF_ZF_prod_set_bool_fun$' ).
tff(func_def_120,type,
'elem$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_121,type,
'inf$': 'ZF$' ).
tff(func_def_122,type,
'image$k': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat_set$' ).
tff(func_def_123,type,
'top$g': 'ZF_ZF_prod_bool_fun$' ).
tff(func_def_124,type,
'inj_on$a': 'ZF_ZF_set_fun$' > 'ZF_set_bool_fun$' ).
tff(func_def_125,type,
'inv_into$c': ( 'Nat_set$' * 'Nat_ZF_fun$' ) > 'ZF_nat_fun$' ).
tff(func_def_126,type,
'fun_app$aa': ( 'Int_ZF_set_fun$' * $int ) > 'ZF_set$' ).
tff(func_def_127,type,
'zet$a': 'ZF_set_set_set$' ).
tff(func_def_128,type,
'power$': 'ZF_ZF_fun$' ).
tff(func_def_129,type,
'sep$': ( 'ZF$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_130,type,
'collect$c': 'ZF_ZF_prod_bool_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_131,type,
'image$d': ( 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set_set$' ).
tff(func_def_132,type,
'domain$': 'ZF_ZF_fun$' ).
tff(func_def_133,type,
'zunion$': ( 'ZF_zet$' * 'ZF_zet$' ) > 'ZF_zet$' ).
tff(func_def_134,type,
'image$': ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_set_set$' ).
tff(func_def_135,type,
'upair$': 'ZF$' > 'ZF_ZF_fun$' ).
tff(func_def_136,type,
'x$': 'ZF$' ).
tff(func_def_137,type,
'suc$': 'Nat_nat_fun$' ).
tff(func_def_138,type,
'nat$': 'ZF$' ).
tff(func_def_139,type,
'sup$a': ( 'ZF_set_set$' * 'ZF_set_set$' ) > 'ZF_set_set$' ).
tff(func_def_140,type,
'trancl$': 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' ).
tff(func_def_141,type,
'fun_app$m': ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_142,type,
'rep_zet$': 'ZF_zet_ZF_set_fun$' ).
tff(func_def_143,type,
'zsubset$': 'ZF_zet$' > 'ZF_zet_bool_fun$' ).
tff(func_def_144,type,
'a$': 'ZF_set$' ).
tff(func_def_145,type,
'image$g': ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set_set$' ).
tff(func_def_146,type,
'image$m': ( 'Nat_ZF_ZF_prod_fun$' * 'Nat_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_147,type,
'implode$': 'ZF_set_ZF_fun$' ).
tff(func_def_148,type,
'explode$': 'ZF_ZF_set_fun$' ).
tff(func_def_149,type,
'product$': 'ZF_ZF_fun$' ).
tff(func_def_150,type,
'subset$': 'ZF$' > 'ZF_bool_fun$' ).
tff(func_def_151,type,
'fun_app$o': ( 'ZF_ZF_prod_set_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).
tff(func_def_152,type,
'fun_app$y': ( 'ZF_set_int_fun$' * 'ZF_set$' ) > $int ).
tff(func_def_156,type,
sK0: 'Int_int_fun$' > $int ).
tff(func_def_157,type,
sK1: 'Int_int_fun$' > $int ).
tff(func_def_158,type,
sK2: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_159,type,
sK3: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_160,type,
sK4: 'ZF_ZF_prod_set$' > 'ZF_ZF_prod$' ).
tff(func_def_161,type,
sK5: ( 'ZF$' * 'ZF$' ) > 'ZF_ZF_fun$' ).
tff(func_def_162,type,
sK6: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_163,type,
sK7: ( 'ZF$' * 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_164,type,
sK8: ( 'ZF_set_set$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_165,type,
sK9: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_166,type,
sK10: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_167,type,
sK11: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_168,type,
sK12: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_169,type,
sK13: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_170,type,
sK14: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_171,type,
sK15: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_172,type,
sK16: ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_173,type,
sK17: ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_174,type,
sK18: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_175,type,
sK19: ( 'ZF_set_set_bool_fun$' * 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_176,type,
sK20: ( 'ZF_set_set_bool_fun$' * 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set_set$' ).
tff(func_def_177,type,
sK21: ( 'ZF_nat_fun$' * 'Nat_ZF_fun$' ) > 'Nat$' ).
tff(func_def_178,type,
sK22: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_179,type,
sK23: ( 'ZF_set_bool_fun$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_180,type,
sK24: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_181,type,
sK25: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_182,type,
sK26: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_183,type,
sK27: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_184,type,
sK28: ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_185,type,
sK29: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).
tff(func_def_186,type,
sK30: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_187,type,
sK31: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_188,type,
sK32: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_189,type,
sK33: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_190,type,
sK34: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_191,type,
sK35: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_192,type,
sK36: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_193,type,
sK37: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_194,type,
sK38: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_195,type,
sK39: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_196,type,
sK40: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_197,type,
sK41: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_198,type,
sK42: ( 'ZF_set$' * 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_199,type,
sK43: ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'Nat$' ).
