%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP322_1 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:39:21 AM UTC 2026
% Result : Theorem 0.19s 0.53s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 18 ( 17 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 213 ( 213 usr; 42 con; 0-4 aty)
% Number of variables : 20 ( 20 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'B_bool_fun_b_bool_fun_fun$': $tType ).
tff(type_def_6,type,
'B_bool_fun_b_bool_fun_bool_fun_fun$': $tType ).
tff(type_def_7,type,
'B_bool_fun_bool_fun$': $tType ).
tff(type_def_8,type,
'B$': $tType ).
tff(type_def_9,type,
'B_bool_fun_b_set_fun$': $tType ).
tff(type_def_10,type,
'B_set_b_set_bool_fun_fun$': $tType ).
tff(type_def_11,type,
'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$': $tType ).
tff(type_def_12,type,
tlbool: $tType ).
tff(type_def_13,type,
'B_set_b_set_b_set_fun_fun$': $tType ).
tff(type_def_14,type,
'B_b_bool_fun_fun$': $tType ).
tff(type_def_15,type,
'B_set$': $tType ).
tff(type_def_16,type,
'B_set_b_bool_fun_fun$': $tType ).
tff(type_def_17,type,
'B_set_bool_fun$': $tType ).
tff(type_def_18,type,
'Bool_bool_fun$': $tType ).
tff(type_def_19,type,
'B_set_b_set_fun$': $tType ).
tff(type_def_20,type,
'B_bool_fun$': $tType ).
tff(type_def_21,type,
'Bool_bool_bool_fun_fun$': $tType ).
tff(func_def_0,type,
def_12: tlbool ).
tff(func_def_1,type,
def_33: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_2,type,
def_15: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_3,type,
def_17: tlbool ).
tff(func_def_4,type,
def_39: tlbool > tlbool ).
tff(func_def_5,type,
'less_eq$a': 'B_bool_fun_b_bool_fun_bool_fun_fun$' ).
tff(func_def_6,type,
'a$': 'B$' ).
tff(func_def_7,type,
'fun_app$b': ( 'B_set_b_set_fun$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_8,type,
def_36: tlbool > tlbool ).
tff(func_def_9,type,
def_6: tlbool ).
tff(func_def_10,type,
def_21: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_11,type,
'collect$': 'B_bool_fun_b_set_fun$' ).
tff(func_def_12,type,
def_29: tlbool ).
tff(func_def_13,type,
def_4: tlbool ).
tff(func_def_14,type,
def_5: tlbool ).
tff(func_def_15,type,
'top$b': 'B_bool_fun$' ).
tff(func_def_16,type,
def_32: tlbool ).
tff(func_def_17,type,
def_8: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_18,type,
'uminus$': 'B_set_b_set_fun$' ).
tff(func_def_19,type,
'fun_app$j': ( 'B_set_b_set_bool_fun_fun$' * 'B_set$' ) > 'B_set_bool_fun$' ).
tff(func_def_20,type,
'fun_app$f': ( 'Bool_bool_bool_fun_fun$' * tlbool ) > 'Bool_bool_fun$' ).
tff(func_def_21,type,
'fun_app$a': ( 'B_set_b_bool_fun_fun$' * 'B_set$' ) > 'B_bool_fun$' ).
tff(func_def_22,type,
def_3: tlbool ).
tff(func_def_23,type,
'fun_app$c': ( 'B_set_b_set_b_set_fun_fun$' * 'B_set$' ) > 'B_set_b_set_fun$' ).
tff(func_def_24,type,
def_22: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_25,type,
def_40: tlbool > tlbool ).
tff(func_def_26,type,
'insert$': 'B$' > 'B_set_b_set_fun$' ).
tff(func_def_27,type,
'fun_app$m': ( 'B_bool_fun_b_bool_fun_bool_fun_fun$' * 'B_bool_fun$' ) > 'B_bool_fun_bool_fun$' ).
tff(func_def_28,type,
'top$': 'B_set$' ).
tff(func_def_29,type,
def_37: ( tlbool * tlbool ) > tlbool ).
tff(func_def_30,type,
tltrue: tlbool ).
tff(func_def_31,type,
def_19: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_32,type,
'inf$': 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' ).
tff(func_def_33,type,
def_24: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_34,type,
'minus$': 'B_set_b_set_b_set_fun_fun$' ).
tff(func_def_35,type,
def_26: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_36,type,
'remove$': 'B$' > 'B_set_b_set_fun$' ).
tff(func_def_37,type,
def_18: tlbool ).
tff(func_def_38,type,
def_2: tlbool ).
