TSTP Solution File: ITP376_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:15:06 EDT 2024
% Result : Theorem 3.92s 0.97s
% Output : Refutation 3.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1790
% Syntax : Number of formulae : 4606 ( 943 unt; 372 typ; 0 def)
% Number of atoms : 12840 (1590 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 13999 (5393 ~;5333 |;1624 &)
% ( 961 <=>; 688 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number arithmetic : 11065 (4252 atm;1378 fun;3005 num;2430 var)
% Number of types : 36 ( 33 usr; 2 ari)
% Number of type conns : 413 ( 317 >; 96 *; 0 +; 0 <<)
% Number of predicates : 859 ( 854 usr; 826 prp; 0-3 aty)
% Number of functors : 330 ( 309 usr; 40 con; 0-3 aty)
% Number of variables : 9314 (8501 !; 813 ?;9314 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Real_real_bool_fun_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Real_num_fun$': $tType ).
tff(type_def_8,type,
'Nat_nat_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'A_ltln_list$': $tType ).
tff(type_def_10,type,
'Num_num_fun$': $tType ).
tff(type_def_11,type,
'Nat_enat_fun$': $tType ).
tff(type_def_12,type,
'Int_real_fun$': $tType ).
tff(type_def_13,type,
'Num_enat_fun$': $tType ).
tff(type_def_14,type,
'Enat$': $tType ).
tff(type_def_15,type,
'Int_int_fun$': $tType ).
tff(type_def_16,type,
'Enat_int_fun$': $tType ).
tff(type_def_17,type,
'Num_bool_fun$': $tType ).
tff(type_def_18,type,
'Nat_nat_fun$': $tType ).
tff(type_def_19,type,
'Num_real_fun$': $tType ).
tff(type_def_20,type,
'Nat$': $tType ).
tff(type_def_21,type,
'Num$': $tType ).
tff(type_def_22,type,
tlbool: $tType ).
tff(type_def_23,type,
'Enat_bool_fun$': $tType ).
tff(type_def_24,type,
'Int_enat_fun$': $tType ).
tff(type_def_25,type,
'Nat_num_fun$': $tType ).
tff(type_def_26,type,
'Enat_num_fun$': $tType ).
tff(type_def_27,type,
'Nat_real_fun$': $tType ).
tff(type_def_28,type,
'Real_int_fun$': $tType ).
tff(type_def_29,type,
'Enat_enat_bool_fun_fun$': $tType ).
tff(type_def_30,type,
'Int_int_bool_fun_fun$': $tType ).
tff(type_def_31,type,
'Nat_bool_fun$': $tType ).
tff(type_def_32,type,
'Real_bool_fun$': $tType ).
tff(type_def_33,type,
'Real_set$': $tType ).
tff(type_def_34,type,
'Nat_int_fun$': $tType ).
tff(type_def_35,type,
'Int_num_fun$': $tType ).
tff(type_def_36,type,
'Num_int_fun$': $tType ).
tff(type_def_37,type,
'Num_num_bool_fun_fun$': $tType ).
tff(func_def_0,type,
'less_eq$': 'Num_num_bool_fun_fun$' ).
tff(func_def_1,type,
'less_eq$a': 'Enat_enat_bool_fun_fun$' ).
tff(func_def_2,type,
'fun_app$p': ( 'Int_int_fun$' * $int ) > $int ).
tff(func_def_3,type,
'dbl$': 'Int_int_fun$' ).
tff(func_def_4,type,
'zero$': 'Nat$' ).
tff(func_def_5,type,
'zero$a': 'Enat$' ).
tff(func_def_6,type,
'numeral$b': 'Num_real_fun$' ).
tff(func_def_7,type,
'power$c': $real > 'Nat_real_fun$' ).
tff(func_def_8,type,
'n$': 'Nat$' ).
tff(func_def_9,type,
'size$a': 'Num$' > 'Nat$' ).
tff(func_def_10,type,
'of_nat$a': 'Nat_nat_fun$' ).
tff(func_def_11,type,
'fun_app$z': ( 'Int_real_fun$' * $int ) > $real ).
tff(func_def_12,type,
'times$b': $int > 'Int_int_fun$' ).
tff(func_def_13,type,
'fun_app$v': ( 'Int_num_fun$' * $int ) > 'Num$' ).
tff(func_def_14,type,
'fun_app$f': ( 'Num_num_bool_fun_fun$' * 'Num$' ) > 'Num_bool_fun$' ).
tff(func_def_15,type,
'ys$': 'A_ltln_list$' ).
tff(func_def_16,type,
'of_nat$': 'Nat_int_fun$' ).
tff(func_def_17,type,
'times$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_18,type,
'less$': 'Num_num_bool_fun_fun$' ).
tff(func_def_19,type,
'dbl$a': $real > $real ).
tff(func_def_20,type,
'less_eq$b': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_21,type,
tltrue: tlbool ).
tff(func_def_22,type,
'fun_app$w': ( 'Enat_num_fun$' * 'Enat$' ) > 'Num$' ).
tff(func_def_23,type,
'uu$': 'Real_set$' > 'Real_bool_fun$' ).
tff(func_def_24,type,
'fun_app$j': ( 'Num_real_fun$' * 'Num$' ) > $real ).
tff(func_def_25,type,
'fun_app$r': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).
tff(func_def_26,type,
'fun_app$a': ( 'Nat_int_fun$' * 'Nat$' ) > $int ).
tff(func_def_27,type,
'pow$': 'Num$' > 'Num_num_fun$' ).
tff(func_def_28,type,
'numeral$c': 'Num$' > 'Nat$' ).
tff(func_def_29,type,
'fun_app$m': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_30,type,
'less$a': 'Enat_enat_bool_fun_fun$' ).
tff(func_def_31,type,
'power$a': $int > 'Nat_int_fun$' ).
tff(func_def_32,type,
'fun_app$x': ( 'Real_num_fun$' * $real ) > 'Num$' ).
tff(func_def_33,type,
'numeral$': 'Num_int_fun$' ).
tff(func_def_34,type,
'power$b': 'Enat$' > 'Nat_enat_fun$' ).
tff(func_def_35,type,
'numeral$a': 'Num_enat_fun$' ).
tff(func_def_36,type,
'fun_app$s': ( 'Real_real_bool_fun_fun$' * $real ) > 'Real_bool_fun$' ).
tff(func_def_37,type,
'fun_app$i': ( 'Num_enat_fun$' * 'Num$' ) > 'Enat$' ).
tff(func_def_38,type,
'times$c': ( 'Enat$' * 'Enat$' ) > 'Enat$' ).
tff(func_def_39,type,
'fun_app$t': ( 'Enat_int_fun$' * 'Enat$' ) > $int ).
tff(func_def_40,type,
'one$': 'Num$' ).
tff(func_def_41,type,
'fun_app$d': ( 'Num_int_fun$' * 'Num$' ) > $int ).
tff(func_def_42,type,
'less$b': 'Nat_nat_bool_fun_fun$' ).
tff(func_def_43,type,
tlfalse: tlbool ).
tff(func_def_44,type,
'nat$': $int > 'Nat$' ).
tff(func_def_45,type,
'fun_app$u': ( 'Real_int_fun$' * $real ) > $int ).
tff(func_def_46,type,
'fun_app$o': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).
tff(func_def_47,type,
'fun_app$c': ( 'Num_num_fun$' * 'Num$' ) > 'Num$' ).
tff(func_def_48,type,
'fun_app$l': ( 'Nat_enat_fun$' * 'Nat$' ) > 'Enat$' ).
tff(func_def_49,type,
'size$': 'A_ltln_list$' > 'Nat$' ).
tff(func_def_50,type,
'of_nat$c': 'Nat_enat_fun$' ).
tff(func_def_51,type,
'fun_app$k': ( 'Nat_num_fun$' * 'Nat$' ) > 'Num$' ).
tff(func_def_52,type,
'fun_app$h': ( 'Enat_enat_bool_fun_fun$' * 'Enat$' ) > 'Enat_bool_fun$' ).
tff(func_def_53,type,
'times$a': 'Num$' > 'Num_num_fun$' ).
tff(func_def_54,type,
'of_nat$b': 'Nat_real_fun$' ).
tff(func_def_55,type,
'fun_app$y': ( 'Int_enat_fun$' * $int ) > 'Enat$' ).
tff(func_def_56,type,
'times$d': ( $real * $real ) > $real ).
tff(func_def_57,type,
'collect$': 'Real_bool_fun$' > 'Real_set$' ).
tff(func_def_58,type,
'power$': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_59,type,
'bit0$': 'Num_num_fun$' ).
tff(func_def_60,type,
'fun_app$b': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_74,type,
sK24: ( $real * $real ) > 'Nat$' ).
tff(func_def_75,type,
sK25: $int > 'Nat$' ).
tff(func_def_76,type,
sK26: $int > 'Nat$' ).
tff(func_def_77,type,
sK27: 'Nat$' > 'Nat$' ).
tff(func_def_78,type,
sK28: 'Nat$' > 'Nat$' ).
tff(func_def_79,type,
sK29: $int > 'Nat$' ).
tff(func_def_80,type,
sK30: $int > 'Nat$' ).
tff(func_def_81,type,
sK31: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_82,type,
sK32: 'Nat$' > 'Nat$' ).
tff(func_def_83,type,
sK33: 'Real_set$' > $real ).
tff(func_def_84,type,
sK34: ( 'Real_set$' * $real ) > $real ).
tff(func_def_85,type,
sK35: ( 'Real_set$' * $real ) > $real ).
tff(func_def_86,type,
sK36: 'Nat$' > 'Nat$' ).
tff(func_def_87,type,
sK37: $real > 'Nat$' ).
tff(func_def_88,type,
sK38: ( $real * 'Nat$' ) > $real ).
tff(func_def_89,type,
sK39: 'Nat$' > 'Nat$' ).
tff(func_def_90,type,
sK40: ( $real * $real ) > 'Nat$' ).
tff(func_def_91,type,
sK41: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_92,type,
sK42: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_93,type,
sK43: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_94,type,
sK44: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_95,type,
sK45: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_96,type,
sK46: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_97,type,
sK47: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_98,type,
sK48: ( 'Nat$' * $real ) > $real ).
tff(func_def_99,type,
sK49: ( 'Nat$' * $real ) > $real ).
tff(func_def_100,type,
sK50: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_101,type,
sK51: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_102,type,
sK52: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_103,type,
sK53: 'Enat_bool_fun$' > 'Enat$' ).
tff(func_def_104,type,
sK54: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_105,type,
sK55: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_106,type,
sK56: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_107,type,
sK57: ( 'Nat$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_108,type,
sK58: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_109,type,
sK59: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_110,type,
sK60: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_111,type,
sK61: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_112,type,
sK62: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_113,type,
sK63: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_114,type,
sK64: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_115,type,
sK65: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_116,type,
sK66: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_117,type,
sK67: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_118,type,
sK68: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_119,type,
sK69: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_120,type,
sK70: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_121,type,
sK71: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_122,type,
sK72: ( 'Nat_bool_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_123,type,
sK73: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_124,type,
sK74: ( 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_125,type,
sK75: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_126,type,
sK76: ( 'Nat$' * 'Nat$' * 'Nat_bool_fun$' ) > 'Nat$' ).
tff(func_def_127,type,
sK77: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_128,type,
sK78: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_129,type,
sK79: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_130,type,
sK80: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_131,type,
sK81: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_132,type,
sK82: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_133,type,
sK83: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_134,type,
sK84: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_135,type,
sK85: 'Nat_nat_bool_fun_fun$' > 'Nat$' ).
tff(func_def_136,type,
sK86: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_137,type,
sK87: 'Nat_real_fun$' > 'Nat$' ).
tff(func_def_138,type,
sK88: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_139,type,
sK89: 'Nat_int_fun$' > 'Nat$' ).
tff(func_def_140,type,
sK90: 'Nat_enat_fun$' > 'Nat$' ).
tff(func_def_141,type,
sK91: 'Nat_enat_fun$' > 'Nat$' ).
tff(func_def_142,type,
sK92: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_143,type,
sK93: 'Nat_num_fun$' > 'Nat$' ).
tff(func_def_144,type,
sK94: 'Real_real_bool_fun_fun$' > $real ).
tff(func_def_145,type,
sK95: 'Real_real_bool_fun_fun$' > $real ).
tff(func_def_146,type,
sK96: 'Real_real_bool_fun_fun$' > $real ).
tff(func_def_147,type,
sK97: 'Real_real_bool_fun_fun$' > $real ).
tff(func_def_148,type,
sK98: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_149,type,
sK99: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_150,type,
sK100: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_151,type,
sK101: 'Int_int_bool_fun_fun$' > $int ).
tff(func_def_152,type,
sK102: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_153,type,
sK103: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_154,type,
sK104: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_155,type,
sK105: 'Enat_enat_bool_fun_fun$' > 'Enat$' ).
tff(func_def_156,type,
sK106: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_157,type,
sK107: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_158,type,
sK108: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_159,type,
sK109: 'Num_num_bool_fun_fun$' > 'Num$' ).
tff(func_def_160,type,
sK110: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_161,type,
sK111: 'Nat_nat_fun$' > 'Nat$' ).
tff(func_def_162,type,
sK112: 'Int_real_fun$' > $int ).
tff(func_def_163,type,
sK113: 'Int_real_fun$' > $int ).
tff(func_def_164,type,
sK114: 'Int_enat_fun$' > $int ).
tff(func_def_165,type,
sK115: 'Int_enat_fun$' > $int ).
tff(func_def_166,type,
sK116: 'Int_num_fun$' > $int ).
tff(func_def_167,type,
sK117: 'Int_num_fun$' > $int ).
tff(func_def_168,type,
sK118: 'Int_int_fun$' > $int ).
tff(func_def_169,type,
sK119: 'Int_int_fun$' > $int ).
tff(func_def_170,type,
sK120: 'Int_real_fun$' > $int ).
tff(func_def_171,type,
sK121: 'Int_real_fun$' > $int ).
tff(func_def_172,type,
sK122: 'Int_int_fun$' > $int ).
tff(func_def_173,type,
sK123: 'Int_int_fun$' > $int ).
tff(func_def_174,type,
sK124: 'Int_enat_fun$' > $int ).
tff(func_def_175,type,
sK125: 'Int_enat_fun$' > $int ).
tff(func_def_176,type,
sK126: 'Int_num_fun$' > $int ).
tff(func_def_177,type,
sK127: 'Int_num_fun$' > $int ).
tff(func_def_178,type,
sK128: 'Int_real_fun$' > $int ).
tff(func_def_179,type,
sK129: 'Int_real_fun$' > $int ).
tff(func_def_180,type,
sK130: 'Int_enat_fun$' > $int ).
tff(func_def_181,type,
sK131: 'Int_enat_fun$' > $int ).
tff(func_def_182,type,
sK132: 'Int_num_fun$' > $int ).
tff(func_def_183,type,
sK133: 'Int_num_fun$' > $int ).
tff(func_def_184,type,
sK134: 'Int_int_fun$' > $int ).
tff(func_def_185,type,
sK135: 'Int_int_fun$' > $int ).
tff(func_def_186,type,
sK136: 'Int_real_fun$' > $int ).
tff(func_def_187,type,
sK137: 'Int_real_fun$' > $int ).
tff(func_def_188,type,
sK138: 'Int_int_fun$' > $int ).
tff(func_def_189,type,
sK139: 'Int_int_fun$' > $int ).
tff(func_def_190,type,
sK140: 'Int_enat_fun$' > $int ).
tff(func_def_191,type,
sK141: 'Int_enat_fun$' > $int ).
tff(func_def_192,type,
sK142: 'Int_num_fun$' > $int ).
tff(func_def_193,type,
sK143: 'Int_num_fun$' > $int ).
tff(func_def_194,type,
sK144: 'Int_real_fun$' > $int ).
tff(func_def_195,type,
sK145: 'Int_real_fun$' > $int ).
tff(func_def_196,type,
sK146: 'Int_real_fun$' > $int ).
tff(func_def_197,type,
sK147: 'Int_real_fun$' > $int ).
tff(func_def_198,type,
sK148: 'Int_enat_fun$' > $int ).
tff(func_def_199,type,
sK149: 'Int_enat_fun$' > $int ).
tff(func_def_200,type,
sK150: 'Int_num_fun$' > $int ).
tff(func_def_201,type,
sK151: 'Int_num_fun$' > $int ).
tff(func_def_202,type,
sK152: 'Int_enat_fun$' > $int ).
tff(func_def_203,type,
sK153: 'Int_enat_fun$' > $int ).
tff(func_def_204,type,
sK154: 'Int_num_fun$' > $int ).
tff(func_def_205,type,
sK155: 'Int_num_fun$' > $int ).
tff(func_def_206,type,
sK156: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_207,type,
sK157: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_208,type,
sK158: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_209,type,
sK159: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_210,type,
sK160: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_211,type,
sK161: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_212,type,
sK162: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_213,type,
sK163: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_214,type,
sK164: 'Num_real_fun$' > 'Num$' ).
tff(func_def_215,type,
sK165: 'Num_real_fun$' > 'Num$' ).
tff(func_def_216,type,
sK166: 'Num_real_fun$' > 'Num$' ).
tff(func_def_217,type,
sK167: 'Num_real_fun$' > 'Num$' ).
tff(func_def_218,type,
sK168: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_219,type,
sK169: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_220,type,
sK170: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_221,type,
sK171: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_222,type,
sK172: 'Num_num_fun$' > 'Num$' ).
tff(func_def_223,type,
sK173: 'Num_num_fun$' > 'Num$' ).
tff(func_def_224,type,
sK174: 'Num_num_fun$' > 'Num$' ).
tff(func_def_225,type,
sK175: 'Num_num_fun$' > 'Num$' ).
tff(func_def_226,type,
sK176: 'Int_int_fun$' > $int ).
tff(func_def_227,type,
sK177: 'Int_int_fun$' > $int ).
tff(func_def_228,type,
sK178: 'Int_int_fun$' > $int ).
tff(func_def_229,type,
sK179: 'Int_int_fun$' > $int ).
tff(func_def_230,type,
sK180: 'Num_int_fun$' > 'Num$' ).
tff(func_def_231,type,
sK181: 'Num_int_fun$' > 'Num$' ).
tff(func_def_232,type,
sK182: 'Num_int_fun$' > 'Num$' ).
tff(func_def_233,type,
sK183: 'Num_int_fun$' > 'Num$' ).
tff(func_def_234,type,
sK184: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_235,type,
sK185: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_236,type,
sK186: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_237,type,
sK187: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_238,type,
sK188: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_239,type,
sK189: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_240,type,
sK190: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_241,type,
sK191: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_242,type,
sK192: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_243,type,
sK193: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_244,type,
sK194: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_245,type,
sK195: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_246,type,
sK196: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_247,type,
sK197: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_248,type,
sK198: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_249,type,
sK199: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_250,type,
sK200: 'Num_real_fun$' > 'Num$' ).
tff(func_def_251,type,
sK201: 'Num_real_fun$' > 'Num$' ).
tff(func_def_252,type,
sK202: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_253,type,
sK203: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_254,type,
sK204: 'Num_num_fun$' > 'Num$' ).
tff(func_def_255,type,
sK205: 'Num_num_fun$' > 'Num$' ).
tff(func_def_256,type,
sK206: 'Num_int_fun$' > 'Num$' ).
tff(func_def_257,type,
sK207: 'Num_int_fun$' > 'Num$' ).
tff(func_def_258,type,
sK208: 'Num_real_fun$' > 'Num$' ).
tff(func_def_259,type,
sK209: 'Num_real_fun$' > 'Num$' ).
tff(func_def_260,type,
sK210: 'Num_int_fun$' > 'Num$' ).
tff(func_def_261,type,
sK211: 'Num_int_fun$' > 'Num$' ).
tff(func_def_262,type,
sK212: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_263,type,
sK213: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_264,type,
sK214: 'Num_num_fun$' > 'Num$' ).
tff(func_def_265,type,
sK215: 'Num_num_fun$' > 'Num$' ).
tff(func_def_266,type,
sK216: 'Num_real_fun$' > 'Num$' ).
tff(func_def_267,type,
sK217: 'Num_real_fun$' > 'Num$' ).
tff(func_def_268,type,
sK218: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_269,type,
sK219: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_270,type,
sK220: 'Num_num_fun$' > 'Num$' ).
tff(func_def_271,type,
sK221: 'Num_num_fun$' > 'Num$' ).
tff(func_def_272,type,
sK222: 'Num_int_fun$' > 'Num$' ).
tff(func_def_273,type,
sK223: 'Num_int_fun$' > 'Num$' ).
tff(func_def_274,type,
sK224: 'Num_real_fun$' > 'Num$' ).
tff(func_def_275,type,
sK225: 'Num_real_fun$' > 'Num$' ).
tff(func_def_276,type,
sK226: 'Num_int_fun$' > 'Num$' ).
tff(func_def_277,type,
sK227: 'Num_int_fun$' > 'Num$' ).
tff(func_def_278,type,
sK228: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_279,type,
sK229: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_280,type,
sK230: 'Num_num_fun$' > 'Num$' ).
tff(func_def_281,type,
sK231: 'Num_num_fun$' > 'Num$' ).
tff(func_def_282,type,
sK232: 'Real_int_fun$' > $real ).
tff(func_def_283,type,
sK233: 'Real_int_fun$' > $real ).
tff(func_def_284,type,
sK234: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_285,type,
sK235: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_286,type,
sK236: 'Int_int_fun$' > $int ).
tff(func_def_287,type,
sK237: 'Int_int_fun$' > $int ).
tff(func_def_288,type,
sK238: 'Num_int_fun$' > 'Num$' ).
tff(func_def_289,type,
sK239: 'Num_int_fun$' > 'Num$' ).
tff(func_def_290,type,
sK240: 'Real_int_fun$' > $real ).
tff(func_def_291,type,
sK241: 'Real_int_fun$' > $real ).
tff(func_def_292,type,
sK242: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_293,type,
sK243: 'Enat_int_fun$' > 'Enat$' ).
tff(func_def_294,type,
sK244: 'Int_int_fun$' > $int ).
tff(func_def_295,type,
sK245: 'Int_int_fun$' > $int ).
tff(func_def_296,type,
sK246: 'Num_int_fun$' > 'Num$' ).
tff(func_def_297,type,
sK247: 'Num_int_fun$' > 'Num$' ).
tff(func_def_298,type,
sK248: 'Int_enat_fun$' > $int ).
tff(func_def_299,type,
sK249: 'Int_enat_fun$' > $int ).
tff(func_def_300,type,
sK250: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_301,type,
sK251: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_302,type,
sK252: 'Int_enat_fun$' > $int ).
tff(func_def_303,type,
sK253: 'Int_enat_fun$' > $int ).
tff(func_def_304,type,
sK254: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_305,type,
sK255: 'Num_enat_fun$' > 'Num$' ).
tff(func_def_306,type,
sK256: 'Real_num_fun$' > $real ).
tff(func_def_307,type,
sK257: 'Real_num_fun$' > $real ).
tff(func_def_308,type,
sK258: 'Int_num_fun$' > $int ).
tff(func_def_309,type,
sK259: 'Int_num_fun$' > $int ).
tff(func_def_310,type,
sK260: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_311,type,
sK261: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_312,type,
sK262: 'Num_num_fun$' > 'Num$' ).
tff(func_def_313,type,
sK263: 'Num_num_fun$' > 'Num$' ).
tff(func_def_314,type,
sK264: 'Real_num_fun$' > $real ).
tff(func_def_315,type,
sK265: 'Real_num_fun$' > $real ).
tff(func_def_316,type,
sK266: 'Int_num_fun$' > $int ).
tff(func_def_317,type,
sK267: 'Int_num_fun$' > $int ).
tff(func_def_318,type,
sK268: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_319,type,
sK269: 'Enat_num_fun$' > 'Enat$' ).
tff(func_def_320,type,
sK270: 'Num_num_fun$' > 'Num$' ).
tff(func_def_321,type,
sK271: 'Num_num_fun$' > 'Num$' ).
tff(pred_def_1,type,
'fun_app$q': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_2,type,
'fun_app$n': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_3,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_4,type,
'fun_app$e': ( 'Num_bool_fun$' * 'Num$' ) > $o ).
tff(pred_def_5,type,
'member$': ( $real * 'Real_set$' ) > $o ).
tff(pred_def_6,type,
'fun_app$g': ( 'Enat_bool_fun$' * 'Enat$' ) > $o ).
tff(pred_def_11,type,
sP0: 'Real_set$' > $o ).
tff(pred_def_12,type,
sP1: 'Nat_bool_fun$' > $o ).
tff(pred_def_13,type,
sP2: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_14,type,
sP3: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_15,type,
sP4: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_16,type,
sP5: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_17,type,
sP6: 'Nat_nat_bool_fun_fun$' > $o ).
tff(pred_def_18,type,
sP7: ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_19,type,
sP8: ( $real * $real * $real ) > $o ).
tff(pred_def_20,type,
sP9: ( $real * $real * $real ) > $o ).
tff(pred_def_21,type,
sP10: ( $real * $real * $real ) > $o ).
tff(pred_def_22,type,
sP11: ( $real * $real * $real ) > $o ).
tff(pred_def_23,type,
sP12: ( $int * $int * $int ) > $o ).
tff(pred_def_24,type,
sP13: ( $int * $int * $int ) > $o ).
tff(pred_def_25,type,
sP14: ( $int * $int * $int ) > $o ).
tff(pred_def_26,type,
sP15: ( $int * $int * $int ) > $o ).
tff(pred_def_27,type,
sP16: ( 'Enat$' * 'Enat$' * 'Enat$' ) > $o ).
tff(pred_def_28,type,
sP17: ( 'Enat$' * 'Enat$' * 'Enat$' ) > $o ).
tff(pred_def_29,type,
sP18: ( 'Enat$' * 'Enat$' * 'Enat$' ) > $o ).
tff(pred_def_30,type,
sP19: ( 'Enat$' * 'Enat$' * 'Enat$' ) > $o ).
tff(pred_def_31,type,
sP20: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_32,type,
sP21: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_33,type,
sP22: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(pred_def_34,type,
sP23: ( 'Num$' * 'Num$' * 'Num$' ) > $o ).
tff(f14705,plain,
$false,
inference(avatar_sat_refutation,[],[f3619,f3623,f3628,f3633,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3665,f3670,f3674,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3755,f3759,f3763,f3767,f3771,f3776,f3781,f3786,f3791,f3795,f3799,f3803,f3807,f3811,f3815,f3819,f3823,f3827,f3831,f3835,f3839,f3854,f3859,f3863,f3867,f3871,f3876,f3881,f3886,f3891,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3963,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4008,f4012,f4016,f4020,f4024,f4028,f4032,f4036,f4040,f4044,f4048,f4064,f4083,f4087,f4092,f4102,f4106,f4110,f4114,f4119,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4179,f4194,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4227,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4271,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4423,f4470,f4592,f4599,f4603,f4607,f4611,f4615,f4619,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4774,f4820,f4959,f4963,f4967,f4971,f4975,f4979,f4983,f4988,f4999,f5003,f5007,f5011,f5016,f5021,f5025,f5030,f5034,f5038,f5049,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5186,f5193,f5224,f5228,f5232,f5252,f5314,f5340,f5344,f5348,f5352,f5369,f5373,f5377,f5381,f5386,f5390,f5394,f5398,f5402,f5406,f5420,f5424,f5428,f5432,f5436,f5440,f5444,f5492,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5596,f5601,f5605,f5609,f5613,f5617,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5660,f5668,f5674,f5676,f5686,f5728,f5883,f5887,f6048,f6052,f6056,f6060,f6064,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6119,f6123,f6127,f6131,f6135,f6139,f6143,f6147,f6151,f6155,f6159,f6163,f6167,f6240,f6307,f6344,f6361,f6365,f6369,f6373,f6377,f6381,f6385,f6389,f6393,f6397,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6458,f6462,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6494,f6506,f6510,f6514,f6518,f6522,f6526,f6530,f6569,f6686,f6765,f6900,f6985,f6989,f6993,f6997,f7001,f7019,f7023,f7027,f7032,f7037,f7041,f7045,f7049,f7053,f7057,f7072,f7076,f7081,f7086,f7090,f7095,f7099,f7103,f7107,f7111,f7124,f7129,f7133,f7141,f7228,f7232,f7292,f7300,f7304,f7318,f7389,f7393,f7397,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7585,f7590,f7595,f7693,f7697,f7701,f7732,f7736,f7740,f7744,f7749,f7753,f7757,f7771,f7775,f7779,f7783,f7787,f7791,f7795,f7799,f7803,f7807,f7811,f7815,f7819,f7823,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7909,f7970,f8075,f8197,f8215,f8219,f8224,f8229,f8233,f8237,f8241,f8245,f8249,f8253,f8269,f8273,f8277,f8281,f8285,f8289,f8293,f8297,f8301,f8305,f8317,f8321,f8325,f8329,f8333,f8337,f8341,f8345,f8349,f8353,f8367,f8371,f8375,f8379,f8383,f8387,f8391,f8395,f8399,f8403,f8407,f8411,f8503,f8507,f8529,f8613,f8677,f8801,f8805,f8809,f8813,f8817,f8833,f8837,f8841,f8845,f8849,f8854,f8858,f8862,f8866,f8870,f9145,f9230,f9234,f9238,f9242,f9246,f9250,f9254,f9258,f9262,f9266,f9270,f9274,f9278,f9282,f9286,f9290,f9294,f9298,f9302,f9306,f9310,f9314,f9318,f9322,f9326,f9330,f9334,f9338,f9342,f9346,f9350,f9412,f9605,f9609,f9613,f9617,f9621,f9625,f9629,f9633,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9695,f9699,f9703,f9707,f9711,f9715,f9719,f9723,f9727,f9731,f9735,f9739,f9743,f9747,f9751,f9755,f9759,f9763,f9767,f9771,f9775,f9779,f9783,f9787,f9791,f9795,f9799,f9803,f9807,f9811,f9815,f9819,f9823,f9945,f10359,f10363,f10367,f10371,f10375,f10379,f10397,f10401,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10434,f10438,f10455,f10460,f10480,f10485,f10502,f10507,f10527,f10531,f10536,f10541,f10546,f10551,f10555,f10559,f10563,f10567,f10571,f10575,f10579,f10583,f10587,f10591,f10595,f10599,f10675,f10888,f10892,f10896,f10900,f10905,f10915,f10920,f10950,f10955,f10965,f10970,f10992,f10997,f11018,f11023,f11045,f11050,f11060,f11065,f11087,f11091,f11095,f11099,f11103,f11107,f11111,f11115,f11119,f11123,f11127,f11131,f11135,f11139,f11143,f11147,f11151,f11257,f11349,f11365,f11369,f11373,f11377,f11381,f11385,f11389,f11393,f11410,f11414,f11418,f11422,f11426,f11430,f11434,f11438,f11442,f11446,f11478,f11482,f11486,f11610,f11844,f11848,f11852,f11856,f11860,f11864,f11869,f11873,f11877,f11881,f11885,f11889,f11893,f11897,f11901,f11905,f12422,f12469,f12473,f12552,f12556,f12567,f12571,f12575,f12579,f12583,f12587,f12591,f12595,f12599,f12603,f12614,f12618,f12622,f12626,f12630,f12634,f12638,f12642,f12765,f13087,f13091,f13095,f13099,f13103,f13223,f13227,f13231,f13235,f13239,f13243,f13247,f13251,f13255,f13259,f13263,f13267,f13271,f13288,f13443,f13447,f13451,f13455,f13459,f13561,f13585,f13589,f13593,f13597,f13601,f13663,f13667,f13671,f13675,f13681,f13697,f13702,f13706,f13710,f13714,f13719,f13724,f13729,f13734,f13739,f13743,f13748,f13754,f13760,f13766,f13772,f13777,f13782,f13786,f14580,f14638,f14697,f14704]) ).
tff(f14704,plain,
( ~ spl272_133
| ~ spl272_240
| ~ spl272_289
| spl272_824 ),
inference(avatar_contradiction_clause,[],[f14703]) ).
tff(f14703,plain,
( $false
| ~ spl272_133
| ~ spl272_240
| ~ spl272_289
| spl272_824 ),
inference(evaluation,[],[f14702]) ).
tff(f14702,plain,
( ~ $less(0,2)
| ~ spl272_133
| ~ spl272_240
| ~ spl272_289
| spl272_824 ),
inference(forward_demodulation,[],[f14698,f5362]) ).
tff(f5362,plain,
( ( 2 = 'fun_app$a'('of_nat$','nat$'(2)) )
| ~ spl272_133
| ~ spl272_240 ),
inference(evaluation,[],[f5358]) ).
tff(f5358,plain,
( ( $sum(2,0) = 'fun_app$a'('of_nat$','nat$'($sum(2,0))) )
| ~ spl272_133
| ~ spl272_240 ),
inference(resolution,[],[f5088,f4238]) ).
tff(f4238,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 ) )
| ~ spl272_133 ),
inference(avatar_component_clause,[],[f4237]) ).
tff(f4237,plain,
( spl272_133
<=> ! [X0: $int] :
( ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_133])]) ).
tff(f5088,plain,
( ! [X0: $int] : ~ $less($sum(2,X0),X0)
| ~ spl272_240 ),
inference(avatar_component_clause,[],[f5087]) ).
tff(f5087,plain,
( spl272_240
<=> ! [X0: $int] : ~ $less($sum(2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_240])]) ).
tff(f14698,plain,
( ~ $less(0,'fun_app$a'('of_nat$','nat$'(2)))
| ~ spl272_289
| spl272_824 ),
inference(resolution,[],[f14696,f5608]) ).
tff(f5608,plain,
( ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ spl272_289 ),
inference(avatar_component_clause,[],[f5607]) ).
tff(f5607,plain,
( spl272_289
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_289])]) ).
tff(f14696,plain,
( ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))))
| spl272_824 ),
inference(avatar_component_clause,[],[f14694]) ).
tff(f14694,plain,
( spl272_824
<=> $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$'))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_824])]) ).
tff(f14697,plain,
( ~ spl272_824
| spl272_110
| ~ spl272_173
| ~ spl272_707 ),
inference(avatar_split_clause,[],[f11527,f11367,f4589,f4116,f14694]) ).
tff(f4116,plain,
( spl272_110
<=> $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_110])]) ).
tff(f4589,plain,
( spl272_173
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$')))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_173])]) ).
tff(f11367,plain,
( spl272_707
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_707])]) ).
tff(f11527,plain,
( $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))
| ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))))
| ~ spl272_173
| ~ spl272_707 ),
inference(resolution,[],[f11368,f4591]) ).
tff(f4591,plain,
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$'))))
| ~ spl272_173 ),
inference(avatar_component_clause,[],[f4589]) ).
tff(f11368,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ spl272_707 ),
inference(avatar_component_clause,[],[f11367]) ).
tff(f14638,plain,
( spl272_823
| ~ spl272_44
| ~ spl272_803
| ~ spl272_804 ),
inference(avatar_split_clause,[],[f14431,f13699,f13694,f3797,f14635]) ).
tff(f14635,plain,
( spl272_823
<=> ( sK26(0) = sK30(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_823])]) ).
tff(f3797,plain,
( spl272_44
<=> ! [X0: 'Nat$'] : ( 'nat$'('fun_app$a'('of_nat$',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_44])]) ).
tff(f13694,plain,
( spl272_803
<=> ( 0 = 'fun_app$a'('of_nat$',sK26(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_803])]) ).
tff(f13699,plain,
( spl272_804
<=> ( 0 = 'fun_app$a'('of_nat$',sK30(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_804])]) ).
tff(f14431,plain,
( ( sK26(0) = sK30(0) )
| ~ spl272_44
| ~ spl272_803
| ~ spl272_804 ),
inference(forward_demodulation,[],[f14158,f13788]) ).
tff(f13788,plain,
( ( 'nat$'(0) = sK26(0) )
| ~ spl272_44
| ~ spl272_803 ),
inference(superposition,[],[f3798,f13696]) ).
tff(f13696,plain,
( ( 0 = 'fun_app$a'('of_nat$',sK26(0)) )
| ~ spl272_803 ),
inference(avatar_component_clause,[],[f13694]) ).
tff(f3798,plain,
( ! [X0: 'Nat$'] : ( 'nat$'('fun_app$a'('of_nat$',X0)) = X0 )
| ~ spl272_44 ),
inference(avatar_component_clause,[],[f3797]) ).
tff(f14158,plain,
( ( 'nat$'(0) = sK30(0) )
| ~ spl272_44
| ~ spl272_804 ),
inference(superposition,[],[f3798,f13701]) ).
tff(f13701,plain,
( ( 0 = 'fun_app$a'('of_nat$',sK30(0)) )
| ~ spl272_804 ),
inference(avatar_component_clause,[],[f13699]) ).
tff(f14580,plain,
( spl272_822
| ~ spl272_44
| ~ spl272_803 ),
inference(avatar_split_clause,[],[f13788,f13694,f3797,f14577]) ).
tff(f14577,plain,
( spl272_822
<=> ( 'nat$'(0) = sK26(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_822])]) ).
tff(f13786,plain,
( spl272_821
| ~ spl272_44
| ~ spl272_170
| ~ spl272_278 ),
inference(avatar_split_clause,[],[f5834,f5561,f4388,f3797,f13784]) ).
tff(f13784,plain,
( spl272_821
<=> ! [X1: 'Nat$'] : ( 1 = 'fun_app$a'('power$a'(1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_821])]) ).
tff(f4388,plain,
( spl272_170
<=> ! [X0: 'Nat$'] : ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_170])]) ).
tff(f5561,plain,
( spl272_278
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_278])]) ).
tff(f5834,plain,
( ! [X1: 'Nat$'] : ( 1 = 'fun_app$a'('power$a'(1),X1) )
| ~ spl272_44
| ~ spl272_170
| ~ spl272_278 ),
inference(forward_demodulation,[],[f5833,f4389]) ).
tff(f4389,plain,
( ! [X0: 'Nat$'] : ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(1)),X0)) )
| ~ spl272_170 ),
inference(avatar_component_clause,[],[f4388]) ).
tff(f5833,plain,
( ! [X1: 'Nat$'] : ( 'fun_app$a'('power$a'(1),X1) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(1)),X1)) )
| ~ spl272_44
| ~ spl272_170
| ~ spl272_278 ),
inference(forward_demodulation,[],[f5823,f4586]) ).
tff(f4586,plain,
( ! [X0: 'Nat$'] : ( 'nat$'(1) = 'fun_app$b'('power$'('nat$'(1)),X0) )
| ~ spl272_44
| ~ spl272_170 ),
inference(superposition,[],[f3798,f4389]) ).
tff(f5823,plain,
( ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(1)),X0)),X1)) = 'fun_app$a'('power$a'(1),X1) )
| ~ spl272_170
| ~ spl272_278 ),
inference(superposition,[],[f5562,f4389]) ).
tff(f5562,plain,
( ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X0)),X1) )
| ~ spl272_278 ),
inference(avatar_component_clause,[],[f5561]) ).
tff(f13782,plain,
( spl272_820
| ~ spl272_170
| ~ spl272_303 ),
inference(avatar_split_clause,[],[f5682,f5666,f4388,f13779]) ).
tff(f13779,plain,
( spl272_820
<=> ( 0 = 'fun_app$p'('times$b'(0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_820])]) ).
tff(f5666,plain,
( spl272_303
<=> ! [X1: 'Nat$'] : ( 0 = 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_303])]) ).
tff(f5682,plain,
( ( 0 = 'fun_app$p'('times$b'(0),1) )
| ~ spl272_170
| ~ spl272_303 ),
inference(superposition,[],[f5667,f4389]) ).
tff(f5667,plain,
( ! [X1: 'Nat$'] : ( 0 = 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X1)) )
| ~ spl272_303 ),
inference(avatar_component_clause,[],[f5666]) ).
tff(f13777,plain,
( spl272_819
| ~ spl272_170
| ~ spl272_302 ),
inference(avatar_split_clause,[],[f5664,f5658,f4388,f13774]) ).
tff(f13774,plain,
( spl272_819
<=> ( 0 = 'fun_app$p'('times$b'(1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_819])]) ).
tff(f5658,plain,
( spl272_302
<=> ! [X0: 'Nat$'] : ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_302])]) ).
tff(f5664,plain,
( ( 0 = 'fun_app$p'('times$b'(1),0) )
| ~ spl272_170
| ~ spl272_302 ),
inference(superposition,[],[f5659,f4389]) ).
tff(f5659,plain,
( ! [X0: 'Nat$'] : ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),0) )
| ~ spl272_302 ),
inference(avatar_component_clause,[],[f5658]) ).
tff(f13772,plain,
( spl272_818
| ~ spl272_40
| ~ spl272_302 ),
inference(avatar_split_clause,[],[f5661,f5658,f3778,f13769]) ).
tff(f13769,plain,
( spl272_818
<=> ( 0 = 'fun_app$p'('times$b'(0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_818])]) ).
tff(f3778,plain,
( spl272_40
<=> ( 0 = 'fun_app$a'('of_nat$','size$a'('one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_40])]) ).
