%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ITP353_1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 11:39:25 AM UTC 2026
% Result : Theorem 0.73s 0.49s
% Output : Refutation 0.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 14 ( 6 ~; 4 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 17 ( 3 atm; 0 fun; 11 num; 3 var)
% Number of types : 24 ( 21 usr; 2 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 56 ( 53 usr; 1 prp; 0-5 aty)
% Number of functors : 180 ( 179 usr; 28 con; 0-3 aty)
% Number of variables : 3 ( 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_fps_int_fps_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Int_fps$': $tType ).
tff(type_def_8,type,
'Real_ereal_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'Nat_fps$': $tType ).
tff(type_def_10,type,
'Ereal_bool_fun$': $tType ).
tff(type_def_11,type,
'Real_fls$': $tType ).
tff(type_def_12,type,
'Nat_real_real_fun_fun$': $tType ).
tff(type_def_13,type,
'Ereal$': $tType ).
tff(type_def_14,type,
'Nat_nat_fun$': $tType ).
tff(type_def_15,type,
'Nat$': $tType ).
tff(type_def_16,type,
'Real_fps_real_fps_fun$': $tType ).
tff(type_def_17,type,
'Ereal_fps$': $tType ).
tff(type_def_18,type,
'Real_fps$': $tType ).
tff(type_def_19,type,
'Ereal_set$': $tType ).
tff(type_def_20,type,
tlbool: $tType ).
tff(type_def_21,type,
'Real_list$': $tType ).
tff(type_def_22,type,
'Real_real_fun$': $tType ).
tff(type_def_23,type,
'Nat_real_fun$': $tType ).
tff(type_def_24,type,
'Nat_bool_fun$': $tType ).
tff(type_def_25,type,
'Real_bool_fun$': $tType ).
tff(func_def_0,type,
'max$': ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_1,type,
'max$a': $real > 'Real_real_fun$' ).
tff(func_def_2,type,
'zero$b': 'Real_fps$' ).
tff(func_def_3,type,
'fun_app$i': ( 'Real_fps_real_fps_fun$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_4,type,
'times$b': ( 'Ereal_fps$' * 'Ereal_fps$' ) > 'Ereal_fps$' ).
tff(func_def_5,type,
'inverse$c': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_6,type,
'one$e': 'Real_fls$' ).
tff(func_def_7,type,
'fps_nth$a': ( 'Ereal_fps$' * 'Nat$' ) > 'Ereal$' ).
tff(func_def_8,type,
'less$': 'Ereal$' > 'Ereal_bool_fun$' ).
tff(func_def_9,type,
'max$b': ( $int * $int ) > $int ).
tff(func_def_10,type,
'times$g': ( 'Real_fps$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_11,type,
'fun_app$f': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_12,type,
'c$a': $real ).
tff(func_def_13,type,
'fun_app$d': ( 'Real_ereal_bool_fun_fun$' * $real ) > 'Ereal_bool_fun$' ).
tff(func_def_14,type,
'size_ereal$': 'Ereal$' > 'Nat$' ).
tff(func_def_15,type,
'uua$': $real > 'Real_bool_fun$' ).
tff(func_def_16,type,
'n$': 'Nat$' ).
tff(func_def_17,type,
'u$': $real ).
tff(func_def_18,type,
'zero$a': 'Real_fls$' ).
tff(func_def_19,type,
'uu$': 'Ereal_set$' > 'Ereal_bool_fun$' ).
tff(func_def_20,type,
'zero$e': 'Nat$' ).
tff(func_def_21,type,
'fps_cutoff$': ( 'Nat$' * 'Ereal_fps$' ) > 'Ereal_fps$' ).
tff(func_def_22,type,
'fps_XD$': 'Int_fps_int_fps_fun$' ).
tff(func_def_23,type,
'fps_tan$': $real > 'Real_fps$' ).
tff(func_def_24,type,
'one$d': 'Int_fps$' ).
tff(func_def_25,type,
'ereal$': $real > 'Ereal$' ).
