%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP404_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 : n017.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 11:33:48 AM UTC 2026
% Result : Theorem 10.21s 2.81s
% Output : Refutation 12.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 1 def)
% Number of atoms : 43 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 42 ( 19 ~; 15 |; 6 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 21 ( 21 atm; 0 fun; 0 num; 0 var)
% Number of types : 33 ( 31 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 22 usr; 2 prp; 0-4 aty)
% Number of functors : 162 ( 162 usr; 42 con; 0-3 aty)
% Number of variables : 14 ( 14 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Nat_set_set$': $tType ).
tff(type_def_6,type,
'Nat_int_set_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'Int_bool_fun$': $tType ).
tff(type_def_8,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'Int_set_set_bool_fun$': $tType ).
tff(type_def_10,type,
'Clock$': $tType ).
tff(type_def_11,type,
'Int_set_set_set$': $tType ).
tff(type_def_12,type,
'Int_set$': $tType ).
tff(type_def_13,type,
'Int_int_fun$': $tType ).
tff(type_def_14,type,
'Int_set_set$': $tType ).
tff(type_def_15,type,
'Nat_bool_fun_set$': $tType ).
tff(type_def_16,type,
'Nat_set_nat_set_bool_fun_fun$': $tType ).
tff(type_def_17,type,
'Int_int_set_bool_fun_fun$': $tType ).
tff(type_def_18,type,
'A_run$': $tType ).
tff(type_def_19,type,
'Nat_nat_fun$': $tType ).
tff(type_def_20,type,
'Nat$': $tType ).
tff(type_def_21,type,
tlbool: $tType ).
tff(type_def_22,type,
'Nat_set_bool_fun$': $tType ).
tff(type_def_23,type,
'Nat_nat_set_bool_fun_fun$': $tType ).
tff(type_def_24,type,
'Nat_set_set_set$': $tType ).
tff(type_def_25,type,
'Int_set_bool_fun$': $tType ).
tff(type_def_26,type,
'Int_set_int_bool_fun_fun$': $tType ).
tff(type_def_27,type,
'Nat_set_set_bool_fun$': $tType ).
tff(type_def_28,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_29,type,
'Nat_bool_fun$': $tType ).
tff(type_def_30,type,
'Int_set_nat_bool_fun_fun$': $tType ).
tff(type_def_31,type,
'Nat_set$': $tType ).
tff(type_def_32,type,
'Nat_int_fun$': $tType ).
tff(type_def_33,type,
'Int_nat_set_bool_fun_fun$': $tType ).
tff(type_def_34,type,
'Nat_int_bool_fun_fun$': $tType ).
tff(type_def_35,type,
'Int_nat_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'uvs$': 'Int_set_int_bool_fun_fun$' ).
tff(func_def_1,type,
'uminus$c': 'Int_bool_fun$' > 'Int_bool_fun$' ).
tff(func_def_2,type,
'collect$c': 'Int_bool_fun$' > 'Int_set$' ).
tff(func_def_3,type,
'less$': 'Nat_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_4,type,
'finite$b': 'Nat_set_set_bool_fun$' ).
tff(func_def_5,type,
'uuw$': ( 'Nat_set$' * 'Nat_int_set_bool_fun_fun$' ) > 'Int_set_nat_bool_fun_fun$' ).
tff(func_def_6,type,
'member$a': 'Int_set$' > 'Int_set_set_bool_fun$' ).
tff(func_def_7,type,
def_5: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_8,type,
'uvj$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_9,type,
'uup$': 'Nat_set_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_10,type,
'uvr$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_11,type,
'uuo$': 'Int_set_set$' > 'Int_set_bool_fun$' ).
tff(func_def_12,type,
'is_empty$': 'Nat_set_bool_fun$' ).
tff(func_def_13,type,
'collect$a': 'Int_set_bool_fun$' > 'Int_set_set$' ).
tff(func_def_14,type,
'uux$': ( 'Nat_set$' * 'Nat_nat_set_bool_fun_fun$' * 'Nat_set$' ) > 'Nat_bool_fun$' ).
tff(func_def_15,type,
'uva$': ( 'Int_set_set$' * 'Int_set_nat_bool_fun_fun$' ) > 'Nat_int_set_bool_fun_fun$' ).
tff(func_def_16,type,
'ordering_top$a': ( 'Nat_nat_bool_fun_fun$' * 'Nat_nat_bool_fun_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_17,type,
'uvo$': $int > 'Int_int_bool_fun_fun$' ).
tff(func_def_18,type,
'bot$e': 'Nat_bool_fun$' ).
tff(func_def_19,type,
'zero$': 'Nat$' ).
tff(func_def_20,type,
'tick_count_strict$': ( 'A_run$' * 'Clock$' ) > 'Nat_nat_fun$' ).
tff(func_def_21,type,
'uvd$': ( 'Nat_set_set$' * 'Nat_set_bool_fun$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_22,type,
'less$d': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_23,type,
'uvi$': 'Nat_set_nat_set_bool_fun_fun$' ).
tff(func_def_24,type,
'uvm$': $int > 'Int_int_bool_fun_fun$' ).
tff(func_def_25,type,
'less_eq$a': 'Int_set_set$' > 'Int_set_set_bool_fun$' ).
tff(func_def_26,type,
'uvl$': 'Int_int_bool_fun_fun$' ).
tff(func_def_27,type,
'bot$j': 'Nat$' ).
tff(func_def_28,type,
'member$': 'Nat_set$' > 'Nat_set_set_bool_fun$' ).
tff(func_def_29,type,
'finite$c': 'Int_set_bool_fun$' ).
tff(func_def_30,type,
'fun_app$m': ( 'Int_int_set_bool_fun_fun$' * $int ) > 'Int_set_bool_fun$' ).
tff(func_def_31,type,
'g$': 'Nat_nat_fun$' ).
tff(func_def_32,type,
'bot$h': 'Int_set_bool_fun$' ).
tff(func_def_33,type,
'n$': 'Nat$' ).