tff(f5661,plain,
( ( 0 = 'fun_app$p'('times$b'(0),0) )
| ~ spl272_40
| ~ spl272_302 ),
inference(superposition,[],[f5659,f3780]) ).
tff(f3780,plain,
( ( 0 = 'fun_app$a'('of_nat$','size$a'('one$')) )
| ~ spl272_40 ),
inference(avatar_component_clause,[],[f3778]) ).
tff(f13766,plain,
( ~ spl272_817
| ~ spl272_170
| ~ spl272_250 ),
inference(avatar_split_clause,[],[f5450,f5338,f4388,f13763]) ).
tff(f13763,plain,
( spl272_817
<=> $less('fun_app$p'('times$b'(1),1),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_817])]) ).
tff(f5338,plain,
( spl272_250
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_250])]) ).
tff(f5450,plain,
( ~ $less('fun_app$p'('times$b'(1),1),1)
| ~ spl272_170
| ~ spl272_250 ),
inference(superposition,[],[f5339,f4389]) ).
tff(f5339,plain,
( ! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0))
| ~ spl272_250 ),
inference(avatar_component_clause,[],[f5338]) ).
tff(f13760,plain,
( ~ spl272_816
| ~ spl272_40
| ~ spl272_250 ),
inference(avatar_split_clause,[],[f5447,f5338,f3778,f13757]) ).
tff(f13757,plain,
( spl272_816
<=> $less('fun_app$p'('times$b'(0),0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_816])]) ).
tff(f5447,plain,
( ~ $less('fun_app$p'('times$b'(0),0),0)
| ~ spl272_40
| ~ spl272_250 ),
inference(superposition,[],[f5339,f3780]) ).
tff(f13754,plain,
( spl272_815
| ~ spl272_62
| ~ spl272_228 ),
inference(avatar_split_clause,[],[f5239,f5032,f3883,f13751]) ).
tff(f13751,plain,
( spl272_815
<=> $less(0,'fun_app$a'('of_nat$','nat$'(2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_815])]) ).
tff(f3883,plain,
( spl272_62
<=> ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_62])]) ).
tff(f5032,plain,
( spl272_228
<=> ! [X0: $real,X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 0.0 != 'fun_app$m'('power$c'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_228])]) ).
tff(f5239,plain,
( $less(0,'fun_app$a'('of_nat$','nat$'(2)))
| ~ spl272_62
| ~ spl272_228 ),
inference(trivial_inequality_removal,[],[f5235]) ).
tff(f5235,plain,
( ( 0.0 != 0.0 )
| $less(0,'fun_app$a'('of_nat$','nat$'(2)))
| ~ spl272_62
| ~ spl272_228 ),
inference(superposition,[],[f5033,f3885]) ).
tff(f3885,plain,
( ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'(2)) )
| ~ spl272_62 ),
inference(avatar_component_clause,[],[f3883]) ).
tff(f5033,plain,
( ! [X0: $real,X1: 'Nat$'] :
( ( 0.0 != 'fun_app$m'('power$c'(X0),X1) )
| $less(0,'fun_app$a'('of_nat$',X1)) )
| ~ spl272_228 ),
inference(avatar_component_clause,[],[f5032]) ).
tff(f13748,plain,
( spl272_814
| ~ spl272_44
| ~ spl272_99
| ~ spl272_170
| ~ spl272_217 ),
inference(avatar_split_clause,[],[f5181,f4977,f4388,f4038,f3797,f13745]) ).
tff(f13745,plain,
( spl272_814
<=> $less(1,'fun_app$a'('of_nat$','nat$'(2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_814])]) ).
tff(f4038,plain,
( spl272_99
<=> ! [X0: 'Nat$'] : ( 'fun_app$b'('power$'(X0),'nat$'(1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_99])]) ).
tff(f4977,plain,
( spl272_217
<=> ! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_217])]) ).
tff(f5181,plain,
( $less(1,'fun_app$a'('of_nat$','nat$'(2)))
| ~ spl272_44
| ~ spl272_99
| ~ spl272_170
| ~ spl272_217 ),
inference(forward_demodulation,[],[f5180,f4039]) ).
tff(f4039,plain,
( ! [X0: 'Nat$'] : ( 'fun_app$b'('power$'(X0),'nat$'(1)) = X0 )
| ~ spl272_99 ),
inference(avatar_component_clause,[],[f4038]) ).
tff(f5180,plain,
( $less(1,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'nat$'(1))))
| ~ spl272_44
| ~ spl272_170
| ~ spl272_217 ),
inference(forward_demodulation,[],[f5177,f4586]) ).
tff(f5177,plain,
( ! [X0: 'Nat$'] : $less(1,'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(1)),X0))))
| ~ spl272_170
| ~ spl272_217 ),
inference(superposition,[],[f4978,f4389]) ).
tff(f4978,plain,
( ! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0)))
| ~ spl272_217 ),
inference(avatar_component_clause,[],[f4977]) ).
tff(f13743,plain,
( spl272_813
| ~ spl272_51
| ~ spl272_770 ),
inference(avatar_split_clause,[],[f13565,f13093,f3825,f13741]) ).
tff(f13741,plain,
( spl272_813
<=> ! [X0: $int] : ~ $less($sum(8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_813])]) ).
tff(f3825,plain,
( spl272_51
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_51])]) ).
tff(f13093,plain,
( spl272_770
<=> ! [X0: $int] : $less(X0,$sum(8,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_770])]) ).
tff(f13565,plain,
( ! [X0: $int] : ~ $less($sum(8,X0),X0)
| ~ spl272_51
| ~ spl272_770 ),
inference(resolution,[],[f13094,f3826]) ).
tff(f3826,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less(X0,X1) )
| ~ spl272_51 ),
inference(avatar_component_clause,[],[f3825]) ).
tff(f13094,plain,
( ! [X0: $int] : $less(X0,$sum(8,X0))
| ~ spl272_770 ),
inference(avatar_component_clause,[],[f13093]) ).
tff(f13739,plain,
( ~ spl272_812
| ~ spl272_40
| ~ spl272_208 ),
inference(avatar_split_clause,[],[f4946,f4740,f3778,f13736]) ).
tff(f13736,plain,
( spl272_812
<=> ( 0.0 = 'fun_app$m'('of_nat$b','nat$'(1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_812])]) ).
tff(f4740,plain,
( spl272_208
<=> ! [X0: 'Nat$'] : ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_208])]) ).
tff(f4946,plain,
( ( 0.0 != 'fun_app$m'('of_nat$b','nat$'(1)) )
| ~ spl272_40
| ~ spl272_208 ),
inference(evaluation,[],[f4940]) ).
tff(f4940,plain,
( ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum(1,0))) )
| ~ spl272_40
| ~ spl272_208 ),
inference(superposition,[],[f4741,f3780]) ).
tff(f4741,plain,
( ! [X0: 'Nat$'] : ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) )
| ~ spl272_208 ),
inference(avatar_component_clause,[],[f4740]) ).
tff(f13734,plain,
( ~ spl272_811
| ~ spl272_170
| ~ spl272_208 ),
inference(avatar_split_clause,[],[f4944,f4740,f4388,f13731]) ).
tff(f13731,plain,
( spl272_811
<=> ( 0.0 = 'fun_app$m'('of_nat$b','nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_811])]) ).
tff(f4944,plain,
( ( 0.0 != 'fun_app$m'('of_nat$b','nat$'(2)) )
| ~ spl272_170
| ~ spl272_208 ),
inference(evaluation,[],[f4943]) ).
tff(f4943,plain,
( ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum(1,1))) )
| ~ spl272_170
| ~ spl272_208 ),
inference(superposition,[],[f4741,f4389]) ).
tff(f13729,plain,
( ~ spl272_810
| ~ spl272_40
| ~ spl272_207 ),
inference(avatar_split_clause,[],[f4928,f4736,f3778,f13726]) ).
tff(f13726,plain,
( spl272_810
<=> ( 'zero$a' = 'fun_app$l'('of_nat$c','nat$'(1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_810])]) ).
tff(f4736,plain,
( spl272_207
<=> ! [X0: 'Nat$'] : ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_207])]) ).
tff(f4928,plain,
( ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'(1)) )
| ~ spl272_40
| ~ spl272_207 ),
inference(evaluation,[],[f4922]) ).
tff(f4922,plain,
( ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum(1,0))) )
| ~ spl272_40
| ~ spl272_207 ),
inference(superposition,[],[f4737,f3780]) ).
tff(f4737,plain,
( ! [X0: 'Nat$'] : ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) )
| ~ spl272_207 ),
inference(avatar_component_clause,[],[f4736]) ).
tff(f13724,plain,
( ~ spl272_809
| ~ spl272_170
| ~ spl272_207 ),
inference(avatar_split_clause,[],[f4926,f4736,f4388,f13721]) ).
tff(f13721,plain,
( spl272_809
<=> ( 'zero$a' = 'fun_app$l'('of_nat$c','nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_809])]) ).
tff(f4926,plain,
( ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'(2)) )
| ~ spl272_170
| ~ spl272_207 ),
inference(evaluation,[],[f4925]) ).
tff(f4925,plain,
( ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum(1,1))) )
| ~ spl272_170
| ~ spl272_207 ),
inference(superposition,[],[f4737,f4389]) ).
tff(f13719,plain,
( spl272_808
| ~ spl272_44
| ~ spl272_170
| ~ spl272_192 ),
inference(avatar_split_clause,[],[f4857,f4676,f4388,f3797,f13716]) ).
tff(f13716,plain,
( spl272_808
<=> $less(0.0,'fun_app$m'('of_nat$b','nat$'(1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_808])]) ).
tff(f4676,plain,
( spl272_192
<=> ! [X0: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_192])]) ).
tff(f4857,plain,
( $less(0.0,'fun_app$m'('of_nat$b','nat$'(1)))
| ~ spl272_44
| ~ spl272_170
| ~ spl272_192 ),
inference(forward_demodulation,[],[f4855,f4586]) ).
tff(f4855,plain,
( ! [X0: 'Nat$'] : $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'('nat$'(1)),X0)))
| ~ spl272_170
| ~ spl272_192 ),
inference(evaluation,[],[f4854]) ).
tff(f4854,plain,
( ! [X0: 'Nat$'] :
( ~ $less(0,1)
| $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'('nat$'(1)),X0))) )
| ~ spl272_170
| ~ spl272_192 ),
inference(superposition,[],[f4677,f4389]) ).
tff(f4677,plain,
( ! [X0: 'Nat$'] :
( ~ $less(0,'fun_app$a'('of_nat$',X0))
| $less(0.0,'fun_app$m'('of_nat$b',X0)) )
| ~ spl272_192 ),
inference(avatar_component_clause,[],[f4676]) ).
tff(f13714,plain,
( spl272_807
| ~ spl272_14
| ~ spl272_182 ),
inference(avatar_split_clause,[],[f4805,f4636,f3672,f13712]) ).
tff(f13712,plain,
( spl272_807
<=> ! [X0: 'Num$'] : ( 0.0 != 'dbl$a'('fun_app$j'('numeral$b',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_807])]) ).
tff(f3672,plain,
( spl272_14
<=> ! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) != 0.0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_14])]) ).
tff(f4636,plain,
( spl272_182
<=> ! [X0: 'Num$'] : ( 'dbl$a'('fun_app$j'('numeral$b',X0)) = 'fun_app$j'('numeral$b','fun_app$c'('bit0$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_182])]) ).
tff(f4805,plain,
( ! [X0: 'Num$'] : ( 0.0 != 'dbl$a'('fun_app$j'('numeral$b',X0)) )
| ~ spl272_14
| ~ spl272_182 ),
inference(superposition,[],[f3673,f4637]) ).
tff(f4637,plain,
( ! [X0: 'Num$'] : ( 'dbl$a'('fun_app$j'('numeral$b',X0)) = 'fun_app$j'('numeral$b','fun_app$c'('bit0$',X0)) )
| ~ spl272_182 ),
inference(avatar_component_clause,[],[f4636]) ).
tff(f3673,plain,
( ! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) != 0.0 )
| ~ spl272_14 ),
inference(avatar_component_clause,[],[f3672]) ).
tff(f13710,plain,
( spl272_806
| ~ spl272_18
| ~ spl272_182 ),
inference(avatar_split_clause,[],[f4804,f4636,f3688,f13708]) ).
tff(f13708,plain,
( spl272_806
<=> ! [X0: 'Num$'] : $less(0.0,'dbl$a'('fun_app$j'('numeral$b',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_806])]) ).
tff(f3688,plain,
( spl272_18
<=> ! [X0: 'Num$'] : $less(0.0,'fun_app$j'('numeral$b',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_18])]) ).
tff(f4804,plain,
( ! [X0: 'Num$'] : $less(0.0,'dbl$a'('fun_app$j'('numeral$b',X0)))
| ~ spl272_18
| ~ spl272_182 ),
inference(superposition,[],[f3689,f4637]) ).
tff(f3689,plain,
( ! [X0: 'Num$'] : $less(0.0,'fun_app$j'('numeral$b',X0))
| ~ spl272_18 ),
inference(avatar_component_clause,[],[f3688]) ).
tff(f13706,plain,
( spl272_805
| ~ spl272_26
| ~ spl272_182 ),
inference(avatar_split_clause,[],[f4803,f4636,f3720,f13704]) ).
tff(f13704,plain,
( spl272_805
<=> ! [X0: 'Num$'] : ~ $less('dbl$a'('fun_app$j'('numeral$b',X0)),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_805])]) ).
tff(f3720,plain,
( spl272_26
<=> ! [X0: 'Num$'] : ~ $less('fun_app$j'('numeral$b',X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_26])]) ).
tff(f4803,plain,
( ! [X0: 'Num$'] : ~ $less('dbl$a'('fun_app$j'('numeral$b',X0)),0.0)
| ~ spl272_26
| ~ spl272_182 ),
inference(superposition,[],[f3721,f4637]) ).
tff(f3721,plain,
( ! [X0: 'Num$'] : ~ $less('fun_app$j'('numeral$b',X0),0.0)
| ~ spl272_26 ),
inference(avatar_component_clause,[],[f3720]) ).
tff(f13702,plain,
( spl272_804
| ~ spl272_1
| ~ spl272_140 ),
inference(avatar_split_clause,[],[f4496,f4265,f3617,f13699]) ).
tff(f3617,plain,
( spl272_1
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_1])]) ).
tff(f4265,plain,
( spl272_140
<=> ! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK30(X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_140])]) ).
tff(f4496,plain,
( ( 0 = 'fun_app$a'('of_nat$',sK30(0)) )
| ~ spl272_1
| ~ spl272_140 ),
inference(resolution,[],[f4266,f3618]) ).
tff(f3618,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl272_1 ),
inference(avatar_component_clause,[],[f3617]) ).
tff(f4266,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( 'fun_app$a'('of_nat$',sK30(X0)) = X0 ) )
| ~ spl272_140 ),
inference(avatar_component_clause,[],[f4265]) ).
tff(f13697,plain,
( spl272_803
| ~ spl272_1
| ~ spl272_137 ),
inference(avatar_split_clause,[],[f4472,f4253,f3617,f13694]) ).
tff(f4253,plain,
( spl272_137
<=> ! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK26(X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_137])]) ).
tff(f4472,plain,
( ( 0 = 'fun_app$a'('of_nat$',sK26(0)) )
| ~ spl272_1
| ~ spl272_137 ),
inference(resolution,[],[f4254,f3618]) ).
tff(f4254,plain,
( ! [X0: $int] :
( $less(X0,0)
| ( 'fun_app$a'('of_nat$',sK26(X0)) = X0 ) )
| ~ spl272_137 ),
inference(avatar_component_clause,[],[f4253]) ).
tff(f13681,plain,
( spl272_802
| ~ spl272_55
| ~ spl272_801 ),
inference(avatar_split_clause,[],[f13677,f13673,f3851,f13679]) ).
tff(f13679,plain,
( spl272_802
<=> ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'size$a'('one$'))
| ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_802])]) ).
tff(f3851,plain,
( spl272_55
<=> ( 'nat$'(0) = 'size$a'('one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_55])]) ).
tff(f13673,plain,
( spl272_801
<=> ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_801])]) ).
tff(f13677,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'size$a'('one$'))
| ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2) )
| ~ spl272_55
| ~ spl272_801 ),
inference(forward_demodulation,[],[f13676,f3853]) ).
tff(f3853,plain,
( ( 'nat$'(0) = 'size$a'('one$') )
| ~ spl272_55 ),
inference(avatar_component_clause,[],[f3851]) ).
tff(f13676,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) )
| ~ spl272_55
| ~ spl272_801 ),
inference(forward_demodulation,[],[f13674,f3853]) ).
tff(f13674,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) )
| ~ spl272_801 ),
inference(avatar_component_clause,[],[f13673]) ).
tff(f13675,plain,
spl272_801,
inference(avatar_split_clause,[],[f3565,f13673]) ).
tff(f3565,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(forward_demodulation,[],[f3564,f848]) ).
tff(f848,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f3564,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK82(X0))))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(forward_demodulation,[],[f3563,f848]) ).
tff(f3563,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK82(X0)),1))),'nat$'($sum(1,'fun_app$a'('of_nat$',sK83(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(forward_demodulation,[],[f2932,f848]) ).
tff(f2932,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK82(X0)),1))),'nat$'($sum('fun_app$a'('of_nat$',sK83(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(cnf_transformation,[],[f1883]) ).
tff(f1883,plain,
! [X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK82(X0)),1))),'nat$'($sum('fun_app$a'('of_nat$',sK83(X0)),1)))
& 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0)) )
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82,sK83,sK84,sK85])],[f1306,f1882,f1881,f1880]) ).
tff(f1880,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'nat$'($sum('fun_app$a'('of_nat$',X4),1)))
& 'fun_app$n'('fun_app$o'(X0,X3),X4) )
=> ( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK82(X0)),1))),'nat$'($sum('fun_app$a'('of_nat$',sK83(X0)),1)))
& 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1881,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X5: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',X5),1)))
=> ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1))) ),
introduced(choice_axiom,[]) ).
tff(f1882,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,X6),'nat$'(0))
=> ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
introduced(choice_axiom,[]) ).
tff(f1306,plain,
! [X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'nat$'($sum('fun_app$a'('of_nat$',X4),1)))
& 'fun_app$n'('fun_app$o'(X0,X3),X4) )
| ? [X5: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',X5),1)))
| ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,X6),'nat$'(0)) ),
inference(flattening,[],[f1305]) ).
tff(f1305,plain,
! [X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X1),X2)
| ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'nat$'($sum('fun_app$a'('of_nat$',X4),1)))
& 'fun_app$n'('fun_app$o'(X0,X3),X4) )
| ? [X5: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',X5),1)))
| ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X0,X6),'nat$'(0)) ),
inference(ennf_transformation,[],[f991]) ).
tff(f991,plain,
! [X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X3: 'Nat$',X4: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X3),X4)
=> 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'nat$'($sum('fun_app$a'('of_nat$',X4),1))) )
& ! [X5: 'Nat$'] : 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',X5),1)))
& ! [X6: 'Nat$'] : 'fun_app$n'('fun_app$o'(X0,X6),'nat$'(0)) )
=> 'fun_app$n'('fun_app$o'(X0,X1),X2) ),
inference(rectify,[],[f172]) ).
tff(f172,axiom,
! [X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X3: 'Nat$',X4: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X3),X4)
=> 'fun_app$n'('fun_app$o'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'nat$'($sum('fun_app$a'('of_nat$',X4),1))) )
& ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X0,X3),'nat$'(0)) )
=> 'fun_app$n'('fun_app$o'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom170) ).
tff(f13671,plain,
spl272_800,
inference(avatar_split_clause,[],[f3556,f13669]) ).
tff(f13669,plain,
( spl272_800
<=> ! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK79(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_800])]) ).
tff(f3556,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK79(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2874,f848]) ).
tff(f2874,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK77(X2)),1)))
| 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK79(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1849]) ).
tff(f1849,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK77(X2)),1)))
| ( ~ 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK80(X2))
& 'fun_app$n'('fun_app$o'(X2,sK79(X2)),sK80(X2))
& 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK79(X2)) )
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78,sK79,sK80,sK81])],[f1288,f1848,f1847,f1846]) ).
tff(f1846,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
=> ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK77(X2)),1))) ),
introduced(choice_axiom,[]) ).
tff(f1847,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X4: 'Nat$',X5: 'Nat$',X6: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X4),X6)
& 'fun_app$n'('fun_app$o'(X2,X5),X6)
& 'fun_app$n'('fun_app$o'(X2,X4),X5) )
=> ( ~ 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK80(X2))
& 'fun_app$n'('fun_app$o'(X2,sK79(X2)),sK80(X2))
& 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK79(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1848,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X7: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X7),X7)
=> ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2)) ),
introduced(choice_axiom,[]) ).
tff(f1288,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ? [X3: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ? [X4: 'Nat$',X5: 'Nat$',X6: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X4),X6)
& 'fun_app$n'('fun_app$o'(X2,X5),X6)
& 'fun_app$n'('fun_app$o'(X2,X4),X5) )
| ? [X7: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X7),X7)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1287]) ).
tff(f1287,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ? [X3: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ? [X4: 'Nat$',X5: 'Nat$',X6: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X4),X6)
& 'fun_app$n'('fun_app$o'(X2,X5),X6)
& 'fun_app$n'('fun_app$o'(X2,X4),X5) )
| ? [X7: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X7),X7)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f986]) ).
tff(f986,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( ( ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& ! [X4: 'Nat$',X5: 'Nat$',X6: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'(X2,X5),X6)
& 'fun_app$n'('fun_app$o'(X2,X4),X5) )
=> 'fun_app$n'('fun_app$o'(X2,X4),X6) )
& ! [X7: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X7),X7)
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'('fun_app$o'(X2,X0),X1) ),
inference(rectify,[],[f786]) ).
tff(f786,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( ( ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& ! [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4) )
=> 'fun_app$n'('fun_app$o'(X2,X3),X5) )
& ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),X3)
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'('fun_app$o'(X2,X0),X1) ),
inference(theory_normalization,[],[f43]) ).
tff(f43,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( ( ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& ! [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4) )
=> 'fun_app$n'('fun_app$o'(X2,X3),X5) )
& ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),X3)
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'('fun_app$o'(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
tff(f13667,plain,
spl272_799,
inference(avatar_split_clause,[],[f3555,f13665]) ).
tff(f13665,plain,
( spl272_799
<=> ! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| 'fun_app$n'('fun_app$o'(X2,sK79(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_799])]) ).
tff(f3555,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| 'fun_app$n'('fun_app$o'(X2,sK79(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2875,f848]) ).
tff(f2875,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK77(X2)),1)))
| 'fun_app$n'('fun_app$o'(X2,sK79(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1849]) ).
tff(f13663,plain,
spl272_798,
inference(avatar_split_clause,[],[f3554,f13661]) ).
tff(f13661,plain,
( spl272_798
<=> ! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_798])]) ).
tff(f3554,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK77(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2876,f848]) ).
tff(f2876,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ~ 'fun_app$n'('fun_app$o'(X2,sK77(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK77(X2)),1)))
| ~ 'fun_app$n'('fun_app$o'(X2,sK78(X2)),sK80(X2))
| ~ 'fun_app$n'('fun_app$o'(X2,sK81(X2)),sK81(X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1849]) ).
tff(f13601,plain,
spl272_797,
inference(avatar_split_clause,[],[f3574,f13599]) ).
tff(f13599,plain,
( spl272_797
<=> ! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK93(X0)))))),'fun_app$k'(X0,sK93(X0)))
| 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_797])]) ).
tff(f3574,plain,
! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK93(X0)))))),'fun_app$k'(X0,sK93(X0)))
| 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2940,f848]) ).
tff(f2940,plain,
! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK93(X0)),1)))),'fun_app$k'(X0,sK93(X0))) ),
inference(cnf_transformation,[],[f1899]) ).
tff(f1899,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK93(X0)),1)))),'fun_app$k'(X0,sK93(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f1322,f1898]) ).
tff(f1898,plain,
! [X0: 'Nat_num_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$k'(X0,X3))
=> ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK93(X0)),1)))),'fun_app$k'(X0,sK93(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1322,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$k'(X0,X3)) ),
inference(flattening,[],[f1321]) ).
tff(f1321,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$k'(X0,X3)) ),
inference(ennf_transformation,[],[f800]) ).
tff(f800,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$k'(X0,X3)) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1)) ),
inference(theory_normalization,[],[f19]) ).
tff(f19,axiom,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$k'(X0,X3)) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X2)),'fun_app$k'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
tff(f13597,plain,
spl272_796,
inference(avatar_split_clause,[],[f3573,f13595]) ).
tff(f13595,plain,
( spl272_796
<=> ! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,sK92(X0))),'fun_app$k'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK92(X0))))))
| 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_796])]) ).
tff(f3573,plain,
! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,sK92(X0))),'fun_app$k'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK92(X0))))))
| 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2939,f848]) ).
tff(f2939,plain,
! [X2: 'Nat$',X0: 'Nat_num_fun$',X1: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,sK92(X0))),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK92(X0)),1)))) ),
inference(cnf_transformation,[],[f1897]) ).
tff(f1897,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,sK92(X0))),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK92(X0)),1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92])],[f1320,f1896]) ).
tff(f1896,plain,
! [X0: 'Nat_num_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X3)),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))))
=> ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,sK92(X0))),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK92(X0)),1)))) ),
introduced(choice_axiom,[]) ).
tff(f1320,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X3)),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(flattening,[],[f1319]) ).
tff(f1319,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X3)),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(ennf_transformation,[],[f799]) ).
tff(f799,plain,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X3)),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2)) ),
inference(theory_normalization,[],[f15]) ).
tff(f15,axiom,
! [X0: 'Nat_num_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X3)),'fun_app$k'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$k'(X0,X1)),'fun_app$k'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
tff(f13593,plain,
spl272_795,
inference(avatar_split_clause,[],[f3572,f13591]) ).
tff(f13591,plain,
( spl272_795
<=> ! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK91(X0)))))),'fun_app$l'(X0,sK91(X0)))
| 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_795])]) ).
tff(f3572,plain,
! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK91(X0)))))),'fun_app$l'(X0,sK91(X0)))
| 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2938,f848]) ).
tff(f2938,plain,
! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK91(X0)),1)))),'fun_app$l'(X0,sK91(X0))) ),
inference(cnf_transformation,[],[f1895]) ).
tff(f1895,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK91(X0)),1)))),'fun_app$l'(X0,sK91(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91])],[f1318,f1894]) ).
tff(f1894,plain,
! [X0: 'Nat_enat_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$l'(X0,X3))
=> ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK91(X0)),1)))),'fun_app$l'(X0,sK91(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1318,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$l'(X0,X3)) ),
inference(flattening,[],[f1317]) ).
tff(f1317,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$l'(X0,X3)) ),
inference(ennf_transformation,[],[f798]) ).
tff(f798,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$l'(X0,X3)) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1)) ),
inference(theory_normalization,[],[f20]) ).
tff(f20,axiom,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))),'fun_app$l'(X0,X3)) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X2)),'fun_app$l'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
tff(f13589,plain,
spl272_794,
inference(avatar_split_clause,[],[f3571,f13587]) ).
tff(f13587,plain,
( spl272_794
<=> ! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,sK90(X0))),'fun_app$l'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK90(X0))))))
| 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_794])]) ).
tff(f3571,plain,
! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,sK90(X0))),'fun_app$l'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK90(X0))))))
| 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2937,f848]) ).
tff(f2937,plain,
! [X2: 'Nat$',X0: 'Nat_enat_fun$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,sK90(X0))),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK90(X0)),1)))) ),
inference(cnf_transformation,[],[f1893]) ).
tff(f1893,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,sK90(X0))),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK90(X0)),1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f1316,f1892]) ).
tff(f1892,plain,
! [X0: 'Nat_enat_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X3)),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))))
=> ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,sK90(X0))),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK90(X0)),1)))) ),
introduced(choice_axiom,[]) ).
tff(f1316,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X3)),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(flattening,[],[f1315]) ).
tff(f1315,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X3)),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(ennf_transformation,[],[f797]) ).
tff(f797,plain,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X3)),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2)) ),
inference(theory_normalization,[],[f16]) ).
tff(f16,axiom,
! [X0: 'Nat_enat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X3)),'fun_app$l'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'(X0,X1)),'fun_app$l'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
tff(f13585,plain,
spl272_793,
inference(avatar_split_clause,[],[f3558,f13583]) ).
tff(f13583,plain,
( spl272_793
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$b'('power$'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_793])]) ).
tff(f3558,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$b'('power$'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(forward_demodulation,[],[f2878,f848]) ).
tff(f2878,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( X0 = X2 )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ( 'fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(cnf_transformation,[],[f1292]) ).
tff(f1292,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( X0 = X2 )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ( 'fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(flattening,[],[f1291]) ).
tff(f1291,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( X0 = X2 )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ( 'fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(ennf_transformation,[],[f318]) ).
tff(f318,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
& 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
& ( 'fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = 'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) )
=> ( X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom316) ).
tff(f13561,plain,
( spl272_792
| ~ spl272_55
| ~ spl272_791 ),
inference(avatar_split_clause,[],[f13461,f13457,f3851,f13559]) ).
tff(f13559,plain,
( spl272_792
<=> ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'size$a'('one$'))
| ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_792])]) ).
tff(f13457,plain,
( spl272_791
<=> ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_791])]) ).
tff(f13461,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'size$a'('one$'))
| ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0)) )
| ~ spl272_55
| ~ spl272_791 ),
inference(forward_demodulation,[],[f13460,f3853]) ).
tff(f13460,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'size$a'('one$')),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) )
| ~ spl272_55
| ~ spl272_791 ),
inference(forward_demodulation,[],[f13458,f3853]) ).
tff(f13458,plain,
( ! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) )
| ~ spl272_791 ),
inference(avatar_component_clause,[],[f13457]) ).
tff(f13459,plain,
spl272_791,
inference(avatar_split_clause,[],[f3566,f13457]) ).
tff(f3566,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK84(X0)))))
| 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(forward_demodulation,[],[f2931,f848]) ).
tff(f2931,plain,
! [X2: 'Nat$',X0: 'Nat_nat_bool_fun_fun$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X0,X1),X2)
| 'fun_app$n'('fun_app$o'(X0,sK82(X0)),sK83(X0))
| ~ 'fun_app$n'('fun_app$o'(X0,'nat$'(0)),'nat$'($sum('fun_app$a'('of_nat$',sK84(X0)),1)))
| ~ 'fun_app$n'('fun_app$o'(X0,sK85(X0)),'nat$'(0)) ),
inference(cnf_transformation,[],[f1883]) ).
tff(f13455,plain,
spl272_790,
inference(avatar_split_clause,[],[f3562,f13453]) ).
tff(f13453,plain,
( spl272_790
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1))))),'fun_app$b'('power$'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_790])]) ).
tff(f3562,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1))))),'fun_app$b'('power$'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2) ),
inference(forward_demodulation,[],[f2882,f848]) ).
tff(f2882,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))),'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(cnf_transformation,[],[f1300]) ).
tff(f1300,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))),'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(flattening,[],[f1299]) ).
tff(f1299,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))),'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(ennf_transformation,[],[f321]) ).
tff(f321,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X2)
& 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))),'fun_app$b'('power$'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) )
=> 'fun_app$n'('fun_app$o'('less_eq$b',X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom319) ).
tff(f13451,plain,
spl272_789,
inference(avatar_split_clause,[],[f3198,f13449]) ).
tff(f13449,plain,
( spl272_789
<=> ! [X0: 'Nat$',X3: 'Nat$',X2: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_789])]) ).
tff(f3198,plain,
! [X2: 'Nat$',X3: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1472]) ).
tff(f1472,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1471]) ).
tff(f1471,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f844]) ).
tff(f844,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ),
inference(theory_normalization,[],[f577]) ).
tff(f577,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> $lesseq('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).
tff(f13447,plain,
spl272_788,
inference(avatar_split_clause,[],[f2958,f13445]) ).
tff(f13445,plain,
( spl272_788
<=> ! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,sK110(X0))),'fun_app$a'('of_nat$','fun_app$b'(X0,sK111(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_788])]) ).
tff(f2958,plain,
! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,sK110(X0))),'fun_app$a'('of_nat$','fun_app$b'(X0,sK111(X0)))) ),
inference(cnf_transformation,[],[f1913]) ).
tff(f1913,plain,
! [X0: 'Nat_nat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,sK110(X0))),'fun_app$a'('of_nat$','fun_app$b'(X0,sK111(X0))))
& $less('fun_app$a'('of_nat$',sK110(X0)),'fun_app$a'('of_nat$',sK111(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f1332,f1912]) ).
tff(f1912,plain,
! [X0: 'Nat_nat_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X3)),'fun_app$a'('of_nat$','fun_app$b'(X0,X4)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
=> ( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,sK110(X0))),'fun_app$a'('of_nat$','fun_app$b'(X0,sK111(X0))))
& $less('fun_app$a'('of_nat$',sK110(X0)),'fun_app$a'('of_nat$',sK111(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1332,plain,
! [X0: 'Nat_nat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X3)),'fun_app$a'('of_nat$','fun_app$b'(X0,X4)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) ) ),
inference(flattening,[],[f1331]) ).
tff(f1331,plain,
! [X0: 'Nat_nat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$',X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X3)),'fun_app$a'('of_nat$','fun_app$b'(X0,X4)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) ) ),
inference(ennf_transformation,[],[f803]) ).
tff(f803,plain,
! [X0: 'Nat_nat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$',X4: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4))
=> $less('fun_app$a'('of_nat$','fun_app$b'(X0,X3)),'fun_app$a'('of_nat$','fun_app$b'(X0,X4))) ) )
=> ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1))) ),
inference(theory_normalization,[],[f580]) ).
tff(f580,axiom,
! [X0: 'Nat_nat_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$',X4: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4))
=> $less('fun_app$a'('of_nat$','fun_app$b'(X0,X3)),'fun_app$a'('of_nat$','fun_app$b'(X0,X4))) ) )
=> $lesseq('fun_app$a'('of_nat$','fun_app$b'(X0,X1)),'fun_app$a'('of_nat$','fun_app$b'(X0,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom578) ).
tff(f13443,plain,
spl272_787,
inference(avatar_split_clause,[],[f2833,f13441]) ).
tff(f13441,plain,
( spl272_787
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_787])]) ).
tff(f2833,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(cnf_transformation,[],[f1825]) ).
tff(f1825,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) )
& ( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2)) ) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(nnf_transformation,[],[f1242]) ).
tff(f1242,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
<=> 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(flattening,[],[f1241]) ).
tff(f1241,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
<=> 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(ennf_transformation,[],[f400]) ).
tff(f400,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
& 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) )
=> ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
<=> 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom398) ).
tff(f13288,plain,
( spl272_786
| ~ spl272_109
| ~ spl272_704 ),
inference(avatar_split_clause,[],[f12610,f11255,f4112,f13286]) ).
tff(f13286,plain,
( spl272_786
<=> ! [X0: $real] : $less(X0,$sum(8.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_786])]) ).
tff(f4112,plain,
( spl272_109
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_109])]) ).
tff(f11255,plain,
( spl272_704
<=> ! [X0: $real] : ~ $less($sum(7.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_704])]) ).
tff(f12610,plain,
( ! [X0: $real] : $less(X0,$sum(8.0,X0))
| ~ spl272_109
| ~ spl272_704 ),
inference(evaluation,[],[f12604]) ).
tff(f12604,plain,
( ! [X0: $real] : $less(X0,$sum(7.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_704 ),
inference(resolution,[],[f11256,f4113]) ).
tff(f4113,plain,
( ! [X0: $real,X1: $real] :
( $less(X1,$sum(X0,1.0))
| $less(X0,X1) )
| ~ spl272_109 ),
inference(avatar_component_clause,[],[f4112]) ).
tff(f11256,plain,
( ! [X0: $real] : ~ $less($sum(7.0,X0),X0)
| ~ spl272_704 ),
inference(avatar_component_clause,[],[f11255]) ).
tff(f13271,plain,
spl272_785,
inference(avatar_split_clause,[],[f3222,f13269]) ).
tff(f13269,plain,
( spl272_785
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK270(X1))),'fun_app$c'(X1,sK271(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_785])]) ).
tff(f3222,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK270(X1))),'fun_app$c'(X1,sK271(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ),
inference(cnf_transformation,[],[f2128]) ).
tff(f2128,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK270(X1))),'fun_app$c'(X1,sK271(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK270(X1)),sK271(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK270,sK271])],[f1496,f2127]) ).
tff(f2127,plain,
! [X1: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK270(X1))),'fun_app$c'(X1,sK271(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK270(X1)),sK271(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1496,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ),
inference(flattening,[],[f1495]) ).
tff(f1495,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ),
inference(ennf_transformation,[],[f263]) ).
tff(f263,axiom,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
tff(f13267,plain,
spl272_784,
inference(avatar_split_clause,[],[f3220,f13265]) ).
tff(f13265,plain,
( spl272_784
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK268(X1))),'fun_app$w'(X1,sK269(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_784])]) ).
tff(f3220,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK268(X1))),'fun_app$w'(X1,sK269(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ),
inference(cnf_transformation,[],[f2126]) ).
tff(f2126,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK268(X1))),'fun_app$w'(X1,sK269(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK268(X1)),sK269(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK268,sK269])],[f1494,f2125]) ).
tff(f2125,plain,
! [X1: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK268(X1))),'fun_app$w'(X1,sK269(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK268(X1)),sK269(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1494,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ),
inference(flattening,[],[f1493]) ).
tff(f1493,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ),
inference(ennf_transformation,[],[f264]) ).
tff(f264,axiom,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
tff(f13263,plain,
spl272_783,
inference(avatar_split_clause,[],[f3214,f13261]) ).
tff(f13261,plain,
( spl272_783
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK262(X1))),'fun_app$c'(X1,sK263(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_783])]) ).
tff(f3214,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK262(X1))),'fun_app$c'(X1,sK263(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ),
inference(cnf_transformation,[],[f2120]) ).
tff(f2120,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK262(X1))),'fun_app$c'(X1,sK263(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK262(X1)),sK263(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK262,sK263])],[f1488,f2119]) ).
tff(f2119,plain,
! [X1: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK262(X1))),'fun_app$c'(X1,sK263(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK262(X1)),sK263(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1488,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ),
inference(flattening,[],[f1487]) ).
tff(f1487,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ),
inference(ennf_transformation,[],[f486]) ).
tff(f486,axiom,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom484) ).
tff(f13259,plain,
spl272_782,
inference(avatar_split_clause,[],[f3212,f13257]) ).
tff(f13257,plain,
( spl272_782
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK260(X1))),'fun_app$w'(X1,sK261(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_782])]) ).
tff(f3212,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK260(X1))),'fun_app$w'(X1,sK261(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ),
inference(cnf_transformation,[],[f2118]) ).
tff(f2118,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK260(X1))),'fun_app$w'(X1,sK261(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK260(X1)),sK261(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK260,sK261])],[f1486,f2117]) ).
tff(f2117,plain,
! [X1: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK260(X1))),'fun_app$w'(X1,sK261(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK260(X1)),sK261(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1486,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ),
inference(flattening,[],[f1485]) ).
tff(f1485,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ),
inference(ennf_transformation,[],[f488]) ).
tff(f488,axiom,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less$a',X2),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
tff(f13255,plain,
spl272_781,
inference(avatar_split_clause,[],[f3206,f13253]) ).
tff(f13253,plain,
( spl272_781
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK254(X1))),'fun_app$i'(X1,sK255(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_781])]) ).
tff(f3206,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK254(X1))),'fun_app$i'(X1,sK255(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ),
inference(cnf_transformation,[],[f2112]) ).
tff(f2112,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK254(X1))),'fun_app$i'(X1,sK255(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK254(X1)),sK255(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK254,sK255])],[f1480,f2111]) ).
tff(f2111,plain,
! [X1: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK254(X1))),'fun_app$i'(X1,sK255(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK254(X1)),sK255(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1480,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ),
inference(flattening,[],[f1479]) ).
tff(f1479,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ),
inference(ennf_transformation,[],[f267]) ).
tff(f267,axiom,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom265) ).
tff(f13251,plain,
spl272_780,
inference(avatar_split_clause,[],[f3202,f13249]) ).
tff(f13249,plain,
( spl272_780
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK250(X1))),'fun_app$i'(X1,sK251(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_780])]) ).
tff(f3202,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK250(X1))),'fun_app$i'(X1,sK251(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ),
inference(cnf_transformation,[],[f2108]) ).
tff(f2108,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK250(X1))),'fun_app$i'(X1,sK251(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK250(X1)),sK251(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK250,sK251])],[f1476,f2107]) ).
tff(f2107,plain,
! [X1: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK250(X1))),'fun_app$i'(X1,sK251(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK250(X1)),sK251(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1476,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ),
inference(flattening,[],[f1475]) ).
tff(f1475,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ),
inference(ennf_transformation,[],[f494]) ).
tff(f494,axiom,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) )
=> 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
tff(f13247,plain,
spl272_779,
inference(avatar_split_clause,[],[f3181,f13245]) ).
tff(f13245,plain,
( spl272_779
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num_num_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK230(X2))),'fun_app$c'(X2,sK231(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_779])]) ).
tff(f3181,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK230(X2))),'fun_app$c'(X2,sK231(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2088]) ).