tff(func_def_26,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_27,type,
'times$f': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_28,type,
'c$': $real ).
tff(func_def_29,type,
'zero$d': 'Int_fps$' ).
tff(func_def_30,type,
'less_eq$': 'Ereal$' > 'Ereal_bool_fun$' ).
tff(func_def_31,type,
'uminus$': 'Ereal$' > 'Ereal$' ).
tff(func_def_32,type,
'fps_ln$': $real > 'Real_fps$' ).
tff(func_def_33,type,
'times$d': ( $int * $int ) > $int ).
tff(func_def_34,type,
'collect$': 'Ereal_bool_fun$' > 'Ereal_set$' ).
tff(func_def_35,type,
'zero$c': 'Ereal_fps$' ).
tff(func_def_36,type,
'fps_nth$c': ( 'Nat_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_37,type,
tltrue: tlbool ).
tff(func_def_38,type,
'times$c': ( 'Int_fps$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_39,type,
'infinity$': 'Ereal$' ).
tff(func_def_40,type,
'fps_Lambert_W$': 'Real_fps$' ).
tff(func_def_41,type,
'uub$': $int > 'Int_bool_fun$' ).
tff(func_def_42,type,
'one$b': 'Nat$' ).
tff(func_def_43,type,
'inverse$a': 'Ereal$' > 'Ereal$' ).
tff(func_def_44,type,
'times$': ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_45,type,
'fps_cutoff$a': ( 'Nat$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_46,type,
'fps_cutoff$b': ( 'Nat$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_47,type,
'radical$': ( 'Nat_real_real_fun_fun$' * 'Nat$' * 'Real_fps$' ) > 'Nat_real_fun$' ).
tff(func_def_48,type,
'fps_XDp$': $real > 'Real_fps_real_fps_fun$' ).
tff(func_def_49,type,
'uminus$a': 'Ereal_fps$' > 'Ereal_fps$' ).
tff(func_def_50,type,
'c$b': 'Ereal$' ).
tff(func_def_51,type,
'fps_deriv$': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_52,type,
'fps_XD$a': 'Real_fps_real_fps_fun$' ).
tff(func_def_53,type,
'inverse$d': 'Ereal_fps$' > 'Ereal_fps$' ).
tff(func_def_54,type,
'times$e': ( 'Nat_fps$' * 'Nat_fps$' ) > 'Nat_fps$' ).
tff(func_def_55,type,
'fps_nth$b': ( 'Int_fps$' * 'Nat$' ) > $int ).
tff(func_def_56,type,
'times$a': $real > 'Real_real_fun$' ).
tff(func_def_57,type,
'inverse$': 'Real_real_fun$' ).
tff(func_def_58,type,
'fun_app$h': ( 'Int_fps_int_fps_fun$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_59,type,
'less_eq$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_60,type,
tlfalse: tlbool ).
tff(func_def_61,type,
'nat$': $int > 'Nat$' ).
tff(func_def_62,type,
'fps_XDp$a': $int > 'Int_fps_int_fps_fun$' ).
tff(func_def_63,type,
'fun_app$c': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_64,type,
'fps_nth$': 'Real_fps$' > 'Nat_real_fun$' ).
tff(func_def_65,type,
'less$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_66,type,
'fun_app$g': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_67,type,
'l$': $real ).
tff(func_def_68,type,
'inverse$b': 'Real_fls$' > 'Real_fls$' ).
tff(func_def_69,type,
'uminus$b': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_70,type,
'fps_hypergeo$': ( 'Real_list$' * 'Real_list$' * $real ) > 'Real_fps$' ).
tff(func_def_71,type,
'one$c': 'Ereal_fps$' ).
tff(func_def_72,type,
'fps_inv$': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_73,type,
'one$': 'Real_fps$' ).
tff(func_def_74,type,
'one$a': 'Ereal$' ).
tff(func_def_75,type,
'zero$': 'Ereal$' ).