tff(func_def_34,type,
'uvp$': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).
tff(func_def_35,type,
'less$a': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_36,type,
'uvh$': 'Nat_bool_fun$' ).
tff(func_def_37,type,
'uuq$': 'Nat_set$' > 'Nat_bool_fun$' ).
tff(func_def_38,type,
'fun_app$a': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_39,type,
'uus$': ( 'Nat_set$' * 'Nat_nat_bool_fun_fun$' ) > 'Nat_nat_bool_fun_fun$' ).
tff(func_def_40,type,
def_7: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_41,type,
'fun_app$o': ( 'Int_set_nat_bool_fun_fun$' * 'Int_set$' ) > 'Nat_bool_fun$' ).
tff(func_def_42,type,
'arg_min_on$a': ( 'Nat_int_fun$' * 'Nat_set$' ) > 'Nat$' ).
tff(func_def_43,type,
'less$b': 'Int_set_set$' > 'Int_set_set_bool_fun$' ).
tff(func_def_44,type,
'collect$d': 'Int_set_set_bool_fun$' > 'Int_set_set_set$' ).
tff(func_def_45,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_46,type,
'bot$': 'Nat_set$' ).
tff(func_def_47,type,
'uuc$': ( 'Int_set_bool_fun$' * 'Int_set_bool_fun$' ) > 'Int_set_bool_fun$' ).
tff(func_def_48,type,
'of_int$': 'Int_int_fun$' ).
tff(func_def_49,type,
'uuk$': 'Int_set_set$' > 'Int_set_set_bool_fun$' ).
tff(func_def_50,type,
'bot$b': 'Nat_set_set$' ).
tff(func_def_51,type,
'bot$a': 'Int_set_set$' ).
tff(func_def_52,type,
'uue$': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_53,type,
def_1: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_54,type,
'ordering_top$': ( 'Nat_set_nat_set_bool_fun_fun$' * 'Nat_set_nat_set_bool_fun_fun$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_55,type,
'uum$': 'Nat_set_nat_set_bool_fun_fun$' ).
tff(func_def_56,type,
'uminus$': 'Nat_set$' > 'Nat_set$' ).
tff(func_def_57,type,
'fun_app$n': ( 'Nat_int_set_bool_fun_fun$' * 'Nat$' ) > 'Int_set_bool_fun$' ).
tff(func_def_58,type,
'uua$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_59,type,
'finite$': 'Nat_set_bool_fun$' ).
tff(func_def_60,type,
'fun_app$s': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_61,type,
tltrue: tlbool ).
tff(func_def_62,type,
def_8: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_63,type,
def_6: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_64,type,
'r$': 'A_run$' ).
tff(func_def_65,type,
'uminus$b': 'Int_set$' > 'Int_set$' ).
tff(func_def_66,type,
'fun_app$g': ( 'Nat_set_nat_set_bool_fun_fun$' * 'Nat_set$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_67,type,
'uuh$': ( 'Nat_set_bool_fun$' * 'Nat_set_bool_fun$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_68,type,
'uub$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_69,type,
'collect$e': 'Nat_set_set_bool_fun$' > 'Nat_set_set_set$' ).
tff(func_def_70,type,
'uvb$': ( 'Int_set_set$' * 'Int_set_int_bool_fun_fun$' ) > 'Int_int_set_bool_fun_fun$' ).
tff(func_def_71,type,
'uvg$': 'Int_bool_fun$' ).
tff(func_def_72,type,
'less$c': 'Nat_set_set$' > 'Nat_set_set_bool_fun$' ).
tff(func_def_73,type,
'f$': 'Nat_nat_fun$' ).
tff(func_def_74,type,
'arg_min_on$': ( 'Int_int_fun$' * 'Int_set$' ) > $int ).
tff(func_def_75,type,
'less_eq$d': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_76,type,
'collect$': 'Nat_bool_fun$' > 'Nat_set$' ).
tff(func_def_77,type,
'sub$': 'A_run$' ).
tff(func_def_78,type,
'less_eq$c': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_79,type,
'fun_app$l': ( 'Int_set_int_bool_fun_fun$' * 'Int_set$' ) > 'Int_bool_fun$' ).
tff(func_def_80,type,
'member$c': 'Int_int_set_bool_fun_fun$' ).
tff(func_def_81,type,
'uut$': ( 'Nat_set$' * 'Nat_int_bool_fun_fun$' ) > 'Int_nat_bool_fun_fun$' ).
tff(func_def_82,type,
'fun_app$k': ( 'Nat_nat_set_bool_fun_fun$' * 'Nat$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_83,type,
'uuy$': ( 'Int_set$' * 'Int_int_set_bool_fun_fun$' ) > 'Int_set_int_bool_fun_fun$' ).
tff(func_def_84,type,
'less_eq$b': 'Nat_set$' > 'Nat_set_bool_fun$' ).
tff(func_def_85,type,
'bot$g': 'Int_bool_fun$' ).
tff(func_def_86,type,
'fun_app$c': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_87,type,
'bot$d': 'Nat_bool_fun_set$' ).
tff(func_def_88,type,
'uvf$': ( 'Int_set$' * 'Int_bool_fun$' ) > 'Int_bool_fun$' ).
tff(func_def_89,type,
'less_eq$': 'Nat_set_set$' > 'Nat_set_set_bool_fun$' ).
tff(func_def_90,type,
'bot$c': 'Int_set$' ).
tff(func_def_91,type,
'uuf$': ( 'Int_bool_fun$' * 'Int_bool_fun$' ) > 'Int_bool_fun$' ).
tff(func_def_92,type,
def_4: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_93,type,
'fun_app$j': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_94,type,
'uminus$a': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).
tff(func_def_95,type,
'uug$': ( 'Int_set_bool_fun$' * 'Int_set_bool_fun$' ) > 'Int_set_bool_fun$' ).
tff(func_def_96,type,
'uuz$': ( 'Int_set$' * 'Int_nat_set_bool_fun_fun$' * 'Nat_set$' ) > 'Int_bool_fun$' ).