tff(func_def_200,type,
sK44: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF$' ).
tff(func_def_201,type,
sK45: ( 'Nat$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_202,type,
sK46: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_203,type,
sK47: 'ZF_zet$' > 'ZF$' ).
tff(func_def_204,type,
sK48: 'Int_ZF_set_fun$' > $int ).
tff(func_def_205,type,
sK49: 'Int_ZF_set_fun$' > $int ).
tff(func_def_206,type,
sK50: 'ZF$' > 'ZF$' ).
tff(func_def_207,type,
sK51: 'ZF$' > 'ZF$' ).
tff(func_def_208,type,
sK52: 'ZF$' > 'ZF$' ).
tff(func_def_209,type,
sK53: 'ZF$' > 'ZF$' ).
tff(func_def_210,type,
sK54: 'ZF$' > 'ZF$' ).
tff(func_def_211,type,
sK55: ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_212,type,
sK56: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_213,type,
sK57: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_214,type,
sK58: 'Nat_ZF_fun$' > 'ZF$' ).
tff(func_def_215,type,
sK59: 'ZF_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_216,type,
sK60: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_217,type,
sK61: ( 'ZF_ZF_fun$' * 'ZF_set_bool_fun$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_218,type,
sK62: ( 'ZF_ZF_fun$' * 'ZF_set_bool_fun$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_219,type,
sK63: 'Nat$' ).
tff(func_def_220,type,
sK64: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_221,type,
sK65: 'ZF$' > 'ZF$' ).
tff(func_def_222,type,
sK66: 'ZF$' > 'ZF$' ).
tff(func_def_223,type,
sK67: 'ZF$' > 'ZF$' ).
tff(func_def_224,type,
sK68: 'ZF$' > 'ZF$' ).
tff(func_def_225,type,
sK69: 'ZF$' > 'ZF$' ).
tff(func_def_226,type,
sK70: ( 'ZF_set$' * 'ZF_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF$' ).
tff(func_def_227,type,
sK71: ( 'ZF_ZF_set_fun$' * 'ZF_set_ZF_fun$' ) > 'ZF$' ).
tff(func_def_228,type,
sK72: ( 'ZF_set_bool_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_229,type,
sK73: ( 'ZF_set_bool_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_set$' ).
tff(func_def_230,type,
sK74: ( 'ZF_zet$' * 'ZF_zet$' ) > 'ZF$' ).
tff(func_def_231,type,
sK75: ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_232,type,
sK76: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_233,type,
sK77: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_234,type,
sK78: 'ZF_nat_fun$' > 'Nat$' ).
tff(func_def_235,type,
sK79: ( 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_236,type,
sK80: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_237,type,
sK81: ( 'ZF_set_bool_fun$' * 'ZF_set_set$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_238,type,
sK82: ( 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_239,type,
sK83: ( 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_240,type,
sK84: ( 'ZF_set_set$' * 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_241,type,
sK85: ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_242,type,
sK86: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_243,type,
sK87: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_244,type,
sK88: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_245,type,
sK89: ( 'ZF_set_set$' * 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_246,type,
sK90: ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_247,type,
sK91: ( 'ZF_zet$' * 'ZF_zet$' ) > 'ZF$' ).
tff(func_def_248,type,
sK92: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).
tff(func_def_249,type,
sK93: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF$' ).
tff(func_def_250,type,
sK94: ( 'ZF_bool_fun$' * 'ZF_set_set$' * 'ZF_set_ZF_fun$' ) > 'ZF$' ).
tff(func_def_251,type,
sK95: 'ZF_ZF_prod_set$' > 'ZF$' ).
tff(func_def_252,type,
sK96: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_253,type,
sK97: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_254,type,
sK98: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_255,type,
sK99: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_256,type,
sK100: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_257,type,
sK101: ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_258,type,
sK102: ( 'Nat$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_259,type,
sK103: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_260,type,
sK104: ( 'ZF_ZF_prod_ZF_set_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_261,type,
sK105: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_262,type,
sK106: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_263,type,
sK107: 'Nat$' > 'Nat$' ).
tff(func_def_264,type,
sK108: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_265,type,
sK109: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_266,type,
sK110: ( 'ZF_set$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_267,type,
sK111: ( 'ZF_set$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_268,type,
sK112: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_269,type,
sK113: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_270,type,
sK114: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_271,type,
sK115: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_272,type,
sK116: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_273,type,
sK117: 'Int_ZF_set_fun$' > $int ).
tff(func_def_274,type,
sK118: 'Int_ZF_set_fun$' > $int ).
tff(func_def_275,type,
sK119: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_276,type,
sK120: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_277,type,
sK121: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_278,type,
sK122: 'ZF_ZF_prod$' ).
tff(func_def_279,type,
sK123: 'Int_int_fun$' > $int ).
tff(func_def_280,type,
sK124: 'Int_int_fun$' > $int ).