tff(f2088,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK230(X2))),'fun_app$c'(X2,sK231(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK230(X2)),sK231(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK230,sK231])],[f1454,f2087]) ).
tff(f2087,plain,
! [X2: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK230(X2))),'fun_app$c'(X2,sK231(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK230(X2)),sK231(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1454,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1453]) ).
tff(f1453,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f273]) ).
tff(f273,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
tff(f13243,plain,
spl272_778,
inference(avatar_split_clause,[],[f3179,f13241]) ).
tff(f13241,plain,
( spl272_778
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Num_enat_fun$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK228(X2))),'fun_app$i'(X2,sK229(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_778])]) ).
tff(f3179,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK228(X2))),'fun_app$i'(X2,sK229(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2086]) ).
tff(f2086,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK228(X2))),'fun_app$i'(X2,sK229(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK228(X2)),sK229(X2)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK228,sK229])],[f1452,f2085]) ).
tff(f2085,plain,
! [X2: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK228(X2))),'fun_app$i'(X2,sK229(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK228(X2)),sK229(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1452,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1451]) ).
tff(f1451,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f274]) ).
tff(f274,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
tff(f13239,plain,
( spl272_777
| ~ spl272_58
| ~ spl272_704 ),
inference(avatar_split_clause,[],[f12608,f11255,f3865,f13237]) ).
tff(f13237,plain,
( spl272_777
<=> ! [X0: $real] : ~ $less($sum(X0,7.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_777])]) ).
tff(f3865,plain,
( spl272_58
<=> ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_58])]) ).
tff(f12608,plain,
( ! [X0: $real] : ~ $less($sum(X0,7.0),X0)
| ~ spl272_58
| ~ spl272_704 ),
inference(superposition,[],[f11256,f3866]) ).
tff(f3866,plain,
( ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl272_58 ),
inference(avatar_component_clause,[],[f3865]) ).
tff(f13235,plain,
spl272_776,
inference(avatar_split_clause,[],[f3165,f13233]) ).
tff(f13233,plain,
( spl272_776
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num_num_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK214(X2))),'fun_app$c'(X2,sK215(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_776])]) ).
tff(f3165,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK214(X2))),'fun_app$c'(X2,sK215(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2072]) ).
tff(f2072,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK214(X2))),'fun_app$c'(X2,sK215(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK214(X2)),sK215(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK214,sK215])],[f1438,f2071]) ).
tff(f2071,plain,
! [X2: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK214(X2))),'fun_app$c'(X2,sK215(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK214(X2)),sK215(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1438,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1437]) ).
tff(f1437,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f476]) ).
tff(f476,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom474) ).
tff(f13231,plain,
spl272_775,
inference(avatar_split_clause,[],[f3163,f13229]) ).
tff(f13229,plain,
( spl272_775
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Num_enat_fun$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK212(X2))),'fun_app$i'(X2,sK213(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_775])]) ).
tff(f3163,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK212(X2))),'fun_app$i'(X2,sK213(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2070]) ).
tff(f2070,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK212(X2))),'fun_app$i'(X2,sK213(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK212(X2)),sK213(X2)) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK212,sK213])],[f1436,f2069]) ).
tff(f2069,plain,
! [X2: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK212(X2))),'fun_app$i'(X2,sK213(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK212(X2)),sK213(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1436,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1435]) ).
tff(f1435,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f478]) ).
tff(f478,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5)) )
& 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom476) ).
tff(f13227,plain,
spl272_774,
inference(avatar_split_clause,[],[f3149,f13225]) ).
tff(f13225,plain,
( spl272_774
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Enat_num_fun$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK198(X2))),'fun_app$w'(X2,sK199(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_774])]) ).
tff(f3149,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK198(X2))),'fun_app$w'(X2,sK199(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2056]) ).
tff(f2056,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK198(X2))),'fun_app$w'(X2,sK199(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK198(X2)),sK199(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198,sK199])],[f1422,f2055]) ).
tff(f2055,plain,
! [X2: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK198(X2))),'fun_app$w'(X2,sK199(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK198(X2)),sK199(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1422,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(flattening,[],[f1421]) ).
tff(f1421,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(ennf_transformation,[],[f277]) ).
tff(f277,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
tff(f13223,plain,
spl272_773,
inference(avatar_split_clause,[],[f3141,f13221]) ).
tff(f13221,plain,
( spl272_773
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Enat_num_fun$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK190(X2))),'fun_app$w'(X2,sK191(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_773])]) ).
tff(f3141,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK190(X2))),'fun_app$w'(X2,sK191(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2048]) ).
tff(f2048,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK190(X2))),'fun_app$w'(X2,sK191(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK190(X2)),sK191(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK190,sK191])],[f1414,f2047]) ).
tff(f2047,plain,
! [X2: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK190(X2))),'fun_app$w'(X2,sK191(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK190(X2)),sK191(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1414,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(flattening,[],[f1413]) ).
tff(f1413,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f484]) ).
tff(f484,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
& 'fun_app$g'('fun_app$h'('less$a',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom482) ).
tff(f13103,plain,
spl272_772,
inference(avatar_split_clause,[],[f3038,f13101]) ).
tff(f13101,plain,
( spl272_772
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_772])]) ).
tff(f3038,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) ) ),
inference(cnf_transformation,[],[f1955]) ).
tff(f1955,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X2) ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(flattening,[],[f1954]) ).
tff(f1954,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X2) ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(nnf_transformation,[],[f381]) ).
tff(f381,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) )
<=> ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).
tff(f13099,plain,
spl272_771,
inference(avatar_split_clause,[],[f3035,f13097]) ).
tff(f13097,plain,
( spl272_771
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_771])]) ).
tff(f3035,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) ) ),
inference(cnf_transformation,[],[f1953]) ).
tff(f1953,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) ) ) ),
inference(flattening,[],[f1952]) ).
tff(f1952,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) ) ) ),
inference(nnf_transformation,[],[f451]) ).
tff(f451,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
<=> ( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
tff(f13095,plain,
( spl272_770
| ~ spl272_107
| ~ spl272_688 ),
inference(avatar_split_clause,[],[f11406,f11089,f4104,f13093]) ).
tff(f4104,plain,
( spl272_107
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_107])]) ).
tff(f11089,plain,
( spl272_688
<=> ! [X0: $int] : ~ $less($sum(7,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_688])]) ).
tff(f11406,plain,
( ! [X0: $int] : $less(X0,$sum(8,X0))
| ~ spl272_107
| ~ spl272_688 ),
inference(evaluation,[],[f11394]) ).
tff(f11394,plain,
( ! [X0: $int] : $less(X0,$sum(7,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_688 ),
inference(resolution,[],[f11090,f4105]) ).
tff(f4105,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl272_107 ),
inference(avatar_component_clause,[],[f4104]) ).
tff(f11090,plain,
( ! [X0: $int] : ~ $less($sum(7,X0),X0)
| ~ spl272_688 ),
inference(avatar_component_clause,[],[f11089]) ).
tff(f13091,plain,
spl272_769,
inference(avatar_split_clause,[],[f2849,f13089]) ).
tff(f13089,plain,
( spl272_769
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_769])]) ).
tff(f2849,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1272]) ).
tff(f1272,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f1271]) ).
tff(f1271,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f439]) ).
tff(f439,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
tff(f13087,plain,
spl272_768,
inference(avatar_split_clause,[],[f2797,f13085]) ).
tff(f13085,plain,
( spl272_768
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_768])]) ).
tff(f2797,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1816]) ).
tff(f1816,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) ) ) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(nnf_transformation,[],[f1190]) ).
tff(f1190,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
<=> ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) ) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f448]) ).
tff(f448,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
=> ( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
<=> ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
tff(f12765,plain,
( spl272_767
| ~ spl272_56
| ~ spl272_688 ),
inference(avatar_split_clause,[],[f11401,f11089,f3857,f12763]) ).
tff(f12763,plain,
( spl272_767
<=> ! [X0: $int] : ~ $less($sum(X0,7),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_767])]) ).
tff(f3857,plain,
( spl272_56
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_56])]) ).
tff(f11401,plain,
( ! [X0: $int] : ~ $less($sum(X0,7),X0)
| ~ spl272_56
| ~ spl272_688 ),
inference(superposition,[],[f11090,f3858]) ).
tff(f3858,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl272_56 ),
inference(avatar_component_clause,[],[f3857]) ).
tff(f12642,plain,
spl272_766,
inference(avatar_split_clause,[],[f3613,f12640]) ).
tff(f12640,plain,
( spl272_766
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_766])]) ).
tff(f3613,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
inference(forward_demodulation,[],[f3058,f848]) ).
tff(f3058,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2))) ),
inference(cnf_transformation,[],[f1967]) ).
tff(f1967,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
& ( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2))) ) ),
inference(nnf_transformation,[],[f551]) ).
tff(f551,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)))
<=> $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
tff(f12638,plain,
spl272_765,
inference(avatar_split_clause,[],[f3612,f12636]) ).
tff(f12636,plain,
( spl272_765
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_765])]) ).
tff(f3612,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
inference(forward_demodulation,[],[f3059,f848]) ).
tff(f3059,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1967]) ).
tff(f12634,plain,
spl272_764,
inference(avatar_split_clause,[],[f3611,f12632]) ).
tff(f12632,plain,
( spl272_764
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_764])]) ).
tff(f3611,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) ) ),
inference(forward_demodulation,[],[f3056,f848]) ).
tff(f3056,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)) ) ),
inference(cnf_transformation,[],[f1966]) ).
tff(f1966,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) )
| ( 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)) != 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)) ) ) ),
inference(nnf_transformation,[],[f552]) ).
tff(f552,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)) )
<=> ( 'fun_app$a'('of_nat$',X1) = 'fun_app$a'('of_nat$',X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
tff(f12630,plain,
spl272_763,
inference(avatar_split_clause,[],[f3610,f12628]) ).
tff(f12628,plain,
( spl272_763
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_763])]) ).
tff(f3610,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'($sum(1,'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) ),
inference(forward_demodulation,[],[f3057,f848]) ).
tff(f3057,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'($sum('fun_app$a'('of_nat$',X0),1)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) ),
inference(cnf_transformation,[],[f1966]) ).
tff(f12626,plain,
spl272_762,
inference(avatar_split_clause,[],[f3570,f12624]) ).
tff(f12624,plain,
( spl272_762
<=> ! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( $less('fun_app$a'(X0,sK89(X0)),'fun_app$a'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK89(X0))))))
| ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_762])]) ).
tff(f3570,plain,
! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( $less('fun_app$a'(X0,sK89(X0)),'fun_app$a'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK89(X0))))))
| ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2936,f848]) ).
tff(f2936,plain,
! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'(X0,sK89(X0)),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK89(X0)),1)))) ),
inference(cnf_transformation,[],[f1891]) ).
tff(f1891,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'(X0,sK89(X0)),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK89(X0)),1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f1314,f1890]) ).
tff(f1890,plain,
! [X0: 'Nat_int_fun$'] :
( ? [X3: 'Nat$'] : $less('fun_app$a'(X0,X3),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))))
=> $less('fun_app$a'(X0,sK89(X0)),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK89(X0)),1)))) ),
introduced(choice_axiom,[]) ).
tff(f1314,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$a'(X0,X3),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(flattening,[],[f1313]) ).
tff(f1313,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$a'(X0,X3),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(ennf_transformation,[],[f796]) ).
tff(f796,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : ~ $less('fun_app$a'(X0,X3),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> ~ $less('fun_app$a'(X0,X1),'fun_app$a'(X0,X2)) ),
inference(theory_normalization,[],[f18]) ).
tff(f18,axiom,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : $lesseq('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$a'(X0,X3)) )
=> $lesseq('fun_app$a'(X0,X2),'fun_app$a'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom16) ).
tff(f12622,plain,
spl272_761,
inference(avatar_split_clause,[],[f3569,f12620]) ).
tff(f12620,plain,
( spl272_761
<=> ! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( $less('fun_app$a'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK88(X0))))),'fun_app$a'(X0,sK88(X0)))
| ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_761])]) ).
tff(f3569,plain,
! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( $less('fun_app$a'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK88(X0))))),'fun_app$a'(X0,sK88(X0)))
| ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2935,f848]) ).
tff(f2935,plain,
! [X2: 'Nat$',X0: 'Nat_int_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK88(X0)),1))),'fun_app$a'(X0,sK88(X0))) ),
inference(cnf_transformation,[],[f1889]) ).
tff(f1889,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK88(X0)),1))),'fun_app$a'(X0,sK88(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f1312,f1888]) ).
tff(f1888,plain,
! [X0: 'Nat_int_fun$'] :
( ? [X3: 'Nat$'] : $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$a'(X0,X3))
=> $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK88(X0)),1))),'fun_app$a'(X0,sK88(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1312,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$a'(X0,X3)) ),
inference(flattening,[],[f1311]) ).
tff(f1311,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$a'(X0,X3)) ),
inference(ennf_transformation,[],[f795]) ).
tff(f795,plain,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : ~ $less('fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$a'(X0,X3)) )
=> ~ $less('fun_app$a'(X0,X2),'fun_app$a'(X0,X1)) ),
inference(theory_normalization,[],[f14]) ).
tff(f14,axiom,
! [X0: 'Nat_int_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : $lesseq('fun_app$a'(X0,X3),'fun_app$a'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> $lesseq('fun_app$a'(X0,X1),'fun_app$a'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
tff(f12618,plain,
spl272_760,
inference(avatar_split_clause,[],[f3568,f12616]) ).
tff(f12616,plain,
( spl272_760
<=> ! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( $less('fun_app$m'(X0,sK87(X0)),'fun_app$m'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK87(X0))))))
| ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_760])]) ).
tff(f3568,plain,
! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( $less('fun_app$m'(X0,sK87(X0)),'fun_app$m'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK87(X0))))))
| ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2934,f848]) ).
tff(f2934,plain,
! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$m'(X0,sK87(X0)),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK87(X0)),1)))) ),
inference(cnf_transformation,[],[f1887]) ).
tff(f1887,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$m'(X0,sK87(X0)),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK87(X0)),1)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f1310,f1886]) ).
tff(f1886,plain,
! [X0: 'Nat_real_fun$'] :
( ? [X3: 'Nat$'] : $less('fun_app$m'(X0,X3),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))))
=> $less('fun_app$m'(X0,sK87(X0)),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK87(X0)),1)))) ),
introduced(choice_axiom,[]) ).
tff(f1310,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$m'(X0,X3),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(flattening,[],[f1309]) ).
tff(f1309,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$m'(X0,X3),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) ),
inference(ennf_transformation,[],[f794]) ).
tff(f794,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : ~ $less('fun_app$m'(X0,X3),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> ~ $less('fun_app$m'(X0,X1),'fun_app$m'(X0,X2)) ),
inference(theory_normalization,[],[f21]) ).
tff(f21,axiom,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : $lesseq('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$m'(X0,X3)) )
=> $lesseq('fun_app$m'(X0,X2),'fun_app$m'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
tff(f12614,plain,
spl272_759,
inference(avatar_split_clause,[],[f3567,f12612]) ).
tff(f12612,plain,
( spl272_759
<=> ! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( $less('fun_app$m'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK86(X0))))),'fun_app$m'(X0,sK86(X0)))
| ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_759])]) ).
tff(f3567,plain,
! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( $less('fun_app$m'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK86(X0))))),'fun_app$m'(X0,sK86(X0)))
| ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2933,f848]) ).
tff(f2933,plain,
! [X2: 'Nat$',X0: 'Nat_real_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK86(X0)),1))),'fun_app$m'(X0,sK86(X0))) ),
inference(cnf_transformation,[],[f1885]) ).
tff(f1885,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK86(X0)),1))),'fun_app$m'(X0,sK86(X0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f1308,f1884]) ).
tff(f1884,plain,
! [X0: 'Nat_real_fun$'] :
( ? [X3: 'Nat$'] : $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$m'(X0,X3))
=> $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK86(X0)),1))),'fun_app$m'(X0,sK86(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1308,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$m'(X0,X3)) ),
inference(flattening,[],[f1307]) ).
tff(f1307,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ? [X3: 'Nat$'] : $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$m'(X0,X3)) ),
inference(ennf_transformation,[],[f793]) ).
tff(f793,plain,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ! [X3: 'Nat$'] : ~ $less('fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1))),'fun_app$m'(X0,X3)) )
=> ~ $less('fun_app$m'(X0,X2),'fun_app$m'(X0,X1)) ),
inference(theory_normalization,[],[f17]) ).
tff(f17,axiom,
! [X0: 'Nat_real_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& ! [X3: 'Nat$'] : $lesseq('fun_app$m'(X0,X3),'fun_app$m'(X0,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))) )
=> $lesseq('fun_app$m'(X0,X1),'fun_app$m'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
tff(f12603,plain,
spl272_758,
inference(avatar_split_clause,[],[f3559,f12601]) ).
tff(f12601,plain,
( spl272_758
<=> ! [X2: $int,X0: $int,X1: 'Nat$'] :
( ( 'fun_app$a'('power$a'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$a'('power$a'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| $less(X2,0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_758])]) ).
tff(f3559,plain,
! [X2: $int,X0: $int,X1: 'Nat$'] :
( ( 'fun_app$a'('power$a'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$a'('power$a'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| $less(X2,0)
| $less(X0,0) ),
inference(forward_demodulation,[],[f2879,f848]) ).
tff(f2879,plain,
! [X2: $int,X0: $int,X1: 'Nat$'] :
( ( X0 = X2 )
| $less(X2,0)
| $less(X0,0)
| ( 'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(cnf_transformation,[],[f1294]) ).
tff(f1294,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( X0 = X2 )
| $less(X2,0)
| $less(X0,0)
| ( 'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(flattening,[],[f1293]) ).
tff(f1293,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( X0 = X2 )
| $less(X2,0)
| $less(X0,0)
| ( 'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(ennf_transformation,[],[f788]) ).
tff(f788,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( ~ $less(X2,0)
& ~ $less(X0,0)
& ( 'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = 'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) )
=> ( X0 = X2 ) ),
inference(theory_normalization,[],[f319]) ).
tff(f319,axiom,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( $lesseq(0,X2)
& $lesseq(0,X0)
& ( 'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = 'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) )
=> ( X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
tff(f12599,plain,
spl272_757,
inference(avatar_split_clause,[],[f3557,f12597]) ).
tff(f12597,plain,
( spl272_757
<=> ! [X2: $real,X0: $real,X1: 'Nat$'] :
( ( 'fun_app$m'('power$c'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$m'('power$c'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| $less(X2,0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_757])]) ).
tff(f3557,plain,
! [X2: $real,X0: $real,X1: 'Nat$'] :
( ( 'fun_app$m'('power$c'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) != 'fun_app$m'('power$c'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) )
| ( X0 = X2 )
| $less(X2,0.0)
| $less(X0,0.0) ),
inference(forward_demodulation,[],[f2877,f848]) ).
tff(f2877,plain,
! [X2: $real,X0: $real,X1: 'Nat$'] :
( ( X0 = X2 )
| $less(X2,0.0)
| $less(X0,0.0)
| ( 'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(cnf_transformation,[],[f1290]) ).
tff(f1290,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( X0 = X2 )
| $less(X2,0.0)
| $less(X0,0.0)
| ( 'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(flattening,[],[f1289]) ).
tff(f1289,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( X0 = X2 )
| $less(X2,0.0)
| $less(X0,0.0)
| ( 'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) != 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) ),
inference(ennf_transformation,[],[f787]) ).
tff(f787,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( ~ $less(X2,0.0)
& ~ $less(X0,0.0)
& ( 'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) )
=> ( X0 = X2 ) ),
inference(theory_normalization,[],[f320]) ).
tff(f320,axiom,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( $lesseq(0.0,X2)
& $lesseq(0.0,X0)
& ( 'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) ) )
=> ( X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom318) ).
tff(f12595,plain,
spl272_756,
inference(avatar_split_clause,[],[f3218,f12593]) ).
tff(f12593,plain,
( spl272_756
<=> ! [X0: 'Num$',X3: $int,X2: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK266(X1))),'fun_app$v'(X1,sK267(X1)))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_756])]) ).
tff(f3218,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK266(X1))),'fun_app$v'(X1,sK267(X1)))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ),
inference(cnf_transformation,[],[f2124]) ).
tff(f2124,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK266(X1))),'fun_app$v'(X1,sK267(X1)))
& ~ $less(sK267(X1),sK266(X1)) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK266,sK267])],[f1492,f2123]) ).
tff(f2123,plain,
! [X1: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK266(X1))),'fun_app$v'(X1,sK267(X1)))
& ~ $less(sK267(X1),sK266(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1492,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ),
inference(flattening,[],[f1491]) ).
tff(f1491,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ),
inference(ennf_transformation,[],[f847]) ).
tff(f847,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& ~ $less(X3,X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3)) ),
inference(theory_normalization,[],[f262]) ).
tff(f262,axiom,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& $lesseq(X2,X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom260) ).
tff(f12591,plain,
spl272_755,
inference(avatar_split_clause,[],[f3216,f12589]) ).
tff(f12589,plain,
( spl272_755
<=> ! [X0: 'Num$',X3: $real,X2: $real,X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,sK264(X1))),'fun_app$x'(X1,sK265(X1)))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_755])]) ).
tff(f3216,plain,
! [X2: $real,X3: $real,X0: 'Num$',X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,sK264(X1))),'fun_app$x'(X1,sK265(X1)))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ),
inference(cnf_transformation,[],[f2122]) ).
tff(f2122,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,sK264(X1))),'fun_app$x'(X1,sK265(X1)))
& ~ $less(sK265(X1),sK264(X1)) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK264,sK265])],[f1490,f2121]) ).
tff(f2121,plain,
! [X1: 'Real_num_fun$'] :
( ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,sK264(X1))),'fun_app$x'(X1,sK265(X1)))
& ~ $less(sK265(X1),sK264(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1490,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ),
inference(flattening,[],[f1489]) ).
tff(f1489,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ),
inference(ennf_transformation,[],[f846]) ).
tff(f846,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( ~ $less(X5,X4)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5)) )
& ~ $less(X3,X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3)) ),
inference(theory_normalization,[],[f265]) ).
tff(f265,axiom,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( $lesseq(X4,X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5)) )
& $lesseq(X2,X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom263) ).
tff(f12587,plain,
spl272_754,
inference(avatar_split_clause,[],[f3210,f12585]) ).
tff(f12585,plain,
( spl272_754
<=> ! [X0: 'Num$',X3: $int,X2: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK258(X1))),'fun_app$v'(X1,sK259(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_754])]) ).
tff(f3210,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK258(X1))),'fun_app$v'(X1,sK259(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ),
inference(cnf_transformation,[],[f2116]) ).
tff(f2116,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK258(X1))),'fun_app$v'(X1,sK259(X1)))
& $less(sK258(X1),sK259(X1)) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK258,sK259])],[f1484,f2115]) ).
tff(f2115,plain,
! [X1: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK258(X1))),'fun_app$v'(X1,sK259(X1)))
& $less(sK258(X1),sK259(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1484,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ),
inference(flattening,[],[f1483]) ).
tff(f1483,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ),
inference(ennf_transformation,[],[f487]) ).
tff(f487,axiom,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& $less(X2,X3)
& 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom485) ).
tff(f12583,plain,
spl272_753,
inference(avatar_split_clause,[],[f3208,f12581]) ).
tff(f12581,plain,
( spl272_753
<=> ! [X0: 'Num$',X3: $real,X2: $real,X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,sK256(X1))),'fun_app$x'(X1,sK257(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_753])]) ).
tff(f3208,plain,
! [X2: $real,X3: $real,X0: 'Num$',X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,sK256(X1))),'fun_app$x'(X1,sK257(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ),
inference(cnf_transformation,[],[f2114]) ).
tff(f2114,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,sK256(X1))),'fun_app$x'(X1,sK257(X1)))
& $less(sK256(X1),sK257(X1)) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK256,sK257])],[f1482,f2113]) ).
tff(f2113,plain,
! [X1: 'Real_num_fun$'] :
( ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,sK256(X1))),'fun_app$x'(X1,sK257(X1)))
& $less(sK256(X1),sK257(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1482,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ),
inference(flattening,[],[f1481]) ).
tff(f1481,plain,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ),
inference(ennf_transformation,[],[f489]) ).
tff(f489,axiom,
! [X0: 'Num$',X1: 'Real_num_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( $less(X4,X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$x'(X1,X4)),'fun_app$x'(X1,X5)) )
& $less(X2,X3)
& 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
tff(f12579,plain,
spl272_752,
inference(avatar_split_clause,[],[f3204,f12577]) ).
tff(f12577,plain,
( spl272_752
<=> ! [X0: 'Enat$',X3: $int,X2: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK252(X1))),'fun_app$y'(X1,sK253(X1)))
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_752])]) ).
tff(f3204,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK252(X1))),'fun_app$y'(X1,sK253(X1)))
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ),
inference(cnf_transformation,[],[f2110]) ).
tff(f2110,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK252(X1))),'fun_app$y'(X1,sK253(X1)))
& ~ $less(sK253(X1),sK252(X1)) )
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK252,sK253])],[f1478,f2109]) ).
tff(f2109,plain,
! [X1: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK252(X1))),'fun_app$y'(X1,sK253(X1)))
& ~ $less(sK253(X1),sK252(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1478,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ),
inference(flattening,[],[f1477]) ).
tff(f1477,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ),
inference(ennf_transformation,[],[f845]) ).
tff(f845,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& ~ $less(X3,X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3)) ),
inference(theory_normalization,[],[f266]) ).
tff(f266,axiom,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& $lesseq(X2,X3)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom264) ).
tff(f12575,plain,
spl272_751,
inference(avatar_split_clause,[],[f3200,f12573]) ).
tff(f12573,plain,
( spl272_751
<=> ! [X0: 'Enat$',X3: $int,X2: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK248(X1))),'fun_app$y'(X1,sK249(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_751])]) ).
tff(f3200,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK248(X1))),'fun_app$y'(X1,sK249(X1)))
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ),
inference(cnf_transformation,[],[f2106]) ).
tff(f2106,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK248(X1))),'fun_app$y'(X1,sK249(X1)))
& $less(sK248(X1),sK249(X1)) )
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK248,sK249])],[f1474,f2105]) ).
tff(f2105,plain,
! [X1: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK248(X1))),'fun_app$y'(X1,sK249(X1)))
& $less(sK248(X1),sK249(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1474,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ),
inference(flattening,[],[f1473]) ).
tff(f1473,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ),
inference(ennf_transformation,[],[f495]) ).
tff(f495,axiom,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& $less(X2,X3)
& 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) )
=> 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
tff(f12571,plain,
spl272_750,
inference(avatar_split_clause,[],[f3093,f12569]) ).
tff(f12569,plain,
( spl272_750
<=> ! [X0: $int,X3: 'Num$',X2: 'Int_num_fun$',X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK142(X2))),'fun_app$v'(X2,sK143(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_750])]) ).
tff(f3093,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK142(X2))),'fun_app$v'(X2,sK143(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f2000]) ).
tff(f2000,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK142(X2))),'fun_app$v'(X2,sK143(X2)))
& ~ $less(sK143(X2),sK142(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143])],[f1366,f1999]) ).
tff(f1999,plain,
! [X2: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK142(X2))),'fun_app$v'(X2,sK143(X2)))
& ~ $less(sK143(X2),sK142(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1366,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ),
inference(flattening,[],[f1365]) ).
tff(f1365,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f826]) ).
tff(f826,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
& ~ $less(X1,X0) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3) ),
inference(theory_normalization,[],[f269]) ).
tff(f269,axiom,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
& $lesseq(X0,X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom267) ).
tff(f12567,plain,
spl272_749,
inference(avatar_split_clause,[],[f3091,f12565]) ).
tff(f12565,plain,
( spl272_749
<=> ! [X0: $int,X3: 'Enat$',X2: 'Int_enat_fun$',X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK140(X2))),'fun_app$y'(X2,sK141(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_749])]) ).
tff(f3091,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK140(X2))),'fun_app$y'(X2,sK141(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1998]) ).
tff(f1998,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK140(X2))),'fun_app$y'(X2,sK141(X2)))
& ~ $less(sK141(X2),sK140(X2)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK140,sK141])],[f1364,f1997]) ).
tff(f1997,plain,
! [X2: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK140(X2))),'fun_app$y'(X2,sK141(X2)))
& ~ $less(sK141(X2),sK140(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1364,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ),
inference(flattening,[],[f1363]) ).
tff(f1363,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f825]) ).
tff(f825,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
& ~ $less(X1,X0) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3) ),
inference(theory_normalization,[],[f270]) ).
tff(f270,axiom,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
& $lesseq(X0,X1) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom268) ).
tff(f12556,plain,
spl272_748,
inference(avatar_split_clause,[],[f3077,f12554]) ).
tff(f12554,plain,
( spl272_748
<=> ! [X0: $int,X3: 'Num$',X2: 'Int_num_fun$',X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK126(X2))),'fun_app$v'(X2,sK127(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_748])]) ).
tff(f3077,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK126(X2))),'fun_app$v'(X2,sK127(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1984]) ).
tff(f1984,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK126(X2))),'fun_app$v'(X2,sK127(X2)))
& $less(sK126(X2),sK127(X2)) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK126,sK127])],[f1350,f1983]) ).
tff(f1983,plain,
! [X2: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK126(X2))),'fun_app$v'(X2,sK127(X2)))
& $less(sK126(X2),sK127(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1350,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(flattening,[],[f1349]) ).
tff(f1349,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f480]) ).
tff(f480,axiom,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
& $less(X0,X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom478) ).
tff(f12552,plain,
spl272_747,
inference(avatar_split_clause,[],[f3075,f12550]) ).
tff(f12550,plain,
( spl272_747
<=> ! [X0: $int,X3: 'Enat$',X2: 'Int_enat_fun$',X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK124(X2))),'fun_app$y'(X2,sK125(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_747])]) ).
tff(f3075,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK124(X2))),'fun_app$y'(X2,sK125(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1982]) ).
tff(f1982,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK124(X2))),'fun_app$y'(X2,sK125(X2)))
& $less(sK124(X2),sK125(X2)) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125])],[f1348,f1981]) ).
tff(f1981,plain,
! [X2: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK124(X2))),'fun_app$y'(X2,sK125(X2)))
& $less(sK124(X2),sK125(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1348,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(flattening,[],[f1347]) ).
tff(f1347,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f482]) ).
tff(f482,axiom,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
& $less(X0,X1) )
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom480) ).
tff(f12473,plain,
spl272_746,
inference(avatar_split_clause,[],[f3487,f12471]) ).
tff(f12471,plain,
( spl272_746
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK50(X0,X1))) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_746])]) ).
tff(f3487,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK50(X0,X1))) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f3486,f848]) ).
tff(f3486,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK50(X0,X1))) )
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2514,f848]) ).
tff(f2514,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK50(X0,X1)),1) )
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f1634,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK50(X0,X1)),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK50(X0,X1))) )
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f1154,f1633]) ).
tff(f1633,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
=> ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK50(X0,X1)),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK50(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1154,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f961]) ).
tff(f961,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
~ ( ! [X2: 'Nat$'] :
~ ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
& ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X0),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f960]) ).
tff(f960,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
~ ( ! [X2: 'Nat$'] :
~ ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
& ( ~ 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(true_and_false_elimination,[],[f569]) ).
tff(f569,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
=> $false )
& ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
=> $false )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
tff(f12469,plain,
spl272_745,
inference(avatar_split_clause,[],[f2957,f12467]) ).
tff(f12467,plain,
( spl272_745
<=> ! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',sK110(X0)),'fun_app$a'('of_nat$',sK111(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_745])]) ).
tff(f2957,plain,
! [X2: 'Nat$',X0: 'Nat_nat_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'(X0,X2)),'fun_app$a'('of_nat$','fun_app$b'(X0,X1)))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',sK110(X0)),'fun_app$a'('of_nat$',sK111(X0))) ),
inference(cnf_transformation,[],[f1913]) ).
tff(f12422,plain,
( spl272_744
| ~ spl272_44
| ~ spl272_55
| ~ spl272_734 ),
inference(avatar_split_clause,[],[f12176,f11866,f3851,f3797,f12419]) ).
tff(f12419,plain,
( spl272_744
<=> ( 'size$'('ys$') = 'size$a'('one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_744])]) ).
tff(f11866,plain,
( spl272_734
<=> ( 'fun_app$a'('of_nat$','size$'('ys$')) = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_734])]) ).
tff(f12176,plain,
( ( 'size$'('ys$') = 'size$a'('one$') )
| ~ spl272_44
| ~ spl272_55
| ~ spl272_734 ),
inference(forward_demodulation,[],[f11948,f3853]) ).
tff(f11948,plain,
( ( 'size$'('ys$') = 'nat$'(0) )
| ~ spl272_44
| ~ spl272_734 ),
inference(superposition,[],[f3798,f11868]) ).
tff(f11868,plain,
( ( 'fun_app$a'('of_nat$','size$'('ys$')) = 0 )
| ~ spl272_734 ),
inference(avatar_component_clause,[],[f11866]) ).
tff(f11905,plain,
spl272_743,
inference(avatar_split_clause,[],[f3548,f11903]) ).
tff(f11903,plain,
( spl272_743
<=> ! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK71(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK71(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_743])]) ).
tff(f3548,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,sK71(X2)),'nat$'($sum(1,'fun_app$a'('of_nat$',sK71(X2)))))
| 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2856,f848]) ).
tff(f2856,plain,
! [X2: 'Nat_nat_bool_fun_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ~ 'fun_app$n'('fun_app$o'(X2,sK71(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK71(X2)),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1832]) ).
tff(f1832,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ~ 'fun_app$n'('fun_app$o'(X2,sK71(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK71(X2)),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f1830,f1831]) ).
tff(f1831,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
=> ~ 'fun_app$n'('fun_app$o'(X2,sK71(X2)),'nat$'($sum('fun_app$a'('of_nat$',sK71(X2)),1))) ),
introduced(choice_axiom,[]) ).
tff(f1830,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ? [X3: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(rectify,[],[f1510]) ).
tff(f1510,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| sP6(X2)
| ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X6),'nat$'($sum('fun_app$a'('of_nat$',X6),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(definition_folding,[],[f1276,f1509]) ).
tff(f1509,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X3),X5)
& 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
| ~ sP6(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f1276,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X3),X5)
& 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
| ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X6),'nat$'($sum('fun_app$a'('of_nat$',X6),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f1275]) ).
tff(f1275,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X2,X0),X1)
| ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X3),X5)
& 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
| ? [X6: 'Nat$'] : ~ 'fun_app$n'('fun_app$o'(X2,X6),'nat$'($sum('fun_app$a'('of_nat$',X6),1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f984]) ).
tff(f984,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( ( ! [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
=> 'fun_app$n'('fun_app$o'(X2,X3),X5) )
& ! [X6: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X6),'nat$'($sum('fun_app$a'('of_nat$',X6),1)))
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'('fun_app$o'(X2,X0),X1) ),
inference(rectify,[],[f555]) ).
tff(f555,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_nat_bool_fun_fun$'] :
( ( ! [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
=> 'fun_app$n'('fun_app$o'(X2,X3),X5) )
& ! [X3: 'Nat$'] : 'fun_app$n'('fun_app$o'(X2,X3),'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'('fun_app$o'(X2,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
tff(f11901,plain,
spl272_742,
inference(avatar_split_clause,[],[f3221,f11899]) ).
tff(f11899,plain,
( spl272_742
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK270(X1)),sK271(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_742])]) ).
tff(f3221,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK270(X1)),sK271(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X2)) ),
inference(cnf_transformation,[],[f2128]) ).
tff(f11897,plain,
spl272_741,
inference(avatar_split_clause,[],[f3219,f11895]) ).
tff(f11895,plain,
( spl272_741
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK268(X1)),sK269(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_741])]) ).
tff(f3219,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK268(X1)),sK269(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X2)) ),
inference(cnf_transformation,[],[f2126]) ).
tff(f11893,plain,
spl272_740,
inference(avatar_split_clause,[],[f3213,f11891]) ).
tff(f11891,plain,
( spl272_740
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK262(X1)),sK263(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_740])]) ).
tff(f3213,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK262(X1)),sK263(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X2)) ),
inference(cnf_transformation,[],[f2120]) ).
tff(f11889,plain,
spl272_739,
inference(avatar_split_clause,[],[f3211,f11887]) ).
tff(f11887,plain,
( spl272_739
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK260(X1)),sK261(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_739])]) ).
tff(f3211,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK260(X1)),sK261(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X2)) ),
inference(cnf_transformation,[],[f2118]) ).
tff(f11885,plain,
spl272_738,
inference(avatar_split_clause,[],[f3205,f11883]) ).
tff(f11883,plain,
( spl272_738
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK254(X1)),sK255(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_738])]) ).
tff(f3205,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK254(X1)),sK255(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X2)) ),
inference(cnf_transformation,[],[f2112]) ).
tff(f11881,plain,
spl272_737,
inference(avatar_split_clause,[],[f3201,f11879]) ).
tff(f11879,plain,
( spl272_737
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK250(X1)),sK251(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_737])]) ).
tff(f3201,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK250(X1)),sK251(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X2)) ),
inference(cnf_transformation,[],[f2108]) ).
tff(f11877,plain,
spl272_736,
inference(avatar_split_clause,[],[f3180,f11875]) ).
tff(f11875,plain,
( spl272_736
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num_num_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK230(X2)),sK231(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_736])]) ).
tff(f3180,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK230(X2)),sK231(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2088]) ).
tff(f11873,plain,
spl272_735,
inference(avatar_split_clause,[],[f3178,f11871]) ).
tff(f11871,plain,
( spl272_735
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Num_enat_fun$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK228(X2)),sK229(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_735])]) ).
tff(f3178,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK228(X2)),sK229(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2086]) ).
tff(f11869,plain,
( spl272_734
| ~ spl272_183
| spl272_727 ),
inference(avatar_split_clause,[],[f11762,f11607,f4640,f11866]) ).
tff(f4640,plain,
( spl272_183
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_183])]) ).
tff(f11607,plain,
( spl272_727
<=> $less(0,'fun_app$a'('of_nat$','size$'('ys$'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_727])]) ).
tff(f11762,plain,
( ( 'fun_app$a'('of_nat$','size$'('ys$')) = 0 )
| ~ spl272_183
| spl272_727 ),
inference(resolution,[],[f11609,f4641]) ).
tff(f4641,plain,
( ! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) = 0 ) )
| ~ spl272_183 ),
inference(avatar_component_clause,[],[f4640]) ).
tff(f11609,plain,
( ~ $less(0,'fun_app$a'('of_nat$','size$'('ys$')))
| spl272_727 ),
inference(avatar_component_clause,[],[f11607]) ).
tff(f11864,plain,
spl272_733,
inference(avatar_split_clause,[],[f3164,f11862]) ).
tff(f11862,plain,
( spl272_733
<=> ! [X0: 'Num$',X3: 'Num$',X2: 'Num_num_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK214(X2)),sK215(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_733])]) ).
tff(f3164,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK214(X2)),sK215(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2072]) ).
tff(f11860,plain,
spl272_732,
inference(avatar_split_clause,[],[f3162,f11858]) ).
tff(f11858,plain,
( spl272_732
<=> ! [X0: 'Num$',X3: 'Enat$',X2: 'Num_enat_fun$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK212(X2)),sK213(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_732])]) ).
tff(f3162,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK212(X2)),sK213(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X1)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2070]) ).
tff(f11856,plain,
spl272_731,
inference(avatar_split_clause,[],[f3148,f11854]) ).
tff(f11854,plain,
( spl272_731
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Enat_num_fun$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK198(X2)),sK199(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_731])]) ).
tff(f3148,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK198(X2)),sK199(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2056]) ).
tff(f11852,plain,
spl272_730,
inference(avatar_split_clause,[],[f3140,f11850]) ).
tff(f11850,plain,
( spl272_730
<=> ! [X0: 'Enat$',X3: 'Num$',X2: 'Enat_num_fun$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK190(X2)),sK191(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_730])]) ).
tff(f3140,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK190(X2)),sK191(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X1)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2048]) ).
tff(f11848,plain,
spl272_729,
inference(avatar_split_clause,[],[f2929,f11846]) ).
tff(f11846,plain,
( spl272_729
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_729])]) ).
tff(f2929,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ),
inference(cnf_transformation,[],[f1532]) ).
tff(f1532,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X0) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X2) )
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ),
inference(definition_folding,[],[f1304,f1531,f1530,f1529,f1528]) ).
tff(f1528,plain,
! [X2: 'Num$',X1: 'Num$',X0: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
| ~ sP20(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
tff(f1529,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X0) )
| ~ sP21(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
tff(f1530,plain,
! [X1: 'Num$',X2: 'Num$',X0: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) )
| ~ sP22(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
tff(f1531,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ~ sP23(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
tff(f1304,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X0) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X2) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X0) )
| ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
inference(ennf_transformation,[],[f990]) ).
tff(f990,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
~ ( ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X0) )
& ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X2) )
& ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
& ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) )
& ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X0) )
& ~ ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
inference(true_and_false_elimination,[],[f207]) ).
tff(f207,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( ( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X0) )
=> $false )
& ( ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X2) )
=> $false )
& ( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
=> $false )
& ( ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) )
=> $false )
& ( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X0) )
=> $false )
& ( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
tff(f11844,plain,
spl272_728,
inference(avatar_split_clause,[],[f2917,f11842]) ).