tff(func_def_97,type,
'dil_inverse$': 'Nat_nat_fun$' > 'Nat_nat_fun$' ).
tff(func_def_98,type,
tlfalse: tlbool ).
tff(func_def_99,type,
'nat$': $int > 'Nat$' ).
tff(func_def_100,type,
'fun_app$p': ( 'Int_nat_bool_fun_fun$' * $int ) > 'Nat_bool_fun$' ).
tff(func_def_101,type,
'uvn$': $int > 'Int_int_bool_fun_fun$' ).
tff(func_def_102,type,
'uvq$': 'Int_bool_fun$' > 'Int_bool_fun$' ).
tff(func_def_103,type,
'finite$a': 'Int_set_set_bool_fun$' ).
tff(func_def_104,type,
'uun$': 'Int_set$' > 'Int_set_bool_fun$' ).
tff(func_def_105,type,
'uvk$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_106,type,
def_2: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_107,type,
'fun_app$q': ( 'Nat_int_bool_fun_fun$' * 'Nat$' ) > 'Int_bool_fun$' ).
tff(func_def_108,type,
'member$b': 'Nat_nat_set_bool_fun_fun$' ).
tff(func_def_109,type,
'uud$': ( 'Nat_set_bool_fun$' * 'Nat_set_bool_fun$' ) > 'Nat_set_bool_fun$' ).
tff(func_def_110,type,
'uve$': ( 'Nat_set$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_111,type,
'collect$b': 'Nat_set_bool_fun$' > 'Nat_set_set$' ).
tff(func_def_112,type,
'fun_app$r': ( 'Int_nat_set_bool_fun_fun$' * $int ) > 'Nat_set_bool_fun$' ).
tff(func_def_113,type,
'uuj$': ( 'Int_bool_fun$' * 'Int_bool_fun$' ) > 'Int_bool_fun$' ).
tff(func_def_114,type,
'uvc$': ( 'Int_set_set$' * 'Int_set_bool_fun$' ) > 'Int_set_bool_fun$' ).
tff(func_def_115,type,
'fun_app$b': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_116,type,
'uuu$': ( 'Int_set$' * 'Int_nat_bool_fun_fun$' ) > 'Nat_int_bool_fun_fun$' ).
tff(func_def_117,type,
'dbl_dec$': 'Int_int_fun$' ).
tff(func_def_118,type,
'uu$': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_119,type,
'uur$': 'Int_set_int_bool_fun_fun$' ).
tff(func_def_120,type,
def_3: ( 'Nat_bool_fun$' * 'Nat$' ) > tlbool ).
tff(func_def_121,type,
'uul$': 'Nat_set_set$' > 'Nat_set_set_bool_fun$' ).
tff(func_def_122,type,
'uuv$': ( 'Int_set$' * 'Int_int_bool_fun_fun$' ) > 'Int_int_bool_fun_fun$' ).
tff(func_def_123,type,
'bot$i': 'Nat_set_bool_fun$' ).
tff(func_def_124,type,
'uui$': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).
tff(func_def_129,type,
sK3: $int > 'Nat$' ).
tff(func_def_130,type,
sK4: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_131,type,
sK5: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_132,type,
sK6: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_133,type,
sK7: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_134,type,
sK8: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_135,type,
sK9: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_136,type,
sK10: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_137,type,
sK11: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_138,type,
sK12: $int > $int ).
tff(func_def_139,type,
sK13: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_140,type,
sK14: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_141,type,
sK15: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_142,type,
sK16: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_143,type,
sK17: $int > 'Nat$' ).
tff(func_def_144,type,
sK18: $int > 'Nat$' ).
tff(func_def_145,type,
sK19: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_146,type,
sK20: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_147,type,
sK21: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_148,type,
sK22: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_149,type,
sK23: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_150,type,
sK24: $int > $int ).
tff(func_def_151,type,
sK25: $int > 'Nat$' ).
tff(func_def_152,type,
sK26: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_153,type,
sK27: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_154,type,
sK28: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_155,type,
sK29: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_156,type,
sK30: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_157,type,
sK31: $int > 'Nat$' ).
tff(func_def_158,type,
sK32: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_159,type,
sK33: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_160,type,
sK34: ( 'Nat_bool_fun$' * $int ) > 'Nat$' ).
tff(func_def_161,type,
sK35: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_162,type,
sK36: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_163,type,
sK37: $int > 'Nat$' ).
tff(func_def_164,type,
sK38: $int > 'Nat$' ).
tff(func_def_165,type,
sK39: 'Nat$' > 'Nat$' ).
tff(pred_def_1,type,
'fun_app$d': ( 'Nat_set_set_bool_fun$' * 'Nat_set_set$' ) > $o ).
tff(pred_def_2,type,
'less$e': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_3,type,
'less$f': ( 'Int_bool_fun$' * 'Int_bool_fun$' ) > $o ).
tff(pred_def_5,type,
'contracting$': ( 'Nat_nat_fun$' * 'A_run$' * 'A_run$' * 'Nat_nat_fun$' ) > $o ).
tff(pred_def_6,type,
'fun_app$': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_7,type,
'fun_app$h': ( 'Int_set_bool_fun$' * 'Int_set$' ) > $o ).
tff(pred_def_8,type,
'member$d': ( 'Nat_bool_fun$' * 'Nat_bool_fun_set$' ) > $o ).
tff(pred_def_9,type,
'finite$f': 'Nat_bool_fun_set$' > $o ).
tff(pred_def_10,type,
'fun_app$e': ( 'Int_set_set_bool_fun$' * 'Int_set_set$' ) > $o ).
tff(pred_def_11,type,
'dense_run$': 'A_run$' > $o ).
tff(pred_def_12,type,
'fun_app$f': ( 'Nat_set_bool_fun$' * 'Nat_set$' ) > $o ).
tff(pred_def_13,type,
'dilating$': ( 'Nat_nat_fun$' * 'A_run$' * 'A_run$' ) > $o ).