tff(func_def_86,type,
sK0: $real ).
tff(func_def_87,type,
sK1: $real > $real ).
tff(func_def_88,type,
sK2: $real > $real ).
tff(func_def_89,type,
sK3: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_90,type,
sK4: $real ).
tff(func_def_91,type,
sK5: ( 'Ereal_set$' * 'Real_ereal_bool_fun_fun$' ) > 'Ereal$' ).
tff(func_def_92,type,
sK6: ( 'Ereal_set$' * 'Real_ereal_bool_fun_fun$' ) > 'Ereal$' ).
tff(func_def_93,type,
sK7: ( 'Ereal_set$' * 'Real_ereal_bool_fun_fun$' * 'Ereal$' ) > $real ).
tff(func_def_94,type,
sK8: ( 'Real_ereal_bool_fun_fun$' * 'Ereal$' ) > $real ).
tff(func_def_95,type,
sK9: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_96,type,
sK10: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_97,type,
sK11: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_98,type,
sK12: ( $real * $real ) > $real ).
tff(func_def_99,type,
sK15: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_100,type,
sK16: ( 'Real_fps$' * 'Real_fps$' ) > 'Nat$' ).
tff(func_def_101,type,
sK17: ( 'Real_fps$' * 'Real_fps$' ) > 'Nat$' ).
tff(func_def_102,type,
sK18: 'Ereal_fps$' > 'Nat$' ).
tff(func_def_103,type,
sK19: 'Int_fps$' > 'Nat$' ).
tff(func_def_104,type,
sK20: 'Real_fps$' > 'Nat$' ).
tff(func_def_105,type,
sK21: 'Ereal$' > $real ).
tff(func_def_106,type,
sK22: 'Ereal$' > $real ).
tff(func_def_107,type,
sK23: 'Ereal$' > $real ).
tff(func_def_108,type,
sK32: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_109,type,
sK33: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_110,type,
sK34: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_111,type,
sK35: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_112,type,
sK36: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_113,type,
sK37: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_114,type,
sK64: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_115,type,
sK65: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_116,type,
sK66: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_117,type,
sK67: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_118,type,
sK68: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_119,type,
sK69: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_120,type,
sK70: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_121,type,
sK71: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_122,type,
sK72: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_123,type,
sK73: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_124,type,
sK74: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_125,type,
sK75: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_126,type,
sK76: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_127,type,
sK77: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_128,type,
sK78: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_129,type,
sK79: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_130,type,
sK80: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_131,type,
sK81: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_132,type,
sK82: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_133,type,
sK83: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_134,type,
sK84: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_135,type,
sK85: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_136,type,
sK86: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_137,type,
sK87: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_138,type,
sK88: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_139,type,
sK89: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_140,type,
sK90: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_141,type,
sK92: 'Ereal_bool_fun$' > 'Ereal$' ).
tff(func_def_142,type,
sK93: 'Ereal_bool_fun$' > $real ).
tff(func_def_143,type,
sK94: 'Ereal_bool_fun$' > 'Ereal$' ).
tff(func_def_144,type,
sK95: 'Ereal_bool_fun$' > $real ).
tff(func_def_145,type,
sK96: 'Ereal_fps$' > 'Nat$' ).
tff(func_def_146,type,
sK97: ( 'Ereal_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_147,type,
sK98: 'Int_fps$' > 'Nat$' ).
tff(func_def_148,type,
sK99: ( 'Int_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_149,type,
sK100: 'Real_fps$' > 'Nat$' ).
tff(func_def_150,type,
sK101: ( 'Real_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_151,type,
sK102: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_152,type,
sK103: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_153,type,
sK104: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_154,type,
sK105: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_155,type,
sK107: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_156,type,
sK108: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_157,type,
sK109: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_158,type,
sK110: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_159,type,
sK113: ( 'Ereal$' * 'Ereal$' * tlbool ) > $real ).
tff(func_def_160,type,
sK114: ( 'Ereal$' * 'Ereal$' * tlbool ) > $real ).