tff(func_def_39,type,
def_16: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_40,type,
def_14: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_41,type,
'less$': 'B_set_b_set_bool_fun_fun$' ).
tff(func_def_42,type,
'sup$b': 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' ).
tff(func_def_43,type,
'fun_app$k': ( 'B_b_bool_fun_fun$' * 'B$' ) > 'B_bool_fun$' ).
tff(func_def_44,type,
def_9: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_45,type,
def_20: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_46,type,
def_10: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_47,type,
def_27: tlbool ).
tff(func_def_48,type,
'sup$': 'B_set_b_set_b_set_fun_fun$' ).
tff(func_def_49,type,
def_34: tlbool ).
tff(func_def_50,type,
'uu$': 'B_set_b_bool_fun_fun$' ).
tff(func_def_51,type,
def_1: tlbool ).
tff(func_def_52,type,
def_25: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_53,type,
def_13: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_54,type,
'uminus$a': 'B_bool_fun_b_bool_fun_fun$' ).
tff(func_def_55,type,
def_41: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_56,type,
'bot$b': 'B_bool_fun$' ).
tff(func_def_57,type,
def_7: tlbool ).
tff(func_def_58,type,
'minus$a': 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' ).
tff(func_def_59,type,
def_38: ( tlbool * tlbool ) > tlbool ).
tff(func_def_60,type,
tlfalse: tlbool ).
tff(func_def_61,type,
'inf$a': 'B_set_b_set_b_set_fun_fun$' ).
tff(func_def_62,type,
def_31: tlbool ).
tff(func_def_63,type,
'the_elem$': 'B_set$' > 'B$' ).
tff(func_def_64,type,
def_28: tlbool ).
tff(func_def_65,type,
'bot$': 'B_set$' ).
tff(func_def_66,type,
def_30: tlbool ).
tff(func_def_67,type,
'b$': 'B$' ).
tff(func_def_68,type,
'less$a': 'B_bool_fun_b_bool_fun_bool_fun_fun$' ).
tff(func_def_69,type,
'less_eq$': 'B_set_b_set_bool_fun_fun$' ).
tff(func_def_70,type,
def_35: tlbool ).
tff(func_def_71,type,
def_42: tlbool > tlbool ).
tff(func_def_72,type,
def_23: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_73,type,
'fun_app$h': ( 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' * 'B_bool_fun$' ) > 'B_bool_fun_b_bool_fun_fun$' ).
tff(func_def_74,type,
'sup$a': 'Bool_bool_bool_fun_fun$' ).
tff(func_def_75,type,
'fun_app$g': ( 'B_bool_fun_b_bool_fun_fun$' * 'B_bool_fun$' ) > 'B_bool_fun$' ).
tff(func_def_76,type,
'fun_app$d': ( 'B_bool_fun_b_set_fun$' * 'B_bool_fun$' ) > 'B_set$' ).
tff(func_def_77,type,
def_11: ( 'B_bool_fun$' * 'B$' ) > tlbool ).
tff(func_def_78,type,
sK0: 'B_bool_fun$' > 'B$' ).
tff(func_def_79,type,
sK1: 'B_bool_fun$' > 'B$' ).
tff(func_def_80,type,
sK2: 'B_set$' > 'B$' ).
tff(func_def_81,type,
sK3: 'B_set$' > 'B$' ).
tff(func_def_82,type,
sK4: 'B_set$' > 'B$' ).
tff(func_def_83,type,
sK5: 'B$' ).
tff(func_def_84,type,
sK6: 'B_set$' > 'B$' ).
tff(func_def_85,type,
sK7: ( 'B$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_86,type,
sK8: ( 'B$' * 'B_set$' * 'B$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_87,type,
sK9: ( 'B$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_88,type,
sK10: ( 'B_bool_fun$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_89,type,
sK11: ( 'B_set$' * 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_90,type,
sK12: ( 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_91,type,
sK13: ( 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_92,type,
sK14: ( 'B_set$' * 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_93,type,
sK15: ( 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_94,type,
sK16: ( 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_95,type,
sK17: ( 'B$' * 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_96,type,
sK18: ( 'B_set$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_97,type,
sK19: 'B_set$' > 'B$' ).
tff(func_def_98,type,
sK20: 'B_set$' > 'B$' ).
tff(func_def_99,type,
sK21: 'B_set$' > 'B$' ).
tff(func_def_100,type,
sK22: 'B_set$' > 'B$' ).
tff(func_def_101,type,
sK23: ( 'B_b_bool_fun_fun$' * 'B_set$' ) > 'B$' ).
tff(func_def_102,type,
sK24: ( 'B_b_bool_fun_fun$' * 'B_set$' ) > 'B$' ).