tff(func_def_281,type,
sK125: ( 'Nat$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_282,type,
sK126: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_283,type,
sK127: ( 'ZF_ZF_fun$' * 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_284,type,
sK128: ( 'ZF_set_bool_fun$' * 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_285,type,
sK129: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_286,type,
sK130: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_287,type,
sK131: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_288,type,
sK132: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_289,type,
sK133: ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_290,type,
sK134: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_291,type,
sK135: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_292,type,
sK136: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_293,type,
sK137: 'ZF_ZF_prod_set$' > 'ZF$' ).
tff(func_def_294,type,
sK138: ( 'ZF_ZF_prod_set$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_295,type,
sK139: ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_296,type,
sK140: ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_297,type,
sK141: ( 'ZF_set_ZF_fun$' * 'ZF_set$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_298,type,
sK142: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_299,type,
sK143: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_300,type,
sK144: 'Int_int_fun$' > $int ).
tff(func_def_301,type,
sK145: 'Int_int_fun$' > $int ).
tff(func_def_302,type,
sK146: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_303,type,
sK147: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_304,type,
sK148: ( 'ZF_ZF_prod_set$' * 'ZF_set$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF$' ).
tff(func_def_305,type,
sK149: ( 'ZF_set_ZF_fun$' * 'ZF_set_set$' * 'ZF$' ) > 'ZF_set$' ).
tff(func_def_306,type,
sK150: 'Int_int_fun$' > $int ).
tff(func_def_307,type,
sK151: 'Int_int_fun$' > $int ).
tff(func_def_308,type,
sK152: ( 'ZF_set$' * 'ZF_set_bool_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_309,type,
sK153: ( 'ZF_set_set$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_310,type,
sK154: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_311,type,
sK155: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_312,type,
sK156: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_313,type,
sK157: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_314,type,
sK158: ( 'ZF_set_ZF_set_fun$' * 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_315,type,
sK159: ( 'ZF_ZF_prod_set$' * 'ZF_set$' * 'ZF_ZF_prod_ZF_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_316,type,
sK160: 'ZF_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_317,type,
sK161: 'ZF_zet_bool_fun$' > 'ZF_set$' ).
tff(func_def_318,type,
sK162: ( 'ZF_bool_fun$' * 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_319,type,
sK163: ( 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_320,type,
sK164: ( 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_321,type,
sK165: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_322,type,
sK166: ( 'ZF_set$' * 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_323,type,
sK167: 'ZF_set_bool_fun$' > 'ZF_zet$' ).
tff(func_def_324,type,
sK168: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_325,type,
sK169: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_326,type,
sK170: 'ZF_ZF_prod_set_ZF_ZF_prod_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_327,type,
sK171: ( 'ZF_set_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_328,type,
sK172: 'ZF$' > 'ZF$' ).
tff(func_def_329,type,
sK173: ( 'ZF_set_set$' * 'ZF_bool_fun$' * 'ZF_set_ZF_fun$' ) > 'ZF_set$' ).
tff(func_def_330,type,
sK174: ( 'ZF_set_set$' * 'ZF_set_set$' * 'ZF_set_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_331,type,
sK175: ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_332,type,
sK176: ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_333,type,
sK177: ( 'ZF$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_334,type,
sK178: ( 'ZF$' * 'ZF$' * 'ZF_ZF_prod_set$' ) > 'Nat$' ).
tff(func_def_335,type,
sK179: 'ZF_set_set$' > 'ZF_set$' ).
tff(func_def_336,type,
sK180: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_337,type,
sK181: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_338,type,
sK182: ( 'Nat_ZF_fun$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_339,type,
sK183: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_340,type,
sK184: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_341,type,
sK185: ( 'ZF_ZF_fun$' * 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_342,type,
sK186: ( 'ZF_nat_fun$' * 'Nat_ZF_fun$' ) > 'ZF$' ).
tff(func_def_343,type,
sK187: ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_zet$' ) > 'ZF$' ).
tff(func_def_344,type,
sK188: 'ZF$' > 'ZF$' ).
tff(func_def_345,type,
sK189: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_346,type,
sK190: 'Nat_ZF_fun$' > 'ZF$' ).
tff(func_def_347,type,
sK191: ( 'Nat_ZF_fun$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_348,type,
sK192: ( 'Nat_ZF_fun$' * 'ZF$' ) > 'Nat$' ).
tff(func_def_349,type,
sK193: ( 'ZF_ZF_prod_set$' * 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_350,type,
sK194: ( 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_351,type,
sK195: 'ZF_ZF_fun$' > 'ZF$' ).
tff(func_def_352,type,
sK196: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_353,type,
sK197: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_354,type,
sK198: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_355,type,
sK199: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_356,type,
sK200: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_357,type,
sK201: ( 'ZF_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF_set$' ).
tff(func_def_358,type,
sK202: ( 'ZF_set$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_359,type,
sK203: ( 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_360,type,
sK204: ( 'ZF_set$' * 'ZF_bool_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_361,type,
sK205: ( 'ZF_nat_fun$' * 'Nat$' ) > 'ZF$' ).
tff(func_def_362,type,
sK206: 'ZF_nat_fun$' > 'Nat$' ).