tff(pred_def_14,type,
'less_eq$g': ( tlbool * tlbool ) > $o ).
tff(pred_def_15,type,
'finite$d': 'Int_set_set_set$' > $o ).
tff(pred_def_16,type,
'less_eq$f': ( 'Int_bool_fun$' * 'Int_bool_fun$' ) > $o ).
tff(pred_def_17,type,
'finite$e': 'Nat_set_set_set$' > $o ).
tff(pred_def_18,type,
'less_eq$e': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > $o ).
tff(pred_def_19,type,
'fun_app$i': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_22,type,
sP0: ( $int * $int * $int ) > $o ).
tff(pred_def_23,type,
sP1: ( $int * $int * $int ) > $o ).
tff(pred_def_24,type,
sP2: ( $int * $int * $int ) > $o ).
tff(f47,conjecture,
'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture46) ).
tff(f48,negated_conjecture,
( ( ~ 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) ) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
tff(f50,axiom,
! [X0: 'Nat$'] : ~ $less('fun_app$b'('of_nat$','fun_app$c'('g$',X0)),'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
tff(f51,axiom,
! [X0: 'Nat$'] : ~ $less('fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)),'fun_app$b'('of_nat$','fun_app$c'('g$',X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
tff(f122,axiom,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( 'fun_app$b'('of_nat$',X0) != 'fun_app$b'('of_nat$',X1) )
<=> ( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
| $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).
tff(f810,plain,
'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')),
inference(flattening,[],[f48]) ).
tff(f1206,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 'fun_app$b'('of_nat$',X0) != 'fun_app$b'('of_nat$',X1) )
| ( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
& ~ $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1)) ) )
& ( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
| $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1))
| ( 'fun_app$b'('of_nat$',X0) = 'fun_app$b'('of_nat$',X1) ) ) ),
inference(nnf_transformation,[],[f122]) ).
tff(f1207,plain,
! [X1: 'Nat$',X0: 'Nat$'] :
( ( ( 'fun_app$b'('of_nat$',X0) != 'fun_app$b'('of_nat$',X1) )
| ( ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
& ~ $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1)) ) )
& ( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
| $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1))
| ( 'fun_app$b'('of_nat$',X0) = 'fun_app$b'('of_nat$',X1) ) ) ),
inference(flattening,[],[f1206]) ).
tff(f1208,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$b'('of_nat$',X0) != 'fun_app$b'('of_nat$',X1) )
| ( ~ $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1))
& ~ $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0)) ) )
& ( $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1))
| $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
| ( 'fun_app$b'('of_nat$',X0) = 'fun_app$b'('of_nat$',X1) ) ) ),
inference(rectify,[],[f1207]) ).
tff(f1539,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$b'('of_nat$',X1),'fun_app$b'('of_nat$',X0))
| ( 'fun_app$b'('of_nat$',X0) = 'fun_app$b'('of_nat$',X1) )
| $less('fun_app$b'('of_nat$',X0),'fun_app$b'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1208]) ).
tff(f1544,plain,
'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')),
inference(cnf_transformation,[],[f810]) ).
tff(f1549,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0)),'fun_app$b'('of_nat$','fun_app$c'('g$',X0))),
inference(cnf_transformation,[],[f51]) ).
tff(f1824,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$b'('of_nat$','fun_app$c'('g$',X0)),'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),X0))),
inference(cnf_transformation,[],[f50]) ).
tff(f1890,definition,
( spl40_1
<=> ( 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) = 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')) ) ),
introduced(definition,[new_symbols(definition,[spl40_1])],[avatar_definition]) ).
tff(f1892,plain,
( ( 'fun_app$b'('of_nat$','fun_app$c'('g$','n$')) != 'fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')) )
| spl40_1 ),
inference(avatar_component_clause,[],[f1890]) ).
tff(f1893,plain,
~ spl40_1,
inference(avatar_split_clause,[],[f1544,f1890]) ).
tff(f1905,plain,
( $less('fun_app$b'('of_nat$','fun_app$c'('dil_inverse$'('f$'),'n$')),'fun_app$b'('of_nat$','fun_app$c'('g$','n$')))
| spl40_1 ),
inference(unit_resulting_resolution,[],[f1539,f1824,f1892]) ).
tff(f2491,plain,
( $false
| spl40_1 ),
inference(forward_subsumption_resolution,[],[f1905,f1549]) ).
tff(f2492,plain,
spl40_1,
inference(avatar_contradiction_clause,[],[f2491]) ).
tff(f2493,plain,
$false,
inference(avatar_smt_refutation,[],[f2492,f1893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP404_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 12:52:50 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 6.76/2.05 % (2524231)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 6.76/2.05 % (2524239)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1770467517:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 6.76/2.05 % (2524240)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1379819214:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 6.76/2.05 % (2524238)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1467200507:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 6.76/2.05 % (2524238)Instruction limit reached!
% 6.76/2.05 % (2524238)------------------------------
% 6.76/2.05 % (2524238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.05 % (2524238)CaDiCaL version: 2.1.3
% 6.76/2.05 % (2524238)Termination reason: Instruction limit
% 6.76/2.05 % (2524238)Termination phase: Property scanning
% 6.76/2.05 % (2524238)Time elapsed: 0.012 s
% 6.76/2.05 % (2524238)Peak memory usage: 85 MB
% 6.76/2.05 % (2524238)Instructions burned: 12 (million)
% 6.76/2.05 % (2524241)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2610240295:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 6.76/2.05 % (2524243)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1759193162:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 6.76/2.05 % (2524242)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3993904067:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 6.76/2.05 % (2524242)Instruction limit reached!
% 6.76/2.05 % (2524242)------------------------------
% 6.76/2.05 % (2524242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.05 % (2524242)CaDiCaL version: 2.1.3
% 6.76/2.05 % (2524242)Termination reason: Instruction limit
% 6.76/2.05 % (2524242)Termination phase: Property scanning
% 6.76/2.05 % (2524242)Time elapsed: 0.006 s
% 6.76/2.05 % (2524242)Peak memory usage: 85 MB
% 6.76/2.05 % (2524242)Instructions burned: 5 (million)
% 6.76/2.05 % (2524241)Instruction limit reached!