tff(f11842,plain,
( spl272_728
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
| 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_728])]) ).
tff(f2917,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
| 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f1527,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2) )
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ),
inference(definition_folding,[],[f1303,f1526,f1525,f1524,f1523]) ).
tff(f1523,plain,
! [X2: 'Enat$',X1: 'Enat$',X0: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
| ~ sP16(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
tff(f1524,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0) )
| ~ sP17(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
tff(f1525,plain,
! [X1: 'Enat$',X2: 'Enat$',X0: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2) )
| ~ sP18(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
tff(f1526,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ~ sP19(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
tff(f1303,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0) )
| ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
inference(ennf_transformation,[],[f989]) ).
tff(f989,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
~ ( ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0) )
& ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2) )
& ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
& ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2) )
& ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0) )
& ~ ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
inference(true_and_false_elimination,[],[f208]) ).
tff(f208,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0) )
=> $false )
& ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2) )
=> $false )
& ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
=> $false )
& ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2) )
=> $false )
& ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0) )
=> $false )
& ( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
tff(f11610,plain,
( ~ spl272_727
| spl272_110
| ~ spl272_173
| ~ spl272_706 ),
inference(avatar_split_clause,[],[f11487,f11363,f4589,f4116,f11607]) ).
tff(f11363,plain,
( spl272_706
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_706])]) ).
tff(f11487,plain,
( $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$')))
| ~ $less(0,'fun_app$a'('of_nat$','size$'('ys$')))
| ~ spl272_173
| ~ spl272_706 ),
inference(resolution,[],[f11364,f4591]) ).
tff(f11364,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ spl272_706 ),
inference(avatar_component_clause,[],[f11363]) ).
tff(f11486,plain,
spl272_726,
inference(avatar_split_clause,[],[f3561,f11484]) ).
tff(f11484,plain,
( spl272_726
<=> ! [X2: $int,X0: $int,X1: 'Nat$'] :
( $less('fun_app$a'('power$a'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))),'fun_app$a'('power$a'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| ~ $less(X2,X0)
| $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_726])]) ).
tff(f3561,plain,
! [X2: $int,X0: $int,X1: 'Nat$'] :
( $less('fun_app$a'('power$a'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))),'fun_app$a'('power$a'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| ~ $less(X2,X0)
| $less(X2,0) ),
inference(forward_demodulation,[],[f2881,f848]) ).
tff(f2881,plain,
! [X2: $int,X0: $int,X1: 'Nat$'] :
( ~ $less(X2,X0)
| $less(X2,0)
| $less('fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(cnf_transformation,[],[f1298]) ).
tff(f1298,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ~ $less(X2,X0)
| $less(X2,0)
| $less('fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(flattening,[],[f1297]) ).
tff(f1297,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ~ $less(X2,X0)
| $less(X2,0)
| $less('fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(ennf_transformation,[],[f790]) ).
tff(f790,plain,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( ~ $less(X2,0)
& ~ $less('fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) )
=> ~ $less(X2,X0) ),
inference(theory_normalization,[],[f322]) ).
tff(f322,axiom,
! [X0: $int,X1: 'Nat$',X2: $int] :
( ( $lesseq(0,X2)
& $lesseq('fun_app$a'('power$a'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$a'('power$a'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) )
=> $lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom320) ).
tff(f11482,plain,
spl272_725,
inference(avatar_split_clause,[],[f3560,f11480]) ).
tff(f11480,plain,
( spl272_725
<=> ! [X2: $real,X0: $real,X1: 'Nat$'] :
( $less('fun_app$m'('power$c'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))),'fun_app$m'('power$c'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| ~ $less(X2,X0)
| $less(X2,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_725])]) ).
tff(f3560,plain,
! [X2: $real,X0: $real,X1: 'Nat$'] :
( $less('fun_app$m'('power$c'(X2),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))),'fun_app$m'('power$c'(X0),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))))
| ~ $less(X2,X0)
| $less(X2,0.0) ),
inference(forward_demodulation,[],[f2880,f848]) ).
tff(f2880,plain,
! [X2: $real,X0: $real,X1: 'Nat$'] :
( ~ $less(X2,X0)
| $less(X2,0.0)
| $less('fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(cnf_transformation,[],[f1296]) ).
tff(f1296,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ~ $less(X2,X0)
| $less(X2,0.0)
| $less('fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(flattening,[],[f1295]) ).
tff(f1295,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ~ $less(X2,X0)
| $less(X2,0.0)
| $less('fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) ),
inference(ennf_transformation,[],[f789]) ).
tff(f789,plain,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( ~ $less(X2,0.0)
& ~ $less('fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) )
=> ~ $less(X2,X0) ),
inference(theory_normalization,[],[f323]) ).
tff(f323,axiom,
! [X0: $real,X1: 'Nat$',X2: $real] :
( ( $lesseq(0.0,X2)
& $lesseq('fun_app$m'('power$c'(X0),'nat$'($sum('fun_app$a'('of_nat$',X1),1))),'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1)))) )
=> $lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom321) ).
tff(f11478,plain,
spl272_724,
inference(avatar_split_clause,[],[f3513,f11476]) ).
tff(f11476,plain,
( spl272_724
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) != $sum(1,'fun_app$a'('of_nat$',X2)) )
| $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_724])]) ).
tff(f3513,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) != $sum(1,'fun_app$a'('of_nat$',X2)) )
| $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) ),
inference(forward_demodulation,[],[f3512,f848]) ).
tff(f3512,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X2),1) ) ),
inference(forward_demodulation,[],[f2718,f848]) ).
tff(f2718,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X2),1) ) ),
inference(cnf_transformation,[],[f1755]) ).
tff(f1755,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X2),1) ) ) )
& ( ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK57(X0,X1)))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK57(X0,X1)),1) ) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1753,f1754]) ).
tff(f1754,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X3))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X3),1) ) )
=> ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK57(X0,X1)))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK57(X0,X1)),1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1753,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X2),1) ) ) )
& ( ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X3))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X3),1) ) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ) ),
inference(rectify,[],[f1752]) ).
tff(f1752,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X2),1) ) ) )
& ( ? [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) ) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ) ),
inference(nnf_transformation,[],[f559]) ).
tff(f559,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
<=> ? [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom557) ).
tff(f11446,plain,
spl272_723,
inference(avatar_split_clause,[],[f3508,f11444]) ).
tff(f11444,plain,
( spl272_723
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK56(X0,X1))) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_723])]) ).
tff(f3508,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK56(X0,X1))) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(forward_demodulation,[],[f3507,f848]) ).
tff(f3507,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK56(X0,X1))) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(forward_demodulation,[],[f2709,f848]) ).
tff(f2709,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK56(X0,X1)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f1749,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ( $less('fun_app$a'('of_nat$',sK56(X0,X1)),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK56(X0,X1)),1) ) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f1747,f1748]) ).
tff(f1748,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X3),1) ) )
=> ( $less('fun_app$a'('of_nat$',sK56(X0,X1)),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK56(X0,X1)),1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1747,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X3),1) ) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(rectify,[],[f1746]) ).
tff(f1746,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ? [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X2),1) ) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(flattening,[],[f1745]) ).
tff(f1745,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ! [X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ? [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X2),1) ) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(nnf_transformation,[],[f574]) ).
tff(f574,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
<=> ( ? [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X2),1) ) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom572) ).
tff(f11442,plain,
spl272_722,
inference(avatar_split_clause,[],[f3503,f11440]) ).
tff(f11440,plain,
( spl272_722
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X2)) )
| $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_722])]) ).
tff(f3503,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X2)) )
| $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f3502,f848]) ).
tff(f3502,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) ),
inference(forward_demodulation,[],[f2712,f848]) ).
tff(f2712,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X2),1) ) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f11438,plain,
spl272_721,
inference(avatar_split_clause,[],[f3488,f11436]) ).
tff(f11436,plain,
( spl272_721
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK50(X0,X1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_721])]) ).
tff(f3488,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK50(X0,X1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2513,f848]) ).
tff(f2513,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK50(X0,X1)))
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1634]) ).
tff(f11434,plain,
spl272_720,
inference(avatar_split_clause,[],[f3485,f11432]) ).
tff(f11432,plain,
( spl272_720
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_720])]) ).
tff(f3485,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',X0)) )
| $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f3484,f848]) ).
tff(f3484,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2512,f848]) ).
tff(f2512,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1153]) ).
tff(f1153,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f1152]) ).
tff(f1152,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X0),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f566]) ).
tff(f566,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X1) != $sum('fun_app$a'('of_nat$',X0),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
tff(f11430,plain,
spl272_719,
inference(avatar_split_clause,[],[f3396,f11428]) ).
tff(f11428,plain,
( spl272_719
<=> ! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK220(X2))),'fun_app$c'(X2,sK221(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_719])]) ).
tff(f3396,plain,
! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK220(X2))),'fun_app$c'(X2,sK221(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3171]) ).
tff(f3171,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK220(X2))),'fun_app$c'(X2,sK221(X2)))
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2078]) ).
tff(f2078,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK220(X2))),'fun_app$c'(X2,sK221(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK220(X2)),sK221(X2)) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK220,sK221])],[f1444,f2077]) ).
tff(f2077,plain,
! [X2: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,sK220(X2))),'fun_app$c'(X2,sK221(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK220(X2)),sK221(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1444,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1443]) ).
tff(f1443,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f305]) ).
tff(f305,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5)) )
& ( 'fun_app$c'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom303) ).
tff(f11426,plain,
spl272_718,
inference(avatar_split_clause,[],[f3394,f11424]) ).
tff(f11424,plain,
( spl272_718
<=> ! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK218(X2))),'fun_app$i'(X2,sK219(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_718])]) ).
tff(f3394,plain,
! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK218(X2))),'fun_app$i'(X2,sK219(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3169]) ).
tff(f3169,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK218(X2))),'fun_app$i'(X2,sK219(X2)))
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2076]) ).
tff(f2076,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK218(X2))),'fun_app$i'(X2,sK219(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK218(X2)),sK219(X2)) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218,sK219])],[f1442,f2075]) ).
tff(f2075,plain,
! [X2: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,sK218(X2))),'fun_app$i'(X2,sK219(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK218(X2)),sK219(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1442,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1441]) ).
tff(f1441,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f306]) ).
tff(f306,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5)) )
& ( 'fun_app$i'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
tff(f11422,plain,
spl272_717,
inference(avatar_split_clause,[],[f3388,f11420]) ).
tff(f11420,plain,
( spl272_717
<=> ! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK204(X2))),'fun_app$c'(X2,sK205(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_717])]) ).
tff(f3388,plain,
! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK204(X2))),'fun_app$c'(X2,sK205(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3155]) ).
tff(f3155,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK204(X2))),'fun_app$c'(X2,sK205(X2)))
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2062]) ).
tff(f2062,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK204(X2))),'fun_app$c'(X2,sK205(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK204(X2)),sK205(X2)) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK204,sK205])],[f1428,f2061]) ).
tff(f2061,plain,
! [X2: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,sK204(X2))),'fun_app$c'(X2,sK205(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK204(X2)),sK205(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1428,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1427]) ).
tff(f1427,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f500]) ).
tff(f500,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X4)),'fun_app$c'(X2,X5)) )
& ( 'fun_app$c'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom498) ).
tff(f11418,plain,
spl272_716,
inference(avatar_split_clause,[],[f3386,f11416]) ).
tff(f11416,plain,
( spl272_716
<=> ! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK202(X2))),'fun_app$i'(X2,sK203(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_716])]) ).
tff(f3386,plain,
! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK202(X2))),'fun_app$i'(X2,sK203(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3153]) ).
tff(f3153,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK202(X2))),'fun_app$i'(X2,sK203(X2)))
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2060]) ).
tff(f2060,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK202(X2))),'fun_app$i'(X2,sK203(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK202(X2)),sK203(X2)) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK202,sK203])],[f1426,f2059]) ).
tff(f2059,plain,
! [X2: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,sK202(X2))),'fun_app$i'(X2,sK203(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK202(X2)),sK203(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1426,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1425]) ).
tff(f1425,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f502]) ).
tff(f502,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X4)),'fun_app$i'(X2,X5)) )
& ( 'fun_app$i'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
tff(f11414,plain,
spl272_715,
inference(avatar_split_clause,[],[f3382,f11412]) ).
tff(f11412,plain,
( spl272_715
<=> ! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK194(X2))),'fun_app$w'(X2,sK195(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_715])]) ).
tff(f3382,plain,
! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK194(X2))),'fun_app$w'(X2,sK195(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(equality_resolution,[],[f3145]) ).
tff(f3145,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK194(X2))),'fun_app$w'(X2,sK195(X2)))
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2052]) ).
tff(f2052,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK194(X2))),'fun_app$w'(X2,sK195(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK194(X2)),sK195(X2)) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194,sK195])],[f1418,f2051]) ).
tff(f2051,plain,
! [X2: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,sK194(X2))),'fun_app$w'(X2,sK195(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK194(X2)),sK195(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1418,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(flattening,[],[f1417]) ).
tff(f1417,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(ennf_transformation,[],[f309]) ).
tff(f309,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5)) )
& ( 'fun_app$w'(X2,X1) = X3 )
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom307) ).
tff(f11410,plain,
spl272_714,
inference(avatar_split_clause,[],[f3378,f11408]) ).
tff(f11408,plain,
( spl272_714
<=> ! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK186(X2))),'fun_app$w'(X2,sK187(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_714])]) ).
tff(f3378,plain,
! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK186(X2))),'fun_app$w'(X2,sK187(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(equality_resolution,[],[f3137]) ).
tff(f3137,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK186(X2))),'fun_app$w'(X2,sK187(X2)))
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2044]) ).
tff(f2044,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK186(X2))),'fun_app$w'(X2,sK187(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK186(X2)),sK187(X2)) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186,sK187])],[f1410,f2043]) ).
tff(f2043,plain,
! [X2: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,sK186(X2))),'fun_app$w'(X2,sK187(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK186(X2)),sK187(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1410,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(flattening,[],[f1409]) ).
tff(f1409,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f508]) ).
tff(f508,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_num_fun$',X3: 'Num$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X4)),'fun_app$w'(X2,X5)) )
& ( 'fun_app$w'(X2,X1) = X3 )
& 'fun_app$g'('fun_app$h'('less$a',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom506) ).
tff(f11393,plain,
spl272_713,
inference(avatar_split_clause,[],[f3366,f11391]) ).
tff(f11391,plain,
( spl272_713
<=> ! [X2: 'Num$',X1: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK174(X1))),'fun_app$c'(X1,sK175(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_713])]) ).
tff(f3366,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK174(X1))),'fun_app$c'(X1,sK175(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3125]) ).
tff(f3125,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK174(X1))),'fun_app$c'(X1,sK175(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2032]) ).
tff(f2032,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK174(X1))),'fun_app$c'(X1,sK175(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK174(X1)),sK175(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK174,sK175])],[f1398,f2031]) ).
tff(f2031,plain,
! [X1: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,sK174(X1))),'fun_app$c'(X1,sK175(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK174(X1)),sK175(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1398,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(flattening,[],[f1397]) ).
tff(f1397,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f295]) ).
tff(f295,axiom,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$c'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).
tff(f11389,plain,
spl272_712,
inference(avatar_split_clause,[],[f3364,f11387]) ).
tff(f11387,plain,
( spl272_712
<=> ! [X2: 'Num$',X1: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK172(X1))),'fun_app$c'(X1,sK173(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_712])]) ).
tff(f3364,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK172(X1))),'fun_app$c'(X1,sK173(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3123]) ).
tff(f3123,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK172(X1))),'fun_app$c'(X1,sK173(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2030]) ).
tff(f2030,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK172(X1))),'fun_app$c'(X1,sK173(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK172(X1)),sK173(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172,sK173])],[f1396,f2029]) ).
tff(f2029,plain,
! [X1: 'Num_num_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,sK172(X1))),'fun_app$c'(X1,sK173(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK172(X1)),sK173(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1396,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(flattening,[],[f1395]) ).
tff(f1395,plain,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f510]) ).
tff(f510,axiom,
! [X0: 'Num$',X1: 'Num_num_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X4)),'fun_app$c'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& ( 'fun_app$c'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom508) ).
tff(f11385,plain,
spl272_711,
inference(avatar_split_clause,[],[f3362,f11383]) ).
tff(f11383,plain,
( spl272_711
<=> ! [X2: 'Num$',X1: 'Num_enat_fun$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK170(X1))),'fun_app$i'(X1,sK171(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_711])]) ).
tff(f3362,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK170(X1))),'fun_app$i'(X1,sK171(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3121]) ).
tff(f3121,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK170(X1))),'fun_app$i'(X1,sK171(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2028]) ).
tff(f2028,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK170(X1))),'fun_app$i'(X1,sK171(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK170(X1)),sK171(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK170,sK171])],[f1394,f2027]) ).
tff(f2027,plain,
! [X1: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,sK170(X1))),'fun_app$i'(X1,sK171(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK170(X1)),sK171(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1394,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(flattening,[],[f1393]) ).
tff(f1393,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f296]) ).
tff(f296,axiom,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$i'(X1,X2) = X0 ) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
tff(f11381,plain,
spl272_710,
inference(avatar_split_clause,[],[f3360,f11379]) ).
tff(f11379,plain,
( spl272_710
<=> ! [X2: 'Num$',X1: 'Num_enat_fun$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK168(X1))),'fun_app$i'(X1,sK169(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_710])]) ).
tff(f3360,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK168(X1))),'fun_app$i'(X1,sK169(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3119]) ).
tff(f3119,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK168(X1))),'fun_app$i'(X1,sK169(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2026]) ).
tff(f2026,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK168(X1))),'fun_app$i'(X1,sK169(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK168(X1)),sK169(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168,sK169])],[f1392,f2025]) ).
tff(f2025,plain,
! [X1: 'Num_enat_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,sK168(X1))),'fun_app$i'(X1,sK169(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK168(X1)),sK169(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1392,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(flattening,[],[f1391]) ).
tff(f1391,plain,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f512]) ).
tff(f512,axiom,
! [X0: 'Enat$',X1: 'Num_enat_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X4)),'fun_app$i'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& ( 'fun_app$i'(X1,X2) = X0 ) )
=> 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).
tff(f11377,plain,
spl272_709,
inference(avatar_split_clause,[],[f3354,f11375]) ).
tff(f11375,plain,
( spl272_709
<=> ! [X2: 'Enat$',X1: 'Enat_num_fun$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK162(X1))),'fun_app$w'(X1,sK163(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_709])]) ).
tff(f3354,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK162(X1))),'fun_app$w'(X1,sK163(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ),
inference(equality_resolution,[],[f3113]) ).
tff(f3113,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK162(X1))),'fun_app$w'(X1,sK163(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2020]) ).
tff(f2020,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK162(X1))),'fun_app$w'(X1,sK163(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK162(X1)),sK163(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162,sK163])],[f1386,f2019]) ).
tff(f2019,plain,
! [X1: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,sK162(X1))),'fun_app$w'(X1,sK163(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK162(X1)),sK163(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1386,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(flattening,[],[f1385]) ).
tff(f1385,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f299]) ).
tff(f299,axiom,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& ( 'fun_app$w'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom297) ).
tff(f11373,plain,
spl272_708,
inference(avatar_split_clause,[],[f3350,f11371]) ).
tff(f11371,plain,
( spl272_708
<=> ! [X2: 'Enat$',X1: 'Enat_num_fun$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK158(X1))),'fun_app$w'(X1,sK159(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_708])]) ).
tff(f3350,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK158(X1))),'fun_app$w'(X1,sK159(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ),
inference(equality_resolution,[],[f3109]) ).
tff(f3109,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK158(X1))),'fun_app$w'(X1,sK159(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2016]) ).
tff(f2016,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK158(X1))),'fun_app$w'(X1,sK159(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK158(X1)),sK159(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158,sK159])],[f1382,f2015]) ).
tff(f2015,plain,
! [X1: 'Enat_num_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,sK158(X1))),'fun_app$w'(X1,sK159(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK158(X1)),sK159(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1382,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(flattening,[],[f1381]) ).
tff(f1381,plain,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f518]) ).
tff(f518,axiom,
! [X0: 'Num$',X1: 'Enat_num_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X4)),'fun_app$w'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less$a',X2),X3)
& ( 'fun_app$w'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom516) ).
tff(f11369,plain,
spl272_707,
inference(avatar_split_clause,[],[f2836,f11367]) ).
tff(f2836,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1246]) ).
tff(f1246,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1245]) ).
tff(f1245,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f587]) ).
tff(f587,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X2)))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom585) ).
tff(f11365,plain,
spl272_706,
inference(avatar_split_clause,[],[f2835,f11363]) ).
tff(f2835,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1244]) ).
tff(f1244,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1243]) ).
tff(f1243,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f781]) ).
tff(f781,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0))) ),
inference(theory_normalization,[],[f601]) ).
tff(f601,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X0)),'fun_app$a'('of_nat$','fun_app$b'('power$'(X2),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom599) ).
tff(f11349,plain,
( spl272_705
| ~ spl272_58
| ~ spl272_667 ),
inference(avatar_split_clause,[],[f11012,f10673,f3865,f11347]) ).
tff(f11347,plain,
( spl272_705
<=> ! [X0: $real] : $less(X0,$sum(X0,7.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_705])]) ).
tff(f10673,plain,
( spl272_667
<=> ! [X0: $real] : $less(X0,$sum(7.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_667])]) ).
tff(f11012,plain,
( ! [X0: $real] : $less(X0,$sum(X0,7.0))
| ~ spl272_58
| ~ spl272_667 ),
inference(superposition,[],[f10674,f3866]) ).
tff(f10674,plain,
( ! [X0: $real] : $less(X0,$sum(7.0,X0))
| ~ spl272_667 ),
inference(avatar_component_clause,[],[f10673]) ).
tff(f11257,plain,
( spl272_704
| ~ spl272_50
| ~ spl272_667 ),
inference(avatar_split_clause,[],[f11006,f10673,f3821,f11255]) ).
tff(f3821,plain,
( spl272_50
<=> ! [X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_50])]) ).
tff(f11006,plain,
( ! [X0: $real] : ~ $less($sum(7.0,X0),X0)
| ~ spl272_50
| ~ spl272_667 ),
inference(resolution,[],[f10674,f3822]) ).
tff(f3822,plain,
( ! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ $less(X0,X1) )
| ~ spl272_50 ),
inference(avatar_component_clause,[],[f3821]) ).
tff(f11151,plain,
spl272_703,
inference(avatar_split_clause,[],[f3553,f11149]) ).
tff(f11149,plain,
( spl272_703
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK76(X0,X1,X2)))))
| 'fun_app$n'(X2,X0)
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_703])]) ).
tff(f3553,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK76(X0,X1,X2)))))
| 'fun_app$n'(X2,X0)
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2871,f848]) ).
tff(f2871,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK76(X0,X1,X2)),1)))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f1845,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| ( ~ 'fun_app$n'(X2,sK76(X0,X1,X2))
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK76(X0,X1,X2)),1)))
& $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f1284,f1844]) ).
tff(f1844,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> ( ~ 'fun_app$n'(X2,sK76(X0,X1,X2))
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK76(X0,X1,X2)),1)))
& $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1284,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1283]) ).
tff(f1283,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f784]) ).
tff(f784,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,X3) )
& 'fun_app$n'(X2,X1)
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,X0) ),
inference(theory_normalization,[],[f595]) ).
tff(f595,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X3)) )
=> 'fun_app$n'(X2,X3) )
& 'fun_app$n'(X2,X1)
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom593) ).
tff(f11147,plain,
spl272_702,
inference(avatar_split_clause,[],[f3552,f11145]) ).
tff(f11145,plain,
( spl272_702
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK75(X0,X1,X2)))))
| 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_702])]) ).
tff(f3552,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK75(X0,X1,X2)))))
| 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2868,f848]) ).
tff(f2868,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK75(X0,X1,X2)),1)))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f1843,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK75(X0,X1,X2)),1)))
& 'fun_app$n'(X2,sK75(X0,X1,X2))
& $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f1282,f1842]) ).
tff(f1842,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> ( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK75(X0,X1,X2)),1)))
& 'fun_app$n'(X2,sK75(X0,X1,X2))
& $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1282,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1281]) ).
tff(f1281,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f783]) ).
tff(f783,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1))) )
& 'fun_app$n'(X2,X0)
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,X1) ),
inference(theory_normalization,[],[f596]) ).
tff(f596,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1))
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X3)) )
=> 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1))) )
& 'fun_app$n'(X2,X0)
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom594) ).
tff(f11143,plain,
spl272_701,
inference(avatar_split_clause,[],[f3550,f11141]) ).
tff(f11141,plain,
( spl272_701
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK73(X1,X2))) )
| 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_701])]) ).
tff(f3550,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK73(X1,X2))) )
| 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2860,f848]) ).
tff(f2860,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK73(X1,X2)),1) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1839]) ).
tff(f1839,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ( ~ 'fun_app$n'(X2,sK73(X1,X2))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK73(X1,X2)),1) ) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f1837,f1838]) ).
tff(f1838,plain,
! [X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X3),1) ) )
=> ( ~ 'fun_app$n'(X2,sK73(X1,X2))
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK73(X1,X2)),1) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1837,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X3),1) ) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(rectify,[],[f1512]) ).
tff(f1512,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ? [X4: 'Nat$'] :
( ~ 'fun_app$n'(X2,X4)
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X4),1) ) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(definition_folding,[],[f1278,f1511]) ).
tff(f1511,plain,
! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
| ~ sP7(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f1278,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
| ? [X4: 'Nat$'] :
( ~ 'fun_app$n'(X2,X4)
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X4),1) ) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f1277]) ).
tff(f1277,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
| ? [X4: 'Nat$'] :
( ~ 'fun_app$n'(X2,X4)
& ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X4),1) ) )
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f985]) ).
tff(f985,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X3) )
& ! [X4: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X4),1) )
=> 'fun_app$n'(X2,X4) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X0) ),
inference(rectify,[],[f554]) ).
tff(f554,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X3) )
& ! [X3: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X3),1) )
=> 'fun_app$n'(X2,X3) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
tff(f11139,plain,
spl272_700,
inference(avatar_split_clause,[],[f3197,f11137]) ).
tff(f11137,plain,
( spl272_700
<=> ! [X0: $int,X3: 'Num$',X2: 'Num$',X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| $less('fun_app$d'(X1,sK247(X1)),'fun_app$d'(X1,sK246(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_700])]) ).
tff(f3197,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| $less('fun_app$d'(X1,sK247(X1)),'fun_app$d'(X1,sK246(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2104]) ).
tff(f2104,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ( $less('fun_app$d'(X1,sK247(X1)),'fun_app$d'(X1,sK246(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK246(X1)),sK247(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK246,sK247])],[f1470,f2103]) ).
tff(f2103,plain,
! [X1: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$d'(X1,sK247(X1)),'fun_app$d'(X1,sK246(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK246(X1)),sK247(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1470,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ),
inference(flattening,[],[f1469]) ).
tff(f1469,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ),
inference(ennf_transformation,[],[f843]) ).
tff(f843,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ~ $less('fun_app$d'(X1,X2),X0) )
=> ~ $less('fun_app$d'(X1,X3),X0) ),
inference(theory_normalization,[],[f259]) ).
tff(f259,axiom,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$d'(X1,X4),'fun_app$d'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& $lesseq(X0,'fun_app$d'(X1,X2)) )
=> $lesseq(X0,'fun_app$d'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom257) ).
tff(f11135,plain,
( spl272_699
| ~ spl272_56
| ~ spl272_649 ),
inference(avatar_split_clause,[],[f10864,f10525,f3857,f11133]) ).
tff(f11133,plain,
( spl272_699
<=> ! [X0: $int] : $less(X0,$sum(X0,7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_699])]) ).
tff(f10525,plain,
( spl272_649
<=> ! [X0: $int] : $less(X0,$sum(7,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_649])]) ).
tff(f10864,plain,
( ! [X0: $int] : $less(X0,$sum(X0,7))
| ~ spl272_56
| ~ spl272_649 ),
inference(superposition,[],[f10526,f3858]) ).
tff(f10526,plain,
( ! [X0: $int] : $less(X0,$sum(7,X0))
| ~ spl272_649 ),
inference(avatar_component_clause,[],[f10525]) ).
tff(f11131,plain,
spl272_698,
inference(avatar_split_clause,[],[f3193,f11129]) ).
tff(f11129,plain,
( spl272_698
<=> ! [X0: $int,X3: 'Enat$',X2: 'Enat$',X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| $less('fun_app$t'(X1,sK243(X1)),'fun_app$t'(X1,sK242(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_698])]) ).
tff(f3193,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| $less('fun_app$t'(X1,sK243(X1)),'fun_app$t'(X1,sK242(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2100]) ).
tff(f2100,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ( $less('fun_app$t'(X1,sK243(X1)),'fun_app$t'(X1,sK242(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK242(X1)),sK243(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK242,sK243])],[f1466,f2099]) ).
tff(f2099,plain,
! [X1: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( $less('fun_app$t'(X1,sK243(X1)),'fun_app$t'(X1,sK242(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK242(X1)),sK243(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1466,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ),
inference(flattening,[],[f1465]) ).
tff(f1465,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ),
inference(ennf_transformation,[],[f841]) ).
tff(f841,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> ~ $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& ~ $less('fun_app$t'(X1,X2),X0) )
=> ~ $less('fun_app$t'(X1,X3),X0) ),
inference(theory_normalization,[],[f260]) ).
tff(f260,axiom,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> $lesseq('fun_app$t'(X1,X4),'fun_app$t'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& $lesseq(X0,'fun_app$t'(X1,X2)) )
=> $lesseq(X0,'fun_app$t'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom258) ).
tff(f11127,plain,
spl272_697,
inference(avatar_split_clause,[],[f3189,f11125]) ).
tff(f11125,plain,
( spl272_697
<=> ! [X0: $int,X3: 'Num$',X2: 'Num$',X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ~ $less('fun_app$d'(X1,sK238(X1)),'fun_app$d'(X1,sK239(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_697])]) ).
tff(f3189,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ~ $less('fun_app$d'(X1,sK238(X1)),'fun_app$d'(X1,sK239(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ),
inference(cnf_transformation,[],[f2096]) ).
tff(f2096,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ( ~ $less('fun_app$d'(X1,sK238(X1)),'fun_app$d'(X1,sK239(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK238(X1)),sK239(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK238,sK239])],[f1462,f2095]) ).
tff(f2095,plain,
! [X1: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$d'(X1,sK238(X1)),'fun_app$d'(X1,sK239(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK238(X1)),sK239(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1462,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ),
inference(flattening,[],[f1461]) ).
tff(f1461,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ),
inference(ennf_transformation,[],[f490]) ).
tff(f490,axiom,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& $less(X0,'fun_app$d'(X1,X2)) )
=> $less(X0,'fun_app$d'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom488) ).
tff(f11123,plain,
spl272_696,
inference(avatar_split_clause,[],[f3185,f11121]) ).
tff(f11121,plain,
( spl272_696
<=> ! [X0: $int,X3: 'Enat$',X2: 'Enat$',X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ~ $less('fun_app$t'(X1,sK234(X1)),'fun_app$t'(X1,sK235(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_696])]) ).
tff(f3185,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ~ $less('fun_app$t'(X1,sK234(X1)),'fun_app$t'(X1,sK235(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ),
inference(cnf_transformation,[],[f2092]) ).
tff(f2092,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ( ~ $less('fun_app$t'(X1,sK234(X1)),'fun_app$t'(X1,sK235(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK234(X1)),sK235(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK234,sK235])],[f1458,f2091]) ).
tff(f2091,plain,
! [X1: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ $less('fun_app$t'(X1,sK234(X1)),'fun_app$t'(X1,sK235(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK234(X1)),sK235(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1458,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ),
inference(flattening,[],[f1457]) ).
tff(f1457,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ),
inference(ennf_transformation,[],[f492]) ).
tff(f492,axiom,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less$a',X2),X3)
& $less(X0,'fun_app$t'(X1,X2)) )
=> $less(X0,'fun_app$t'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom490) ).
tff(f11119,plain,
spl272_695,
inference(avatar_split_clause,[],[f3177,f11117]) ).
tff(f11117,plain,
( spl272_695
<=> ! [X0: 'Num$',X3: $int,X2: 'Num_int_fun$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| $less('fun_app$d'(X2,sK227(X2)),'fun_app$d'(X2,sK226(X2)))
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_695])]) ).
tff(f3177,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| $less('fun_app$d'(X2,sK227(X2)),'fun_app$d'(X2,sK226(X2)))
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2084]) ).
tff(f2084,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ( $less('fun_app$d'(X2,sK227(X2)),'fun_app$d'(X2,sK226(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK226(X2)),sK227(X2)) )
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK226,sK227])],[f1450,f2083]) ).
tff(f2083,plain,
! [X2: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$d'(X2,sK227(X2)),'fun_app$d'(X2,sK226(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK226(X2)),sK227(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1450,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1449]) ).
tff(f1449,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f839]) ).
tff(f839,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4)) )
& ~ $less(X3,'fun_app$d'(X2,X1))
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> ~ $less(X3,'fun_app$d'(X2,X0)) ),
inference(theory_normalization,[],[f272]) ).
tff(f272,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$d'(X2,X4),'fun_app$d'(X2,X5)) )
& $lesseq('fun_app$d'(X2,X1),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> $lesseq('fun_app$d'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).
tff(f11115,plain,
spl272_694,
inference(avatar_split_clause,[],[f3175,f11113]) ).
tff(f11113,plain,
( spl272_694
<=> ! [X0: 'Num$',X3: $real,X2: 'Num_real_fun$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| $less('fun_app$j'(X2,sK225(X2)),'fun_app$j'(X2,sK224(X2)))
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_694])]) ).
tff(f3175,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| $less('fun_app$j'(X2,sK225(X2)),'fun_app$j'(X2,sK224(X2)))
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2082]) ).
tff(f2082,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ( $less('fun_app$j'(X2,sK225(X2)),'fun_app$j'(X2,sK224(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK224(X2)),sK225(X2)) )
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK224,sK225])],[f1448,f2081]) ).
tff(f2081,plain,
! [X2: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$j'(X2,sK225(X2)),'fun_app$j'(X2,sK224(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK224(X2)),sK225(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1448,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1447]) ).
tff(f1447,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f838]) ).
tff(f838,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4)) )
& ~ $less(X3,'fun_app$j'(X2,X1))
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> ~ $less(X3,'fun_app$j'(X2,X0)) ),
inference(theory_normalization,[],[f275]) ).
tff(f275,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$j'(X2,X4),'fun_app$j'(X2,X5)) )
& $lesseq('fun_app$j'(X2,X1),X3)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> $lesseq('fun_app$j'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom273) ).
tff(f11111,plain,
spl272_693,
inference(avatar_split_clause,[],[f3161,f11109]) ).
tff(f11109,plain,
( spl272_693
<=> ! [X0: 'Num$',X3: $int,X2: 'Num_int_fun$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| ~ $less('fun_app$d'(X2,sK210(X2)),'fun_app$d'(X2,sK211(X2)))
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_693])]) ).
tff(f3161,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| ~ $less('fun_app$d'(X2,sK210(X2)),'fun_app$d'(X2,sK211(X2)))
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2068]) ).
tff(f2068,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ( ~ $less('fun_app$d'(X2,sK210(X2)),'fun_app$d'(X2,sK211(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK210(X2)),sK211(X2)) )
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK210,sK211])],[f1434,f2067]) ).
tff(f2067,plain,
! [X2: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$d'(X2,sK210(X2)),'fun_app$d'(X2,sK211(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK210(X2)),sK211(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1434,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1433]) ).
tff(f1433,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f477]) ).
tff(f477,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5)) )
& $less('fun_app$d'(X2,X1),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> $less('fun_app$d'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom475) ).
tff(f11107,plain,
spl272_692,
inference(avatar_split_clause,[],[f3159,f11105]) ).
tff(f11105,plain,
( spl272_692
<=> ! [X0: 'Num$',X3: $real,X2: 'Num_real_fun$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| ~ $less('fun_app$j'(X2,sK208(X2)),'fun_app$j'(X2,sK209(X2)))
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_692])]) ).
tff(f3159,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| ~ $less('fun_app$j'(X2,sK208(X2)),'fun_app$j'(X2,sK209(X2)))
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2066]) ).
tff(f2066,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ( ~ $less('fun_app$j'(X2,sK208(X2)),'fun_app$j'(X2,sK209(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK208(X2)),sK209(X2)) )
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK208,sK209])],[f1432,f2065]) ).
tff(f2065,plain,
! [X2: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$j'(X2,sK208(X2)),'fun_app$j'(X2,sK209(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK208(X2)),sK209(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1432,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1431]) ).
tff(f1431,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f479]) ).
tff(f479,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5)) )
& $less('fun_app$j'(X2,X1),X3)
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> $less('fun_app$j'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom477) ).
tff(f11103,plain,
spl272_691,
inference(avatar_split_clause,[],[f3147,f11101]) ).
tff(f11101,plain,
( spl272_691
<=> ! [X0: 'Enat$',X3: $int,X2: 'Enat_int_fun$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| $less('fun_app$t'(X2,sK197(X2)),'fun_app$t'(X2,sK196(X2)))
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_691])]) ).
tff(f3147,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| $less('fun_app$t'(X2,sK197(X2)),'fun_app$t'(X2,sK196(X2)))
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2054]) ).
tff(f2054,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ( $less('fun_app$t'(X2,sK197(X2)),'fun_app$t'(X2,sK196(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK196(X2)),sK197(X2)) )
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196,sK197])],[f1420,f2053]) ).
tff(f2053,plain,
! [X2: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( $less('fun_app$t'(X2,sK197(X2)),'fun_app$t'(X2,sK196(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK196(X2)),sK197(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1420,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(flattening,[],[f1419]) ).
tff(f1419,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(ennf_transformation,[],[f835]) ).
tff(f835,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> ~ $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4)) )
& ~ $less(X3,'fun_app$t'(X2,X1))
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> ~ $less(X3,'fun_app$t'(X2,X0)) ),
inference(theory_normalization,[],[f276]) ).
tff(f276,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> $lesseq('fun_app$t'(X2,X4),'fun_app$t'(X2,X5)) )
& $lesseq('fun_app$t'(X2,X1),X3)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> $lesseq('fun_app$t'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom274) ).
tff(f11099,plain,
spl272_690,
inference(avatar_split_clause,[],[f3139,f11097]) ).
tff(f11097,plain,
( spl272_690
<=> ! [X0: 'Enat$',X3: $int,X2: 'Enat_int_fun$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| ~ $less('fun_app$t'(X2,sK188(X2)),'fun_app$t'(X2,sK189(X2)))
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_690])]) ).
tff(f3139,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| ~ $less('fun_app$t'(X2,sK188(X2)),'fun_app$t'(X2,sK189(X2)))
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2046]) ).
tff(f2046,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ( ~ $less('fun_app$t'(X2,sK188(X2)),'fun_app$t'(X2,sK189(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK188(X2)),sK189(X2)) )
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK188,sK189])],[f1412,f2045]) ).
tff(f2045,plain,
! [X2: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ $less('fun_app$t'(X2,sK188(X2)),'fun_app$t'(X2,sK189(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK188(X2)),sK189(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1412,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(flattening,[],[f1411]) ).
tff(f1411,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f485]) ).
tff(f485,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5)) )
& $less('fun_app$t'(X2,X1),X3)
& 'fun_app$g'('fun_app$h'('less$a',X0),X1) )
=> $less('fun_app$t'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
tff(f11095,plain,
spl272_689,
inference(avatar_split_clause,[],[f3039,f11093]) ).
tff(f11093,plain,
( spl272_689
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_689])]) ).
tff(f3039,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X2) ) ),
inference(cnf_transformation,[],[f1955]) ).
tff(f11091,plain,
( spl272_688
| ~ spl272_51
| ~ spl272_649 ),
inference(avatar_split_clause,[],[f10853,f10525,f3825,f11089]) ).
tff(f10853,plain,
( ! [X0: $int] : ~ $less($sum(7,X0),X0)
| ~ spl272_51
| ~ spl272_649 ),
inference(resolution,[],[f10526,f3826]) ).
tff(f11087,plain,
spl272_687,
inference(avatar_split_clause,[],[f3037,f11085]) ).
tff(f11085,plain,
( spl272_687
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_687])]) ).
tff(f3037,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X1) != 'fun_app$a'('of_nat$',X2) ) ),
inference(cnf_transformation,[],[f1953]) ).
tff(f11065,plain,
( spl272_686
| ~ spl272_181
| ~ spl272_278
| ~ spl272_685 ),
inference(avatar_split_clause,[],[f11061,f11058,f5561,f4632,f11063]) ).
tff(f11063,plain,
( spl272_686
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1))
| 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_686])]) ).
tff(f4632,plain,
( spl272_181
<=> ! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) = 'fun_app$a'('of_nat$','nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_181])]) ).
tff(f11058,plain,
( spl272_685
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_685])]) ).
tff(f11061,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1))
| 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_685 ),
inference(forward_demodulation,[],[f11059,f5822]) ).
tff(f5822,plain,
( ! [X0: 'Num$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) = 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) )
| ~ spl272_181
| ~ spl272_278 ),
inference(superposition,[],[f5562,f4633]) ).