tff(func_def_103,type,
sK25: ( 'B_set$' * 'B_set$' ) > 'B$' ).
tff(func_def_104,type,
sK26: ( 'B_bool_fun$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_105,type,
sK27: ( 'B_b_bool_fun_fun$' * 'B_b_bool_fun_fun$' ) > 'B$' ).
tff(func_def_106,type,
sK28: ( 'B_b_bool_fun_fun$' * 'B_b_bool_fun_fun$' ) > 'B$' ).
tff(func_def_107,type,
sK29: ( 'B_b_bool_fun_fun$' * 'B_set$' ) > 'B$' ).
tff(func_def_108,type,
sK30: ( 'B_b_bool_fun_fun$' * 'B_set$' ) > 'B$' ).
tff(func_def_109,type,
sK31: ( 'B_bool_fun$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_110,type,
sK32: ( 'B_set$' * 'B_set$' ) > 'B$' ).
tff(func_def_111,type,
sK33: ( 'B_set$' * 'B_set$' ) > 'B$' ).
tff(func_def_112,type,
sK34: ( 'B_set$' * 'B_b_bool_fun_fun$' ) > 'B$' ).
tff(func_def_113,type,
sK35: ( 'B_set$' * 'B_b_bool_fun_fun$' ) > 'B$' ).
tff(func_def_114,type,
sK36: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_115,type,
sK37: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_116,type,
sK38: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_117,type,
sK39: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_118,type,
sK40: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_119,type,
sK41: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_120,type,
sK42: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_121,type,
sK43: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_122,type,
sK44: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_123,type,
sK45: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_124,type,
sK46: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_125,type,
sK47: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_126,type,
sK48: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_127,type,
sK49: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_128,type,
sK50: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_129,type,
sK51: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_130,type,
sK52: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_131,type,
sK53: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_132,type,
sK54: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_133,type,
sK55: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_134,type,
sK56: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_135,type,
sK57: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_136,type,
sK58: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_137,type,
sK59: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_138,type,
sK60: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_139,type,
sK61: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_140,type,
sK62: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_141,type,
sK63: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_142,type,
sK64: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_143,type,
sK65: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_144,type,
sK66: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_145,type,
sK67: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_146,type,
sK68: ( 'B_bool_fun$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_147,type,
sK69: ( 'B_bool_fun$' * 'B_bool_fun$' ) > 'B$' ).
tff(func_def_148,type,
sK70: ( 'B_b_bool_fun_fun$' * 'B$' * 'B_set$' ) > 'B$' ).
tff(func_def_149,type,
sK71: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_150,type,
sK72: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_151,type,
sK73: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_152,type,
sK74: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_153,type,
sK75: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_154,type,
sK76: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_155,type,
sK77: 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_156,type,
sK78: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_157,type,
sK79: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_158,type,
sK80: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_159,type,
sK81: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_160,type,
sK82: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_161,type,
sK83: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_162,type,
sK84: 'B_set_b_set_b_set_fun_fun$' > 'B_set$' ).
tff(func_def_163,type,
sK85: ( 'B_set$' * 'B_set$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_164,type,
sK86: ( 'B_set$' * 'B_set$' * 'B_set$' ) > 'B_set$' ).
tff(func_def_165,type,
sK87: 'B_set$' > 'B$' ).
tff(func_def_166,type,
sK88: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_167,type,
sK89: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_168,type,
sK90: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_169,type,
sK91: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_170,type,
sK92: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_171,type,
sK93: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_172,type,
sK94: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_173,type,
sK95: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_174,type,
sK96: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_175,type,
sK97: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_176,type,
sK98: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_177,type,
sK99: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_178,type,
sK100: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_179,type,
sK101: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_180,type,
sK102: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_181,type,
sK103: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_182,type,
sK104: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_183,type,
sK105: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_184,type,
sK106: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_185,type,
sK107: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_186,type,
sK108: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_187,type,
sK109: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_188,type,
sK110: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_189,type,
sK111: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_190,type,
sK112: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_191,type,
sK113: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_192,type,
sK114: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_193,type,
sK115: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_194,type,
sK116: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_195,type,
sK117: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_196,type,
sK118: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_197,type,
sK119: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_198,type,
sK120: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_199,type,
sK121: 'B_bool_fun_b_set_fun$' > 'B_bool_fun$' ).
tff(func_def_200,type,
sK122: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_201,type,
sK123: 'B_set_b_bool_fun_fun$' > 'B_set$' ).
tff(func_def_202,type,
sK124: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_203,type,
sK125: 'B_bool_fun_b_bool_fun_fun$' > 'B_bool_fun$' ).