% 6.76/2.05 % (2524241)------------------------------
% 6.76/2.05 % (2524241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.05 % (2524241)CaDiCaL version: 2.1.3
% 6.76/2.05 % (2524241)Termination reason: Instruction limit
% 6.76/2.05 % (2524241)Termination phase: Property scanning
% 6.76/2.05 % (2524241)Time elapsed: 0.008 s
% 6.76/2.05 % (2524241)Peak memory usage: 85 MB
% 6.76/2.05 % (2524241)Instructions burned: 8 (million)
% 6.76/2.05 % (2524244)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=288970537:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 6.76/2.05 % (2524244)Instruction limit reached!
% 6.76/2.05 % (2524244)------------------------------
% 6.76/2.05 % (2524244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.05 % (2524244)CaDiCaL version: 2.1.3
% 6.76/2.05 % (2524244)Termination reason: Instruction limit
% 6.76/2.05 % (2524244)Termination phase: Property scanning
% 6.76/2.05 % (2524244)Time elapsed: 0.035 s
% 6.76/2.05 % (2524244)Peak memory usage: 88 MB
% 6.76/2.05 % (2524244)Instructions burned: 33 (million)
% 6.76/2.05 % (2524243)Instruction limit reached!
% 6.76/2.05 % (2524243)------------------------------
% 6.76/2.05 % (2524243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.76/2.05 % (2524243)CaDiCaL version: 2.1.3
% 6.76/2.05 % (2524243)Termination reason: Instruction limit
% 6.76/2.05 % (2524243)Termination phase: Property scanning
% 6.76/2.05 % (2524243)Time elapsed: 0.044 s
% 6.76/2.05 % (2524243)Peak memory usage: 88 MB
% 6.76/2.05 % (2524243)Instructions burned: 46 (million)
% 6.76/2.05 % (2524239)Instruction limit reached!
% 6.76/2.05 % (2524239)------------------------------
% 6.76/2.05 % (2524239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.76/2.05 % (2524239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524239)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524239)Termination reason: Instruction limit
% 7.70/2.31 % (2524239)Termination phase: Saturation
% 7.70/2.31 % (2524239)Time elapsed: 0.184 s
% 7.70/2.31 % (2524239)Peak memory usage: 119 MB
% 7.70/2.31 % (2524239)Instructions burned: 308 (million)
% 7.70/2.31 % (2524240)Instruction limit reached!
% 7.70/2.31 % (2524240)------------------------------
% 7.70/2.31 % (2524240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524240)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524240)Termination reason: Instruction limit
% 7.70/2.31 % (2524240)Termination phase: Saturation
% 7.70/2.31 % (2524240)Time elapsed: 0.259 s
% 7.70/2.31 % (2524240)Peak memory usage: 119 MB
% 7.70/2.31 % (2524240)Instructions burned: 201 (million)
% 7.70/2.31 % (2524253)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3450826822:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2996 on theBenchmark for (2996ds/14Mi)
% 7.70/2.31 % (2524256)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1584294542:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 7.70/2.31 % (2524255)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=2197126792:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2996 on theBenchmark for (2996ds/29Mi)
% 7.70/2.31 % (2524253)Instruction limit reached!
% 7.70/2.31 % (2524253)------------------------------
% 7.70/2.31 % (2524253)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524253)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524253)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524253)Termination reason: Instruction limit
% 7.70/2.31 % (2524253)Termination phase: Preprocessing 1
% 7.70/2.31 % (2524253)Time elapsed: 0.014 s
% 7.70/2.31 % (2524253)Peak memory usage: 86 MB
% 7.70/2.31 % (2524253)Instructions burned: 14 (million)
% 7.70/2.31 % (2524256)Instruction limit reached!
% 7.70/2.31 % (2524256)------------------------------
% 7.70/2.31 % (2524256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524256)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524256)Termination reason: Instruction limit
% 7.70/2.31 % (2524256)Termination phase: Preprocessing 3
% 7.70/2.31 % (2524256)Time elapsed: 0.017 s
% 7.70/2.31 % (2524256)Peak memory usage: 87 MB
% 7.70/2.31 % (2524256)Instructions burned: 16 (million)
% 7.70/2.31 % (2524259)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=2758106070:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 7.70/2.31 % (2524258)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=528116280:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 7.70/2.31 % (2524255)Instruction limit reached!
% 7.70/2.31 % (2524255)------------------------------
% 7.70/2.31 % (2524255)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524255)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524255)Termination reason: Instruction limit
% 7.70/2.31 % (2524255)Termination phase: Clausification
% 7.70/2.31 % (2524255)Time elapsed: 0.032 s
% 7.70/2.31 % (2524255)Peak memory usage: 87 MB
% 7.70/2.31 % (2524255)Instructions burned: 30 (million)
% 7.70/2.31 % (2524258)Instruction limit reached!
% 7.70/2.31 % (2524258)------------------------------
% 7.70/2.31 % (2524258)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.70/2.31 % (2524258)CaDiCaL version: 2.1.3
% 7.70/2.31 % (2524258)Termination reason: Instruction limit
% 7.70/2.31 % (2524258)Termination phase: Preprocessing 3
% 7.70/2.31 % (2524258)Time elapsed: 0.028 s
% 7.70/2.31 % (2524258)Peak memory usage: 87 MB
% 7.70/2.31 % (2524258)Instructions burned: 27 (million)
% 7.70/2.31 % (2524259)Instruction limit reached!
% 7.70/2.31 % (2524259)------------------------------
% 7.70/2.31 % (2524259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.70/2.31 % (2524259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524259)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524259)Termination reason: Instruction limit
% 8.77/2.57 % (2524259)Termination phase: Saturation
% 8.77/2.57 % (2524259)Time elapsed: 0.042 s
% 8.77/2.57 % (2524259)Peak memory usage: 90 MB
% 8.77/2.57 % (2524259)Instructions burned: 85 (million)
% 8.77/2.57 % (2524257)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2075571186:i=24:canc=force:rtra=on_2996 on theBenchmark for (2996ds/24Mi)
% 8.77/2.57 % (2524257)Instruction limit reached!