tff(func_def_363,type,
sK207: ( 'ZF_ZF_fun$' * 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_364,type,
sK208: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_365,type,
sK209: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_366,type,
sK210: ( 'ZF_set$' * 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF_set$' ).
tff(func_def_367,type,
sK211: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_368,type,
sK212: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_369,type,
sK213: 'ZF_set$' ).
tff(func_def_370,type,
sK214: ( 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_set$' ).
tff(func_def_371,type,
sK215: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_372,type,
sK216: 'ZF_set$' > 'ZF$' ).
tff(func_def_373,type,
sK217: ( 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_374,type,
sK218: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_375,type,
sK219: ( 'ZF_set_set$' * 'ZF_set$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_376,type,
sK220: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_377,type,
sK221: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_378,type,
sK222: ( 'ZF_ZF_prod$' * 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_fun$' ) > 'ZF_set$' ).
tff(func_def_379,type,
sK223: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_380,type,
sK224: 'ZF_set_ZF_set_fun$' > 'ZF_set$' ).
tff(func_def_381,type,
sK225: ( 'ZF_ZF_ZF_prod_fun$' * 'ZF_set$' * 'ZF_ZF_prod$' ) > 'ZF$' ).
tff(func_def_382,type,
sK226: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_383,type,
sK227: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_384,type,
sK228: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_385,type,
sK229: ( 'ZF$' * 'ZF_set$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_386,type,
sK230: ( 'ZF_set_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_387,type,
sK231: ( 'ZF_set_ZF_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_388,type,
sK232: 'ZF_zet$' > 'ZF_set$' ).
tff(func_def_389,type,
sK233: ( 'ZF$' * 'Nat_ZF_fun$' ) > 'Nat$' ).
tff(func_def_390,type,
sK234: 'Int_ZF_set_fun$' > $int ).
tff(func_def_391,type,
sK235: 'Int_ZF_set_fun$' > $int ).
tff(func_def_392,type,
sK236: ( 'ZF_zet$' * 'ZF$' * 'ZF_ZF_fun$' ) > 'ZF$' ).
tff(func_def_393,type,
sK237: 'ZF_ZF_fun$' > 'ZF$' ).
tff(func_def_394,type,
sK238: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_395,type,
sK239: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_396,type,
sK240: ( 'ZF_ZF_prod_ZF_fun$' * 'ZF_ZF_prod_set$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_397,type,
sK241: 'Int_ZF_set_fun$' > $int ).
tff(func_def_398,type,
sK242: 'Int_ZF_set_fun$' > $int ).
tff(func_def_399,type,
sK243: ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'ZF$' ).
tff(func_def_400,type,
sK244: ( 'Nat_ZF_fun$' * 'ZF_nat_fun$' ) > 'Nat$' ).
tff(func_def_401,type,
sK245: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_402,type,
sK246: 'ZF_ZF_prod_set_ZF_set_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_403,type,
sK247: ( 'ZF_set_set$' * 'ZF_set_bool_fun$' ) > 'ZF_set$' ).
tff(func_def_404,type,
sK248: ( 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_405,type,
sK249: ( 'ZF_set_set$' * 'ZF_set_bool_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_406,type,
sK250: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_407,type,
sK251: 'ZF_set_int_fun$' > 'ZF_set$' ).
tff(func_def_408,type,
sK252: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_409,type,
sK253: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_410,type,
sK254: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_set$' * 'ZF_ZF_ZF_prod_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_411,type,
sK255: 'Nat_set$' > 'Nat$' ).
tff(func_def_412,type,
sK256: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_413,type,
sK257: ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_414,type,
sK258: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_fun$' * 'ZF_set$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_415,type,
sK259: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_ZF_set_fun$' ) > 'ZF$' ).
tff(func_def_416,type,
sK260: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_set_set$' * 'ZF_set_ZF_ZF_prod_fun$' ) > 'ZF_set$' ).
tff(func_def_417,type,
sK261: ( 'ZF_set$' * 'ZF_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_418,type,
sK262: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_419,type,
sK263: ( 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_bool_fun$' ) > 'ZF_ZF_prod$' ).
tff(func_def_420,type,
sK264: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_421,type,
sK265: 'ZF$' > 'ZF$' ).
tff(func_def_422,type,
sK266: 'ZF$' > 'ZF$' ).
tff(func_def_423,type,
sK267: 'ZF$' > 'ZF$' ).
tff(func_def_424,type,
sK268: ( 'ZF_ZF_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_425,type,
sK269: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_426,type,
sK270: 'ZF_ZF_prod_set_int_fun$' > 'ZF_ZF_prod_set$' ).
tff(func_def_427,type,
sK271: 'ZF$' ).
tff(func_def_428,type,
sK272: ( 'ZF_ZF_set_fun$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_429,type,
sK273: ( 'ZF_set_set$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_430,type,
sK274: ( 'ZF$' * 'ZF_ZF_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_431,type,
sK275: ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_432,type,
sK276: ( 'ZF_bool_fun$' * 'ZF_bool_fun$' ) > 'ZF$' ).