tff(f4633,plain,
( ! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) = 'fun_app$a'('of_nat$','nat$'('fun_app$d'('numeral$',X0))) )
| ~ spl272_181 ),
inference(avatar_component_clause,[],[f4632]) ).
tff(f11059,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1))) )
| ~ spl272_685 ),
inference(avatar_component_clause,[],[f11058]) ).
tff(f11060,plain,
spl272_685,
inference(avatar_split_clause,[],[f3026,f11058]) ).
tff(f3026,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1))) ),
inference(cnf_transformation,[],[f1947]) ).
tff(f1947,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1))) )
& ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
inference(nnf_transformation,[],[f813]) ).
tff(f813,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1))) ),
inference(theory_normalization,[],[f72]) ).
tff(f72,axiom,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
tff(f11050,plain,
( spl272_684
| ~ spl272_181
| ~ spl272_278
| ~ spl272_683 ),
inference(avatar_split_clause,[],[f11046,f11043,f5561,f4632,f11048]) ).
tff(f11048,plain,
( spl272_684
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_684])]) ).
tff(f11043,plain,
( spl272_683
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_683])]) ).
tff(f11046,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_683 ),
inference(forward_demodulation,[],[f11044,f5822]) ).
tff(f11044,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_683 ),
inference(avatar_component_clause,[],[f11043]) ).
tff(f11045,plain,
spl272_683,
inference(avatar_split_clause,[],[f3025,f11043]) ).
tff(f3025,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ),
inference(cnf_transformation,[],[f1947]) ).
tff(f11023,plain,
( spl272_682
| ~ spl272_181
| ~ spl272_278
| ~ spl272_681 ),
inference(avatar_split_clause,[],[f11019,f11016,f5561,f4632,f11021]) ).
tff(f11021,plain,
( spl272_682
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_682])]) ).
tff(f11016,plain,
( spl272_681
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_681])]) ).
tff(f11019,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_681 ),
inference(forward_demodulation,[],[f11017,f5822]) ).
tff(f11017,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) )
| ~ spl272_681 ),
inference(avatar_component_clause,[],[f11016]) ).
tff(f11018,plain,
spl272_681,
inference(avatar_split_clause,[],[f3024,f11016]) ).
tff(f3024,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1946]) ).
tff(f1946,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) )
& ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
inference(nnf_transformation,[],[f419]) ).
tff(f419,axiom,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom417) ).
tff(f10997,plain,
( spl272_680
| ~ spl272_181
| ~ spl272_278
| ~ spl272_679 ),
inference(avatar_split_clause,[],[f10993,f10990,f5561,f4632,f10995]) ).
tff(f10995,plain,
( spl272_680
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_680])]) ).
tff(f10990,plain,
( spl272_679
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_679])]) ).
tff(f10993,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_679 ),
inference(forward_demodulation,[],[f10991,f5822]) ).
tff(f10991,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) )
| ~ spl272_679 ),
inference(avatar_component_clause,[],[f10990]) ).
tff(f10992,plain,
spl272_679,
inference(avatar_split_clause,[],[f3023,f10990]) ).
tff(f3023,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('numeral$c'(X0)),X1)),'fun_app$b'('of_nat$a',X2)) ),
inference(cnf_transformation,[],[f1946]) ).
tff(f10970,plain,
( spl272_678
| ~ spl272_181
| ~ spl272_278
| ~ spl272_677 ),
inference(avatar_split_clause,[],[f10966,f10963,f5561,f4632,f10968]) ).
tff(f10968,plain,
( spl272_678
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_678])]) ).
tff(f10963,plain,
( spl272_677
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_677])]) ).
tff(f10966,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_677 ),
inference(forward_demodulation,[],[f10964,f5822]) ).
tff(f10964,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0)) )
| ~ spl272_677 ),
inference(avatar_component_clause,[],[f10963]) ).
tff(f10965,plain,
spl272_677,
inference(avatar_split_clause,[],[f3022,f10963]) ).
tff(f3022,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1945]) ).
tff(f1945,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0)) )
& ( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
inference(nnf_transformation,[],[f812]) ).
tff(f812,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
<=> ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f69]) ).
tff(f69,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
<=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
tff(f10955,plain,
( spl272_676
| ~ spl272_181
| ~ spl272_278
| ~ spl272_675 ),
inference(avatar_split_clause,[],[f10951,f10948,f5561,f4632,f10953]) ).
tff(f10953,plain,
( spl272_676
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_676])]) ).
tff(f10948,plain,
( spl272_675
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_675])]) ).
tff(f10951,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_675 ),
inference(forward_demodulation,[],[f10949,f5822]) ).
tff(f10949,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_675 ),
inference(avatar_component_clause,[],[f10948]) ).
tff(f10950,plain,
spl272_675,
inference(avatar_split_clause,[],[f3021,f10948]) ).
tff(f3021,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ),
inference(cnf_transformation,[],[f1945]) ).
tff(f10920,plain,
( spl272_674
| ~ spl272_181
| ~ spl272_278
| ~ spl272_673 ),
inference(avatar_split_clause,[],[f10916,f10913,f5561,f4632,f10918]) ).
tff(f10918,plain,
( spl272_674
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_674])]) ).
tff(f10913,plain,
( spl272_673
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_673])]) ).
tff(f10916,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_673 ),
inference(forward_demodulation,[],[f10914,f5822]) ).
tff(f10914,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) )
| ~ spl272_673 ),
inference(avatar_component_clause,[],[f10913]) ).
tff(f10915,plain,
spl272_673,
inference(avatar_split_clause,[],[f3020,f10913]) ).
tff(f3020,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
inference(cnf_transformation,[],[f1944]) ).
tff(f1944,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) )
& ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
inference(nnf_transformation,[],[f416]) ).
tff(f416,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2))
<=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
tff(f10905,plain,
( spl272_672
| ~ spl272_181
| ~ spl272_278
| ~ spl272_671 ),
inference(avatar_split_clause,[],[f10901,f10898,f5561,f4632,f10903]) ).
tff(f10903,plain,
( spl272_672
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_672])]) ).
tff(f10898,plain,
( spl272_671
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_671])]) ).
tff(f10901,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_671 ),
inference(forward_demodulation,[],[f10899,f5822]) ).
tff(f10899,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) )
| ~ spl272_671 ),
inference(avatar_component_clause,[],[f10898]) ).
tff(f10900,plain,
spl272_671,
inference(avatar_split_clause,[],[f3019,f10898]) ).
tff(f3019,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('numeral$c'(X1)),X2)) ),
inference(cnf_transformation,[],[f1944]) ).
tff(f10896,plain,
spl272_670,
inference(avatar_split_clause,[],[f2806,f10894]) ).
tff(f10894,plain,
( spl272_670
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_670])]) ).
tff(f2806,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1198]) ).
tff(f1198,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X0)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f765]) ).
tff(f765,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
=> ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X0))) ),
inference(theory_normalization,[],[f575]) ).
tff(f575,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> $lesseq('fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X0)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom573) ).
tff(f10892,plain,
spl272_669,
inference(avatar_split_clause,[],[f2805,f10890]) ).
tff(f10890,plain,
( spl272_669
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_669])]) ).
tff(f2805,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1197]) ).
tff(f1197,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f764]) ).
tff(f764,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
=> ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ),
inference(theory_normalization,[],[f576]) ).
tff(f576,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> $lesseq('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
tff(f10888,plain,
spl272_668,
inference(avatar_split_clause,[],[f2490,f10886]) ).
tff(f10886,plain,
( spl272_668
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( X0 = X1 )
| ( 'fun_app$b'('power$'(X0),'nat$'(2)) != 'fun_app$b'('power$'(X1),'nat$'(2)) )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_668])]) ).
tff(f2490,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( X0 = X1 )
| ( 'fun_app$b'('power$'(X0),'nat$'(2)) != 'fun_app$b'('power$'(X1),'nat$'(2)) )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f1628,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ( 'fun_app$b'('power$'(X0),'nat$'(2)) = 'fun_app$b'('power$'(X1),'nat$'(2)) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$b'('power$'(X0),'nat$'(2)) != 'fun_app$b'('power$'(X1),'nat$'(2)) ) ) )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(nnf_transformation,[],[f1122]) ).
tff(f1122,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$b'('power$'(X0),'nat$'(2)) = 'fun_app$b'('power$'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(flattening,[],[f1121]) ).
tff(f1121,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$b'('power$'(X0),'nat$'(2)) = 'fun_app$b'('power$'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(ennf_transformation,[],[f76]) ).
tff(f76,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
& 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) )
=> ( ( 'fun_app$b'('power$'(X0),'nat$'(2)) = 'fun_app$b'('power$'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom74) ).
tff(f10675,plain,
( spl272_667
| ~ spl272_109
| ~ spl272_624 ),
inference(avatar_split_clause,[],[f10305,f9821,f4112,f10673]) ).
tff(f9821,plain,
( spl272_624
<=> ! [X0: $real] : ~ $less($sum(6.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_624])]) ).
tff(f10305,plain,
( ! [X0: $real] : $less(X0,$sum(7.0,X0))
| ~ spl272_109
| ~ spl272_624 ),
inference(evaluation,[],[f10299]) ).
tff(f10299,plain,
( ! [X0: $real] : $less(X0,$sum(6.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_624 ),
inference(resolution,[],[f9822,f4113]) ).
tff(f9822,plain,
( ! [X0: $real] : ~ $less($sum(6.0,X0),X0)
| ~ spl272_624 ),
inference(avatar_component_clause,[],[f9821]) ).
tff(f10599,plain,
spl272_666,
inference(avatar_split_clause,[],[f3551,f10597]) ).
tff(f10597,plain,
( spl272_666
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK74(X0,X2)))))
| 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_666])]) ).
tff(f3551,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum(1,'fun_app$a'('of_nat$',sK74(X0,X2)))))
| 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2864,f848]) ).
tff(f2864,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK74(X0,X2)),1)))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f1841,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK74(X0,X2)),1)))
& 'fun_app$n'(X2,sK74(X0,X2))
& ~ $less('fun_app$a'('of_nat$',sK74(X0,X2)),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f1280,f1840]) ).
tff(f1840,plain,
! [X0: 'Nat$',X2: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> ( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',sK74(X0,X2)),1)))
& 'fun_app$n'(X2,sK74(X0,X2))
& ~ $less('fun_app$a'('of_nat$',sK74(X0,X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1280,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1279]) ).
tff(f1279,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( 'fun_app$n'(X2,X1)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& 'fun_app$n'(X2,X3)
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f782]) ).
tff(f782,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,X3)
& ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1))) )
& 'fun_app$n'(X2,X0)
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
=> 'fun_app$n'(X2,X1) ),
inference(theory_normalization,[],[f44]) ).
tff(f44,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat_bool_fun$'] :
( ( ! [X3: 'Nat$'] :
( ( 'fun_app$n'(X2,X3)
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X3)) )
=> 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1))) )
& 'fun_app$n'(X2,X0)
& $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> 'fun_app$n'(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
tff(f10595,plain,
spl272_665,
inference(avatar_split_clause,[],[f3547,f10593]) ).
tff(f10593,plain,
( spl272_665
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_665])]) ).
tff(f3547,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2850,f848]) ).
tff(f2850,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1274]) ).
tff(f1274,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(flattening,[],[f1273]) ).
tff(f1273,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f556]) ).
tff(f556,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) )
=> $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
tff(f10591,plain,
spl272_664,
inference(avatar_split_clause,[],[f3506,f10589]) ).
tff(f10589,plain,
( spl272_664
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| $less('fun_app$a'('of_nat$',sK56(X0,X1)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_664])]) ).
tff(f3506,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| $less('fun_app$a'('of_nat$',sK56(X0,X1)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(forward_demodulation,[],[f2710,f848]) ).
tff(f2710,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK56(X0,X1)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f10587,plain,
spl272_663,
inference(avatar_split_clause,[],[f3464,f10585]) ).
tff(f10585,plain,
( spl272_663
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_663])]) ).
tff(f3464,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2415,f848]) ).
tff(f2415,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1604]) ).
tff(f1604,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(nnf_transformation,[],[f1048]) ).
tff(f1048,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) ) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f553]) ).
tff(f553,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom551) ).
tff(f10583,plain,
spl272_662,
inference(avatar_split_clause,[],[f3346,f10581]) ).
tff(f10581,plain,
( spl272_662
<=> ! [X2: $int,X1: 'Int_num_fun$',X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK154(X1))),'fun_app$v'(X1,sK155(X1)))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_662])]) ).
tff(f3346,plain,
! [X2: $int,X3: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK154(X1))),'fun_app$v'(X1,sK155(X1)))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3105]) ).
tff(f3105,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK154(X1))),'fun_app$v'(X1,sK155(X1)))
| $less(X3,X2)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2012]) ).
tff(f2012,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK154(X1))),'fun_app$v'(X1,sK155(X1)))
& ~ $less(sK155(X1),sK154(X1)) )
| $less(X3,X2)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK154,sK155])],[f1378,f2011]) ).
tff(f2011,plain,
! [X1: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,sK154(X1))),'fun_app$v'(X1,sK155(X1)))
& ~ $less(sK155(X1),sK154(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1378,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(flattening,[],[f1377]) ).
tff(f1377,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f829]) ).
tff(f829,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& ~ $less(X3,X2)
& ( 'fun_app$v'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3)) ),
inference(theory_normalization,[],[f291]) ).
tff(f291,axiom,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& $lesseq(X2,X3)
& ( 'fun_app$v'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom289) ).
tff(f10579,plain,
spl272_661,
inference(avatar_split_clause,[],[f3344,f10577]) ).
tff(f10577,plain,
( spl272_661
<=> ! [X2: $int,X1: 'Int_enat_fun$',X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK152(X1))),'fun_app$y'(X1,sK153(X1)))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_661])]) ).
tff(f3344,plain,
! [X2: $int,X3: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK152(X1))),'fun_app$y'(X1,sK153(X1)))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3103]) ).
tff(f3103,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK152(X1))),'fun_app$y'(X1,sK153(X1)))
| $less(X3,X2)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2010]) ).
tff(f2010,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK152(X1))),'fun_app$y'(X1,sK153(X1)))
& ~ $less(sK153(X1),sK152(X1)) )
| $less(X3,X2)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153])],[f1376,f2009]) ).
tff(f2009,plain,
! [X1: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,sK152(X1))),'fun_app$y'(X1,sK153(X1)))
& ~ $less(sK153(X1),sK152(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1376,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(flattening,[],[f1375]) ).
tff(f1375,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f828]) ).
tff(f828,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& ~ $less(X3,X2)
& ( 'fun_app$y'(X1,X2) = X0 ) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3)) ),
inference(theory_normalization,[],[f292]) ).
tff(f292,axiom,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& $lesseq(X2,X3)
& ( 'fun_app$y'(X1,X2) = X0 ) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
tff(f10575,plain,
( spl272_660
| ~ spl272_58
| ~ spl272_624 ),
inference(avatar_split_clause,[],[f10303,f9821,f3865,f10573]) ).
tff(f10573,plain,
( spl272_660
<=> ! [X0: $real] : ~ $less($sum(X0,6.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_660])]) ).
tff(f10303,plain,
( ! [X0: $real] : ~ $less($sum(X0,6.0),X0)
| ~ spl272_58
| ~ spl272_624 ),
inference(superposition,[],[f9822,f3866]) ).
tff(f10571,plain,
spl272_659,
inference(avatar_split_clause,[],[f3342,f10569]) ).
tff(f10569,plain,
( spl272_659
<=> ! [X2: $int,X1: 'Int_num_fun$',X3: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK150(X1))),'fun_app$v'(X1,sK151(X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_659])]) ).
tff(f3342,plain,
! [X2: $int,X3: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK150(X1))),'fun_app$v'(X1,sK151(X1)))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3101]) ).
tff(f3101,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK150(X1))),'fun_app$v'(X1,sK151(X1)))
| ~ $less(X2,X3)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2008]) ).
tff(f2008,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK150(X1))),'fun_app$v'(X1,sK151(X1)))
& $less(sK150(X1),sK151(X1)) )
| ~ $less(X2,X3)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151])],[f1374,f2007]) ).
tff(f2007,plain,
! [X1: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,sK150(X1))),'fun_app$v'(X1,sK151(X1)))
& $less(sK150(X1),sK151(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1374,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(flattening,[],[f1373]) ).
tff(f1373,plain,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f514]) ).
tff(f514,axiom,
! [X0: 'Num$',X1: 'Int_num_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X4)),'fun_app$v'(X1,X5)) )
& $less(X2,X3)
& ( 'fun_app$v'(X1,X2) = X0 ) )
=> 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).
tff(f10567,plain,
spl272_658,
inference(avatar_split_clause,[],[f3340,f10565]) ).
tff(f10565,plain,
( spl272_658
<=> ! [X2: $int,X1: 'Int_enat_fun$',X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK148(X1))),'fun_app$y'(X1,sK149(X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_658])]) ).
tff(f3340,plain,
! [X2: $int,X3: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK148(X1))),'fun_app$y'(X1,sK149(X1)))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3099]) ).
tff(f3099,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK148(X1))),'fun_app$y'(X1,sK149(X1)))
| ~ $less(X2,X3)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2006]) ).
tff(f2006,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK148(X1))),'fun_app$y'(X1,sK149(X1)))
& $less(sK148(X1),sK149(X1)) )
| ~ $less(X2,X3)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148,sK149])],[f1372,f2005]) ).
tff(f2005,plain,
! [X1: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,sK148(X1))),'fun_app$y'(X1,sK149(X1)))
& $less(sK148(X1),sK149(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1372,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(flattening,[],[f1371]) ).
tff(f1371,plain,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f516]) ).
tff(f516,axiom,
! [X0: 'Enat$',X1: 'Int_enat_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X4)),'fun_app$y'(X1,X5)) )
& $less(X2,X3)
& ( 'fun_app$y'(X1,X2) = X0 ) )
=> 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom514) ).
tff(f10563,plain,
spl272_657,
inference(avatar_split_clause,[],[f3332,f10561]) ).
tff(f10561,plain,
( spl272_657
<=> ! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK132(X2))),'fun_app$v'(X2,sK133(X2)))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_657])]) ).
tff(f3332,plain,
! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK132(X2))),'fun_app$v'(X2,sK133(X2)))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3083]) ).
tff(f3083,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK132(X2))),'fun_app$v'(X2,sK133(X2)))
| ( 'fun_app$v'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1990]) ).
tff(f1990,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK132(X2))),'fun_app$v'(X2,sK133(X2)))
& ~ $less(sK133(X2),sK132(X2)) )
| ( 'fun_app$v'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK132,sK133])],[f1356,f1989]) ).
tff(f1989,plain,
! [X2: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,sK132(X2))),'fun_app$v'(X2,sK133(X2)))
& ~ $less(sK133(X2),sK132(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1356,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
| ( 'fun_app$v'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(flattening,[],[f1355]) ).
tff(f1355,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& ~ $less(X5,X4) )
| ( 'fun_app$v'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f821]) ).
tff(f821,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& ( 'fun_app$v'(X2,X1) = X3 )
& ~ $less(X1,X0) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3) ),
inference(theory_normalization,[],[f301]) ).
tff(f301,axiom,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& ( 'fun_app$v'(X2,X1) = X3 )
& $lesseq(X0,X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom299) ).
tff(f10559,plain,
spl272_656,
inference(avatar_split_clause,[],[f3330,f10557]) ).
tff(f10557,plain,
( spl272_656
<=> ! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK130(X2))),'fun_app$y'(X2,sK131(X2)))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_656])]) ).
tff(f3330,plain,
! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK130(X2))),'fun_app$y'(X2,sK131(X2)))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3081]) ).
tff(f3081,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK130(X2))),'fun_app$y'(X2,sK131(X2)))
| ( 'fun_app$y'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1988]) ).
tff(f1988,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK130(X2))),'fun_app$y'(X2,sK131(X2)))
& ~ $less(sK131(X2),sK130(X2)) )
| ( 'fun_app$y'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130,sK131])],[f1354,f1987]) ).
tff(f1987,plain,
! [X2: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
=> ( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,sK130(X2))),'fun_app$y'(X2,sK131(X2)))
& ~ $less(sK131(X2),sK130(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1354,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
| ( 'fun_app$y'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(flattening,[],[f1353]) ).
tff(f1353,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& ~ $less(X5,X4) )
| ( 'fun_app$y'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f820]) ).
tff(f820,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& ( 'fun_app$y'(X2,X1) = X3 )
& ~ $less(X1,X0) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3) ),
inference(theory_normalization,[],[f302]) ).
tff(f302,axiom,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& ( 'fun_app$y'(X2,X1) = X3 )
& $lesseq(X0,X1) )
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom300) ).
tff(f10555,plain,
spl272_655,
inference(avatar_split_clause,[],[f3324,f10553]) ).
tff(f10553,plain,
( spl272_655
<=> ! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK116(X2))),'fun_app$v'(X2,sK117(X2)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_655])]) ).
tff(f3324,plain,
! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK116(X2))),'fun_app$v'(X2,sK117(X2)))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3067]) ).
tff(f3067,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK116(X2))),'fun_app$v'(X2,sK117(X2)))
| ( 'fun_app$v'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1974]) ).
tff(f1974,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK116(X2))),'fun_app$v'(X2,sK117(X2)))
& $less(sK116(X2),sK117(X2)) )
| ( 'fun_app$v'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK116,sK117])],[f1340,f1973]) ).
tff(f1973,plain,
! [X2: 'Int_num_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,sK116(X2))),'fun_app$v'(X2,sK117(X2)))
& $less(sK116(X2),sK117(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1340,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$v'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(flattening,[],[f1339]) ).
tff(f1339,plain,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$v'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f504]) ).
tff(f504,axiom,
! [X0: $int,X1: $int,X2: 'Int_num_fun$',X3: 'Num$'] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X4)),'fun_app$v'(X2,X5)) )
& ( 'fun_app$v'(X2,X1) = X3 )
& $less(X0,X1) )
=> 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom502) ).
tff(f10551,plain,
spl272_654,
inference(avatar_split_clause,[],[f3322,f10549]) ).
tff(f10549,plain,
( spl272_654
<=> ! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK114(X2))),'fun_app$y'(X2,sK115(X2)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_654])]) ).
tff(f3322,plain,
! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK114(X2))),'fun_app$y'(X2,sK115(X2)))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3065]) ).
tff(f3065,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK114(X2))),'fun_app$y'(X2,sK115(X2)))
| ( 'fun_app$y'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1972]) ).
tff(f1972,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK114(X2))),'fun_app$y'(X2,sK115(X2)))
& $less(sK114(X2),sK115(X2)) )
| ( 'fun_app$y'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114,sK115])],[f1338,f1971]) ).
tff(f1971,plain,
! [X2: 'Int_enat_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
=> ( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,sK114(X2))),'fun_app$y'(X2,sK115(X2)))
& $less(sK114(X2),sK115(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1338,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$y'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(flattening,[],[f1337]) ).
tff(f1337,plain,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| ? [X4: $int,X5: $int] :
( ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$y'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f506]) ).
tff(f506,axiom,
! [X0: $int,X1: $int,X2: 'Int_enat_fun$',X3: 'Enat$'] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X4)),'fun_app$y'(X2,X5)) )
& ( 'fun_app$y'(X2,X1) = X3 )
& $less(X0,X1) )
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom504) ).
tff(f10546,plain,
spl272_653,
inference(avatar_split_clause,[],[f3008,f10544]) ).
tff(f10544,plain,
( spl272_653
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_653])]) ).
tff(f3008,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1938]) ).
tff(f1938,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) )
& ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2)) ) ),
inference(nnf_transformation,[],[f420]) ).
tff(f420,axiom,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom418) ).
tff(f10541,plain,
spl272_652,
inference(avatar_split_clause,[],[f3007,f10539]) ).
tff(f10539,plain,
( spl272_652
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_652])]) ).
tff(f3007,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1938]) ).
tff(f10536,plain,
spl272_651,
inference(avatar_split_clause,[],[f3004,f10534]) ).
tff(f10534,plain,
( spl272_651
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_651])]) ).
tff(f3004,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
inference(cnf_transformation,[],[f1936]) ).
tff(f1936,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) )
& ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2)) ) ),
inference(nnf_transformation,[],[f417]) ).
tff(f417,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
<=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom415) ).
tff(f10531,plain,
spl272_650,
inference(avatar_split_clause,[],[f3003,f10529]) ).
tff(f10529,plain,
( spl272_650
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_650])]) ).
tff(f3003,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2)) ),
inference(cnf_transformation,[],[f1936]) ).
tff(f10527,plain,
( spl272_649
| ~ spl272_107
| ~ spl272_602 ),
inference(avatar_split_clause,[],[f10048,f9733,f4104,f10525]) ).
tff(f9733,plain,
( spl272_602
<=> ! [X0: $int] : ~ $less($sum(6,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_602])]) ).
tff(f10048,plain,
( ! [X0: $int] : $less(X0,$sum(7,X0))
| ~ spl272_107
| ~ spl272_602 ),
inference(evaluation,[],[f10036]) ).
tff(f10036,plain,
( ! [X0: $int] : $less(X0,$sum(6,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_602 ),
inference(resolution,[],[f9734,f4105]) ).
tff(f9734,plain,
( ! [X0: $int] : ~ $less($sum(6,X0),X0)
| ~ spl272_602 ),
inference(avatar_component_clause,[],[f9733]) ).
tff(f10507,plain,
( spl272_648
| ~ spl272_181
| ~ spl272_278
| ~ spl272_647 ),
inference(avatar_split_clause,[],[f10503,f10500,f5561,f4632,f10505]) ).
tff(f10505,plain,
( spl272_648
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_648])]) ).
tff(f10500,plain,
( spl272_647
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_647])]) ).
tff(f10503,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_647 ),
inference(forward_demodulation,[],[f10501,f5822]) ).
tff(f10501,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) )
| ~ spl272_647 ),
inference(avatar_component_clause,[],[f10500]) ).
tff(f10502,plain,
spl272_647,
inference(avatar_split_clause,[],[f2992,f10500]) ).
tff(f2992,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1930]) ).
tff(f1930,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) )
& ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) ) ),
inference(nnf_transformation,[],[f421]) ).
tff(f421,axiom,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2))
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom419) ).
tff(f10485,plain,
( spl272_646
| ~ spl272_181
| ~ spl272_278
| ~ spl272_645 ),
inference(avatar_split_clause,[],[f10481,f10478,f5561,f4632,f10483]) ).
tff(f10483,plain,
( spl272_646
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_646])]) ).
tff(f10478,plain,
( spl272_645
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_645])]) ).
tff(f10481,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_645 ),
inference(forward_demodulation,[],[f10479,f5822]) ).
tff(f10479,plain,
( ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) )
| ~ spl272_645 ),
inference(avatar_component_clause,[],[f10478]) ).
tff(f10480,plain,
spl272_645,
inference(avatar_split_clause,[],[f2991,f10478]) ).
tff(f2991,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)),'fun_app$a'('of_nat$',X2))
| ~ $less('fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),X1),'fun_app$m'('of_nat$b',X2)) ),
inference(cnf_transformation,[],[f1930]) ).
tff(f10460,plain,
( spl272_644
| ~ spl272_181
| ~ spl272_278
| ~ spl272_643 ),
inference(avatar_split_clause,[],[f10456,f10453,f5561,f4632,f10458]) ).
tff(f10458,plain,
( spl272_644
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_644])]) ).
tff(f10453,plain,
( spl272_643
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_643])]) ).
tff(f10456,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_643 ),
inference(forward_demodulation,[],[f10454,f5822]) ).
tff(f10454,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) )
| ~ spl272_643 ),
inference(avatar_component_clause,[],[f10453]) ).
tff(f10455,plain,
spl272_643,
inference(avatar_split_clause,[],[f2988,f10453]) ).
tff(f2988,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
inference(cnf_transformation,[],[f1928]) ).
tff(f1928,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) )
& ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) ) ),
inference(nnf_transformation,[],[f418]) ).
tff(f418,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2))
<=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
tff(f10438,plain,
( spl272_642
| ~ spl272_56
| ~ spl272_602 ),
inference(avatar_split_clause,[],[f10043,f9733,f3857,f10436]) ).
tff(f10436,plain,
( spl272_642
<=> ! [X0: $int] : ~ $less($sum(X0,6),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_642])]) ).
tff(f10043,plain,
( ! [X0: $int] : ~ $less($sum(X0,6),X0)
| ~ spl272_56
| ~ spl272_602 ),
inference(superposition,[],[f9734,f3858]) ).
tff(f10434,plain,
( spl272_641
| ~ spl272_181
| ~ spl272_278
| ~ spl272_640 ),
inference(avatar_split_clause,[],[f10430,f10427,f5561,f4632,f10432]) ).
tff(f10432,plain,
( spl272_641
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_641])]) ).
tff(f10427,plain,
( spl272_640
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_640])]) ).
tff(f10430,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('power$a'('fun_app$d'('numeral$',X1)),X2))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) )
| ~ spl272_181
| ~ spl272_278
| ~ spl272_640 ),
inference(forward_demodulation,[],[f10428,f5822]) ).
tff(f10428,plain,
( ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) )
| ~ spl272_640 ),
inference(avatar_component_clause,[],[f10427]) ).
tff(f10429,plain,
spl272_640,
inference(avatar_split_clause,[],[f2987,f10427]) ).
tff(f2987,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2)) ),
inference(cnf_transformation,[],[f1928]) ).
tff(f10425,plain,
spl272_639,
inference(avatar_split_clause,[],[f2976,f10423]) ).
tff(f10423,plain,
( spl272_639
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_639])]) ).
tff(f2976,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) ) ),
inference(cnf_transformation,[],[f1922]) ).
tff(f1922,plain,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) ) )
& ( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) ) ) ),
inference(nnf_transformation,[],[f140]) ).
tff(f140,axiom,
! [X0: 'Num$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) )
<=> ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
tff(f10421,plain,
spl272_638,
inference(avatar_split_clause,[],[f2975,f10419]) ).
tff(f10419,plain,
( spl272_638
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_638])]) ).
tff(f2975,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X2) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X0))),X1)) )
| ( 'fun_app$a'('of_nat$',X2) != 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),X1) ) ),
inference(cnf_transformation,[],[f1922]) ).
tff(f10417,plain,
spl272_637,
inference(avatar_split_clause,[],[f2966,f10415]) ).
tff(f10415,plain,
( spl272_637
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_637])]) ).
tff(f2966,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
inference(cnf_transformation,[],[f1917]) ).
tff(f1917,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) ) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
tff(f10413,plain,
spl272_636,
inference(avatar_split_clause,[],[f2965,f10411]) ).
tff(f10411,plain,
( spl272_636
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_636])]) ).
tff(f2965,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X1)),X2) ) ),
inference(cnf_transformation,[],[f1917]) ).
tff(f10409,plain,
spl272_635,
inference(avatar_split_clause,[],[f2964,f10407]) ).
tff(f10407,plain,
( spl272_635
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$l'('of_nat$c',X0) = 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_635])]) ).
tff(f2964,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$l'('of_nat$c',X0) = 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
inference(cnf_transformation,[],[f1916]) ).
tff(f1916,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( ( 'fun_app$l'('of_nat$c',X0) = 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$l'('of_nat$c',X0) != 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) ) ) ),
inference(nnf_transformation,[],[f143]) ).
tff(f143,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( 'fun_app$l'('of_nat$c',X0) = 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom141) ).
tff(f10405,plain,
spl272_634,
inference(avatar_split_clause,[],[f2963,f10403]) ).
tff(f10403,plain,
( spl272_634
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$l'('of_nat$c',X0) != 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_634])]) ).
tff(f2963,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$l'('of_nat$c',X0) != 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X1)),X2) ) ),
inference(cnf_transformation,[],[f1916]) ).
tff(f10401,plain,
spl272_633,
inference(avatar_split_clause,[],[f2870,f10399]) ).
tff(f10399,plain,
( spl272_633
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_633])]) ).
tff(f2870,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f10397,plain,
spl272_632,
inference(avatar_split_clause,[],[f2869,f10395]) ).
tff(f10395,plain,
( spl272_632
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| ~ $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_632])]) ).
tff(f2869,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| ~ $less('fun_app$a'('of_nat$',sK76(X0,X1,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f10379,plain,
spl272_631,
inference(avatar_split_clause,[],[f2866,f10377]) ).
tff(f10377,plain,
( spl272_631
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_631])]) ).
tff(f2866,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f10375,plain,
spl272_630,
inference(avatar_split_clause,[],[f2865,f10373]) ).
tff(f10373,plain,
( spl272_630
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_630])]) ).
tff(f2865,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ $less('fun_app$a'('of_nat$',sK75(X0,X1,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f10371,plain,
spl272_629,
inference(avatar_split_clause,[],[f2823,f10369]) ).
tff(f10369,plain,
( spl272_629
<=> ! [X2: 'Nat$',X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_629])]) ).
tff(f2823,plain,
! [X2: 'Nat$',X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1824]) ).
tff(f1824,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( ( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| $less(X1,X0) )
& ( ~ $less(X1,X0)
| $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2)) ) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(nnf_transformation,[],[f1224]) ).
tff(f1224,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
<=> ~ $less(X1,X0) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(flattening,[],[f1223]) ).
tff(f1223,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
<=> ~ $less(X1,X0) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(ennf_transformation,[],[f775]) ).
tff(f775,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& ~ $less(X1,0.0)
& ~ $less(X0,0.0) )
=> ( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
<=> ~ $less(X1,X0) ) ),
inference(theory_normalization,[],[f402]) ).
tff(f402,axiom,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& $lesseq(0.0,X1)
& $lesseq(0.0,X0) )
=> ( $lesseq('fun_app$m'('power$c'(X0),X2),'fun_app$m'('power$c'(X1),X2))
<=> $lesseq(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom400) ).
tff(f10367,plain,
spl272_628,
inference(avatar_split_clause,[],[f2817,f10365]) ).
tff(f10365,plain,
( spl272_628
<=> ! [X4: 'Nat$',X0: 'Nat_bool_fun$',X2: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4)
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_628])]) ).
tff(f2817,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$',X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4)
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1823]) ).
tff(f1823,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4) )
& 'fun_app$n'(X0,sK66(X0)) )
| ( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
& 'fun_app$n'(X0,sK67(X0,X2)) )
| ~ 'fun_app$n'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67])],[f1820,f1822,f1821]) ).
tff(f1821,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4) )
& 'fun_app$n'(X0,X3) )
=> ( ! [X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4) )
& 'fun_app$n'(X0,sK66(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1822,plain,
! [X0: 'Nat_bool_fun$',X2: 'Nat$'] :
( ? [X5: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X5))
& 'fun_app$n'(X0,X5) )
=> ( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
& 'fun_app$n'(X0,sK67(X0,X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1820,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4) )
& 'fun_app$n'(X0,X3) )
| ? [X5: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X5))
& 'fun_app$n'(X0,X5) )
| ~ 'fun_app$n'(X0,X1) ),
inference(rectify,[],[f1212]) ).
tff(f1212,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ? [X4: 'Nat$'] :
( ! [X5: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
| ~ 'fun_app$n'(X0,X5) )
& 'fun_app$n'(X0,X4) )
| ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ 'fun_app$n'(X0,X1) ),
inference(flattening,[],[f1211]) ).
tff(f1211,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ? [X4: 'Nat$'] :
( ! [X5: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
| ~ 'fun_app$n'(X0,X5) )
& 'fun_app$n'(X0,X4) )
| ? [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ 'fun_app$n'(X0,X1) ),
inference(ennf_transformation,[],[f983]) ).
tff(f983,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
=> ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3)) )
& 'fun_app$n'(X0,X1) )
=> ? [X4: 'Nat$'] :
( ! [X5: 'Nat$'] :
( 'fun_app$n'(X0,X5)
=> ~ $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5)) )
& 'fun_app$n'(X0,X4) ) ),
inference(rectify,[],[f769]) ).
tff(f769,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
=> ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3)) )
& 'fun_app$n'(X0,X1) )
=> ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( 'fun_app$n'(X0,X4)
=> ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
& 'fun_app$n'(X0,X3) ) ),
inference(theory_normalization,[],[f35]) ).
tff(f35,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$',X2: 'Nat$'] :
( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
=> $lesseq('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& 'fun_app$n'(X0,X1) )
=> ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( 'fun_app$n'(X0,X4)
=> $lesseq('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X3)) )
& 'fun_app$n'(X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom33) ).
tff(f10363,plain,
spl272_627,
inference(avatar_split_clause,[],[f2811,f10361]) ).
tff(f10361,plain,
( spl272_627
<=> ! [X2: 'Nat$',X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_627])]) ).
tff(f2811,plain,
! [X2: 'Nat$',X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0)
| $less(X0,0) ),
inference(cnf_transformation,[],[f1819]) ).
tff(f1819,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( ( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| $less(X1,X0) )
& ( ~ $less(X1,X0)
| $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2)) ) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0)
| $less(X0,0) ),
inference(nnf_transformation,[],[f1208]) ).
tff(f1208,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
<=> ~ $less(X1,X0) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0)
| $less(X0,0) ),
inference(flattening,[],[f1207]) ).
tff(f1207,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
<=> ~ $less(X1,X0) )
| ~ $less(0,'fun_app$a'('of_nat$',X2))
| $less(X1,0)
| $less(X0,0) ),
inference(ennf_transformation,[],[f768]) ).
tff(f768,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& ~ $less(X1,0)
& ~ $less(X0,0) )
=> ( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
<=> ~ $less(X1,X0) ) ),
inference(theory_normalization,[],[f401]) ).
tff(f401,axiom,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& $lesseq(0,X1)
& $lesseq(0,X0) )
=> ( $lesseq('fun_app$a'('power$a'(X0),X2),'fun_app$a'('power$a'(X1),X2))
<=> $lesseq(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom399) ).
tff(f10359,plain,
spl272_626,
inference(avatar_split_clause,[],[f2526,f10357]) ).
tff(f10357,plain,
( spl272_626
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$b'('power$'(X1),'nat$'(2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_626])]) ).
tff(f2526,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$b'('power$'(X1),'nat$'(2))) ),
inference(cnf_transformation,[],[f1173]) ).
tff(f1173,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$b'('power$'(X1),'nat$'(2))) ),
inference(flattening,[],[f1172]) ).
tff(f1172,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$b'('power$'(X1),'nat$'(2))) ),
inference(ennf_transformation,[],[f336]) ).
tff(f336,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X1)
& 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$b'('power$'(X1),'nat$'(2))) )
=> 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
tff(f9945,plain,
( spl272_625
| ~ spl272_58
| ~ spl272_573 ),
inference(avatar_split_clause,[],[f9689,f9410,f3865,f9943]) ).
tff(f9943,plain,
( spl272_625
<=> ! [X0: $real] : $less(X0,$sum(X0,6.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_625])]) ).
tff(f9410,plain,
( spl272_573
<=> ! [X0: $real] : $less(X0,$sum(6.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_573])]) ).
tff(f9689,plain,
( ! [X0: $real] : $less(X0,$sum(X0,6.0))
| ~ spl272_58
| ~ spl272_573 ),
inference(superposition,[],[f9411,f3866]) ).
tff(f9411,plain,
( ! [X0: $real] : $less(X0,$sum(6.0,X0))
| ~ spl272_573 ),
inference(avatar_component_clause,[],[f9410]) ).
tff(f9823,plain,
( spl272_624
| ~ spl272_50
| ~ spl272_573 ),
inference(avatar_split_clause,[],[f9684,f9410,f3821,f9821]) ).
tff(f9684,plain,
( ! [X0: $real] : ~ $less($sum(6.0,X0),X0)
| ~ spl272_50
| ~ spl272_573 ),
inference(resolution,[],[f9411,f3822]) ).
tff(f9819,plain,
spl272_623,
inference(avatar_split_clause,[],[f3606,f9817]) ).
tff(f9817,plain,
( spl272_623
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_623])]) ).
tff(f3606,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
inference(forward_demodulation,[],[f3033,f2347]) ).
tff(f2347,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1) ),
inference(cnf_transformation,[],[f120]) ).
tff(f120,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom118) ).
tff(f3033,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2)) ),
inference(cnf_transformation,[],[f1951]) ).
tff(f1951,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) )
& ( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
inference(nnf_transformation,[],[f815]) ).
tff(f815,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
inference(theory_normalization,[],[f132]) ).
tff(f132,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom130) ).
tff(f9815,plain,
spl272_622,
inference(avatar_split_clause,[],[f3605,f9813]) ).
tff(f9813,plain,
( spl272_622
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_622])]) ).
tff(f3605,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
inference(forward_demodulation,[],[f3034,f2347]) ).
tff(f3034,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
inference(cnf_transformation,[],[f1951]) ).
tff(f9811,plain,
spl272_621,
inference(avatar_split_clause,[],[f3604,f9809]) ).
tff(f9809,plain,
( spl272_621
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_621])]) ).
tff(f3604,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(forward_demodulation,[],[f3031,f2347]) ).
tff(f3031,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2)) ),
inference(cnf_transformation,[],[f1950]) ).
tff(f1950,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) )
& ( $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2)) ) ),
inference(nnf_transformation,[],[f410]) ).
tff(f410,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
<=> $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
tff(f9807,plain,
spl272_620,
inference(avatar_split_clause,[],[f3603,f9805]) ).