tff(func_def_204,type,
sK126: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_205,type,
sK127: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_206,type,
sK128: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_207,type,
sK129: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_208,type,
sK130: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_209,type,
sK131: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_210,type,
sK132: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_211,type,
sK133: 'B_set_b_set_fun$' > 'B_set$' ).
tff(func_def_212,type,
sK134: ( 'B_set$' * 'B_set$' ) > 'B$' ).
tff(pred_def_1,type,
'semilattice_neutr$': ( 'Bool_bool_bool_fun_fun$' * tlbool ) > $o ).
tff(pred_def_2,type,
'fun_app$i': ( 'B_set_bool_fun$' * 'B_set$' ) > $o ).
tff(pred_def_5,type,
'semilattice_neutr$b': ( 'B_set_b_set_b_set_fun_fun$' * 'B_set$' ) > $o ).
tff(pred_def_6,type,
'less_eq$b': ( tlbool * tlbool ) > $o ).
tff(pred_def_7,type,
'member$': ( 'B$' * 'B_set$' ) > $o ).
tff(pred_def_8,type,
'uminus$b': tlbool > $o ).
tff(pred_def_9,type,
'is_empty$': 'B_set$' > $o ).
tff(pred_def_10,type,
'semilattice_neutr$a': ( 'B_bool_fun_b_bool_fun_b_bool_fun_fun_fun$' * 'B_bool_fun$' ) > $o ).
tff(pred_def_11,type,
'is_singleton$': 'B_set$' > $o ).
tff(pred_def_12,type,
'fun_app$e': ( 'Bool_bool_fun$' * tlbool ) > $o ).
tff(pred_def_13,type,
'pairwise$': ( 'B_b_bool_fun_fun$' * 'B_set$' ) > $o ).
tff(pred_def_14,type,
'ordering_top$': ( 'B_bool_fun_b_bool_fun_bool_fun_fun$' * 'B_bool_fun_b_bool_fun_bool_fun_fun$' * 'B_bool_fun$' ) > $o ).
tff(pred_def_15,type,
'ordering_top$a': ( 'B_set_b_set_bool_fun_fun$' * 'B_set_b_set_bool_fun_fun$' * 'B_set$' ) > $o ).
tff(pred_def_16,type,
'fun_app$': ( 'B_bool_fun$' * 'B$' ) > $o ).
tff(pred_def_17,type,
'fun_app$l': ( 'B_bool_fun_bool_fun$' * 'B_bool_fun$' ) > $o ).
tff(pred_def_18,type,
'minus$b': ( tlbool * tlbool ) > $o ).
tff(pred_def_19,type,
'ordering_top_axioms$': ( 'B_set_b_set_bool_fun_fun$' * 'B_set$' ) > $o ).
tff(f2,conjecture,
'top$' = 'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('a$'),'bot$'))),'fun_app$b'('insert$'('a$'),'bot$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
tff(f3,negated_conjecture,
( ( ~ 'top$' ) = 'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('a$'),'bot$'))),'fun_app$b'('insert$'('a$'),'bot$')) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,axiom,
'a$' = 'b$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f5,axiom,
! [X0: 'B$',X1: 'B_set$'] : ( 'fun_app$b'('insert$'(X0),'fun_app$b'('fun_app$c'('minus$',X1),'fun_app$b'('insert$'(X0),'bot$'))) = 'fun_app$b'('insert$'(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
tff(f12,axiom,
! [X0: 'B_set$',X1: 'B$',X2: 'B_set$'] : ( 'fun_app$b'('fun_app$c'('sup$',X0),'fun_app$b'('insert$'(X1),X2)) = 'fun_app$b'('insert$'(X1),'fun_app$b'('fun_app$c'('sup$',X0),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
tff(f68,axiom,
! [X0: 'B$'] : ( 'fun_app$b'('insert$'(X0),'top$') = 'top$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
tff(f160,axiom,
! [X0: 'B_set$'] : ( 'fun_app$b'('fun_app$c'('sup$',X0),'bot$') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
tff(f167,axiom,
! [X0: 'B$',X1: 'B_set$'] : ( 'fun_app$b'('remove$'(X0),X1) = 'fun_app$b'('fun_app$c'('minus$',X1),'fun_app$b'('insert$'(X0),'bot$')) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
tff(f681,plain,
'top$' != 'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('a$'),'bot$'))),'fun_app$b'('insert$'('a$'),'bot$')),
inference(flattening,[],[f3]) ).
tff(f1119,plain,
'top$' != 'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('a$'),'bot$'))),'fun_app$b'('insert$'('a$'),'bot$')),
inference(cnf_transformation,[],[f681]) ).