tff(func_def_433,type,
sK277: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_434,type,
sK278: 'ZF_set_ZF_ZF_prod_set_fun$' > 'ZF_set$' ).
tff(func_def_435,type,
sK279: ( 'ZF_bool_fun$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_436,type,
sK280: 'ZF_bool_fun$' > 'ZF$' ).
tff(func_def_437,type,
sK281: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_438,type,
sK282: 'Int_ZF_ZF_prod_set_fun$' > $int ).
tff(func_def_439,type,
sK283: ( 'ZF_set_bool_fun$' * 'ZF_set_ZF_set_fun$' * 'ZF_set_set$' ) > 'ZF_set$' ).
tff(func_def_440,type,
sK284: ( 'ZF_set_bool_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_ZF_set_fun$' ) > 'ZF_set$' ).
tff(func_def_441,type,
sK285: ( 'Nat_nat_fun$' * 'Nat_nat_fun$' ) > 'Nat$' ).
tff(func_def_442,type,
sK286: ( 'ZF$' * 'ZF$' ) > 'ZF$' ).
tff(func_def_443,type,
sK287: 'ZF_set$' > 'ZF_zet$' ).
tff(func_def_444,type,
sK288: ( 'ZF_ZF_prod_bool_fun$' * 'ZF_set_ZF_ZF_prod_fun$' * 'ZF_set_set$' ) > 'ZF_ZF_prod$' ).
tff(func_def_445,type,
sK289: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set_bool_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_446,type,
sK290: ( 'ZF_ZF_prod_ZF_ZF_prod_fun$' * 'ZF_ZF_prod_set$' * 'ZF_ZF_prod_set_bool_fun$' ) > 'ZF_ZF_prod_set$' ).
tff(func_def_447,type,
sK291: ( 'ZF_set$' * 'ZF_set$' ) > 'ZF$' ).
tff(func_def_448,type,
sF292: 'ZF_set$' ).
tff(func_def_449,type,
sF293: 'ZF$' ).
tff(func_def_450,type,
sF294: 'ZF_set_bool_fun$' ).
tff(pred_def_1,type,
'strict_mono$a': 'Int_ZF_set_fun$' > $o ).
tff(pred_def_2,type,
'fun_app$b': ( 'ZF_bool_fun$' * 'ZF$' ) > $o ).
tff(pred_def_3,type,
'member$d': ( 'ZF_set_set$' * 'ZF_set_set_set$' ) > $o ).
tff(pred_def_4,type,
'less_eq$d': ( 'Nat_set$' * 'Nat_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$ah': ( 'ZF_zet_bool_fun$' * 'ZF_zet$' ) > $o ).
tff(pred_def_6,type,
'relChain$b': ( 'ZF_ZF_prod_set$' * 'ZF_int_fun$' ) > $o ).
tff(pred_def_7,type,
'fun_app$': ( 'ZF_ZF_prod_bool_fun$' * 'ZF_ZF_prod$' ) > $o ).
tff(pred_def_8,type,
'fun_app$ae': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_9,type,
'relChain$': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_set_fun$' ) > $o ).
tff(pred_def_10,type,
'fun_app$d': ( 'ZF_set_set_bool_fun$' * 'ZF_set_set$' ) > $o ).
tff(pred_def_11,type,
'member$c': ( 'Nat$' * 'Nat_set$' ) > $o ).
tff(pred_def_12,type,
'fun_app$a': ( 'ZF_ZF_prod_set_bool_fun$' * 'ZF_ZF_prod_set$' ) > $o ).
tff(pred_def_13,type,
'relChain$a': ( 'ZF_ZF_prod_set$' * 'ZF_ZF_ZF_prod_set_fun$' ) > $o ).
tff(pred_def_14,type,
'inj_on$': ( 'Nat_ZF_fun$' * 'Nat_set$' ) > $o ).
tff(pred_def_15,type,
'strict_mono$': 'Nat_nat_fun$' > $o ).
tff(pred_def_16,type,
'strict_mono$b': 'Int_ZF_ZF_prod_set_fun$' > $o ).
tff(pred_def_17,type,
'zin$a': ( 'ZF_set$' * 'ZF_set_zet$' ) > $o ).
tff(pred_def_18,type,
'zin$b': ( 'ZF_ZF_prod$' * 'ZF_ZF_prod_zet$' ) > $o ).
tff(pred_def_19,type,
'strict_mono_on$c': ( 'Int_int_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_20,type,
'bijection$a': 'Nat_nat_fun$' > $o ).
tff(pred_def_21,type,
'strict_mono_on$a': ( 'Int_ZF_set_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_22,type,
'strict_mono_on$b': ( 'Int_ZF_ZF_prod_set_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_23,type,
'fun_app$c': ( 'ZF_set_bool_fun$' * 'ZF_set$' ) > $o ).
tff(pred_def_24,type,
'fun_app$x': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_25,type,
'strict_mono_on$': ( 'Nat_nat_fun$' * 'Nat_set$' ) > $o ).