tff(f9805,plain,
( spl272_620
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_620])]) ).
tff(f3603,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1))),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(forward_demodulation,[],[f3032,f2347]) ).
tff(f3032,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)),'fun_app$b'('of_nat$a',X2))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X2)) ),
inference(cnf_transformation,[],[f1950]) ).
tff(f9803,plain,
spl272_619,
inference(avatar_split_clause,[],[f3602,f9801]) ).
tff(f9801,plain,
( spl272_619
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_619])]) ).
tff(f3602,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f3029,f2347]) ).
tff(f3029,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2)) ),
inference(cnf_transformation,[],[f1949]) ).
tff(f1949,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) )
& ( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2)) ) ),
inference(nnf_transformation,[],[f814]) ).
tff(f814,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
<=> ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f135]) ).
tff(f135,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
<=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).
tff(f9799,plain,
spl272_618,
inference(avatar_split_clause,[],[f3601,f9797]) ).
tff(f9797,plain,
( spl272_618
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_618])]) ).
tff(f3601,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f3030,f2347]) ).
tff(f3030,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1949]) ).
tff(f9795,plain,
spl272_617,
inference(avatar_split_clause,[],[f3600,f9793]) ).
tff(f9793,plain,
( spl272_617
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_617])]) ).
tff(f3600,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
inference(forward_demodulation,[],[f3027,f2347]) ).
tff(f3027,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2)) ),
inference(cnf_transformation,[],[f1948]) ).
tff(f1948,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) )
& ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)))
| ~ 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2)) ) ),
inference(nnf_transformation,[],[f407]) ).
tff(f407,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
<=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
tff(f9791,plain,
spl272_616,
inference(avatar_split_clause,[],[f3599,f9789]) ).
tff(f9789,plain,
( spl272_616
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_616])]) ).
tff(f3599,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
inference(forward_demodulation,[],[f3028,f2347]) ).
tff(f3028,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','fun_app$b'('of_nat$a',X0)),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2))) ),
inference(cnf_transformation,[],[f1948]) ).
tff(f9787,plain,
spl272_615,
inference(avatar_split_clause,[],[f3419,f9785]) ).
tff(f9785,plain,
( spl272_615
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_615])]) ).
tff(f3419,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(evaluation,[],[f2497]) ).
tff(f2497,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1128]) ).
tff(f1128,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1127]) ).
tff(f1127,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f441]) ).
tff(f441,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum(0,1),'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
tff(f9783,plain,
spl272_614,
inference(avatar_split_clause,[],[f3418,f9781]) ).
tff(f9781,plain,
( spl272_614
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_614])]) ).
tff(f3418,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(evaluation,[],[f2498]) ).
tff(f2498,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1130]) ).
tff(f1130,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1129]) ).
tff(f1129,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f442]) ).
tff(f442,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum(0,1),'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> $less('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
tff(f9779,plain,
( spl272_613
| ~ spl272_56
| ~ spl272_557 ),
inference(avatar_split_clause,[],[f9574,f9288,f3857,f9777]) ).
tff(f9777,plain,
( spl272_613
<=> ! [X0: $int] : $less(X0,$sum(X0,6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_613])]) ).
tff(f9288,plain,
( spl272_557
<=> ! [X0: $int] : $less(X0,$sum(6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_557])]) ).
tff(f9574,plain,
( ! [X0: $int] : $less(X0,$sum(X0,6))
| ~ spl272_56
| ~ spl272_557 ),
inference(superposition,[],[f9289,f3858]) ).
tff(f9289,plain,
( ! [X0: $int] : $less(X0,$sum(6,X0))
| ~ spl272_557 ),
inference(avatar_component_clause,[],[f9288]) ).
tff(f9775,plain,
spl272_612,
inference(avatar_split_clause,[],[f3261,f9773]) ).
tff(f9773,plain,
( spl272_612
<=> ! [X0: 'Nat$',X3: $real] :
( ( sK49(X0,'fun_app$m'('power$c'(X3),X0)) = X3 )
| ~ $less(0.0,X3)
| ~ $less(0.0,'fun_app$m'('power$c'(X3),X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_612])]) ).
tff(f3261,plain,
! [X3: $real,X0: 'Nat$'] :
( ( sK49(X0,'fun_app$m'('power$c'(X3),X0)) = X3 )
| ~ $less(0.0,X3)
| ~ $less(0.0,'fun_app$m'('power$c'(X3),X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(equality_resolution,[],[f2496]) ).
tff(f2496,plain,
! [X3: $real,X0: 'Nat$',X1: $real] :
( ( sK49(X0,X1) = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3)
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f1632,plain,
! [X0: 'Nat$',X1: $real] :
( ( ! [X3: $real] :
( ( sK49(X0,X1) = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3) )
& ( 'fun_app$m'('power$c'(sK49(X0,X1)),X0) = X1 )
& $less(0.0,sK49(X0,X1)) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f1126,f1631]) ).
tff(f1631,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ! [X3: $real] :
( ( X2 = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3) )
& ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
=> ( ! [X3: $real] :
( ( sK49(X0,X1) = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3) )
& ( 'fun_app$m'('power$c'(sK49(X0,X1)),X0) = X1 )
& $less(0.0,sK49(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1126,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ! [X3: $real] :
( ( X2 = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3) )
& ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1125]) ).
tff(f1125,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ! [X3: $real] :
( ( X2 = X3 )
| ( 'fun_app$m'('power$c'(X3),X0) != X1 )
| ~ $less(0.0,X3) )
& ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f635]) ).
tff(f635,axiom,
! [X0: 'Nat$',X1: $real] :
( ( $less(0.0,X1)
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> ? [X2: $real] :
( ! [X3: $real] :
( ( ( 'fun_app$m'('power$c'(X3),X0) = X1 )
& $less(0.0,X3) )
=> ( X2 = X3 ) )
& ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom633) ).
tff(f9771,plain,
spl272_611,
inference(avatar_split_clause,[],[f3217,f9769]) ).
tff(f9769,plain,
( spl272_611
<=> ! [X0: 'Num$',X3: $int,X2: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ $less(sK267(X1),sK266(X1))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_611])]) ).
tff(f3217,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ $less(sK267(X1),sK266(X1))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X2)) ),
inference(cnf_transformation,[],[f2124]) ).
tff(f9767,plain,
spl272_610,
inference(avatar_split_clause,[],[f3215,f9765]) ).
tff(f9765,plain,
( spl272_610
<=> ! [X0: 'Num$',X3: $real,X2: $real,X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ~ $less(sK265(X1),sK264(X1))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_610])]) ).
tff(f3215,plain,
! [X2: $real,X3: $real,X0: 'Num$',X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X3))
| ~ $less(sK265(X1),sK264(X1))
| $less(X3,X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$x'(X1,X2)) ),
inference(cnf_transformation,[],[f2122]) ).
tff(f9763,plain,
spl272_609,
inference(avatar_split_clause,[],[f3209,f9761]) ).
tff(f9761,plain,
( spl272_609
<=> ! [X0: 'Num$',X3: $int,X2: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| $less(sK258(X1),sK259(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_609])]) ).
tff(f3209,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| $less(sK258(X1),sK259(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X2)) ),
inference(cnf_transformation,[],[f2116]) ).
tff(f9759,plain,
spl272_608,
inference(avatar_split_clause,[],[f3207,f9757]) ).
tff(f9757,plain,
( spl272_608
<=> ! [X0: 'Num$',X3: $real,X2: $real,X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| $less(sK256(X1),sK257(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_608])]) ).
tff(f3207,plain,
! [X2: $real,X3: $real,X0: 'Num$',X1: 'Real_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X3))
| $less(sK256(X1),sK257(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$x'(X1,X2)) ),
inference(cnf_transformation,[],[f2114]) ).
tff(f9755,plain,
spl272_607,
inference(avatar_split_clause,[],[f3203,f9753]) ).
tff(f9753,plain,
( spl272_607
<=> ! [X0: 'Enat$',X3: $int,X2: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ $less(sK253(X1),sK252(X1))
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_607])]) ).
tff(f3203,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ $less(sK253(X1),sK252(X1))
| $less(X3,X2)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X2)) ),
inference(cnf_transformation,[],[f2110]) ).
tff(f9751,plain,
spl272_606,
inference(avatar_split_clause,[],[f3199,f9749]) ).
tff(f9749,plain,
( spl272_606
<=> ! [X0: 'Enat$',X3: $int,X2: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| $less(sK248(X1),sK249(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_606])]) ).
tff(f3199,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| $less(sK248(X1),sK249(X1))
| ~ $less(X2,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X2)) ),
inference(cnf_transformation,[],[f2106]) ).
tff(f9747,plain,
spl272_605,
inference(avatar_split_clause,[],[f3196,f9745]) ).
tff(f9745,plain,
( spl272_605
<=> ! [X0: $int,X3: 'Num$',X2: 'Num$',X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',sK246(X1)),sK247(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_605])]) ).
tff(f3196,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',sK246(X1)),sK247(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| $less('fun_app$d'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2104]) ).
tff(f9743,plain,
spl272_604,
inference(avatar_split_clause,[],[f3195,f9741]) ).
tff(f9741,plain,
( spl272_604
<=> ! [X0: $int,X3: $int,X2: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| $less('fun_app$p'(X1,sK245(X1)),'fun_app$p'(X1,sK244(X1)))
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_604])]) ).
tff(f3195,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| $less('fun_app$p'(X1,sK245(X1)),'fun_app$p'(X1,sK244(X1)))
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2102]) ).
tff(f2102,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ( $less('fun_app$p'(X1,sK245(X1)),'fun_app$p'(X1,sK244(X1)))
& ~ $less(sK245(X1),sK244(X1)) )
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK244,sK245])],[f1468,f2101]) ).
tff(f2101,plain,
! [X1: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$p'(X1,sK245(X1)),'fun_app$p'(X1,sK244(X1)))
& ~ $less(sK245(X1),sK244(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1468,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ),
inference(flattening,[],[f1467]) ).
tff(f1467,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ),
inference(ennf_transformation,[],[f842]) ).
tff(f842,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4)) )
& ~ $less(X3,X2)
& ~ $less('fun_app$p'(X1,X2),X0) )
=> ~ $less('fun_app$p'(X1,X3),X0) ),
inference(theory_normalization,[],[f258]) ).
tff(f258,axiom,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$p'(X1,X4),'fun_app$p'(X1,X5)) )
& $lesseq(X2,X3)
& $lesseq(X0,'fun_app$p'(X1,X2)) )
=> $lesseq(X0,'fun_app$p'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom256) ).
tff(f9739,plain,
spl272_603,
inference(avatar_split_clause,[],[f3192,f9737]) ).
tff(f9737,plain,
( spl272_603
<=> ! [X0: $int,X3: 'Enat$',X2: 'Enat$',X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK242(X1)),sK243(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_603])]) ).
tff(f3192,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK242(X1)),sK243(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| $less('fun_app$t'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2100]) ).
tff(f9735,plain,
( spl272_602
| ~ spl272_51
| ~ spl272_557 ),
inference(avatar_split_clause,[],[f9569,f9288,f3825,f9733]) ).
tff(f9569,plain,
( ! [X0: $int] : ~ $less($sum(6,X0),X0)
| ~ spl272_51
| ~ spl272_557 ),
inference(resolution,[],[f9289,f3826]) ).
tff(f9731,plain,
spl272_601,
inference(avatar_split_clause,[],[f3191,f9729]) ).
tff(f9729,plain,
( spl272_601
<=> ! [X0: $int,X3: $real,X2: $real,X1: 'Real_int_fun$'] :
( ~ $less('fun_app$u'(X1,X3),X0)
| $less('fun_app$u'(X1,sK241(X1)),'fun_app$u'(X1,sK240(X1)))
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_601])]) ).
tff(f3191,plain,
! [X2: $real,X3: $real,X0: $int,X1: 'Real_int_fun$'] :
( ~ $less('fun_app$u'(X1,X3),X0)
| $less('fun_app$u'(X1,sK241(X1)),'fun_app$u'(X1,sK240(X1)))
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2098]) ).
tff(f2098,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ~ $less('fun_app$u'(X1,X3),X0)
| ( $less('fun_app$u'(X1,sK241(X1)),'fun_app$u'(X1,sK240(X1)))
& ~ $less(sK241(X1),sK240(X1)) )
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK240,sK241])],[f1464,f2097]) ).
tff(f2097,plain,
! [X1: 'Real_int_fun$'] :
( ? [X4: $real,X5: $real] :
( $less('fun_app$u'(X1,X5),'fun_app$u'(X1,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$u'(X1,sK241(X1)),'fun_app$u'(X1,sK240(X1)))
& ~ $less(sK241(X1),sK240(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1464,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ~ $less('fun_app$u'(X1,X3),X0)
| ? [X4: $real,X5: $real] :
( $less('fun_app$u'(X1,X5),'fun_app$u'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ),
inference(flattening,[],[f1463]) ).
tff(f1463,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ~ $less('fun_app$u'(X1,X3),X0)
| ? [X4: $real,X5: $real] :
( $less('fun_app$u'(X1,X5),'fun_app$u'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ),
inference(ennf_transformation,[],[f840]) ).
tff(f840,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$u'(X1,X5),'fun_app$u'(X1,X4)) )
& ~ $less(X3,X2)
& ~ $less('fun_app$u'(X1,X2),X0) )
=> ~ $less('fun_app$u'(X1,X3),X0) ),
inference(theory_normalization,[],[f261]) ).
tff(f261,axiom,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$u'(X1,X4),'fun_app$u'(X1,X5)) )
& $lesseq(X2,X3)
& $lesseq(X0,'fun_app$u'(X1,X2)) )
=> $lesseq(X0,'fun_app$u'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom259) ).
tff(f9727,plain,
spl272_600,
inference(avatar_split_clause,[],[f3188,f9725]) ).
tff(f9725,plain,
( spl272_600
<=> ! [X0: $int,X3: 'Num$',X2: 'Num$',X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK238(X1)),sK239(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_600])]) ).
tff(f3188,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK238(X1)),sK239(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ~ $less(X0,'fun_app$d'(X1,X2)) ),
inference(cnf_transformation,[],[f2096]) ).
tff(f9723,plain,
spl272_599,
inference(avatar_split_clause,[],[f3187,f9721]) ).
tff(f9721,plain,
( spl272_599
<=> ! [X0: $int,X3: $int,X2: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| ~ $less('fun_app$p'(X1,sK236(X1)),'fun_app$p'(X1,sK237(X1)))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_599])]) ).
tff(f3187,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| ~ $less('fun_app$p'(X1,sK236(X1)),'fun_app$p'(X1,sK237(X1)))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ),
inference(cnf_transformation,[],[f2094]) ).
tff(f2094,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ( ~ $less('fun_app$p'(X1,sK236(X1)),'fun_app$p'(X1,sK237(X1)))
& $less(sK236(X1),sK237(X1)) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK236,sK237])],[f1460,f2093]) ).
tff(f2093,plain,
! [X1: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$p'(X1,sK236(X1)),'fun_app$p'(X1,sK237(X1)))
& $less(sK236(X1),sK237(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1460,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ),
inference(flattening,[],[f1459]) ).
tff(f1459,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ),
inference(ennf_transformation,[],[f491]) ).
tff(f491,axiom,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5)) )
& $less(X2,X3)
& $less(X0,'fun_app$p'(X1,X2)) )
=> $less(X0,'fun_app$p'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom489) ).
tff(f9719,plain,
spl272_598,
inference(avatar_split_clause,[],[f3184,f9717]) ).
tff(f9717,plain,
( spl272_598
<=> ! [X0: $int,X3: 'Enat$',X2: 'Enat$',X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK234(X1)),sK235(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_598])]) ).
tff(f3184,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK234(X1)),sK235(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ~ $less(X0,'fun_app$t'(X1,X2)) ),
inference(cnf_transformation,[],[f2092]) ).
tff(f9715,plain,
spl272_597,
inference(avatar_split_clause,[],[f3183,f9713]) ).
tff(f9713,plain,
( spl272_597
<=> ! [X0: $int,X3: $real,X2: $real,X1: 'Real_int_fun$'] :
( $less(X0,'fun_app$u'(X1,X3))
| ~ $less('fun_app$u'(X1,sK232(X1)),'fun_app$u'(X1,sK233(X1)))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_597])]) ).
tff(f3183,plain,
! [X2: $real,X3: $real,X0: $int,X1: 'Real_int_fun$'] :
( $less(X0,'fun_app$u'(X1,X3))
| ~ $less('fun_app$u'(X1,sK232(X1)),'fun_app$u'(X1,sK233(X1)))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ),
inference(cnf_transformation,[],[f2090]) ).
tff(f2090,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( $less(X0,'fun_app$u'(X1,X3))
| ( ~ $less('fun_app$u'(X1,sK232(X1)),'fun_app$u'(X1,sK233(X1)))
& $less(sK232(X1),sK233(X1)) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK232,sK233])],[f1456,f2089]) ).
tff(f2089,plain,
! [X1: 'Real_int_fun$'] :
( ? [X4: $real,X5: $real] :
( ~ $less('fun_app$u'(X1,X4),'fun_app$u'(X1,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$u'(X1,sK232(X1)),'fun_app$u'(X1,sK233(X1)))
& $less(sK232(X1),sK233(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1456,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( $less(X0,'fun_app$u'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ $less('fun_app$u'(X1,X4),'fun_app$u'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ),
inference(flattening,[],[f1455]) ).
tff(f1455,plain,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( $less(X0,'fun_app$u'(X1,X3))
| ? [X4: $real,X5: $real] :
( ~ $less('fun_app$u'(X1,X4),'fun_app$u'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ),
inference(ennf_transformation,[],[f493]) ).
tff(f493,axiom,
! [X0: $int,X1: 'Real_int_fun$',X2: $real,X3: $real] :
( ( ! [X4: $real,X5: $real] :
( $less(X4,X5)
=> $less('fun_app$u'(X1,X4),'fun_app$u'(X1,X5)) )
& $less(X2,X3)
& $less(X0,'fun_app$u'(X1,X2)) )
=> $less(X0,'fun_app$u'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom491) ).
tff(f9711,plain,
spl272_596,
inference(avatar_split_clause,[],[f3176,f9709]) ).
tff(f9709,plain,
( spl272_596
<=> ! [X0: 'Num$',X3: $int,X2: 'Num_int_fun$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK226(X2)),sK227(X2))
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_596])]) ).
tff(f3176,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK226(X2)),sK227(X2))
| $less(X3,'fun_app$d'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2084]) ).
tff(f9707,plain,
spl272_595,
inference(avatar_split_clause,[],[f3174,f9705]) ).
tff(f9705,plain,
( spl272_595
<=> ! [X0: 'Num$',X3: $real,X2: 'Num_real_fun$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK224(X2)),sK225(X2))
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_595])]) ).
tff(f3174,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK224(X2)),sK225(X2))
| $less(X3,'fun_app$j'(X2,X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2082]) ).
tff(f9703,plain,
spl272_594,
inference(avatar_split_clause,[],[f3160,f9701]) ).
tff(f9701,plain,
( spl272_594
<=> ! [X0: 'Num$',X3: $int,X2: 'Num_int_fun$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK210(X2)),sK211(X2))
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_594])]) ).
tff(f3160,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK210(X2)),sK211(X2))
| ~ $less('fun_app$d'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2068]) ).
tff(f9699,plain,
spl272_593,
inference(avatar_split_clause,[],[f3158,f9697]) ).
tff(f9697,plain,
( spl272_593
<=> ! [X0: 'Num$',X3: $real,X2: 'Num_real_fun$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK208(X2)),sK209(X2))
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_593])]) ).
tff(f3158,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK208(X2)),sK209(X2))
| ~ $less('fun_app$j'(X2,X1),X3)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2066]) ).
tff(f9695,plain,
spl272_592,
inference(avatar_split_clause,[],[f3146,f9693]) ).
tff(f9693,plain,
( spl272_592
<=> ! [X0: 'Enat$',X3: $int,X2: 'Enat_int_fun$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK196(X2)),sK197(X2))
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_592])]) ).
tff(f3146,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK196(X2)),sK197(X2))
| $less(X3,'fun_app$t'(X2,X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2054]) ).
tff(f9681,plain,
spl272_591,
inference(avatar_split_clause,[],[f3138,f9679]) ).
tff(f9679,plain,
( spl272_591
<=> ! [X0: 'Enat$',X3: $int,X2: 'Enat_int_fun$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK188(X2)),sK189(X2))
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_591])]) ).
tff(f3138,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK188(X2)),sK189(X2))
| ~ $less('fun_app$t'(X2,X1),X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2046]) ).
tff(f9677,plain,
spl272_590,
inference(avatar_split_clause,[],[f3092,f9675]) ).
tff(f9675,plain,
( spl272_590
<=> ! [X0: $int,X3: 'Num$',X2: 'Int_num_fun$',X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ $less(sK143(X2),sK142(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_590])]) ).
tff(f3092,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ $less(sK143(X2),sK142(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X1)),X3)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f2000]) ).
tff(f9673,plain,
spl272_589,
inference(avatar_split_clause,[],[f3090,f9671]) ).
tff(f9671,plain,
( spl272_589
<=> ! [X0: $int,X3: 'Enat$',X2: 'Int_enat_fun$',X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ $less(sK141(X2),sK140(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_589])]) ).
tff(f3090,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ $less(sK141(X2),sK140(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X1)),X3)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1998]) ).
tff(f9669,plain,
spl272_588,
inference(avatar_split_clause,[],[f3089,f9667]) ).
tff(f9667,plain,
( spl272_588
<=> ! [X0: $int,X3: $int,X2: 'Int_int_fun$',X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| $less('fun_app$p'(X2,sK139(X2)),'fun_app$p'(X2,sK138(X2)))
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_588])]) ).
tff(f3089,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| $less('fun_app$p'(X2,sK139(X2)),'fun_app$p'(X2,sK138(X2)))
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1996]) ).
tff(f1996,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ( $less('fun_app$p'(X2,sK139(X2)),'fun_app$p'(X2,sK138(X2)))
& ~ $less(sK139(X2),sK138(X2)) )
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138,sK139])],[f1362,f1995]) ).
tff(f1995,plain,
! [X2: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$p'(X2,sK139(X2)),'fun_app$p'(X2,sK138(X2)))
& ~ $less(sK139(X2),sK138(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1362,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ),
inference(flattening,[],[f1361]) ).
tff(f1361,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ),
inference(ennf_transformation,[],[f824]) ).
tff(f824,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4)) )
& ~ $less(X3,'fun_app$p'(X2,X1))
& ~ $less(X1,X0) )
=> ~ $less(X3,'fun_app$p'(X2,X0)) ),
inference(theory_normalization,[],[f268]) ).
tff(f268,axiom,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$p'(X2,X4),'fun_app$p'(X2,X5)) )
& $lesseq('fun_app$p'(X2,X1),X3)
& $lesseq(X0,X1) )
=> $lesseq('fun_app$p'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom266) ).
tff(f9665,plain,
spl272_587,
inference(avatar_split_clause,[],[f3087,f9663]) ).
tff(f9663,plain,
( spl272_587
<=> ! [X0: $int,X3: $real,X2: 'Int_real_fun$',X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| $less('fun_app$z'(X2,sK137(X2)),'fun_app$z'(X2,sK136(X2)))
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_587])]) ).
tff(f3087,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| $less('fun_app$z'(X2,sK137(X2)),'fun_app$z'(X2,sK136(X2)))
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1994]) ).
tff(f1994,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ( $less('fun_app$z'(X2,sK137(X2)),'fun_app$z'(X2,sK136(X2)))
& ~ $less(sK137(X2),sK136(X2)) )
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136,sK137])],[f1360,f1993]) ).
tff(f1993,plain,
! [X2: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$z'(X2,sK137(X2)),'fun_app$z'(X2,sK136(X2)))
& ~ $less(sK137(X2),sK136(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1360,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ),
inference(flattening,[],[f1359]) ).
tff(f1359,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ),
inference(ennf_transformation,[],[f823]) ).
tff(f823,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4)) )
& ~ $less(X3,'fun_app$z'(X2,X1))
& ~ $less(X1,X0) )
=> ~ $less(X3,'fun_app$z'(X2,X0)) ),
inference(theory_normalization,[],[f271]) ).
tff(f271,axiom,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$z'(X2,X4),'fun_app$z'(X2,X5)) )
& $lesseq('fun_app$z'(X2,X1),X3)
& $lesseq(X0,X1) )
=> $lesseq('fun_app$z'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom269) ).
tff(f9661,plain,
spl272_586,
inference(avatar_split_clause,[],[f3076,f9659]) ).
tff(f9659,plain,
( spl272_586
<=> ! [X0: $int,X3: 'Num$',X2: 'Int_num_fun$',X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| $less(sK126(X2),sK127(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_586])]) ).
tff(f3076,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| $less(sK126(X2),sK127(X2))
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1984]) ).
tff(f9657,plain,
spl272_585,
inference(avatar_split_clause,[],[f3074,f9655]) ).
tff(f9655,plain,
( spl272_585
<=> ! [X0: $int,X3: 'Enat$',X2: 'Int_enat_fun$',X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| $less(sK124(X2),sK125(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_585])]) ).
tff(f3074,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| $less(sK124(X2),sK125(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X1)),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1982]) ).
tff(f9653,plain,
spl272_584,
inference(avatar_split_clause,[],[f3073,f9651]) ).
tff(f9651,plain,
( spl272_584
<=> ! [X0: $int,X3: $int,X2: 'Int_int_fun$',X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ~ $less('fun_app$p'(X2,sK122(X2)),'fun_app$p'(X2,sK123(X2)))
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_584])]) ).
tff(f3073,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ~ $less('fun_app$p'(X2,sK122(X2)),'fun_app$p'(X2,sK123(X2)))
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1980]) ).
tff(f1980,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ( ~ $less('fun_app$p'(X2,sK122(X2)),'fun_app$p'(X2,sK123(X2)))
& $less(sK122(X2),sK123(X2)) )
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122,sK123])],[f1346,f1979]) ).
tff(f1979,plain,
! [X2: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$p'(X2,sK122(X2)),'fun_app$p'(X2,sK123(X2)))
& $less(sK122(X2),sK123(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1346,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(flattening,[],[f1345]) ).
tff(f1345,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f481]) ).
tff(f481,axiom,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5)) )
& $less('fun_app$p'(X2,X1),X3)
& $less(X0,X1) )
=> $less('fun_app$p'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom479) ).
tff(f9649,plain,
spl272_583,
inference(avatar_split_clause,[],[f3071,f9647]) ).
tff(f9647,plain,
( spl272_583
<=> ! [X0: $int,X3: $real,X2: 'Int_real_fun$',X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| ~ $less('fun_app$z'(X2,sK120(X2)),'fun_app$z'(X2,sK121(X2)))
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_583])]) ).
tff(f3071,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| ~ $less('fun_app$z'(X2,sK120(X2)),'fun_app$z'(X2,sK121(X2)))
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1978]) ).
tff(f1978,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ( ~ $less('fun_app$z'(X2,sK120(X2)),'fun_app$z'(X2,sK121(X2)))
& $less(sK120(X2),sK121(X2)) )
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK120,sK121])],[f1344,f1977]) ).
tff(f1977,plain,
! [X2: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$z'(X2,sK120(X2)),'fun_app$z'(X2,sK121(X2)))
& $less(sK120(X2),sK121(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1344,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(flattening,[],[f1343]) ).
tff(f1343,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f483]) ).
tff(f483,axiom,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5)) )
& $less('fun_app$z'(X2,X1),X3)
& $less(X0,X1) )
=> $less('fun_app$z'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom481) ).
tff(f9645,plain,
spl272_582,
inference(avatar_split_clause,[],[f3047,f9643]) ).
tff(f9643,plain,
( spl272_582
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_582])]) ).
tff(f3047,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1))) ),
inference(cnf_transformation,[],[f1961]) ).
tff(f1961,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ~ $less(0,'fun_app$a'('of_nat$',X1)) )
& ( ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X1)) )
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1))) ) ),
inference(flattening,[],[f1960]) ).
tff(f1960,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
| ~ $less(0,'fun_app$a'('of_nat$',X1)) )
& ( ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X1)) )
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1))) ) ),
inference(nnf_transformation,[],[f382]) ).
tff(f382,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X2)),'fun_app$a'('of_nat$',X1)))
<=> ( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom380) ).
tff(f9633,plain,
spl272_581,
inference(avatar_split_clause,[],[f3044,f9631]) ).
tff(f9631,plain,
( spl272_581
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_581])]) ).
tff(f3044,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ),
inference(cnf_transformation,[],[f1959]) ).
tff(f1959,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( ( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ) ),
inference(flattening,[],[f1958]) ).
tff(f1958,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( ( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2))) ) ),
inference(nnf_transformation,[],[f384]) ).
tff(f384,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)))
<=> ( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2))
& $less(0,'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom382) ).
tff(f9629,plain,
spl272_580,
inference(avatar_split_clause,[],[f2960,f9627]) ).
tff(f9627,plain,
( spl272_580
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('numeral$c'(X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_580])]) ).
tff(f2960,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('numeral$c'(X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
inference(cnf_transformation,[],[f1914]) ).
tff(f1914,plain,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('numeral$c'(X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('power$'('numeral$c'(X1)),X2) ) ) ),
inference(nnf_transformation,[],[f142]) ).
tff(f142,axiom,
! [X0: 'Nat$',X1: 'Num$',X2: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('numeral$c'(X1)),X2) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom140) ).
tff(f9625,plain,
spl272_579,
inference(avatar_split_clause,[],[f2959,f9623]) ).
tff(f9623,plain,
( spl272_579
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('power$'('numeral$c'(X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_579])]) ).
tff(f2959,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Num$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'('fun_app$d'('numeral$',X1))),X2)) )
| ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('power$'('numeral$c'(X1)),X2) ) ),
inference(cnf_transformation,[],[f1914]) ).
tff(f9621,plain,
spl272_578,
inference(avatar_split_clause,[],[f2905,f9619]) ).
tff(f9619,plain,
( spl272_578
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less(X2,X1)
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_578])]) ).
tff(f2905,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less(X2,X1)
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ),
inference(cnf_transformation,[],[f1522]) ).
tff(f1522,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ),
inference(definition_folding,[],[f1302,f1521,f1520,f1519,f1518]) ).
tff(f1518,plain,
! [X1: $int,X2: $int,X0: $int] :
( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
| ~ sP12(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
tff(f1519,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ~ sP13(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f1520,plain,
! [X2: $int,X1: $int,X0: $int] :
( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ~ sP14(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f1521,plain,
! [X1: $int,X0: $int,X2: $int] :
( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ~ sP15(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
tff(f1302,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
| ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ( ~ $less(X2,X1)
& ~ $less(X1,X0) ) ),
inference(ennf_transformation,[],[f988]) ).
tff(f988,plain,
! [X0: $int,X1: $int,X2: $int] :
~ ( ~ ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
& ~ ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
& ~ ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
& ~ ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
& ~ ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
& ~ ( ~ $less(X2,X1)
& ~ $less(X1,X0) ) ),
inference(true_and_false_elimination,[],[f792]) ).
tff(f792,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
=> $false )
& ( ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
=> $false )
& ( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
=> $false )
& ( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
=> $false )
& ( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
=> $false )
& ( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
=> $false ) )
=> $false ),
inference(theory_normalization,[],[f206]) ).
tff(f206,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( ( ( $lesseq(X0,X1)
& $lesseq(X2,X0) )
=> $false )
& ( ( $lesseq(X2,X0)
& $lesseq(X1,X2) )
=> $false )
& ( ( $lesseq(X1,X0)
& $lesseq(X2,X1) )
=> $false )
& ( ( $lesseq(X2,X1)
& $lesseq(X0,X2) )
=> $false )
& ( ( $lesseq(X0,X2)
& $lesseq(X1,X0) )
=> $false )
& ( ( $lesseq(X1,X2)
& $lesseq(X0,X1) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
tff(f9617,plain,
spl272_577,
inference(avatar_split_clause,[],[f2893,f9615]) ).
tff(f9615,plain,
( spl272_577
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ $less(X2,X1)
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_577])]) ).
tff(f2893,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ $less(X2,X1)
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ),
inference(cnf_transformation,[],[f1517]) ).
tff(f1517,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ),
inference(definition_folding,[],[f1301,f1516,f1515,f1514,f1513]) ).
tff(f1513,plain,
! [X1: $real,X2: $real,X0: $real] :
( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
| ~ sP8(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f1514,plain,
! [X0: $real,X2: $real,X1: $real] :
( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ~ sP9(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f1515,plain,
! [X2: $real,X1: $real,X0: $real] :
( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ~ sP10(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f1516,plain,
! [X1: $real,X0: $real,X2: $real] :
( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ~ sP11(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
tff(f1301,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
| ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ( ~ $less(X2,X1)
& ~ $less(X1,X0) ) ),
inference(ennf_transformation,[],[f987]) ).
tff(f987,plain,
! [X0: $real,X1: $real,X2: $real] :
~ ( ~ ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
& ~ ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
& ~ ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
& ~ ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
& ~ ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
& ~ ( ~ $less(X2,X1)
& ~ $less(X1,X0) ) ),
inference(true_and_false_elimination,[],[f791]) ).
tff(f791,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
=> $false )
& ( ( ~ $less(X0,X2)
& ~ $less(X2,X1) )
=> $false )
& ( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
=> $false )
& ( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
=> $false )
& ( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
=> $false )
& ( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
=> $false ) )
=> $false ),
inference(theory_normalization,[],[f209]) ).
tff(f209,axiom,
! [X0: $real,X1: $real,X2: $real] :
( ( ( ( $lesseq(X0,X1)
& $lesseq(X2,X0) )
=> $false )
& ( ( $lesseq(X2,X0)
& $lesseq(X1,X2) )
=> $false )
& ( ( $lesseq(X1,X0)
& $lesseq(X2,X1) )
=> $false )
& ( ( $lesseq(X2,X1)
& $lesseq(X0,X2) )
=> $false )
& ( ( $lesseq(X0,X2)
& $lesseq(X1,X0) )
=> $false )
& ( ( $lesseq(X1,X2)
& $lesseq(X0,X1) )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
tff(f9613,plain,
spl272_576,
inference(avatar_split_clause,[],[f2862,f9611]) ).
tff(f9611,plain,
( spl272_576
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ $less('fun_app$a'('of_nat$',sK74(X0,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_576])]) ).
tff(f2862,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| ~ $less('fun_app$a'('of_nat$',sK74(X0,X2)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f9609,plain,
spl272_575,
inference(avatar_split_clause,[],[f2758,f9607]) ).
tff(f9607,plain,
( spl272_575
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_575])]) ).
tff(f2758,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1779]) ).
tff(f1779,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
& ( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ) ),
inference(nnf_transformation,[],[f762]) ).
tff(f762,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))))
<=> ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))))
<=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f9605,plain,
spl272_574,
inference(avatar_split_clause,[],[f2757,f9603]) ).
tff(f9603,plain,
( spl272_574
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_574])]) ).
tff(f2757,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X1),'nat$'(2))),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ),
inference(cnf_transformation,[],[f1779]) ).
tff(f9412,plain,
( spl272_573
| ~ spl272_109
| ~ spl272_524 ),
inference(avatar_split_clause,[],[f8877,f8611,f4112,f9410]) ).
tff(f8611,plain,
( spl272_524
<=> ! [X0: $real] : ~ $less($sum(5.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_524])]) ).
tff(f8877,plain,
( ! [X0: $real] : $less(X0,$sum(6.0,X0))
| ~ spl272_109
| ~ spl272_524 ),
inference(evaluation,[],[f8871]) ).
tff(f8871,plain,
( ! [X0: $real] : $less(X0,$sum(5.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_524 ),
inference(resolution,[],[f8612,f4113]) ).
tff(f8612,plain,
( ! [X0: $real] : ~ $less($sum(5.0,X0),X0)
| ~ spl272_524 ),
inference(avatar_component_clause,[],[f8611]) ).
tff(f9350,plain,
spl272_572,
inference(avatar_split_clause,[],[f3401,f9348]) ).
tff(f9348,plain,
( spl272_572
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_572])]) ).
tff(f3401,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ),
inference(duplicate_literal_removal,[],[f2916]) ).
tff(f2916,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| sP19(X0,X1,X2)
| sP18(X1,X2,X0)
| sP17(X2,X0,X1)
| sP16(X2,X1,X0) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f9346,plain,
spl272_571,
inference(avatar_split_clause,[],[f3400,f9344]) ).
tff(f9344,plain,
( spl272_571
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_571])]) ).
tff(f3400,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ),
inference(duplicate_literal_removal,[],[f2928]) ).
tff(f2928,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',X2),X0)
| sP23(X0,X1,X2)
| sP22(X1,X2,X0)
| sP21(X2,X0,X1)
| sP20(X2,X1,X0) ),
inference(cnf_transformation,[],[f1532]) ).
tff(f9342,plain,
spl272_570,
inference(avatar_split_clause,[],[f3398,f9340]) ).
tff(f9340,plain,
( spl272_570
<=> ! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'(X2,X1),'fun_app$d'(X2,X0))
| $less('fun_app$d'(X2,sK223(X2)),'fun_app$d'(X2,sK222(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_570])]) ).
tff(f3398,plain,
! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'(X2,X1),'fun_app$d'(X2,X0))
| $less('fun_app$d'(X2,sK223(X2)),'fun_app$d'(X2,sK222(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3173]) ).
tff(f3173,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| $less('fun_app$d'(X2,sK223(X2)),'fun_app$d'(X2,sK222(X2)))
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2080]) ).
tff(f2080,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ( $less('fun_app$d'(X2,sK223(X2)),'fun_app$d'(X2,sK222(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK222(X2)),sK223(X2)) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK222,sK223])],[f1446,f2079]) ).
tff(f2079,plain,
! [X2: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$d'(X2,sK223(X2)),'fun_app$d'(X2,sK222(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK222(X2)),sK223(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1446,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1445]) ).
tff(f1445,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f837]) ).
tff(f837,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$d'(X2,X5),'fun_app$d'(X2,X4)) )
& ( 'fun_app$d'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> ~ $less(X3,'fun_app$d'(X2,X0)) ),
inference(theory_normalization,[],[f304]) ).
tff(f304,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$d'(X2,X4),'fun_app$d'(X2,X5)) )
& ( 'fun_app$d'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> $lesseq('fun_app$d'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
tff(f9338,plain,
spl272_569,
inference(avatar_split_clause,[],[f3397,f9336]) ).
tff(f9336,plain,
( spl272_569
<=> ! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| 'fun_app$e'('fun_app$f'('less_eq$',sK220(X2)),sK221(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_569])]) ).
tff(f3397,plain,
! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| 'fun_app$e'('fun_app$f'('less_eq$',sK220(X2)),sK221(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3170]) ).
tff(f3170,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK220(X2)),sK221(X2))
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2078]) ).
tff(f9334,plain,
( spl272_568
| ~ spl272_58
| ~ spl272_524 ),
inference(avatar_split_clause,[],[f8875,f8611,f3865,f9332]) ).
tff(f9332,plain,
( spl272_568
<=> ! [X0: $real] : ~ $less($sum(X0,5.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_568])]) ).
tff(f8875,plain,
( ! [X0: $real] : ~ $less($sum(X0,5.0),X0)
| ~ spl272_58
| ~ spl272_524 ),
inference(superposition,[],[f8612,f3866]) ).
tff(f9330,plain,
spl272_567,
inference(avatar_split_clause,[],[f3395,f9328]) ).
tff(f9328,plain,
( spl272_567
<=> ! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| 'fun_app$e'('fun_app$f'('less_eq$',sK218(X2)),sK219(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_567])]) ).
tff(f3395,plain,
! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| 'fun_app$e'('fun_app$f'('less_eq$',sK218(X2)),sK219(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3168]) ).
tff(f3168,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less_eq$',sK218(X2)),sK219(X2))
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2076]) ).
tff(f9326,plain,
spl272_566,
inference(avatar_split_clause,[],[f3392,f9324]) ).
tff(f9324,plain,
( spl272_566
<=> ! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'(X2,X1),'fun_app$j'(X2,X0))
| $less('fun_app$j'(X2,sK217(X2)),'fun_app$j'(X2,sK216(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_566])]) ).
tff(f3392,plain,
! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'(X2,X1),'fun_app$j'(X2,X0))
| $less('fun_app$j'(X2,sK217(X2)),'fun_app$j'(X2,sK216(X2)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3167]) ).
tff(f3167,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| $less('fun_app$j'(X2,sK217(X2)),'fun_app$j'(X2,sK216(X2)))
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2074]) ).
tff(f2074,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ( $less('fun_app$j'(X2,sK217(X2)),'fun_app$j'(X2,sK216(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK216(X2)),sK217(X2)) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK216,sK217])],[f1440,f2073]) ).
tff(f2073,plain,
! [X2: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$j'(X2,sK217(X2)),'fun_app$j'(X2,sK216(X2)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK216(X2)),sK217(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1440,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1439]) ).
tff(f1439,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f836]) ).
tff(f836,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$j'(X2,X5),'fun_app$j'(X2,X4)) )
& ( 'fun_app$j'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> ~ $less(X3,'fun_app$j'(X2,X0)) ),
inference(theory_normalization,[],[f307]) ).
tff(f307,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$j'(X2,X4),'fun_app$j'(X2,X5)) )
& ( 'fun_app$j'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> $lesseq('fun_app$j'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).