% 8.77/2.57 % (2524257)------------------------------
% 8.77/2.57 % (2524257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.57 % (2524257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524257)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524257)Termination reason: Instruction limit
% 8.77/2.57 % (2524257)Termination phase: Preprocessing 3
% 8.77/2.57 % (2524257)Time elapsed: 0.025 s
% 8.77/2.57 % (2524257)Peak memory usage: 87 MB
% 8.77/2.57 % (2524257)Instructions burned: 24 (million)
% 8.77/2.57 % (2524260)ott+1002_1_si=on:sp=occurrence:spb=goal:lcm=predicate:random_seed=926569443:i=2:bd=preordered:nm=2:ins=3:rtra=on:inst=on:tar=off_2995 on theBenchmark for (2995ds/2Mi)
% 8.77/2.57 % (2524260)Instruction limit reached!
% 8.77/2.57 % (2524260)------------------------------
% 8.77/2.57 % (2524260)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.57 % (2524260)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524260)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524260)Termination reason: Instruction limit
% 8.77/2.57 % (2524260)Termination phase: shuffling
% 8.77/2.57 % (2524260)Time elapsed: 0.003 s
% 8.77/2.57 % (2524260)Peak memory usage: 85 MB
% 8.77/2.57 % (2524260)Instructions burned: 2 (million)
% 8.77/2.57 % (2524265)dis+1010_1_to=kbo:sil=128000:tgt=full:si=on:tha=off:random_seed=1643652829:i=181:rtra=on:ss=axioms:ev=cautious_2994 on theBenchmark for (2994ds/181Mi)
% 8.77/2.57 % (2524266)lrs+10_2_to=lpo:sil=64000:si=on:sos=on:gve=force:lcm=reverse:uwa=one_side_interpreted:random_seed=3771336606:i=4:ep=RST:ins=2:rtra=on_2994 on theBenchmark for (2994ds/4Mi)
% 8.77/2.57 % (2524266)Instruction limit reached!
% 8.77/2.57 % (2524266)------------------------------
% 8.77/2.57 % (2524266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.57 % (2524266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524266)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524266)Termination reason: Instruction limit
% 8.77/2.57 % (2524266)Termination phase: Property scanning
% 8.77/2.57 % (2524266)Time elapsed: 0.005 s
% 8.77/2.57 % (2524266)Peak memory usage: 86 MB
% 8.77/2.57 % (2524266)Instructions burned: 4 (million)
% 8.77/2.57 % (2524270)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=2735197322:i=8:ep=RST:nm=16:rtra=on:gtg=exists_top_2993 on theBenchmark for (2993ds/8Mi)
% 8.77/2.57 % (2524270)Instruction limit reached!
% 8.77/2.57 % (2524270)------------------------------
% 8.77/2.57 % (2524270)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.57 % (2524268)dis+1010_128_isp=bottom:to=lpo:thi=overlap:prc=on:sas=z3:si=on:fd=preordered:random_seed=76893635:i=66:thsqd=64:thsqc=16:rtra=on:thsq=on:ev=force_2994 on theBenchmark for (2994ds/66Mi)
% 8.77/2.57 % (2524270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524270)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524270)Termination reason: Instruction limit
% 8.77/2.57 % (2524270)Termination phase: Property scanning
% 8.77/2.57 % (2524270)Time elapsed: 0.005 s
% 8.77/2.57 % (2524270)Peak memory usage: 86 MB
% 8.77/2.57 % (2524270)Instructions burned: 11 (million)
% 8.77/2.57 % (2524269)lrs+10_1_thi=all:si=on:fd=off:random_seed=3971085088:i=53:rtra=on:gtg=all_2993 on theBenchmark for (2993ds/53Mi)
% 8.77/2.57 % (2524272)lrs+10_1_to=lakbo:sil=128000:si=on:alasca=on:sp=occurrence:random_seed=73917805:st=3:i=2:rtra=on:ss=axioms_2993 on theBenchmark for (2993ds/2Mi)
% 8.77/2.57 % (2524272)Instruction limit reached!
% 8.77/2.57 % (2524272)------------------------------
% 8.77/2.57 % (2524272)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.77/2.57 % (2524272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.77/2.57 % (2524272)CaDiCaL version: 2.1.3
% 8.77/2.57 % (2524272)Termination reason: Instruction limit
% 10.21/2.81 % (2524272)Termination phase: shuffling
% 10.21/2.81 % (2524272)Time elapsed: 0.003 s
% 10.21/2.81 % (2524272)Peak memory usage: 85 MB
% 10.21/2.81 % (2524272)Instructions burned: 2 (million)
% 10.21/2.81 % (2524269)Instruction limit reached!
% 10.21/2.81 % (2524269)------------------------------
% 10.21/2.81 % (2524269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524269)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524269)Termination reason: Instruction limit
% 10.21/2.81 % (2524269)Termination phase: Property scanning
% 10.21/2.81 % (2524269)Time elapsed: 0.052 s
% 10.21/2.81 % (2524269)Peak memory usage: 88 MB
% 10.21/2.81 % (2524269)Instructions burned: 53 (million)
% 10.21/2.81 % (2524274)dis+1002_1_to=lpo:sil=64000:si=on:flr=on:random_seed=3194847251:i=2:doe=on:canc=force:asg=cautious:rtra=on_2993 on theBenchmark for (2993ds/2Mi)
% 10.21/2.81 % (2524274)Instruction limit reached!