tff(pred_def_26,type,
'member$e': ( $int * 'Int_set$' ) > $o ).
tff(pred_def_27,type,
'strict_mono$c': 'Int_int_fun$' > $o ).
tff(pred_def_28,type,
'bijection$': 'ZF_ZF_fun$' > $o ).
tff(f4,conjecture,
( 'fun_app$c'('member$a'('y$'),'a$')
& ( 'fun_app$e'('implode$','fun_app$f'('f$','y$')) = 'fun_app$e'('implode$','fun_app$f'('f$','y$')) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture3) ).
tff(f5,negated_conjecture,
~ ( 'fun_app$c'('member$a'('y$'),'a$')
& ( 'fun_app$e'('implode$','fun_app$f'('f$','y$')) = 'fun_app$e'('implode$','fun_app$f'('f$','y$')) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,axiom,
'fun_app$c'('member$a'('y$'),'a$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f1513,plain,
( ( 'fun_app$e'('implode$','fun_app$f'('f$','y$')) != 'fun_app$e'('implode$','fun_app$f'('f$','y$')) )
| ~ 'fun_app$c'('member$a'('y$'),'a$') ),
inference(ennf_transformation,[],[f5]) ).
tff(f2466,plain,
'fun_app$c'('member$a'('y$'),'a$'),
inference(cnf_transformation,[],[f6]) ).
tff(f3046,plain,
( ( 'fun_app$e'('implode$','fun_app$f'('f$','y$')) != 'fun_app$e'('implode$','fun_app$f'('f$','y$')) )
| ~ 'fun_app$c'('member$a'('y$'),'a$') ),
inference(cnf_transformation,[],[f1513]) ).
tff(f3768,definition,
sF292 = 'fun_app$f'('f$','y$'),
introduced(definition,[new_symbols(definition,[sF292])],[function_definition]) ).
tff(f3769,plain,
'fun_app$f'('f$','y$') = sF292,
inference(reorient_equations,[],[f3768]) ).
tff(f3770,definition,
sF293 = 'fun_app$e'('implode$',sF292),
introduced(definition,[new_symbols(definition,[sF293])],[function_definition]) ).
tff(f3771,plain,
'fun_app$e'('implode$',sF292) = sF293,
inference(reorient_equations,[],[f3770]) ).
tff(f3772,definition,
sF294 = 'member$a'('y$'),
introduced(definition,[new_symbols(definition,[sF294])],[function_definition]) ).
tff(f3773,plain,
'member$a'('y$') = sF294,
inference(reorient_equations,[],[f3772]) ).
tff(f3774,plain,
( ~ 'fun_app$c'(sF294,'a$')
| ( sF293 != sF293 ) ),
inference(definition_folding,[],[f3046,f3773,f3771,f3769,f3771,f3769]) ).
tff(f3783,plain,
~ 'fun_app$c'(sF294,'a$'),
inference(trivial_inequality_removal,[],[f3774]) ).
tff(f3858,definition,
( spl295_5
<=> 'fun_app$c'(sF294,'a$') ),
introduced(definition,[new_symbols(definition,[spl295_5])],[avatar_definition]) ).
tff(f3861,plain,
~ spl295_5,
inference(avatar_split_clause,[],[f3783,f3858]) ).
tff(f3873,definition,
( spl295_8
<=> 'fun_app$c'('member$a'('y$'),'a$') ),
introduced(definition,[new_symbols(definition,[spl295_8])],[avatar_definition]) ).
tff(f3876,plain,
spl295_8,
inference(avatar_split_clause,[],[f2466,f3873]) ).
tff(f3913,definition,
( spl295_16
<=> ( 'member$a'('y$') = sF294 ) ),
introduced(definition,[new_symbols(definition,[spl295_16])],[avatar_definition]) ).
tff(f3916,plain,
spl295_16,
inference(avatar_split_clause,[],[f3773,f3913]) ).
tff(f3972,plain,
$false,
inference(avatar_smt_refutation,[],[f3916,f3876,f3861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP296_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n001.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 12:59:15 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.38/1.45 % (3545296)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.38/1.45 % (3545301)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=4146637006:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.38/1.45 % (3545301)Instruction limit reached!
% 3.38/1.45 % (3545301)------------------------------
% 3.38/1.45 % (3545301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545301)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545301)Termination reason: Instruction limit
% 3.38/1.45 % (3545301)Termination phase: shuffling
% 3.38/1.45 % (3545301)Time elapsed: 0.004 s
% 3.38/1.45 % (3545301)Peak memory usage: 86 MB
% 3.38/1.45 % (3545301)Instructions burned: 16 (million)
% 3.38/1.45 % (3545303)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1907936176:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.38/1.45 % (3545304)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2752813296:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.38/1.45 % (3545304)Instruction limit reached!