tff(f9322,plain,
spl272_565,
inference(avatar_split_clause,[],[f3390,f9320]) ).
tff(f9320,plain,
( spl272_565
<=> ! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),'fun_app$d'(X2,X1))
| ~ $less('fun_app$d'(X2,sK206(X2)),'fun_app$d'(X2,sK207(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_565])]) ).
tff(f3390,plain,
! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),'fun_app$d'(X2,X1))
| ~ $less('fun_app$d'(X2,sK206(X2)),'fun_app$d'(X2,sK207(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3157]) ).
tff(f3157,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| ~ $less('fun_app$d'(X2,sK206(X2)),'fun_app$d'(X2,sK207(X2)))
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2064]) ).
tff(f2064,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ( ~ $less('fun_app$d'(X2,sK206(X2)),'fun_app$d'(X2,sK207(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK206(X2)),sK207(X2)) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK206,sK207])],[f1430,f2063]) ).
tff(f2063,plain,
! [X2: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$d'(X2,sK206(X2)),'fun_app$d'(X2,sK207(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK206(X2)),sK207(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1430,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1429]) ).
tff(f1429,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( $less('fun_app$d'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f501]) ).
tff(f501,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_int_fun$',X3: $int] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$d'(X2,X4),'fun_app$d'(X2,X5)) )
& ( 'fun_app$d'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> $less('fun_app$d'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
tff(f9318,plain,
spl272_564,
inference(avatar_split_clause,[],[f3389,f9316]) ).
tff(f9316,plain,
( spl272_564
<=> ! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK204(X2)),sK205(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_564])]) ).
tff(f3389,plain,
! [X2: 'Num_num_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),'fun_app$c'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK204(X2)),sK205(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3154]) ).
tff(f3154,plain,
! [X2: 'Num_num_fun$',X3: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK204(X2)),sK205(X2))
| ( 'fun_app$c'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2062]) ).
tff(f9314,plain,
spl272_563,
inference(avatar_split_clause,[],[f3387,f9312]) ).
tff(f9312,plain,
( spl272_563
<=> ! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK202(X2)),sK203(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_563])]) ).
tff(f3387,plain,
! [X2: 'Num_enat_fun$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),'fun_app$i'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK202(X2)),sK203(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3152]) ).
tff(f3152,plain,
! [X2: 'Num_enat_fun$',X3: 'Enat$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X2,X0)),X3)
| 'fun_app$e'('fun_app$f'('less$',sK202(X2)),sK203(X2))
| ( 'fun_app$i'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2060]) ).
tff(f9310,plain,
spl272_562,
inference(avatar_split_clause,[],[f3384,f9308]) ).
tff(f9308,plain,
( spl272_562
<=> ! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),'fun_app$j'(X2,X1))
| ~ $less('fun_app$j'(X2,sK200(X2)),'fun_app$j'(X2,sK201(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_562])]) ).
tff(f3384,plain,
! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),'fun_app$j'(X2,X1))
| ~ $less('fun_app$j'(X2,sK200(X2)),'fun_app$j'(X2,sK201(X2)))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3151]) ).
tff(f3151,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| ~ $less('fun_app$j'(X2,sK200(X2)),'fun_app$j'(X2,sK201(X2)))
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2058]) ).
tff(f2058,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ( ~ $less('fun_app$j'(X2,sK200(X2)),'fun_app$j'(X2,sK201(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK200(X2)),sK201(X2)) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK200,sK201])],[f1424,f2057]) ).
tff(f2057,plain,
! [X2: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$j'(X2,sK200(X2)),'fun_app$j'(X2,sK201(X2)))
& 'fun_app$e'('fun_app$f'('less$',sK200(X2)),sK201(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1424,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1423]) ).
tff(f1423,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( $less('fun_app$j'(X2,X0),X3)
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f503]) ).
tff(f503,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num_real_fun$',X3: $real] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$j'(X2,X4),'fun_app$j'(X2,X5)) )
& ( 'fun_app$j'(X2,X1) = X3 )
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> $less('fun_app$j'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
tff(f9306,plain,
spl272_561,
inference(avatar_split_clause,[],[f3383,f9304]) ).
tff(f9304,plain,
( spl272_561
<=> ! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK194(X2)),sK195(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_561])]) ).
tff(f3383,plain,
! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK194(X2)),sK195(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(equality_resolution,[],[f3144]) ).
tff(f3144,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK194(X2)),sK195(X2))
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2052]) ).
tff(f9302,plain,
spl272_560,
inference(avatar_split_clause,[],[f3380,f9300]) ).
tff(f9300,plain,
( spl272_560
<=> ! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X1),'fun_app$t'(X2,X0))
| $less('fun_app$t'(X2,sK193(X2)),'fun_app$t'(X2,sK192(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_560])]) ).
tff(f3380,plain,
! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X1),'fun_app$t'(X2,X0))
| $less('fun_app$t'(X2,sK193(X2)),'fun_app$t'(X2,sK192(X2)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(equality_resolution,[],[f3143]) ).
tff(f3143,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| $less('fun_app$t'(X2,sK193(X2)),'fun_app$t'(X2,sK192(X2)))
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2050]) ).
tff(f2050,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ( $less('fun_app$t'(X2,sK193(X2)),'fun_app$t'(X2,sK192(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK192(X2)),sK193(X2)) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK192,sK193])],[f1416,f2049]) ).
tff(f2049,plain,
! [X2: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( $less('fun_app$t'(X2,sK193(X2)),'fun_app$t'(X2,sK192(X2)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK192(X2)),sK193(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1416,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(flattening,[],[f1415]) ).
tff(f1415,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(ennf_transformation,[],[f834]) ).
tff(f834,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> ~ $less('fun_app$t'(X2,X5),'fun_app$t'(X2,X4)) )
& ( 'fun_app$t'(X2,X1) = X3 )
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> ~ $less(X3,'fun_app$t'(X2,X0)) ),
inference(theory_normalization,[],[f308]) ).
tff(f308,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> $lesseq('fun_app$t'(X2,X4),'fun_app$t'(X2,X5)) )
& ( 'fun_app$t'(X2,X1) = X3 )
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> $lesseq('fun_app$t'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
tff(f9298,plain,
spl272_559,
inference(avatar_split_clause,[],[f3379,f9296]) ).
tff(f9296,plain,
( spl272_559
<=> ! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| 'fun_app$g'('fun_app$h'('less$a',sK186(X2)),sK187(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_559])]) ).
tff(f3379,plain,
! [X2: 'Enat_num_fun$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),'fun_app$w'(X2,X1))
| 'fun_app$g'('fun_app$h'('less$a',sK186(X2)),sK187(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(equality_resolution,[],[f3136]) ).
tff(f3136,plain,
! [X2: 'Enat_num_fun$',X3: 'Num$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X2,X0)),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK186(X2)),sK187(X2))
| ( 'fun_app$w'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2044]) ).
tff(f9294,plain,
spl272_558,
inference(avatar_split_clause,[],[f3376,f9292]) ).
tff(f9292,plain,
( spl272_558
<=> ! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),'fun_app$t'(X2,X1))
| ~ $less('fun_app$t'(X2,sK184(X2)),'fun_app$t'(X2,sK185(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_558])]) ).
tff(f3376,plain,
! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),'fun_app$t'(X2,X1))
| ~ $less('fun_app$t'(X2,sK184(X2)),'fun_app$t'(X2,sK185(X2)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(equality_resolution,[],[f3135]) ).
tff(f3135,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| ~ $less('fun_app$t'(X2,sK184(X2)),'fun_app$t'(X2,sK185(X2)))
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2042]) ).
tff(f2042,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ( ~ $less('fun_app$t'(X2,sK184(X2)),'fun_app$t'(X2,sK185(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK184(X2)),sK185(X2)) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK184,sK185])],[f1408,f2041]) ).
tff(f2041,plain,
! [X2: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ $less('fun_app$t'(X2,sK184(X2)),'fun_app$t'(X2,sK185(X2)))
& 'fun_app$g'('fun_app$h'('less$a',sK184(X2)),sK185(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1408,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(flattening,[],[f1407]) ).
tff(f1407,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( $less('fun_app$t'(X2,X0),X3)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f509]) ).
tff(f509,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat_int_fun$',X3: $int] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> $less('fun_app$t'(X2,X4),'fun_app$t'(X2,X5)) )
& ( 'fun_app$t'(X2,X1) = X3 )
& 'fun_app$g'('fun_app$h'('less$a',X0),X1) )
=> $less('fun_app$t'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).
tff(f9290,plain,
( spl272_557
| ~ spl272_107
| ~ spl272_519 ),
inference(avatar_split_clause,[],[f8750,f8405,f4104,f9288]) ).
tff(f8405,plain,
( spl272_519
<=> ! [X0: $int] : ~ $less($sum(5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_519])]) ).
tff(f8750,plain,
( ! [X0: $int] : $less(X0,$sum(6,X0))
| ~ spl272_107
| ~ spl272_519 ),
inference(evaluation,[],[f8738]) ).
tff(f8738,plain,
( ! [X0: $int] : $less(X0,$sum(5,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_519 ),
inference(resolution,[],[f8406,f4105]) ).
tff(f8406,plain,
( ! [X0: $int] : ~ $less($sum(5,X0),X0)
| ~ spl272_519 ),
inference(avatar_component_clause,[],[f8405]) ).
tff(f9286,plain,
spl272_556,
inference(avatar_split_clause,[],[f3374,f9284]) ).
tff(f9284,plain,
( spl272_556
<=> ! [X2: 'Num$',X1: 'Num_int_fun$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),'fun_app$d'(X1,X2))
| $less('fun_app$d'(X1,sK183(X1)),'fun_app$d'(X1,sK182(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_556])]) ).
tff(f3374,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),'fun_app$d'(X1,X2))
| $less('fun_app$d'(X1,sK183(X1)),'fun_app$d'(X1,sK182(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3133]) ).
tff(f3133,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| $less('fun_app$d'(X1,sK183(X1)),'fun_app$d'(X1,sK182(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2040]) ).
tff(f2040,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ( $less('fun_app$d'(X1,sK183(X1)),'fun_app$d'(X1,sK182(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK182(X1)),sK183(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182,sK183])],[f1406,f2039]) ).
tff(f2039,plain,
! [X1: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$d'(X1,sK183(X1)),'fun_app$d'(X1,sK182(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK182(X1)),sK183(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1406,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(flattening,[],[f1405]) ).
tff(f1405,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f833]) ).
tff(f833,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$d'(X1,X5),'fun_app$d'(X1,X4)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$d'(X1,X2) = X0 ) )
=> ~ $less('fun_app$d'(X1,X3),X0) ),
inference(theory_normalization,[],[f294]) ).
tff(f294,axiom,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$d'(X1,X4),'fun_app$d'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$d'(X1,X2) = X0 ) )
=> $lesseq(X0,'fun_app$d'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
tff(f9282,plain,
spl272_555,
inference(avatar_split_clause,[],[f3372,f9280]) ).
tff(f9280,plain,
( spl272_555
<=> ! [X2: 'Num$',X1: 'Num_int_fun$',X3: 'Num$'] :
( $less('fun_app$d'(X1,X2),'fun_app$d'(X1,X3))
| ~ $less('fun_app$d'(X1,sK180(X1)),'fun_app$d'(X1,sK181(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_555])]) ).
tff(f3372,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_int_fun$'] :
( $less('fun_app$d'(X1,X2),'fun_app$d'(X1,X3))
| ~ $less('fun_app$d'(X1,sK180(X1)),'fun_app$d'(X1,sK181(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3131]) ).
tff(f3131,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ~ $less('fun_app$d'(X1,sK180(X1)),'fun_app$d'(X1,sK181(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2038]) ).
tff(f2038,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ( ~ $less('fun_app$d'(X1,sK180(X1)),'fun_app$d'(X1,sK181(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK180(X1)),sK181(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK180,sK181])],[f1404,f2037]) ).
tff(f2037,plain,
! [X1: 'Num_int_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$d'(X1,sK180(X1)),'fun_app$d'(X1,sK181(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK180(X1)),sK181(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1404,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(flattening,[],[f1403]) ).
tff(f1403,plain,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$d'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f511]) ).
tff(f511,axiom,
! [X0: $int,X1: 'Num_int_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$d'(X1,X4),'fun_app$d'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& ( 'fun_app$d'(X1,X2) = X0 ) )
=> $less(X0,'fun_app$d'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).
tff(f9278,plain,
spl272_554,
inference(avatar_split_clause,[],[f3367,f9276]) ).
tff(f9276,plain,
( spl272_554
<=> ! [X2: 'Num$',X1: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK174(X1)),sK175(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_554])]) ).
tff(f3367,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK174(X1)),sK175(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3124]) ).
tff(f3124,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK174(X1)),sK175(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2032]) ).
tff(f9274,plain,
spl272_553,
inference(avatar_split_clause,[],[f3365,f9272]) ).
tff(f9272,plain,
( spl272_553
<=> ! [X2: 'Num$',X1: 'Num_num_fun$',X3: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK172(X1)),sK173(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_553])]) ).
tff(f3365,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'(X1,X2)),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK172(X1)),sK173(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3122]) ).
tff(f3122,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Num$',X1: 'Num_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$c'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK172(X1)),sK173(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$c'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2030]) ).
tff(f9270,plain,
spl272_552,
inference(avatar_split_clause,[],[f3363,f9268]) ).
tff(f9268,plain,
( spl272_552
<=> ! [X2: 'Num$',X1: 'Num_enat_fun$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK170(X1)),sK171(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_552])]) ).
tff(f3363,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK170(X1)),sK171(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3120]) ).
tff(f3120,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less_eq$',sK170(X1)),sK171(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2028]) ).
tff(f9266,plain,
spl272_551,
inference(avatar_split_clause,[],[f3361,f9264]) ).
tff(f9264,plain,
( spl272_551
<=> ! [X2: 'Num$',X1: 'Num_enat_fun$',X3: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK168(X1)),sK169(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_551])]) ).
tff(f3361,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'(X1,X2)),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK168(X1)),sK169(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3118]) ).
tff(f3118,plain,
! [X2: 'Num$',X3: 'Num$',X0: 'Enat$',X1: 'Num_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$i'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK168(X1)),sK169(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$i'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2026]) ).
tff(f9262,plain,
spl272_550,
inference(avatar_split_clause,[],[f3358,f9260]) ).
tff(f9260,plain,
( spl272_550
<=> ! [X2: 'Num$',X1: 'Num_real_fun$',X3: 'Num$'] :
( ~ $less('fun_app$j'(X1,X3),'fun_app$j'(X1,X2))
| $less('fun_app$j'(X1,sK167(X1)),'fun_app$j'(X1,sK166(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_550])]) ).
tff(f3358,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_real_fun$'] :
( ~ $less('fun_app$j'(X1,X3),'fun_app$j'(X1,X2))
| $less('fun_app$j'(X1,sK167(X1)),'fun_app$j'(X1,sK166(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3117]) ).
tff(f3117,plain,
! [X2: 'Num$',X3: 'Num$',X0: $real,X1: 'Num_real_fun$'] :
( ~ $less('fun_app$j'(X1,X3),X0)
| $less('fun_app$j'(X1,sK167(X1)),'fun_app$j'(X1,sK166(X1)))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2024]) ).
tff(f2024,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$j'(X1,X3),X0)
| ( $less('fun_app$j'(X1,sK167(X1)),'fun_app$j'(X1,sK166(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK166(X1)),sK167(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166,sK167])],[f1390,f2023]) ).
tff(f2023,plain,
! [X1: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X1,X5),'fun_app$j'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
=> ( $less('fun_app$j'(X1,sK167(X1)),'fun_app$j'(X1,sK166(X1)))
& 'fun_app$e'('fun_app$f'('less_eq$',sK166(X1)),sK167(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1390,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$j'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X1,X5),'fun_app$j'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(flattening,[],[f1389]) ).
tff(f1389,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ~ $less('fun_app$j'(X1,X3),X0)
| ? [X4: 'Num$',X5: 'Num$'] :
( $less('fun_app$j'(X1,X5),'fun_app$j'(X1,X4))
& 'fun_app$e'('fun_app$f'('less_eq$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f831]) ).
tff(f831,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> ~ $less('fun_app$j'(X1,X5),'fun_app$j'(X1,X4)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$j'(X1,X2) = X0 ) )
=> ~ $less('fun_app$j'(X1,X3),X0) ),
inference(theory_normalization,[],[f297]) ).
tff(f297,axiom,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X4),X5)
=> $lesseq('fun_app$j'(X1,X4),'fun_app$j'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
& ( 'fun_app$j'(X1,X2) = X0 ) )
=> $lesseq(X0,'fun_app$j'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom295) ).
tff(f9258,plain,
spl272_549,
inference(avatar_split_clause,[],[f3356,f9256]) ).
tff(f9256,plain,
( spl272_549
<=> ! [X2: 'Num$',X1: 'Num_real_fun$',X3: 'Num$'] :
( $less('fun_app$j'(X1,X2),'fun_app$j'(X1,X3))
| ~ $less('fun_app$j'(X1,sK164(X1)),'fun_app$j'(X1,sK165(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_549])]) ).
tff(f3356,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_real_fun$'] :
( $less('fun_app$j'(X1,X2),'fun_app$j'(X1,X3))
| ~ $less('fun_app$j'(X1,sK164(X1)),'fun_app$j'(X1,sK165(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3115]) ).
tff(f3115,plain,
! [X2: 'Num$',X3: 'Num$',X0: $real,X1: 'Num_real_fun$'] :
( $less(X0,'fun_app$j'(X1,X3))
| ~ $less('fun_app$j'(X1,sK164(X1)),'fun_app$j'(X1,sK165(X1)))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2022]) ).
tff(f2022,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$j'(X1,X3))
| ( ~ $less('fun_app$j'(X1,sK164(X1)),'fun_app$j'(X1,sK165(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK164(X1)),sK165(X1)) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164,sK165])],[f1388,f2021]) ).
tff(f2021,plain,
! [X1: 'Num_real_fun$'] :
( ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X1,X4),'fun_app$j'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
=> ( ~ $less('fun_app$j'(X1,sK164(X1)),'fun_app$j'(X1,sK165(X1)))
& 'fun_app$e'('fun_app$f'('less$',sK164(X1)),sK165(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1388,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$j'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X1,X4),'fun_app$j'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(flattening,[],[f1387]) ).
tff(f1387,plain,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( $less(X0,'fun_app$j'(X1,X3))
| ? [X4: 'Num$',X5: 'Num$'] :
( ~ $less('fun_app$j'(X1,X4),'fun_app$j'(X1,X5))
& 'fun_app$e'('fun_app$f'('less$',X4),X5) )
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f513]) ).
tff(f513,axiom,
! [X0: $real,X1: 'Num_real_fun$',X2: 'Num$',X3: 'Num$'] :
( ( ! [X4: 'Num$',X5: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X4),X5)
=> $less('fun_app$j'(X1,X4),'fun_app$j'(X1,X5)) )
& 'fun_app$e'('fun_app$f'('less$',X2),X3)
& ( 'fun_app$j'(X1,X2) = X0 ) )
=> $less(X0,'fun_app$j'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).
tff(f9254,plain,
spl272_548,
inference(avatar_split_clause,[],[f3355,f9252]) ).
tff(f9252,plain,
( spl272_548
<=> ! [X2: 'Enat$',X1: 'Enat_num_fun$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK162(X1)),sK163(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_548])]) ).
tff(f3355,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK162(X1)),sK163(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ),
inference(equality_resolution,[],[f3112]) ).
tff(f3112,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK162(X1)),sK163(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2020]) ).
tff(f9250,plain,
spl272_547,
inference(avatar_split_clause,[],[f3352,f9248]) ).
tff(f9248,plain,
( spl272_547
<=> ! [X2: 'Enat$',X1: 'Enat_int_fun$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),'fun_app$t'(X1,X2))
| $less('fun_app$t'(X1,sK161(X1)),'fun_app$t'(X1,sK160(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_547])]) ).
tff(f3352,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),'fun_app$t'(X1,X2))
| $less('fun_app$t'(X1,sK161(X1)),'fun_app$t'(X1,sK160(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ),
inference(equality_resolution,[],[f3111]) ).
tff(f3111,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| $less('fun_app$t'(X1,sK161(X1)),'fun_app$t'(X1,sK160(X1)))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2018]) ).
tff(f2018,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ( $less('fun_app$t'(X1,sK161(X1)),'fun_app$t'(X1,sK160(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK160(X1)),sK161(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK160,sK161])],[f1384,f2017]) ).
tff(f2017,plain,
! [X1: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
=> ( $less('fun_app$t'(X1,sK161(X1)),'fun_app$t'(X1,sK160(X1)))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK160(X1)),sK161(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1384,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(flattening,[],[f1383]) ).
tff(f1383,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| ? [X4: 'Enat$',X5: 'Enat$'] :
( $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4))
& 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f830]) ).
tff(f830,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> ~ $less('fun_app$t'(X1,X5),'fun_app$t'(X1,X4)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& ( 'fun_app$t'(X1,X2) = X0 ) )
=> ~ $less('fun_app$t'(X1,X3),X0) ),
inference(theory_normalization,[],[f298]) ).
tff(f298,axiom,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X4),X5)
=> $lesseq('fun_app$t'(X1,X4),'fun_app$t'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
& ( 'fun_app$t'(X1,X2) = X0 ) )
=> $lesseq(X0,'fun_app$t'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom296) ).
tff(f9246,plain,
( spl272_546
| ~ spl272_56
| ~ spl272_519 ),
inference(avatar_split_clause,[],[f8745,f8405,f3857,f9244]) ).
tff(f9244,plain,
( spl272_546
<=> ! [X0: $int] : ~ $less($sum(X0,5),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_546])]) ).
tff(f8745,plain,
( ! [X0: $int] : ~ $less($sum(X0,5),X0)
| ~ spl272_56
| ~ spl272_519 ),
inference(superposition,[],[f8406,f3858]) ).
tff(f9242,plain,
spl272_545,
inference(avatar_split_clause,[],[f3351,f9240]) ).
tff(f9240,plain,
( spl272_545
<=> ! [X2: 'Enat$',X1: 'Enat_num_fun$',X3: 'Enat$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK158(X1)),sK159(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_545])]) ).
tff(f3351,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$w'(X1,X2)),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK158(X1)),sK159(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ),
inference(equality_resolution,[],[f3108]) ).
tff(f3108,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: 'Num$',X1: 'Enat_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$w'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK158(X1)),sK159(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$w'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2016]) ).
tff(f9238,plain,
spl272_544,
inference(avatar_split_clause,[],[f3348,f9236]) ).
tff(f9236,plain,
( spl272_544
<=> ! [X2: 'Enat$',X1: 'Enat_int_fun$',X3: 'Enat$'] :
( $less('fun_app$t'(X1,X2),'fun_app$t'(X1,X3))
| ~ $less('fun_app$t'(X1,sK156(X1)),'fun_app$t'(X1,sK157(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_544])]) ).
tff(f3348,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_int_fun$'] :
( $less('fun_app$t'(X1,X2),'fun_app$t'(X1,X3))
| ~ $less('fun_app$t'(X1,sK156(X1)),'fun_app$t'(X1,sK157(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ),
inference(equality_resolution,[],[f3107]) ).
tff(f3107,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ~ $less('fun_app$t'(X1,sK156(X1)),'fun_app$t'(X1,sK157(X1)))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2014]) ).
tff(f2014,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ( ~ $less('fun_app$t'(X1,sK156(X1)),'fun_app$t'(X1,sK157(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK156(X1)),sK157(X1)) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156,sK157])],[f1380,f2013]) ).
tff(f2013,plain,
! [X1: 'Enat_int_fun$'] :
( ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
=> ( ~ $less('fun_app$t'(X1,sK156(X1)),'fun_app$t'(X1,sK157(X1)))
& 'fun_app$g'('fun_app$h'('less$a',sK156(X1)),sK157(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1380,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(flattening,[],[f1379]) ).
tff(f1379,plain,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( $less(X0,'fun_app$t'(X1,X3))
| ? [X4: 'Enat$',X5: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5))
& 'fun_app$g'('fun_app$h'('less$a',X4),X5) )
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f519]) ).
tff(f519,axiom,
! [X0: $int,X1: 'Enat_int_fun$',X2: 'Enat$',X3: 'Enat$'] :
( ( ! [X4: 'Enat$',X5: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X4),X5)
=> $less('fun_app$t'(X1,X4),'fun_app$t'(X1,X5)) )
& 'fun_app$g'('fun_app$h'('less$a',X2),X3)
& ( 'fun_app$t'(X1,X2) = X0 ) )
=> $less(X0,'fun_app$t'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
tff(f9234,plain,
spl272_543,
inference(avatar_split_clause,[],[f2837,f9232]) ).
tff(f9232,plain,
( spl272_543
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_543])]) ).
tff(f2837,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ),
inference(cnf_transformation,[],[f1248]) ).
tff(f1248,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ),
inference(flattening,[],[f1247]) ).
tff(f1247,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
| ~ 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) ),
inference(ennf_transformation,[],[f191]) ).
tff(f191,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
& 'fun_app$n'('fun_app$o'('less_eq$b',X0),X1) )
=> 'fun_app$n'('fun_app$o'('less_eq$b','fun_app$b'('power$'(X0),X2)),'fun_app$b'('power$'(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom189) ).
tff(f9230,plain,
spl272_542,
inference(avatar_split_clause,[],[f2790,f9228]) ).
tff(f9228,plain,
( spl272_542
<=> ! [X2: $int,X0: 'Num$',X1: 'Num$'] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$p'('times$b'('fun_app$d'('numeral$',X1)),X2)) = 'fun_app$p'('times$b'('fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_542])]) ).
tff(f2790,plain,
! [X2: $int,X0: 'Num$',X1: 'Num$'] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$p'('times$b'('fun_app$d'('numeral$',X1)),X2)) = 'fun_app$p'('times$b'('fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1))),X2) ),
inference(cnf_transformation,[],[f369]) ).
tff(f369,axiom,
! [X0: 'Num$',X1: 'Num$',X2: $int] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$p'('times$b'('fun_app$d'('numeral$',X1)),X2)) = 'fun_app$p'('times$b'('fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1))),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom367) ).
tff(f9145,plain,
( spl272_541
| ~ spl272_55
| ~ spl272_535 ),
inference(avatar_split_clause,[],[f8850,f8847,f3851,f9143]) ).
tff(f9143,plain,
( spl272_541
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',sK46(X0))))))
| 'fun_app$n'(X0,X1)
| sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_541])]) ).
tff(f8847,plain,
( spl272_535
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',sK46(X0))))))
| 'fun_app$n'(X0,X1)
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_535])]) ).
tff(f8850,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',sK46(X0))))))
| 'fun_app$n'(X0,X1)
| sP1(X0) )
| ~ spl272_55
| ~ spl272_535 ),
inference(forward_demodulation,[],[f8848,f3853]) ).
tff(f8848,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',sK46(X0))))))
| 'fun_app$n'(X0,X1)
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_535 ),
inference(avatar_component_clause,[],[f8847]) ).
tff(f8870,plain,
spl272_540,
inference(avatar_split_clause,[],[f3580,f8868]) ).
tff(f8868,plain,
( spl272_540
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_540])]) ).
tff(f3580,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
inference(forward_demodulation,[],[f2971,f2347]) ).
tff(f2971,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2) ) ),
inference(cnf_transformation,[],[f1920]) ).
tff(f1920,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$b'('of_nat$a',X0) != 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2) ) ) ),
inference(nnf_transformation,[],[f126]) ).
tff(f126,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).
tff(f8866,plain,
spl272_539,
inference(avatar_split_clause,[],[f3579,f8864]) ).
tff(f8864,plain,
( spl272_539
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_539])]) ).
tff(f3579,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
inference(forward_demodulation,[],[f2972,f2347]) ).
tff(f2972,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('of_nat$a',X0) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
inference(cnf_transformation,[],[f1920]) ).
tff(f8862,plain,
spl272_538,
inference(avatar_split_clause,[],[f3526,f8860]) ).
tff(f8860,plain,
( spl272_538
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_538])]) ).
tff(f3526,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2734,f2347]) ).
tff(f2734,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)) ),
inference(cnf_transformation,[],[f1766]) ).
tff(f1766,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)) ) ),
inference(flattening,[],[f1765]) ).
tff(f1765,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1)) ) ),
inference(nnf_transformation,[],[f413]) ).
tff(f413,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1))
<=> ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
tff(f8858,plain,
spl272_537,
inference(avatar_split_clause,[],[f3516,f8856]) ).
tff(f8856,plain,
( spl272_537
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK57(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_537])]) ).
tff(f3516,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK57(X0,X1))) ) ),
inference(forward_demodulation,[],[f3515,f848]) ).
tff(f3515,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK57(X0,X1))) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2716,f848]) ).
tff(f2716,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK57(X0,X1)),1) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1755]) ).
tff(f8854,plain,
spl272_536,
inference(avatar_split_clause,[],[f3491,f8852]) ).
tff(f8852,plain,
( spl272_536
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK51(X0,X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_536])]) ).
tff(f3491,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK51(X0,X1))) ) ),
inference(forward_demodulation,[],[f3490,f848]) ).
tff(f3490,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK51(X0,X1))) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2519,f848]) ).
tff(f2519,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK51(X0,X1)),1) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1636]) ).
tff(f1636,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK51(X0,X1)),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK51(X0,X1))) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f1160,f1635]) ).
tff(f1635,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
=> ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK51(X0,X1)),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK51(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1160,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f964]) ).
tff(f964,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
~ ( ! [X2: 'Nat$'] :
~ ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
& $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(true_and_false_elimination,[],[f567]) ).
tff(f567,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
& $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X2)) )
=> $false )
& $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom565) ).
tff(f8849,plain,
spl272_535,
inference(avatar_split_clause,[],[f3482,f8847]) ).
tff(f3482,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',sK46(X0))))))
| 'fun_app$n'(X0,X1)
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(forward_demodulation,[],[f2486,f848]) ).
tff(f2486,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',sK46(X0))),1)))
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1625]) ).
tff(f1625,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',sK46(X0))),1)))
& 'fun_app$n'(X0,sK46(X0)) )
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1500,f1624]) ).
tff(f1624,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1)))
& 'fun_app$n'(X0,X2) )
=> ( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',sK46(X0))),1)))
& 'fun_app$n'(X0,sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1500,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1)))
& 'fun_app$n'(X0,X2) )
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(definition_folding,[],[f1118,f1499]) ).
tff(f1499,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X3))))
& $less(0,'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f1118,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1)))
& 'fun_app$n'(X0,X2) )
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X3))))
& $less(0,'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(flattening,[],[f1117]) ).
tff(f1117,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1)))
& 'fun_app$n'(X0,X2) )
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X3))))
& $less(0,'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f953]) ).
tff(f953,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
=> 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1))) )
& ! [X3: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
=> 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X3)))) )
& 'fun_app$n'(X0,'nat$'(0)) )
=> 'fun_app$n'(X0,X1) ),
inference(rectify,[],[f588]) ).
tff(f588,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
=> 'fun_app$n'(X0,'nat$'($sum($product(2,'fun_app$a'('of_nat$',X2)),1))) )
& ! [X2: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X2))
& 'fun_app$n'(X0,X2) )
=> 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X2)))) )
& 'fun_app$n'(X0,'nat$'(0)) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom586) ).
tff(f8845,plain,
spl272_534,
inference(avatar_split_clause,[],[f3417,f8843]) ).
tff(f8843,plain,
( spl272_534
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(1,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(1,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_534])]) ).
tff(f3417,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(1,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less(1,'fun_app$a'('of_nat$',X1))
| ~ $less(1,'fun_app$a'('of_nat$',X0)) ),
inference(evaluation,[],[f2511]) ).
tff(f2511,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(0,1),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1151]) ).
tff(f1151,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(0,1),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1150]) ).
tff(f1150,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(0,1),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X1))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f436]) ).
tff(f436,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less($sum(0,1),'fun_app$a'('of_nat$',X1))
& $less($sum(0,1),'fun_app$a'('of_nat$',X0)) )
=> $less($sum(0,1),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom434) ).
tff(f8841,plain,
spl272_533,
inference(avatar_split_clause,[],[f3407,f8839]) ).
tff(f8839,plain,
( spl272_533
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1)
| $less('fun_app$a'('of_nat$',X1),1)
| $less('fun_app$a'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_533])]) ).
tff(f3407,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1)
| $less('fun_app$a'('of_nat$',X1),1)
| $less('fun_app$a'('of_nat$',X0),1) ),
inference(evaluation,[],[f2756]) ).
tff(f2756,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1))
| $less('fun_app$a'('of_nat$',X1),$sum(0,1))
| $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ),
inference(cnf_transformation,[],[f1778]) ).
tff(f1778,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1))
| $less('fun_app$a'('of_nat$',X1),$sum(0,1))
| $less('fun_app$a'('of_nat$',X0),$sum(0,1)) )
& ( ( ~ $less('fun_app$a'('of_nat$',X1),$sum(0,1))
& ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1)) )
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1)) ) ),
inference(flattening,[],[f1777]) ).
tff(f1777,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1))
| $less('fun_app$a'('of_nat$',X1),$sum(0,1))
| $less('fun_app$a'('of_nat$',X0),$sum(0,1)) )
& ( ( ~ $less('fun_app$a'('of_nat$',X1),$sum(0,1))
& ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1)) )
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1)) ) ),
inference(nnf_transformation,[],[f761]) ).
tff(f761,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1))
<=> ( ~ $less('fun_app$a'('of_nat$',X1),$sum(0,1))
& ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ) ),
inference(theory_normalization,[],[f406]) ).
tff(f406,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq($sum(0,1),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
<=> ( $lesseq($sum(0,1),'fun_app$a'('of_nat$',X1))
& $lesseq($sum(0,1),'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom404) ).
tff(f8837,plain,
spl272_532,
inference(avatar_split_clause,[],[f2980,f8835]) ).
tff(f8835,plain,
( spl272_532
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_532])]) ).
tff(f2980,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
inference(cnf_transformation,[],[f1924]) ).
tff(f1924,plain,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) ) ) ),
inference(nnf_transformation,[],[f127]) ).
tff(f127,axiom,
! [X0: 'Nat$',X1: 'Nat$',X2: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom125) ).
tff(f8833,plain,
spl272_531,
inference(avatar_split_clause,[],[f2979,f8831]) ).
tff(f8831,plain,
( spl272_531
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_531])]) ).
tff(f2979,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X1),X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X1)),X2) ) ),
inference(cnf_transformation,[],[f1924]) ).
tff(f8817,plain,
spl272_530,
inference(avatar_split_clause,[],[f2728,f8815]) ).
tff(f8815,plain,
( spl272_530
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 0 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_530])]) ).
tff(f2728,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 0 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ),
inference(cnf_transformation,[],[f1762]) ).
tff(f1762,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 0 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(flattening,[],[f1761]) ).
tff(f1761,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 0 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(nnf_transformation,[],[f378]) ).
tff(f378,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
<=> ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom376) ).
tff(f8813,plain,
spl272_529,
inference(avatar_split_clause,[],[f2460,f8811]) ).
tff(f8811,plain,
( spl272_529
<=> ! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( 'fun_app$a'('power$a'(X0),'nat$'(2)) != 'fun_app$a'('power$a'(X1),'nat$'(2)) )
| $less(X1,0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_529])]) ).
tff(f2460,plain,
! [X0: $int,X1: $int] :
( ( X0 = X1 )
| ( 'fun_app$a'('power$a'(X0),'nat$'(2)) != 'fun_app$a'('power$a'(X1),'nat$'(2)) )
| $less(X1,0)
| $less(X0,0) ),
inference(cnf_transformation,[],[f1611]) ).
tff(f1611,plain,
! [X0: $int,X1: $int] :
( ( ( ( 'fun_app$a'('power$a'(X0),'nat$'(2)) = 'fun_app$a'('power$a'(X1),'nat$'(2)) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$a'('power$a'(X0),'nat$'(2)) != 'fun_app$a'('power$a'(X1),'nat$'(2)) ) ) )
| $less(X1,0)
| $less(X0,0) ),
inference(nnf_transformation,[],[f1092]) ).
tff(f1092,plain,
! [X0: $int,X1: $int] :
( ( ( 'fun_app$a'('power$a'(X0),'nat$'(2)) = 'fun_app$a'('power$a'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| $less(X1,0)
| $less(X0,0) ),
inference(flattening,[],[f1091]) ).
tff(f1091,plain,
! [X0: $int,X1: $int] :
( ( ( 'fun_app$a'('power$a'(X0),'nat$'(2)) = 'fun_app$a'('power$a'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| $less(X1,0)
| $less(X0,0) ),
inference(ennf_transformation,[],[f715]) ).
tff(f715,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ( ( 'fun_app$a'('power$a'(X0),'nat$'(2)) = 'fun_app$a'('power$a'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) ) ),
inference(theory_normalization,[],[f77]) ).
tff(f77,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(0,X1)
& $lesseq(0,X0) )
=> ( ( 'fun_app$a'('power$a'(X0),'nat$'(2)) = 'fun_app$a'('power$a'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom75) ).
tff(f8809,plain,
spl272_528,
inference(avatar_split_clause,[],[f2456,f8807]) ).
tff(f8807,plain,
( spl272_528
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'fun_app$m'('power$c'(X0),'nat$'(2)) != 'fun_app$m'('power$c'(X1),'nat$'(2)) )
| $less(X1,0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_528])]) ).
tff(f2456,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'fun_app$m'('power$c'(X0),'nat$'(2)) != 'fun_app$m'('power$c'(X1),'nat$'(2)) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1608]) ).
tff(f1608,plain,
! [X0: $real,X1: $real] :
( ( ( ( 'fun_app$m'('power$c'(X0),'nat$'(2)) = 'fun_app$m'('power$c'(X1),'nat$'(2)) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$m'('power$c'(X0),'nat$'(2)) != 'fun_app$m'('power$c'(X1),'nat$'(2)) ) ) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(nnf_transformation,[],[f1088]) ).
tff(f1088,plain,
! [X0: $real,X1: $real] :
( ( ( 'fun_app$m'('power$c'(X0),'nat$'(2)) = 'fun_app$m'('power$c'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(flattening,[],[f1087]) ).
tff(f1087,plain,
! [X0: $real,X1: $real] :
( ( ( 'fun_app$m'('power$c'(X0),'nat$'(2)) = 'fun_app$m'('power$c'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(ennf_transformation,[],[f713]) ).
tff(f713,plain,
! [X0: $real,X1: $real] :
( ( ~ $less(X1,0.0)
& ~ $less(X0,0.0) )
=> ( ( 'fun_app$m'('power$c'(X0),'nat$'(2)) = 'fun_app$m'('power$c'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) ) ),
inference(theory_normalization,[],[f78]) ).
tff(f78,axiom,
! [X0: $real,X1: $real] :
( ( $lesseq(0.0,X1)
& $lesseq(0.0,X0) )
=> ( ( 'fun_app$m'('power$c'(X0),'nat$'(2)) = 'fun_app$m'('power$c'(X1),'nat$'(2)) )
<=> ( X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom76) ).
tff(f8805,plain,
spl272_527,
inference(avatar_split_clause,[],[f2361,f8803]) ).
tff(f8803,plain,
( spl272_527
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'fun_app$b'('times$'('fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_527])]) ).
tff(f2361,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'fun_app$b'('times$'('fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a',X1)) ),
inference(cnf_transformation,[],[f390]) ).
tff(f390,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'fun_app$b'('times$'('fun_app$b'('of_nat$a',X0)),'fun_app$b'('of_nat$a',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom388) ).
tff(f8801,plain,
spl272_526,
inference(avatar_split_clause,[],[f2359,f8799]) ).
tff(f8799,plain,
( spl272_526
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$a'('of_nat$','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_526])]) ).
tff(f2359,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$a'('of_nat$','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) ),
inference(cnf_transformation,[],[f629]) ).
tff(f629,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$a'('of_nat$','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).
tff(f8677,plain,
( spl272_525
| ~ spl272_58
| ~ spl272_477 ),
inference(avatar_split_clause,[],[f8361,f8073,f3865,f8675]) ).
tff(f8675,plain,
( spl272_525
<=> ! [X0: $real] : $less(X0,$sum(X0,5.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_525])]) ).
tff(f8073,plain,
( spl272_477
<=> ! [X0: $real] : $less(X0,$sum(5.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_477])]) ).
tff(f8361,plain,
( ! [X0: $real] : $less(X0,$sum(X0,5.0))
| ~ spl272_58
| ~ spl272_477 ),
inference(superposition,[],[f8074,f3866]) ).
tff(f8074,plain,
( ! [X0: $real] : $less(X0,$sum(5.0,X0))
| ~ spl272_477 ),
inference(avatar_component_clause,[],[f8073]) ).
tff(f8613,plain,
( spl272_524
| ~ spl272_50
| ~ spl272_477 ),
inference(avatar_split_clause,[],[f8356,f8073,f3821,f8611]) ).
tff(f8356,plain,
( ! [X0: $real] : ~ $less($sum(5.0,X0),X0)
| ~ spl272_50
| ~ spl272_477 ),
inference(resolution,[],[f8074,f3822]) ).