% 10.21/2.81 % (2524274)------------------------------
% 10.21/2.81 % (2524274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524274)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524274)Termination reason: Instruction limit
% 10.21/2.81 % (2524274)Termination phase: Property scanning
% 10.21/2.81 % (2524274)Time elapsed: 0.002 s
% 10.21/2.81 % (2524274)Peak memory usage: 85 MB
% 10.21/2.81 % (2524274)Instructions burned: 3 (million)
% 10.21/2.81 % (2524268)Instruction limit reached!
% 10.21/2.81 % (2524268)------------------------------
% 10.21/2.81 % (2524268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524268)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524268)Termination reason: Instruction limit
% 10.21/2.81 % (2524268)Termination phase: Saturation
% 10.21/2.81 % (2524268)Time elapsed: 0.117 s
% 10.21/2.81 % (2524268)Peak memory usage: 130 MB
% 10.21/2.81 % (2524268)Instructions burned: 66 (million)
% 10.21/2.81 % (2524265)Instruction limit reached!
% 10.21/2.81 % (2524265)------------------------------
% 10.21/2.81 % (2524265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524265)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524265)Termination reason: Instruction limit
% 10.21/2.81 % (2524265)Termination phase: Saturation
% 10.21/2.81 % (2524265)Time elapsed: 0.182 s
% 10.21/2.81 % (2524265)Peak memory usage: 91 MB
% 10.21/2.81 % (2524265)Instructions burned: 181 (million)
% 10.21/2.81 % (2524278)lrs+1011_16:1_to=kbo:sil=128000:sas=z3:si=on:sos=theory:erd=off:urr=full:random_seed=619735575:i=127:doe=on:rtra=on_2992 on theBenchmark for (2992ds/127Mi)
% 10.21/2.81 % (2524281)dis+10_1_si=on:random_seed=1434836350:i=10:ep=R:rtra=on_2991 on theBenchmark for (2991ds/10Mi)
% 10.21/2.81 % (2524281)Instruction limit reached!
% 10.21/2.81 % (2524281)------------------------------
% 10.21/2.81 % (2524281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524281)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524281)Termination reason: Instruction limit
% 10.21/2.81 % (2524281)Termination phase: Property scanning
% 10.21/2.81 % (2524281)Time elapsed: 0.010 s
% 10.21/2.81 % (2524281)Peak memory usage: 86 MB
% 10.21/2.81 % (2524281)Instructions burned: 10 (million)
% 10.21/2.81 % (2524284)lrs-1011_64_to=lpo:si=on:sp=unary_first:sos=on:br=off:random_seed=3290617093:i=26:canc=cautious:av=off:rtra=on_2990 on theBenchmark for (2990ds/26Mi)
% 10.21/2.81 % (2524284)Instruction limit reached!
% 10.21/2.81 % (2524284)------------------------------
% 10.21/2.81 % (2524284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524284)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524284)Termination reason: Instruction limit
% 10.21/2.81 % (2524284)Termination phase: Preprocessing 3
% 10.21/2.81 % (2524284)Time elapsed: 0.015 s
% 10.21/2.81 % (2524284)Peak memory usage: 87 MB
% 10.21/2.81 % (2524284)Instructions burned: 27 (million)
% 10.21/2.81 % (2524286)dis+1011_5_anc=all:tgt=full:si=on:sp=const_frequency:spb=non_intro:fd=preordered:sac=on:random_seed=2788136333:avsq=on:i=35:doe=on:thsqd=64:nm=64:fsr=off:thsqc=32:rtra=on:tac=light:ss=included:thsq=on:ev=off:sgt=32_2990 on theBenchmark for (2990ds/35Mi)
% 10.21/2.81 % (2524287)ott+10_8:1_to=lpo:sil=128000:si=on:fs=off:spb=goal_then_units:uwa=alasca_main:random_seed=1204100114:i=2:fsr=off:rtra=on:inst=on_2990 on theBenchmark for (2990ds/2Mi)
% 10.21/2.81 % (2524287)Instruction limit reached!
% 10.21/2.81 % (2524287)------------------------------
% 10.21/2.81 % (2524287)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524287)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524287)Termination reason: Instruction limit
% 10.21/2.81 % (2524287)Termination phase: shuffling
% 10.21/2.81 % (2524287)Time elapsed: 0.003 s
% 10.21/2.81 % (2524287)Peak memory usage: 85 MB
% 10.21/2.81 % (2524287)Instructions burned: 2 (million)
% 10.21/2.81 % (2524289)lrs-1011_1_to=kbo:sil=128000:prc=on:si=on:fs=off:tha=off:random_seed=4050372875:i=370:ep=RS:fsr=off:rtra=on_2990 on theBenchmark for (2990ds/370Mi)
% 10.21/2.81 % (2524288)dis+21_1_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=off:s2agt=16:random_seed=121424861:s2a=on:i=8:kws=inv_precedence:doe=on:rtra=on_2990 on theBenchmark for (2990ds/8Mi)
% 10.21/2.81 % (2524286)Instruction limit reached!
% 10.21/2.81 % (2524286)------------------------------
% 10.21/2.81 % (2524286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524286)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524286)Termination reason: Instruction limit
% 10.21/2.81 % (2524286)Termination phase: Property scanning
% 10.21/2.81 % (2524286)Time elapsed: 0.036 s
% 10.21/2.81 % (2524286)Peak memory usage: 88 MB
% 10.21/2.81 % (2524286)Instructions burned: 35 (million)
% 10.21/2.81 % (2524278)Instruction limit reached!
% 10.21/2.81 % (2524278)------------------------------
% 10.21/2.81 % (2524278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524278)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524278)Termination reason: Instruction limit
% 10.21/2.81 % (2524278)Termination phase: Saturation
% 10.21/2.81 % (2524278)Time elapsed: 0.164 s
% 10.21/2.81 % (2524278)Peak memory usage: 118 MB
% 10.21/2.81 % (2524278)Instructions burned: 128 (million)
% 10.21/2.81 % (2524288)Instruction limit reached!