tff(f1120,plain,
'a$' = 'b$',
inference(cnf_transformation,[],[f4]) ).
tff(f1121,plain,
! [X0: 'B$',X1: 'B_set$'] : ( 'fun_app$b'('insert$'(X0),'fun_app$b'('fun_app$c'('minus$',X1),'fun_app$b'('insert$'(X0),'bot$'))) = 'fun_app$b'('insert$'(X0),X1) ),
inference(cnf_transformation,[],[f5]) ).
tff(f1128,plain,
! [X2: 'B_set$',X0: 'B_set$',X1: 'B$'] : ( 'fun_app$b'('fun_app$c'('sup$',X0),'fun_app$b'('insert$'(X1),X2)) = 'fun_app$b'('insert$'(X1),'fun_app$b'('fun_app$c'('sup$',X0),X2)) ),
inference(cnf_transformation,[],[f12]) ).
tff(f1231,plain,
! [X0: 'B$'] : ( 'top$' = 'fun_app$b'('insert$'(X0),'top$') ),
inference(cnf_transformation,[],[f68]) ).
tff(f1393,plain,
! [X0: 'B_set$'] : ( 'fun_app$b'('fun_app$c'('sup$',X0),'bot$') = X0 ),
inference(cnf_transformation,[],[f160]) ).
tff(f1407,plain,
! [X0: 'B$',X1: 'B_set$'] : ( 'fun_app$b'('fun_app$c'('minus$',X1),'fun_app$b'('insert$'(X0),'bot$')) = 'fun_app$b'('remove$'(X0),X1) ),
inference(cnf_transformation,[],[f167]) ).
tff(f2233,plain,
'top$' != 'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('b$'),'bot$'))),'fun_app$b'('insert$'('b$'),'bot$')),
inference(definition_unfolding,[],[f1119,f1120,f1120]) ).
tff(f2769,plain,
! [X0: 'B$',X1: 'B_set$'] : ( 'fun_app$b'('insert$'(X0),X1) = 'fun_app$b'('insert$'(X0),'fun_app$b'('remove$'(X0),X1)) ),
inference(forward_demodulation,[],[f1121,f1407]) ).
tff(f2770,plain,
'top$' != 'fun_app$b'('insert$'('b$'),'fun_app$b'('fun_app$c'('sup$','fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('b$'),'bot$'))),'bot$')),
inference(forward_demodulation,[],[f2233,f1128]) ).
tff(f2773,plain,
'top$' != 'fun_app$b'('insert$'('b$'),'fun_app$b'('fun_app$c'('minus$','top$'),'fun_app$b'('insert$'('b$'),'bot$'))),
inference(forward_demodulation,[],[f2770,f1393]) ).
tff(f2774,plain,
'top$' != 'fun_app$b'('insert$'('b$'),'fun_app$b'('remove$'('b$'),'top$')),
inference(forward_demodulation,[],[f2773,f1407]) ).
tff(f2775,plain,
'top$' != 'fun_app$b'('insert$'('b$'),'top$'),
inference(forward_demodulation,[],[f2774,f2769]) ).
tff(f2776,plain,
$false,
inference(forward_subsumption_resolution,[],[f2775,f1231]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP322_1 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n026.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 12:57:11 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.53 % (2817674)Will run a generic schedule for satisfiability detection.
% 0.19/0.53 % (2817703)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=934497249:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.53 % (2817698)% WARNING: option uhcvi not known.
% 0.19/0.53 % (2817698)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1873274362:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.53 % (2817697)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=900268109_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.53 % (2817702)dis+10_1_sil=32000:sp=arity:random_seed=3404371438:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.53 % (2817700)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2568572524:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.53 % (2817705)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1690460038:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.53 % (2817706)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4144378370:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.53 % (2817703) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2817674-2817703"...
% 0.19/0.53 % (2817703)...printing done.
% 0.19/0.53 % (2817703)Refutation found. Thanks to Tanya!
% 0.19/0.53 % SZS status Theorem for theBenchmark
% 0.19/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.53 % (2817703)------------------------------
% 0.19/0.53 % (2817703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.53 % (2817703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.53 % (2817703)CaDiCaL version: 2.1.3
% 0.19/0.53 % (2817703)Termination reason: Refutation
% 0.19/0.53 % (2817703)Time elapsed: 0.030 s
% 0.19/0.53 % (2817703)Peak memory usage: 14 MB
% 0.19/0.53 % (2817703)Instructions burned: 99 (million)
% 0.19/0.53 % (2817674)Success in time 0.091 s
% 0.19/0.53 % Vampire exiting
%------------------------------------------------------------------------------