% 3.38/1.45 % (3545304)------------------------------
% 3.38/1.45 % (3545304)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545304)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545304)Termination reason: Instruction limit
% 3.38/1.45 % (3545304)Termination phase: Property scanning
% 3.38/1.45 % (3545304)Time elapsed: 0.005 s
% 3.38/1.45 % (3545304)Peak memory usage: 86 MB
% 3.38/1.45 % (3545304)Instructions burned: 8 (million)
% 3.38/1.45 % (3545302)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1528316627:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.38/1.45 % (3545305)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3649726122:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.38/1.45 % (3545305)Instruction limit reached!
% 3.38/1.45 % (3545305)------------------------------
% 3.38/1.45 % (3545305)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545305)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545305)Termination reason: Instruction limit
% 3.38/1.45 % (3545305)Termination phase: Property scanning
% 3.38/1.45 % (3545305)Time elapsed: 0.005 s
% 3.38/1.45 % (3545305)Peak memory usage: 86 MB
% 3.38/1.45 % (3545305)Instructions burned: 4 (million)
% 3.38/1.45 % (3545306)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1941772245:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.38/1.45 % (3545307)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2267660040:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.38/1.45 % (3545307)Instruction limit reached!
% 3.38/1.45 % (3545307)------------------------------
% 3.38/1.45 % (3545307)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545307)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545307)Termination reason: Instruction limit
% 3.38/1.45 % (3545307)Termination phase: Preprocessing 3
% 3.38/1.45 % (3545307)Time elapsed: 0.020 s
% 3.38/1.45 % (3545307)Peak memory usage: 88 MB
% 3.38/1.45 % (3545307)Instructions burned: 33 (million)
% 3.38/1.45 % (3545306)Instruction limit reached!
% 3.38/1.45 % (3545306)------------------------------
% 3.38/1.45 % (3545306)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545306)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545306)Termination reason: Instruction limit
% 3.38/1.45 % (3545306)Termination phase: Property scanning
% 3.38/1.45 % (3545306)Time elapsed: 0.028 s
% 3.38/1.45 % (3545306)Peak memory usage: 89 MB
% 3.38/1.45 % (3545306)Instructions burned: 46 (million)
% 3.38/1.45 % (3545309)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2038441076:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.38/1.45 % (3545309)Instruction limit reached!
% 3.38/1.45 % (3545309)------------------------------
% 3.38/1.45 % (3545309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545309)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545309)Termination reason: Instruction limit
% 3.38/1.45 % (3545309)Termination phase: Preprocessing 1
% 3.38/1.45 % (3545309)Time elapsed: 0.005 s
% 3.38/1.45 % (3545309)Peak memory usage: 86 MB
% 3.38/1.45 % (3545309)Instructions burned: 16 (million)
% 3.38/1.45 % (3545302)First to succeed.
% 3.38/1.45 % (3545302)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3545296"
% 3.38/1.45 % (3545313)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=709234295:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.38/1.45 % (3545317)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1751745312:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.38/1.45 % (3545321)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=671845654:i=85:gtgl=4:rtra=on:gtg=exists_sym_2997 on theBenchmark for (2997ds/85Mi)
% 3.38/1.45 % (3545313)Instruction limit reached!
% 3.38/1.45 % (3545313)------------------------------
% 3.38/1.45 % (3545313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545313)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545313)Termination reason: Instruction limit
% 3.38/1.45 % (3545313)Termination phase: Preprocessing 3
% 3.38/1.45 % (3545313)Time elapsed: 0.018 s
% 3.38/1.45 % (3545313)Peak memory usage: 88 MB
% 3.38/1.45 % (3545313)Instructions burned: 30 (million)
% 3.38/1.45 % (3545303)Instruction limit reached!
% 3.38/1.45 % (3545303)------------------------------
% 3.38/1.45 % (3545303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545303)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545303)Termination reason: Instruction limit
% 3.38/1.45 % (3545303)Termination phase: Saturation
% 3.38/1.45 % (3545303)Time elapsed: 0.154 s
% 3.38/1.45 % (3545303)Peak memory usage: 119 MB
% 3.38/1.45 % (3545303)Instructions burned: 201 (million)
% 3.38/1.45 % (3545317)Instruction limit reached!
% 3.38/1.45 % (3545317)------------------------------
% 3.38/1.45 % (3545317)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545317)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545317)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545317)Termination reason: Instruction limit
% 3.38/1.45 % (3545317)Termination phase: Preprocessing 3
% 3.38/1.45 % (3545317)Time elapsed: 0.012 s
% 3.38/1.45 % (3545317)Peak memory usage: 87 MB
% 3.38/1.45 % (3545317)Instructions burned: 18 (million)
% 3.38/1.45 % (3545321)Instruction limit reached!
% 3.38/1.45 % (3545321)------------------------------
% 3.38/1.45 % (3545321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545321)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545321)Termination reason: Instruction limit
% 3.38/1.45 % (3545321)Termination phase: Saturation
% 3.38/1.45 % (3545321)Time elapsed: 0.024 s
% 3.38/1.45 % (3545321)Peak memory usage: 90 MB
% 3.38/1.45 % (3545321)Instructions burned: 88 (million)
% 3.38/1.45 % (3545318)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2504701952:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.38/1.45 % (3545320)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=2215931726:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.38/1.45 % (3545318)Instruction limit reached!