tff(func_def_161,type,
sK115: ( 'Ereal$' * 'Ereal$' * tlbool ) > 'Ereal$' ).
tff(func_def_162,type,
sK116: ( 'Ereal$' * 'Ereal$' * tlbool ) > 'Ereal$' ).
tff(func_def_163,type,
sK117: ( 'Ereal$' * 'Ereal$' * tlbool ) > $real ).
tff(func_def_164,type,
sK118: ( 'Ereal$' * 'Ereal$' * tlbool ) > $real ).
tff(func_def_165,type,
sK123: ( 'Ereal$' * $real ) > $real ).
tff(func_def_166,type,
sK134: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_167,type,
sK135: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_168,type,
sK136: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_169,type,
sK137: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_170,type,
sK138: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_171,type,
sK139: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_172,type,
sK140: 'Int_fps$' > 'Int_fps$' ).
tff(func_def_173,type,
sK141: 'Int_fps$' > $int ).
tff(func_def_174,type,
sK142: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_175,type,
sK143: 'Real_fps$' > $real ).
tff(func_def_176,type,
sK144: 'Int_fps$' > 'Int_fps$' ).
tff(func_def_177,type,
sK145: 'Int_fps$' > $int ).
tff(func_def_178,type,
sK146: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_179,type,
sK147: 'Real_fps$' > $real ).
tff(func_def_180,type,
sK148: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_181,type,
sK149: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_182,type,
sK150: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_183,type,
sK151: 'Ereal_set$' > 'Ereal$' ).
tff(func_def_184,type,
sK152: ( 'Ereal_set$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_185,type,
sK153: 'Ereal_set$' > 'Ereal$' ).
tff(func_def_186,type,
sK154: ( 'Ereal_set$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_187,type,
sK155: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_188,type,
sK156: 'Ereal$' > $real ).
tff(pred_def_1,type,
'fun_app$e': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_2,type,
'fun_app$a': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_3,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_4,type,
'member$': ( 'Ereal$' * 'Ereal_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$b': ( 'Ereal_bool_fun$' * 'Ereal$' ) > $o ).
tff(pred_def_10,type,
sP13: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_12,type,
sP24: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_13,type,
sP25: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_14,type,
sP26: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_15,type,
sP27: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_16,type,
sP28: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_17,type,
sP29: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_18,type,
sP30: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_20,type,
sP38: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_21,type,
sP39: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_22,type,
sP40: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_23,type,
sP41: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_24,type,
sP42: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_25,type,
sP43: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_26,type,
sP44: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_27,type,
sP45: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_28,type,
sP46: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_29,type,
sP47: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_30,type,
sP48: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_31,type,
sP49: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_32,type,
sP50: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_33,type,
sP51: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_34,type,
sP52: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_35,type,
sP53: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_36,type,
sP54: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_37,type,
sP55: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_38,type,
sP56: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_39,type,
sP57: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_40,type,
sP58: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_41,type,
sP59: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_42,type,
sP60: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_43,type,
sP61: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_44,type,
sP62: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_47,type,
sP106: ( $real * $real * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_48,type,
sP111: ( $real * $real * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_50,type,
sP119: ( $real * tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_51,type,
sP120: ( 'Ereal$' * tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_52,type,
sP121: ( 'Ereal$' * tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_53,type,
sP122: ( $real * $real * tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_54,type,
sP124: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_55,type,
sP125: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_56,type,
sP126: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_57,type,
sP127: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_58,type,
sP128: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_59,type,
sP129: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_60,type,
sP130: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_61,type,
sP131: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_62,type,
sP132: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(f4,conjecture,
'ereal$'('fun_app$c'('inverse$','c$')) = 'inverse$a'('ereal$'('c$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture3) ).