% 10.21/2.81 % (2524288)------------------------------
% 10.21/2.81 % (2524288)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524288)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524288)Termination reason: Instruction limit
% 10.21/2.81 % (2524288)Termination phase: Property scanning
% 10.21/2.81 % (2524288)Time elapsed: 0.011 s
% 10.21/2.81 % (2524288)Peak memory usage: 86 MB
% 10.21/2.81 % (2524288)Instructions burned: 11 (million)
% 10.21/2.81 % (2524293)ott+1002_1_to=lpo:thi=overlap:prc=on:bsd=on:si=on:gve=cautious:thigen=on:tha=some:random_seed=2119245479:i=13:av=off:rtra=on:gtg=exists_sym:ev=force_2989 on theBenchmark for (2989ds/13Mi)
% 10.21/2.81 % (2524293)Instruction limit reached!
% 10.21/2.81 % (2524293)------------------------------
% 10.21/2.81 % (2524293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524293)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524293)Termination reason: Instruction limit
% 10.21/2.81 % (2524293)Termination phase: Property scanning
% 10.21/2.81 % (2524293)Time elapsed: 0.012 s
% 10.21/2.81 % (2524293)Peak memory usage: 85 MB
% 10.21/2.81 % (2524293)Instructions burned: 14 (million)
% 10.21/2.81 % (2524295)lrs+1002_1_to=lpo:sil=128000:sas=z3:si=on:sos=on:urr=on:tha=off:random_seed=3274933820:i=226:rtra=on:gtg=position:ss=axioms_2988 on theBenchmark for (2988ds/226Mi)
% 10.21/2.81 % (2524295)First to succeed.
% 10.21/2.81 % (2524295)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2524231"
% 10.21/2.81 % (2524303)lrs+1010_1_to=lpo:prlc=on:sil=128000:prc=on:drc=off:si=on:sp=const_max:thsqr=8,1:tha=some:nwc=5:random_seed=2002121419:i=75:doe=on:thsqd=64:canc=force:thsqc=64:rtra=on:thsq=on_2987 on theBenchmark for (2987ds/75Mi)
% 10.21/2.81 % (2524299)lrs+1010_5_to=lpo:sil=128000:si=on:sp=const_frequency:sos=theory:tha=off:random_seed=2748382294:i=10:rtra=on_2988 on theBenchmark for (2988ds/10Mi)
% 10.21/2.81 % (2524301)lrs+1002_1_to=lpo:thi=strong:sas=z3:si=on:sp=const_frequency:tha=off:random_seed=3859497996:i=71:rtra=on:gtg=exists_top_2987 on theBenchmark for (2987ds/71Mi)
% 10.21/2.81 % (2524299)Instruction limit reached!
% 10.21/2.81 % (2524299)------------------------------
% 10.21/2.81 % (2524299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524299)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524299)Termination reason: Instruction limit
% 10.21/2.81 % (2524299)Termination phase: Preprocessing 1
% 10.21/2.81 % (2524299)Time elapsed: 0.011 s
% 10.21/2.81 % (2524299)Peak memory usage: 86 MB
% 10.21/2.81 % (2524299)Instructions burned: 11 (million)
% 10.21/2.81 % (2524303)Instruction limit reached!
% 10.21/2.81 % (2524303)------------------------------
% 10.21/2.81 % (2524303)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524303)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524303)Termination reason: Instruction limit
% 10.21/2.81 % (2524303)Termination phase: Saturation
% 10.21/2.81 % (2524303)Time elapsed: 0.046 s
% 10.21/2.81 % (2524303)Peak memory usage: 91 MB
% 10.21/2.81 % (2524303)Instructions burned: 75 (million)
% 10.21/2.81 % (2524305)ott+21_1_to=kbo:tgt=full:sas=z3:si=on:tha=off:random_seed=2900852201:i=130:kws=inv_frequency:nm=0:rtra=on:gtg=exists_all_2987 on theBenchmark for (2987ds/130Mi)
% 10.21/2.81 % (2524304)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=52650796:i=294:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2987 on theBenchmark for (2987ds/294Mi)
% 10.21/2.81 % (2524289)Instruction limit reached!
% 10.21/2.81 % (2524289)------------------------------
% 10.21/2.81 % (2524289)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524289)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524289)Termination reason: Instruction limit
% 10.21/2.81 % (2524289)Termination phase: Saturation
% 10.21/2.81 % (2524289)Time elapsed: 0.350 s
% 10.21/2.81 % (2524289)Peak memory usage: 94 MB
% 10.21/2.81 % (2524289)Instructions burned: 370 (million)
% 10.21/2.81 % (2524301)Instruction limit reached!
% 10.21/2.81 % (2524301)------------------------------
% 10.21/2.81 % (2524301)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.21/2.81 % (2524301)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.21/2.81 % (2524301)CaDiCaL version: 2.1.3
% 10.21/2.81 % (2524301)Termination reason: Instruction limit
% 10.21/2.81 % (2524301)Termination phase: Saturation
% 10.21/2.81 % (2524301)Time elapsed: 0.120 s
% 10.21/2.81 % (2524301)Peak memory usage: 130 MB
% 10.21/2.81 % (2524301)Instructions burned: 71 (million)
% 10.21/2.81 % (2524295)Refutation found. Thanks to Tanya!
% 10.21/2.81 % SZS status Theorem for theBenchmark
% 10.21/2.81 % SZS output start Proof for theBenchmark
% See solution above
% 12.28/2.99 % (2524295)------------------------------
% 12.28/2.99 % (2524295)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.28/2.99 % (2524295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.28/2.99 % (2524295)CaDiCaL version: 2.1.3
% 12.28/2.99 % (2524295)Termination reason: Refutation
% 12.28/2.99 % (2524295)Time elapsed: 0.059 s
% 12.28/2.99 % (2524295)Peak memory usage: 118 MB
% 12.28/2.99 % (2524295)Instructions burned: 80 (million)
% 12.28/2.99 % (2524295)------------------------------
% 12.28/2.99 % (2524295)------------------------------
% 12.28/2.99 % (2524231)Success in time 1.683 s
% 12.28/2.99 % Vampire exiting
%------------------------------------------------------------------------------