% 3.38/1.45 % (3545318)------------------------------
% 3.38/1.45 % (3545318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545318)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545318)Termination reason: Instruction limit
% 3.38/1.45 % (3545318)Termination phase: Preprocessing 3
% 3.38/1.45 % (3545318)Time elapsed: 0.015 s
% 3.38/1.45 % (3545318)Peak memory usage: 87 MB
% 3.38/1.45 % (3545318)Instructions burned: 25 (million)
% 3.38/1.45 % (3545320)Instruction limit reached!
% 3.38/1.45 % (3545320)------------------------------
% 3.38/1.45 % (3545320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545320)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545320)Termination reason: Instruction limit
% 3.38/1.45 % (3545320)Termination phase: Preprocessing 3
% 3.38/1.45 % (3545320)Time elapsed: 0.018 s
% 3.38/1.45 % (3545320)Peak memory usage: 88 MB
% 3.38/1.45 % (3545320)Instructions burned: 28 (million)
% 3.38/1.45 % (3545328)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=407298543:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2996 on theBenchmark for (2996ds/66Mi)
% 3.38/1.45 % (3545325)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=738204238:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2996 on theBenchmark for (2996ds/2Mi)
% 3.38/1.45 % (3545325)Instruction limit reached!
% 3.38/1.45 % (3545325)------------------------------
% 3.38/1.45 % (3545325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545325)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545325)Termination reason: Instruction limit
% 3.38/1.45 % (3545325)Termination phase: shuffling
% 3.38/1.45 % (3545325)Time elapsed: 0.003 s
% 3.38/1.45 % (3545325)Peak memory usage: 85 MB
% 3.38/1.45 % (3545325)Instructions burned: 2 (million)
% 3.38/1.45 % (3545328)Instruction limit reached!
% 3.38/1.45 % (3545328)------------------------------
% 3.38/1.45 % (3545328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545328)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545328)Termination reason: Instruction limit
% 3.38/1.45 % (3545328)Termination phase: Saturation
% 3.38/1.45 % (3545328)Time elapsed: 0.038 s
% 3.38/1.45 % (3545328)Peak memory usage: 95 MB
% 3.38/1.45 % (3545328)Instructions burned: 66 (million)
% 3.38/1.45 % (3545327)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=1369172300:i=4:ep=RST:ins=2:rtra=on_2996 on theBenchmark for (2996ds/4Mi)
% 3.38/1.45 % (3545326)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=2657981580:i=181:rtra=on:ss=axioms:ev=cautious_2996 on theBenchmark for (2996ds/181Mi)
% 3.38/1.45 % (3545327)Instruction limit reached!
% 3.38/1.45 % (3545327)------------------------------
% 3.38/1.45 % (3545327)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545327)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545327)Termination reason: Instruction limit
% 3.38/1.45 % (3545327)Termination phase: Property scanning
% 3.38/1.45 % (3545327)Time elapsed: 0.005 s
% 3.38/1.45 % (3545327)Peak memory usage: 86 MB
% 3.38/1.45 % (3545327)Instructions burned: 4 (million)
% 3.38/1.45 % (3545326)Also succeeded, but the first one will report.
% 3.38/1.45 % (3545331)lrs+10_1_thi=all:si=on:fd=off:random_seed=2715844205:i=53:rtra=on:gtg=all_2996 on theBenchmark for (2996ds/53Mi)
% 3.38/1.45 % (3545332)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=419828512:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2996 on theBenchmark for (2996ds/8Mi)
% 3.38/1.45 % (3545332)Instruction limit reached!
% 3.38/1.45 % (3545332)------------------------------
% 3.38/1.45 % (3545332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.38/1.45 % (3545332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.38/1.45 % (3545332)CaDiCaL version: 2.1.3
% 3.38/1.45 % (3545332)Termination reason: Instruction limit
% 3.38/1.45 % (3545332)Termination phase: Property scanning
% 3.38/1.45 % (3545332)Time elapsed: 0.008 s
% 3.38/1.45 % (3545332)Peak memory usage: 85 MB
% 3.38/1.45 % (3545332)Instructions burned: 8 (million)
% 3.38/1.45 % (3545302)Refutation found. Thanks to Tanya!
% 3.38/1.45 % SZS status Theorem for theBenchmark
% 3.38/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.71 % (3545302)------------------------------
% 0.17/1.71 % (3545302)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.71 % (3545302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.71 % (3545302)CaDiCaL version: 2.1.3
% 0.17/1.71 % (3545302)Termination reason: Refutation
% 0.17/1.71 % (3545302)Time elapsed: 0.077 s
% 0.17/1.71 % (3545302)Peak memory usage: 118 MB
% 0.17/1.71 % (3545302)Instructions burned: 91 (million)
% 0.17/1.71 % (3545302)------------------------------
% 0.17/1.71 % (3545302)------------------------------
% 0.17/1.71 % (3545296)Success in time 0.596 s
% 0.17/1.71 % Vampire exiting
%------------------------------------------------------------------------------