tff(f5,negated_conjecture,
( ( ~ 'ereal$'('fun_app$c'('inverse$','c$')) ) = 'inverse$a'('ereal$'('c$')) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f7,axiom,
$less(0/1,'c$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f21,axiom,
! [X0: $real] :
( ( ( X0 = 0/1 )
=> ( 'inverse$a'('ereal$'(X0)) = 'infinity$' ) )
& ( ( X0 != 0/1 )
=> ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
tff(f747,plain,
'ereal$'('fun_app$c'('inverse$','c$')) != 'inverse$a'('ereal$'('c$')),
inference(flattening,[],[f5]) ).
tff(f765,plain,
! [X0: $real] :
( ( ( 'inverse$a'('ereal$'(X0)) = 'infinity$' )
| ( 0/1 != X0 ) )
& ( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0/1 = X0 ) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f1167,plain,
'ereal$'('fun_app$c'('inverse$','c$')) != 'inverse$a'('ereal$'('c$')),
inference(cnf_transformation,[],[f747]) ).
tff(f1169,plain,
$less(0/1,'c$'),
inference(cnf_transformation,[],[f7]) ).
tff(f1187,plain,
! [X0: $real] :
( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0/1 = X0 ) ),
inference(cnf_transformation,[],[f765]) ).
tff(f6037,plain,
( ( 'inverse$a'('ereal$'('c$')) != 'inverse$a'('ereal$'('c$')) )
| ( 'c$' = 0/1 ) ),
inference(superposition,[],[f1167,f1187]) ).
tff(f6065,plain,
'c$' = 0/1,
inference(trivial_inequality_removal,[],[f6037]) ).
tff(f6086,plain,
$less(0/1,0/1),
inference(superposition,[],[f1169,f6065]) ).
tff(f6098,plain,
$false,
inference(evaluation,[],[f6086]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP353_1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.31 % Computer : n012.cluster.edu
% 0.06/0.31 % Model : x86_64 x86_64
% 0.06/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.31 % Memory : 8046.5625MB
% 0.06/0.31 % OS : Linux 6.8.0-71-generic
% 0.06/0.31 % CPULimit : 300
% 0.06/0.31 % WCLimit : 300
% 0.06/0.31 % DateTime : Sun Sep 27 12:55:04 UTC 2026
% 0.06/0.31 % CPUTime :
% 0.06/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.06/0.34 Running first-order model finding
% 0.06/0.34 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
% 0.73/0.49 % (2366415)Will run a generic schedule for satisfiability detection.
% 0.73/0.49 % (2366426)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=211725645:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.73/0.49 % (2366421)% WARNING: option uhcvi not known.
% 0.73/0.49 % (2366422)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3788437765:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.73/0.49 % (2366423)dis+10_1_sil=32000:sp=arity:random_seed=3468960766:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.73/0.49 % (2366420)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3118766889_2999 on theBenchmark for (2999ds/0Mi)
% 0.73/0.49 % (2366424)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1884451553:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.73/0.49 % (2366421)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2416857372:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.73/0.49 % (2366425)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3686753798:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.49 % (2366420)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.73/0.49 % (2366420)Terminated due to inappropriate strategy.
% 0.73/0.49 % (2366420)------------------------------
% 0.73/0.49 % (2366420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366420)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366420)Termination reason: Inappropriate
% 0.73/0.49 % (2366420)Time elapsed: 0.033 s
% 0.73/0.49 % (2366420)Peak memory usage: 12 MB
% 0.73/0.49 % (2366420)Instructions burned: 72 (million)
% 0.73/0.49 % (2366420)------------------------------
% 0.73/0.49 % (2366420)------------------------------
% 0.73/0.49 % (2366426)Instruction limit reached!
% 0.73/0.49 % (2366426)------------------------------
% 0.73/0.49 % (2366426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366426)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366426)Termination reason: Instruction limit
% 0.73/0.49 % (2366426)Termination phase: Saturation
% 0.73/0.49 % (2366426)Time elapsed: 0.051 s
% 0.73/0.49 % (2366426)Peak memory usage: 15 MB
% 0.73/0.49 % (2366426)Instructions burned: 159 (million)
% 0.73/0.49 % (2366423)Instruction limit reached!
% 0.73/0.49 % (2366423)------------------------------
% 0.73/0.49 % (2366423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366423)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366423)Termination reason: Instruction limit
% 0.73/0.49 % (2366423)Termination phase: Saturation
% 0.73/0.49 % (2366423)Time elapsed: 0.052 s
% 0.73/0.49 % (2366423)Peak memory usage: 13 MB
% 0.73/0.49 % (2366423)Instructions burned: 104 (million)
% 0.73/0.49 % (2366424)Instruction limit reached!
% 0.73/0.49 % (2366424)------------------------------
% 0.73/0.49 % (2366424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366424)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366424)Termination reason: Instruction limit
% 0.73/0.49 % (2366424)Termination phase: Saturation
% 0.73/0.49 % (2366424)Time elapsed: 0.053 s
% 0.73/0.49 % (2366424)Peak memory usage: 14 MB
% 0.73/0.49 % (2366424)Instructions burned: 116 (million)
% 0.73/0.49 % (2366434)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=281774:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.73/0.49 % (2366435)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1941871064:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.73/0.49 % (2366425)Instruction limit reached!
% 0.73/0.49 % (2366425)------------------------------
% 0.73/0.49 % (2366425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366425)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366425)Termination reason: Instruction limit
% 0.73/0.49 % (2366425)Termination phase: Saturation
% 0.73/0.49 % (2366425)Time elapsed: 0.066 s
% 0.73/0.49 % (2366425)Peak memory usage: 14 MB
% 0.73/0.49 % (2366425)Instructions burned: 131 (million)
% 0.73/0.49 % (2366436)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3888789246:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.73/0.49 % (2366437)ott-21_1_sil=16000:fs=off:random_seed=3804404076:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.73/0.49 % (2366434)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.73/0.49 % (2366434)Terminated due to inappropriate strategy.
% 0.73/0.49 % (2366434)------------------------------
% 0.73/0.49 % (2366434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366434)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366434)Termination reason: Inappropriate
% 0.73/0.49 % (2366434)Time elapsed: 0.030 s
% 0.73/0.49 % (2366434)Peak memory usage: 12 MB
% 0.73/0.49 % (2366434)Instructions burned: 61 (million)
% 0.73/0.49 % (2366434)------------------------------
% 0.73/0.49 % (2366434)------------------------------
% 0.73/0.49 % (2366440)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=4243550278:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.73/0.49 % (2366435)Instruction limit reached!
% 0.73/0.49 % (2366435)------------------------------
% 0.73/0.49 % (2366435)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366435)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366435)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366435)Termination reason: Instruction limit
% 0.73/0.49 % (2366435)Termination phase: Saturation
% 0.73/0.49 % (2366435)Time elapsed: 0.040 s
% 0.73/0.49 % (2366435)Peak memory usage: 14 MB
% 0.73/0.49 % (2366435)Instructions burned: 132 (million)
% 0.73/0.49 % (2366421) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2366415-2366421"...
% 0.73/0.49 % (2366443)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=56785434:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.73/0.49 % (2366421)...printing done.
% 0.73/0.49 % (2366421)Refutation found. Thanks to Tanya!
% 0.73/0.49 % SZS status Theorem for theBenchmark
% 0.73/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.73/0.49 % (2366421)------------------------------
% 0.73/0.49 % (2366421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.73/0.49 % (2366421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.73/0.49 % (2366421)CaDiCaL version: 2.1.3
% 0.73/0.49 % (2366421)Termination reason: Refutation
% 0.73/0.49 % (2366421)Time elapsed: 0.108 s
% 0.73/0.49 % (2366421)Peak memory usage: 15 MB
% 0.73/0.49 % (2366421)Instructions burned: 196 (million)
% 0.73/0.49 % (2366415)Success in time 0.147 s
% 0.73/0.49 % Vampire exiting
%------------------------------------------------------------------------------