tff(f8529,plain,
( spl272_523
| ~ spl272_56
| ~ spl272_473 ),
inference(avatar_split_clause,[],[f8262,f7853,f3857,f8527]) ).
tff(f8527,plain,
( spl272_523
<=> ! [X0: $int] : $less(X0,$sum(X0,5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_523])]) ).
tff(f7853,plain,
( spl272_473
<=> ! [X0: $int] : $less(X0,$sum(5,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_473])]) ).
tff(f8262,plain,
( ! [X0: $int] : $less(X0,$sum(X0,5))
| ~ spl272_56
| ~ spl272_473 ),
inference(superposition,[],[f7854,f3858]) ).
tff(f7854,plain,
( ! [X0: $int] : $less(X0,$sum(5,X0))
| ~ spl272_473 ),
inference(avatar_component_clause,[],[f7853]) ).
tff(f8507,plain,
( spl272_522
| ~ spl272_55
| ~ spl272_481 ),
inference(avatar_split_clause,[],[f8225,f8222,f3851,f8505]) ).
tff(f8505,plain,
( spl272_522
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1)))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_522])]) ).
tff(f8222,plain,
( spl272_481
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_481])]) ).
tff(f8225,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1)))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_481 ),
inference(forward_demodulation,[],[f8223,f3853]) ).
tff(f8223,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_481 ),
inference(avatar_component_clause,[],[f8222]) ).
tff(f8503,plain,
( spl272_521
| ~ spl272_55
| ~ spl272_480 ),
inference(avatar_split_clause,[],[f8220,f8217,f3851,f8501]) ).
tff(f8501,plain,
( spl272_521
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_521])]) ).
tff(f8217,plain,
( spl272_480
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_480])]) ).
tff(f8220,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_480 ),
inference(forward_demodulation,[],[f8218,f3853]) ).
tff(f8218,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_480 ),
inference(avatar_component_clause,[],[f8217]) ).
tff(f8411,plain,
spl272_520,
inference(avatar_split_clause,[],[f3474,f8409]) ).
tff(f8409,plain,
( spl272_520
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),$sum(1,'fun_app$a'('of_nat$',X0)))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK39(X1))) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_520])]) ).
tff(f3474,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),$sum(1,'fun_app$a'('of_nat$',X0)))
| ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK39(X1))) ) ),
inference(forward_demodulation,[],[f3473,f848]) ).
tff(f3473,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(1,'fun_app$a'('of_nat$',sK39(X1))) )
| $less('fun_app$a'('of_nat$',X1),$sum('fun_app$a'('of_nat$',X0),1)) ),
inference(forward_demodulation,[],[f2446,f848]) ).
tff(f2446,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK39(X1)),1) )
| $less('fun_app$a'('of_nat$',X1),$sum('fun_app$a'('of_nat$',X0),1)) ),
inference(cnf_transformation,[],[f1607]) ).
tff(f1607,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK39(X1)),1) )
| $less('fun_app$a'('of_nat$',X1),$sum('fun_app$a'('of_nat$',X0),1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f1077,f1606]) ).
tff(f1606,plain,
! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
=> ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',sK39(X1)),1) ) ),
introduced(choice_axiom,[]) ).
tff(f1077,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) )
| $less('fun_app$a'('of_nat$',X1),$sum('fun_app$a'('of_nat$',X0),1)) ),
inference(ennf_transformation,[],[f709]) ).
tff(f709,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),$sum('fun_app$a'('of_nat$',X0),1))
=> ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) ) ),
inference(theory_normalization,[],[f49]) ).
tff(f49,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1))
=> ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = $sum('fun_app$a'('of_nat$',X2),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).
tff(f8407,plain,
( spl272_519
| ~ spl272_51
| ~ spl272_473 ),
inference(avatar_split_clause,[],[f8257,f7853,f3825,f8405]) ).
tff(f8257,plain,
( ! [X0: $int] : ~ $less($sum(5,X0),X0)
| ~ spl272_51
| ~ spl272_473 ),
inference(resolution,[],[f7854,f3826]) ).
tff(f8403,plain,
spl272_518,
inference(avatar_split_clause,[],[f3403,f8401]) ).
tff(f8401,plain,
( spl272_518
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_518])]) ).
tff(f3403,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ),
inference(duplicate_literal_removal,[],[f2892]) ).
tff(f2892,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ $less(X0,X2)
| sP11(X1,X0,X2)
| sP10(X2,X1,X0)
| sP9(X0,X2,X1)
| sP8(X1,X2,X0) ),
inference(cnf_transformation,[],[f1517]) ).
tff(f8399,plain,
spl272_517,
inference(avatar_split_clause,[],[f3402,f8397]) ).
tff(f8397,plain,
( spl272_517
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_517])]) ).
tff(f3402,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ),
inference(duplicate_literal_removal,[],[f2904]) ).
tff(f2904,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ $less(X0,X2)
| sP15(X1,X0,X2)
| sP14(X2,X1,X0)
| sP13(X0,X2,X1)
| sP12(X1,X2,X0) ),
inference(cnf_transformation,[],[f1522]) ).
tff(f8395,plain,
spl272_516,
inference(avatar_split_clause,[],[f3399,f8393]) ).
tff(f8393,plain,
( spl272_516
<=> ! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'(X2,X1),'fun_app$d'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK222(X2)),sK223(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_516])]) ).
tff(f3399,plain,
! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'(X2,X1),'fun_app$d'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK222(X2)),sK223(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3172]) ).
tff(f3172,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$d'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK222(X2)),sK223(X2))
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2080]) ).
tff(f8391,plain,
spl272_515,
inference(avatar_split_clause,[],[f3393,f8389]) ).
tff(f8389,plain,
( spl272_515
<=> ! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'(X2,X1),'fun_app$j'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK216(X2)),sK217(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_515])]) ).
tff(f3393,plain,
! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'(X2,X1),'fun_app$j'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK216(X2)),sK217(X2))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(equality_resolution,[],[f3166]) ).
tff(f3166,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( ~ $less(X3,'fun_app$j'(X2,X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK216(X2)),sK217(X2))
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f2074]) ).
tff(f8387,plain,
spl272_514,
inference(avatar_split_clause,[],[f3391,f8385]) ).
tff(f8385,plain,
( spl272_514
<=> ! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),'fun_app$d'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK206(X2)),sK207(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_514])]) ).
tff(f3391,plain,
! [X2: 'Num_int_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),'fun_app$d'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK206(X2)),sK207(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3156]) ).
tff(f3156,plain,
! [X2: 'Num_int_fun$',X3: $int,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK206(X2)),sK207(X2))
| ( 'fun_app$d'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2064]) ).
tff(f8383,plain,
spl272_513,
inference(avatar_split_clause,[],[f3385,f8381]) ).
tff(f8381,plain,
( spl272_513
<=> ! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),'fun_app$j'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK200(X2)),sK201(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_513])]) ).
tff(f3385,plain,
! [X2: 'Num_real_fun$',X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),'fun_app$j'(X2,X1))
| 'fun_app$e'('fun_app$f'('less$',sK200(X2)),sK201(X2))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(equality_resolution,[],[f3150]) ).
tff(f3150,plain,
! [X2: 'Num_real_fun$',X3: $real,X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'(X2,X0),X3)
| 'fun_app$e'('fun_app$f'('less$',sK200(X2)),sK201(X2))
| ( 'fun_app$j'(X2,X1) != X3 )
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f2058]) ).
tff(f8379,plain,
spl272_512,
inference(avatar_split_clause,[],[f3381,f8377]) ).
tff(f8377,plain,
( spl272_512
<=> ! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X1),'fun_app$t'(X2,X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK192(X2)),sK193(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_512])]) ).
tff(f3381,plain,
! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( ~ $less('fun_app$t'(X2,X1),'fun_app$t'(X2,X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK192(X2)),sK193(X2))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(equality_resolution,[],[f3142]) ).
tff(f3142,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( ~ $less(X3,'fun_app$t'(X2,X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK192(X2)),sK193(X2))
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f2050]) ).
tff(f8375,plain,
spl272_511,
inference(avatar_split_clause,[],[f3377,f8373]) ).
tff(f8373,plain,
( spl272_511
<=> ! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),'fun_app$t'(X2,X1))
| 'fun_app$g'('fun_app$h'('less$a',sK184(X2)),sK185(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_511])]) ).
tff(f3377,plain,
! [X2: 'Enat_int_fun$',X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),'fun_app$t'(X2,X1))
| 'fun_app$g'('fun_app$h'('less$a',sK184(X2)),sK185(X2))
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(equality_resolution,[],[f3134]) ).
tff(f3134,plain,
! [X2: 'Enat_int_fun$',X3: $int,X0: 'Enat$',X1: 'Enat$'] :
( $less('fun_app$t'(X2,X0),X3)
| 'fun_app$g'('fun_app$h'('less$a',sK184(X2)),sK185(X2))
| ( 'fun_app$t'(X2,X1) != X3 )
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f2042]) ).
tff(f8371,plain,
spl272_510,
inference(avatar_split_clause,[],[f3375,f8369]) ).
tff(f8369,plain,
( spl272_510
<=> ! [X2: 'Num$',X1: 'Num_int_fun$',X3: 'Num$'] :
( ~ $less('fun_app$d'(X1,X3),'fun_app$d'(X1,X2))
| 'fun_app$e'('fun_app$f'('less_eq$',sK182(X1)),sK183(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_510])]) ).
tff(f3375,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),'fun_app$d'(X1,X2))
| 'fun_app$e'('fun_app$f'('less_eq$',sK182(X1)),sK183(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3132]) ).
tff(f3132,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( ~ $less('fun_app$d'(X1,X3),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',sK182(X1)),sK183(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2040]) ).
tff(f8367,plain,
spl272_509,
inference(avatar_split_clause,[],[f3373,f8365]) ).
tff(f8365,plain,
( spl272_509
<=> ! [X2: 'Num$',X1: 'Num_int_fun$',X3: 'Num$'] :
( $less('fun_app$d'(X1,X2),'fun_app$d'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK180(X1)),sK181(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_509])]) ).
tff(f3373,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_int_fun$'] :
( $less('fun_app$d'(X1,X2),'fun_app$d'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK180(X1)),sK181(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3130]) ).
tff(f3130,plain,
! [X2: 'Num$',X3: 'Num$',X0: $int,X1: 'Num_int_fun$'] :
( $less(X0,'fun_app$d'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK180(X1)),sK181(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$d'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2038]) ).
tff(f8353,plain,
spl272_508,
inference(avatar_split_clause,[],[f3370,f8351]) ).
tff(f8351,plain,
( spl272_508
<=> ! [X2: $int,X1: 'Int_int_fun$',X3: $int] :
( ~ $less('fun_app$p'(X1,X3),'fun_app$p'(X1,X2))
| $less('fun_app$p'(X1,sK179(X1)),'fun_app$p'(X1,sK178(X1)))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_508])]) ).
tff(f3370,plain,
! [X2: $int,X3: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),'fun_app$p'(X1,X2))
| $less('fun_app$p'(X1,sK179(X1)),'fun_app$p'(X1,sK178(X1)))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3129]) ).
tff(f3129,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| $less('fun_app$p'(X1,sK179(X1)),'fun_app$p'(X1,sK178(X1)))
| $less(X3,X2)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2036]) ).
tff(f2036,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ( $less('fun_app$p'(X1,sK179(X1)),'fun_app$p'(X1,sK178(X1)))
& ~ $less(sK179(X1),sK178(X1)) )
| $less(X3,X2)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK178,sK179])],[f1402,f2035]) ).
tff(f2035,plain,
! [X1: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$p'(X1,sK179(X1)),'fun_app$p'(X1,sK178(X1)))
& ~ $less(sK179(X1),sK178(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1402,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(flattening,[],[f1401]) ).
tff(f1401,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f832]) ).
tff(f832,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$p'(X1,X5),'fun_app$p'(X1,X4)) )
& ~ $less(X3,X2)
& ( 'fun_app$p'(X1,X2) = X0 ) )
=> ~ $less('fun_app$p'(X1,X3),X0) ),
inference(theory_normalization,[],[f290]) ).
tff(f290,axiom,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$p'(X1,X4),'fun_app$p'(X1,X5)) )
& $lesseq(X2,X3)
& ( 'fun_app$p'(X1,X2) = X0 ) )
=> $lesseq(X0,'fun_app$p'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom288) ).
tff(f8349,plain,
spl272_507,
inference(avatar_split_clause,[],[f3368,f8347]) ).
tff(f8347,plain,
( spl272_507
<=> ! [X2: $int,X1: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X1,X2),'fun_app$p'(X1,X3))
| ~ $less('fun_app$p'(X1,sK176(X1)),'fun_app$p'(X1,sK177(X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_507])]) ).
tff(f3368,plain,
! [X2: $int,X3: $int,X1: 'Int_int_fun$'] :
( $less('fun_app$p'(X1,X2),'fun_app$p'(X1,X3))
| ~ $less('fun_app$p'(X1,sK176(X1)),'fun_app$p'(X1,sK177(X1)))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3127]) ).
tff(f3127,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| ~ $less('fun_app$p'(X1,sK176(X1)),'fun_app$p'(X1,sK177(X1)))
| ~ $less(X2,X3)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2034]) ).
tff(f2034,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ( ~ $less('fun_app$p'(X1,sK176(X1)),'fun_app$p'(X1,sK177(X1)))
& $less(sK176(X1),sK177(X1)) )
| ~ $less(X2,X3)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK176,sK177])],[f1400,f2033]) ).
tff(f2033,plain,
! [X1: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$p'(X1,sK176(X1)),'fun_app$p'(X1,sK177(X1)))
& $less(sK176(X1),sK177(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1400,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(flattening,[],[f1399]) ).
tff(f1399,plain,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$p'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f515]) ).
tff(f515,axiom,
! [X0: $int,X1: 'Int_int_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$p'(X1,X4),'fun_app$p'(X1,X5)) )
& $less(X2,X3)
& ( 'fun_app$p'(X1,X2) = X0 ) )
=> $less(X0,'fun_app$p'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).
tff(f8345,plain,
spl272_506,
inference(avatar_split_clause,[],[f3359,f8343]) ).
tff(f8343,plain,
( spl272_506
<=> ! [X2: 'Num$',X1: 'Num_real_fun$',X3: 'Num$'] :
( ~ $less('fun_app$j'(X1,X3),'fun_app$j'(X1,X2))
| 'fun_app$e'('fun_app$f'('less_eq$',sK166(X1)),sK167(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_506])]) ).
tff(f3359,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_real_fun$'] :
( ~ $less('fun_app$j'(X1,X3),'fun_app$j'(X1,X2))
| 'fun_app$e'('fun_app$f'('less_eq$',sK166(X1)),sK167(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3) ),
inference(equality_resolution,[],[f3116]) ).
tff(f3116,plain,
! [X2: 'Num$',X3: 'Num$',X0: $real,X1: 'Num_real_fun$'] :
( ~ $less('fun_app$j'(X1,X3),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',sK166(X1)),sK167(X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2024]) ).
tff(f8341,plain,
spl272_505,
inference(avatar_split_clause,[],[f3357,f8339]) ).
tff(f8339,plain,
( spl272_505
<=> ! [X2: 'Num$',X1: 'Num_real_fun$',X3: 'Num$'] :
( $less('fun_app$j'(X1,X2),'fun_app$j'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK164(X1)),sK165(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_505])]) ).
tff(f3357,plain,
! [X2: 'Num$',X3: 'Num$',X1: 'Num_real_fun$'] :
( $less('fun_app$j'(X1,X2),'fun_app$j'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK164(X1)),sK165(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3) ),
inference(equality_resolution,[],[f3114]) ).
tff(f3114,plain,
! [X2: 'Num$',X3: 'Num$',X0: $real,X1: 'Num_real_fun$'] :
( $less(X0,'fun_app$j'(X1,X3))
| 'fun_app$e'('fun_app$f'('less$',sK164(X1)),sK165(X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X2),X3)
| ( 'fun_app$j'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2022]) ).
tff(f8337,plain,
spl272_504,
inference(avatar_split_clause,[],[f3353,f8335]) ).
tff(f8335,plain,
( spl272_504
<=> ! [X2: 'Enat$',X1: 'Enat_int_fun$',X3: 'Enat$'] :
( ~ $less('fun_app$t'(X1,X3),'fun_app$t'(X1,X2))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK160(X1)),sK161(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_504])]) ).
tff(f3353,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),'fun_app$t'(X1,X2))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK160(X1)),sK161(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3) ),
inference(equality_resolution,[],[f3110]) ).
tff(f3110,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( ~ $less('fun_app$t'(X1,X3),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',sK160(X1)),sK161(X1))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2018]) ).
tff(f8333,plain,
spl272_503,
inference(avatar_split_clause,[],[f3349,f8331]) ).
tff(f8331,plain,
( spl272_503
<=> ! [X2: 'Enat$',X1: 'Enat_int_fun$',X3: 'Enat$'] :
( $less('fun_app$t'(X1,X2),'fun_app$t'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK156(X1)),sK157(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_503])]) ).
tff(f3349,plain,
! [X2: 'Enat$',X3: 'Enat$',X1: 'Enat_int_fun$'] :
( $less('fun_app$t'(X1,X2),'fun_app$t'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK156(X1)),sK157(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3) ),
inference(equality_resolution,[],[f3106]) ).
tff(f3106,plain,
! [X2: 'Enat$',X3: 'Enat$',X0: $int,X1: 'Enat_int_fun$'] :
( $less(X0,'fun_app$t'(X1,X3))
| 'fun_app$g'('fun_app$h'('less$a',sK156(X1)),sK157(X1))
| ~ 'fun_app$g'('fun_app$h'('less$a',X2),X3)
| ( 'fun_app$t'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2014]) ).
tff(f8329,plain,
spl272_502,
inference(avatar_split_clause,[],[f3338,f8327]) ).
tff(f8327,plain,
( spl272_502
<=> ! [X2: $int,X1: 'Int_real_fun$',X3: $int] :
( ~ $less('fun_app$z'(X1,X3),'fun_app$z'(X1,X2))
| $less('fun_app$z'(X1,sK147(X1)),'fun_app$z'(X1,sK146(X1)))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_502])]) ).
tff(f3338,plain,
! [X2: $int,X3: $int,X1: 'Int_real_fun$'] :
( ~ $less('fun_app$z'(X1,X3),'fun_app$z'(X1,X2))
| $less('fun_app$z'(X1,sK147(X1)),'fun_app$z'(X1,sK146(X1)))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3097]) ).
tff(f3097,plain,
! [X2: $int,X3: $int,X0: $real,X1: 'Int_real_fun$'] :
( ~ $less('fun_app$z'(X1,X3),X0)
| $less('fun_app$z'(X1,sK147(X1)),'fun_app$z'(X1,sK146(X1)))
| $less(X3,X2)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2004]) ).
tff(f2004,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$z'(X1,X3),X0)
| ( $less('fun_app$z'(X1,sK147(X1)),'fun_app$z'(X1,sK146(X1)))
& ~ $less(sK147(X1),sK146(X1)) )
| $less(X3,X2)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK146,sK147])],[f1370,f2003]) ).
tff(f2003,plain,
! [X1: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X1,X5),'fun_app$z'(X1,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$z'(X1,sK147(X1)),'fun_app$z'(X1,sK146(X1)))
& ~ $less(sK147(X1),sK146(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1370,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$z'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X1,X5),'fun_app$z'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(flattening,[],[f1369]) ).
tff(f1369,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ~ $less('fun_app$z'(X1,X3),X0)
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X1,X5),'fun_app$z'(X1,X4))
& ~ $less(X5,X4) )
| $less(X3,X2)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f827]) ).
tff(f827,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$z'(X1,X5),'fun_app$z'(X1,X4)) )
& ~ $less(X3,X2)
& ( 'fun_app$z'(X1,X2) = X0 ) )
=> ~ $less('fun_app$z'(X1,X3),X0) ),
inference(theory_normalization,[],[f293]) ).
tff(f293,axiom,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$z'(X1,X4),'fun_app$z'(X1,X5)) )
& $lesseq(X2,X3)
& ( 'fun_app$z'(X1,X2) = X0 ) )
=> $lesseq(X0,'fun_app$z'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
tff(f8325,plain,
spl272_501,
inference(avatar_split_clause,[],[f3336,f8323]) ).
tff(f8323,plain,
( spl272_501
<=> ! [X2: $int,X1: 'Int_real_fun$',X3: $int] :
( $less('fun_app$z'(X1,X2),'fun_app$z'(X1,X3))
| ~ $less('fun_app$z'(X1,sK144(X1)),'fun_app$z'(X1,sK145(X1)))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_501])]) ).
tff(f3336,plain,
! [X2: $int,X3: $int,X1: 'Int_real_fun$'] :
( $less('fun_app$z'(X1,X2),'fun_app$z'(X1,X3))
| ~ $less('fun_app$z'(X1,sK144(X1)),'fun_app$z'(X1,sK145(X1)))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3095]) ).
tff(f3095,plain,
! [X2: $int,X3: $int,X0: $real,X1: 'Int_real_fun$'] :
( $less(X0,'fun_app$z'(X1,X3))
| ~ $less('fun_app$z'(X1,sK144(X1)),'fun_app$z'(X1,sK145(X1)))
| ~ $less(X2,X3)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2002]) ).
tff(f2002,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$z'(X1,X3))
| ( ~ $less('fun_app$z'(X1,sK144(X1)),'fun_app$z'(X1,sK145(X1)))
& $less(sK144(X1),sK145(X1)) )
| ~ $less(X2,X3)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK144,sK145])],[f1368,f2001]) ).
tff(f2001,plain,
! [X1: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X1,X4),'fun_app$z'(X1,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$z'(X1,sK144(X1)),'fun_app$z'(X1,sK145(X1)))
& $less(sK144(X1),sK145(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1368,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$z'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X1,X4),'fun_app$z'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(flattening,[],[f1367]) ).
tff(f1367,plain,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( $less(X0,'fun_app$z'(X1,X3))
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X1,X4),'fun_app$z'(X1,X5))
& $less(X4,X5) )
| ~ $less(X2,X3)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(ennf_transformation,[],[f517]) ).
tff(f517,axiom,
! [X0: $real,X1: 'Int_real_fun$',X2: $int,X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$z'(X1,X4),'fun_app$z'(X1,X5)) )
& $less(X2,X3)
& ( 'fun_app$z'(X1,X2) = X0 ) )
=> $less(X0,'fun_app$z'(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
tff(f8321,plain,
spl272_500,
inference(avatar_split_clause,[],[f3334,f8319]) ).
tff(f8319,plain,
( spl272_500
<=> ! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$p'(X2,X1),'fun_app$p'(X2,X0))
| $less('fun_app$p'(X2,sK135(X2)),'fun_app$p'(X2,sK134(X2)))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_500])]) ).
tff(f3334,plain,
! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$p'(X2,X1),'fun_app$p'(X2,X0))
| $less('fun_app$p'(X2,sK135(X2)),'fun_app$p'(X2,sK134(X2)))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3085]) ).
tff(f3085,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| $less('fun_app$p'(X2,sK135(X2)),'fun_app$p'(X2,sK134(X2)))
| ( 'fun_app$p'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1992]) ).
tff(f1992,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ( $less('fun_app$p'(X2,sK135(X2)),'fun_app$p'(X2,sK134(X2)))
& ~ $less(sK135(X2),sK134(X2)) )
| ( 'fun_app$p'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134,sK135])],[f1358,f1991]) ).
tff(f1991,plain,
! [X2: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$p'(X2,sK135(X2)),'fun_app$p'(X2,sK134(X2)))
& ~ $less(sK135(X2),sK134(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1358,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
| ( 'fun_app$p'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(flattening,[],[f1357]) ).
tff(f1357,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4))
& ~ $less(X5,X4) )
| ( 'fun_app$p'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f822]) ).
tff(f822,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$p'(X2,X5),'fun_app$p'(X2,X4)) )
& ( 'fun_app$p'(X2,X1) = X3 )
& ~ $less(X1,X0) )
=> ~ $less(X3,'fun_app$p'(X2,X0)) ),
inference(theory_normalization,[],[f300]) ).
tff(f300,axiom,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$p'(X2,X4),'fun_app$p'(X2,X5)) )
& ( 'fun_app$p'(X2,X1) = X3 )
& $lesseq(X0,X1) )
=> $lesseq('fun_app$p'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom298) ).
tff(f8317,plain,
spl272_499,
inference(avatar_split_clause,[],[f3328,f8315]) ).
tff(f8315,plain,
( spl272_499
<=> ! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$z'(X2,X1),'fun_app$z'(X2,X0))
| $less('fun_app$z'(X2,sK129(X2)),'fun_app$z'(X2,sK128(X2)))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_499])]) ).
tff(f3328,plain,
! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$z'(X2,X1),'fun_app$z'(X2,X0))
| $less('fun_app$z'(X2,sK129(X2)),'fun_app$z'(X2,sK128(X2)))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3079]) ).
tff(f3079,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| $less('fun_app$z'(X2,sK129(X2)),'fun_app$z'(X2,sK128(X2)))
| ( 'fun_app$z'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1986]) ).
tff(f1986,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ( $less('fun_app$z'(X2,sK129(X2)),'fun_app$z'(X2,sK128(X2)))
& ~ $less(sK129(X2),sK128(X2)) )
| ( 'fun_app$z'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128,sK129])],[f1352,f1985]) ).
tff(f1985,plain,
! [X2: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
=> ( $less('fun_app$z'(X2,sK129(X2)),'fun_app$z'(X2,sK128(X2)))
& ~ $less(sK129(X2),sK128(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1352,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
| ( 'fun_app$z'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(flattening,[],[f1351]) ).
tff(f1351,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ? [X4: $int,X5: $int] :
( $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4))
& ~ $less(X5,X4) )
| ( 'fun_app$z'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f819]) ).
tff(f819,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( ~ $less(X5,X4)
=> ~ $less('fun_app$z'(X2,X5),'fun_app$z'(X2,X4)) )
& ( 'fun_app$z'(X2,X1) = X3 )
& ~ $less(X1,X0) )
=> ~ $less(X3,'fun_app$z'(X2,X0)) ),
inference(theory_normalization,[],[f303]) ).
tff(f303,axiom,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( $lesseq(X4,X5)
=> $lesseq('fun_app$z'(X2,X4),'fun_app$z'(X2,X5)) )
& ( 'fun_app$z'(X2,X1) = X3 )
& $lesseq(X0,X1) )
=> $lesseq('fun_app$z'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom301) ).
tff(f8305,plain,
spl272_498,
inference(avatar_split_clause,[],[f3326,f8303]) ).
tff(f8303,plain,
( spl272_498
<=> ! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),'fun_app$p'(X2,X1))
| ~ $less('fun_app$p'(X2,sK118(X2)),'fun_app$p'(X2,sK119(X2)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_498])]) ).
tff(f3326,plain,
! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),'fun_app$p'(X2,X1))
| ~ $less('fun_app$p'(X2,sK118(X2)),'fun_app$p'(X2,sK119(X2)))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3069]) ).
tff(f3069,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ~ $less('fun_app$p'(X2,sK118(X2)),'fun_app$p'(X2,sK119(X2)))
| ( 'fun_app$p'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1976]) ).
tff(f1976,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ( ~ $less('fun_app$p'(X2,sK118(X2)),'fun_app$p'(X2,sK119(X2)))
& $less(sK118(X2),sK119(X2)) )
| ( 'fun_app$p'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK118,sK119])],[f1342,f1975]) ).
tff(f1975,plain,
! [X2: 'Int_int_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$p'(X2,sK118(X2)),'fun_app$p'(X2,sK119(X2)))
& $less(sK118(X2),sK119(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1342,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$p'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(flattening,[],[f1341]) ).
tff(f1341,plain,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$p'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f505]) ).
tff(f505,axiom,
! [X0: $int,X1: $int,X2: 'Int_int_fun$',X3: $int] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$p'(X2,X4),'fun_app$p'(X2,X5)) )
& ( 'fun_app$p'(X2,X1) = X3 )
& $less(X0,X1) )
=> $less('fun_app$p'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom503) ).
tff(f8301,plain,
spl272_497,
inference(avatar_split_clause,[],[f3320,f8299]) ).
tff(f8299,plain,
( spl272_497
<=> ! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),'fun_app$z'(X2,X1))
| ~ $less('fun_app$z'(X2,sK112(X2)),'fun_app$z'(X2,sK113(X2)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_497])]) ).
tff(f3320,plain,
! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),'fun_app$z'(X2,X1))
| ~ $less('fun_app$z'(X2,sK112(X2)),'fun_app$z'(X2,sK113(X2)))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3063]) ).
tff(f3063,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| ~ $less('fun_app$z'(X2,sK112(X2)),'fun_app$z'(X2,sK113(X2)))
| ( 'fun_app$z'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1970]) ).
tff(f1970,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ( ~ $less('fun_app$z'(X2,sK112(X2)),'fun_app$z'(X2,sK113(X2)))
& $less(sK112(X2),sK113(X2)) )
| ( 'fun_app$z'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f1336,f1969]) ).
tff(f1969,plain,
! [X2: 'Int_real_fun$'] :
( ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
=> ( ~ $less('fun_app$z'(X2,sK112(X2)),'fun_app$z'(X2,sK113(X2)))
& $less(sK112(X2),sK113(X2)) ) ),
introduced(choice_axiom,[]) ).
tff(f1336,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$z'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(flattening,[],[f1335]) ).
tff(f1335,plain,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( $less('fun_app$z'(X2,X0),X3)
| ? [X4: $int,X5: $int] :
( ~ $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5))
& $less(X4,X5) )
| ( 'fun_app$z'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f507]) ).
tff(f507,axiom,
! [X0: $int,X1: $int,X2: 'Int_real_fun$',X3: $real] :
( ( ! [X4: $int,X5: $int] :
( $less(X4,X5)
=> $less('fun_app$z'(X2,X4),'fun_app$z'(X2,X5)) )
& ( 'fun_app$z'(X2,X1) = X3 )
& $less(X0,X1) )
=> $less('fun_app$z'(X2,X0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom505) ).
tff(f8297,plain,
spl272_496,
inference(avatar_split_clause,[],[f2956,f8295]) ).
tff(f8295,plain,
( spl272_496
<=> ! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
| ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_496])]) ).
tff(f2956,plain,
! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
| ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0)) ),
inference(cnf_transformation,[],[f1911]) ).
tff(f1911,plain,
! [X0: 'Num_num_bool_fun_fun$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ( ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
& 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0)) )
| ( ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0))
& 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107,sK108,sK109])],[f1330,f1910,f1909]) ).
tff(f1909,plain,
! [X0: 'Num_num_bool_fun_fun$'] :
( ? [X3: 'Num$',X4: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X3),X4)
& 'fun_app$e'('fun_app$f'(X0,X4),X3) )
=> ( ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
& 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1910,plain,
! [X0: 'Num_num_bool_fun_fun$'] :
( ? [X5: 'Num$',X6: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X5),X6)
& 'fun_app$e'('fun_app$f'('less_eq$',X5),X6) )
=> ( ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0))
& 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1330,plain,
! [X0: 'Num_num_bool_fun_fun$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ? [X3: 'Num$',X4: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X3),X4)
& 'fun_app$e'('fun_app$f'(X0,X4),X3) )
| ? [X5: 'Num$',X6: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X5),X6)
& 'fun_app$e'('fun_app$f'('less_eq$',X5),X6) ) ),
inference(flattening,[],[f1329]) ).
tff(f1329,plain,
! [X0: 'Num_num_bool_fun_fun$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ? [X3: 'Num$',X4: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X3),X4)
& 'fun_app$e'('fun_app$f'(X0,X4),X3) )
| ? [X5: 'Num$',X6: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'(X0,X5),X6)
& 'fun_app$e'('fun_app$f'('less_eq$',X5),X6) ) ),
inference(ennf_transformation,[],[f995]) ).
tff(f995,plain,
! [X0: 'Num_num_bool_fun_fun$',X1: 'Num$',X2: 'Num$'] :
( ( ! [X3: 'Num$',X4: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X4),X3)
=> 'fun_app$e'('fun_app$f'(X0,X3),X4) )
& ! [X5: 'Num$',X6: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X5),X6)
=> 'fun_app$e'('fun_app$f'(X0,X5),X6) ) )
=> 'fun_app$e'('fun_app$f'(X0,X1),X2) ),
inference(rectify,[],[f235]) ).
tff(f235,axiom,
! [X0: 'Num_num_bool_fun_fun$',X1: 'Num$',X2: 'Num$'] :
( ( ! [X3: 'Num$',X4: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X4),X3)
=> 'fun_app$e'('fun_app$f'(X0,X3),X4) )
& ! [X3: 'Num$',X4: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X3),X4)
=> 'fun_app$e'('fun_app$f'(X0,X3),X4) ) )
=> 'fun_app$e'('fun_app$f'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom233) ).
tff(f8293,plain,
spl272_495,
inference(avatar_split_clause,[],[f2955,f8291]) ).
tff(f8291,plain,
( spl272_495
<=> ! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_495])]) ).
tff(f2955,plain,
! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| ~ 'fun_app$e'('fun_app$f'(X0,sK106(X0)),sK107(X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ),
inference(cnf_transformation,[],[f1911]) ).
tff(f8289,plain,
spl272_494,
inference(avatar_split_clause,[],[f2954,f8287]) ).
tff(f8287,plain,
( spl272_494
<=> ! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0))
| ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_494])]) ).
tff(f2954,plain,
! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0))
| ~ 'fun_app$e'('fun_app$f'(X0,sK108(X0)),sK109(X0)) ),
inference(cnf_transformation,[],[f1911]) ).
tff(f8285,plain,
spl272_493,
inference(avatar_split_clause,[],[f2953,f8283]) ).
tff(f8283,plain,
( spl272_493
<=> ! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_493])]) ).
tff(f2953,plain,
! [X2: 'Num$',X0: 'Num_num_bool_fun_fun$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'(X0,X1),X2)
| 'fun_app$e'('fun_app$f'(X0,sK107(X0)),sK106(X0))
| 'fun_app$e'('fun_app$f'('less_eq$',sK108(X0)),sK109(X0)) ),
inference(cnf_transformation,[],[f1911]) ).
tff(f8281,plain,
spl272_492,
inference(avatar_split_clause,[],[f2952,f8279]) ).
tff(f8279,plain,
( spl272_492
<=> ! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
| ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_492])]) ).
tff(f2952,plain,
! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
| ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0)) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f1908,plain,
! [X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ( ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
& 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0)) )
| ( ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103,sK104,sK105])],[f1328,f1907,f1906]) ).
tff(f1906,plain,
! [X0: 'Enat_enat_bool_fun_fun$'] :
( ? [X3: 'Enat$',X4: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X3),X4)
& 'fun_app$g'('fun_app$h'(X0,X4),X3) )
=> ( ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
& 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1907,plain,
! [X0: 'Enat_enat_bool_fun_fun$'] :
( ? [X5: 'Enat$',X6: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X5),X6)
& 'fun_app$g'('fun_app$h'('less_eq$a',X5),X6) )
=> ( ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0))
& 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1328,plain,
! [X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ? [X3: 'Enat$',X4: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X3),X4)
& 'fun_app$g'('fun_app$h'(X0,X4),X3) )
| ? [X5: 'Enat$',X6: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X5),X6)
& 'fun_app$g'('fun_app$h'('less_eq$a',X5),X6) ) ),
inference(flattening,[],[f1327]) ).
tff(f1327,plain,
! [X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ? [X3: 'Enat$',X4: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X3),X4)
& 'fun_app$g'('fun_app$h'(X0,X4),X3) )
| ? [X5: 'Enat$',X6: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'(X0,X5),X6)
& 'fun_app$g'('fun_app$h'('less_eq$a',X5),X6) ) ),
inference(ennf_transformation,[],[f994]) ).
tff(f994,plain,
! [X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$',X2: 'Enat$'] :
( ( ! [X3: 'Enat$',X4: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X4),X3)
=> 'fun_app$g'('fun_app$h'(X0,X3),X4) )
& ! [X5: 'Enat$',X6: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X5),X6)
=> 'fun_app$g'('fun_app$h'(X0,X5),X6) ) )
=> 'fun_app$g'('fun_app$h'(X0,X1),X2) ),
inference(rectify,[],[f236]) ).
tff(f236,axiom,
! [X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$',X2: 'Enat$'] :
( ( ! [X3: 'Enat$',X4: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X4),X3)
=> 'fun_app$g'('fun_app$h'(X0,X3),X4) )
& ! [X3: 'Enat$',X4: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X3),X4)
=> 'fun_app$g'('fun_app$h'(X0,X3),X4) ) )
=> 'fun_app$g'('fun_app$h'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
tff(f8277,plain,
spl272_491,
inference(avatar_split_clause,[],[f2951,f8275]) ).
tff(f8275,plain,
( spl272_491
<=> ! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_491])]) ).
tff(f2951,plain,
! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| ~ 'fun_app$g'('fun_app$h'(X0,sK102(X0)),sK103(X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f8273,plain,
spl272_490,
inference(avatar_split_clause,[],[f2950,f8271]) ).
tff(f8271,plain,
( spl272_490
<=> ! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0))
| ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_490])]) ).
tff(f2950,plain,
! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0))
| ~ 'fun_app$g'('fun_app$h'(X0,sK104(X0)),sK105(X0)) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f8269,plain,
spl272_489,
inference(avatar_split_clause,[],[f2949,f8267]) ).
tff(f8267,plain,
( spl272_489
<=> ! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_489])]) ).
tff(f2949,plain,
! [X2: 'Enat$',X0: 'Enat_enat_bool_fun_fun$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'(X0,X1),X2)
| 'fun_app$g'('fun_app$h'(X0,sK103(X0)),sK102(X0))
| 'fun_app$g'('fun_app$h'('less_eq$a',sK104(X0)),sK105(X0)) ),
inference(cnf_transformation,[],[f1908]) ).
tff(f8253,plain,
spl272_488,
inference(avatar_split_clause,[],[f2948,f8251]) ).
tff(f8251,plain,
( spl272_488
<=> ! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
| ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_488])]) ).
tff(f2948,plain,
! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
| ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0)) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f1905,plain,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ( ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
& 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0)) )
| ( ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0))
& ~ $less(sK101(X0),sK100(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99,sK100,sK101])],[f1326,f1904,f1903]) ).
tff(f1903,plain,
! [X0: 'Int_int_bool_fun_fun$'] :
( ? [X3: $int,X4: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X3),X4)
& 'fun_app$q'('fun_app$r'(X0,X4),X3) )
=> ( ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
& 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1904,plain,
! [X0: 'Int_int_bool_fun_fun$'] :
( ? [X5: $int,X6: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X5),X6)
& ~ $less(X6,X5) )
=> ( ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0))
& ~ $less(sK101(X0),sK100(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1326,plain,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ? [X3: $int,X4: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X3),X4)
& 'fun_app$q'('fun_app$r'(X0,X4),X3) )
| ? [X5: $int,X6: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X5),X6)
& ~ $less(X6,X5) ) ),
inference(flattening,[],[f1325]) ).
tff(f1325,plain,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ? [X3: $int,X4: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X3),X4)
& 'fun_app$q'('fun_app$r'(X0,X4),X3) )
| ? [X5: $int,X6: $int] :
( ~ 'fun_app$q'('fun_app$r'(X0,X5),X6)
& ~ $less(X6,X5) ) ),
inference(ennf_transformation,[],[f993]) ).
tff(f993,plain,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( ( ! [X3: $int,X4: $int] :
( 'fun_app$q'('fun_app$r'(X0,X4),X3)
=> 'fun_app$q'('fun_app$r'(X0,X3),X4) )
& ! [X5: $int,X6: $int] :
( ~ $less(X6,X5)
=> 'fun_app$q'('fun_app$r'(X0,X5),X6) ) )
=> 'fun_app$q'('fun_app$r'(X0,X1),X2) ),
inference(rectify,[],[f802]) ).
tff(f802,plain,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( ( ! [X3: $int,X4: $int] :
( 'fun_app$q'('fun_app$r'(X0,X4),X3)
=> 'fun_app$q'('fun_app$r'(X0,X3),X4) )
& ! [X3: $int,X4: $int] :
( ~ $less(X4,X3)
=> 'fun_app$q'('fun_app$r'(X0,X3),X4) ) )
=> 'fun_app$q'('fun_app$r'(X0,X1),X2) ),
inference(theory_normalization,[],[f234]) ).
tff(f234,axiom,
! [X0: 'Int_int_bool_fun_fun$',X1: $int,X2: $int] :
( ( ! [X3: $int,X4: $int] :
( 'fun_app$q'('fun_app$r'(X0,X4),X3)
=> 'fun_app$q'('fun_app$r'(X0,X3),X4) )
& ! [X3: $int,X4: $int] :
( $lesseq(X3,X4)
=> 'fun_app$q'('fun_app$r'(X0,X3),X4) ) )
=> 'fun_app$q'('fun_app$r'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).
tff(f8249,plain,
spl272_487,
inference(avatar_split_clause,[],[f2946,f8247]) ).
tff(f8247,plain,
( spl272_487
<=> ! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0))
| ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_487])]) ).
tff(f2946,plain,
! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0))
| ~ 'fun_app$q'('fun_app$r'(X0,sK100(X0)),sK101(X0)) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f8245,plain,
spl272_486,
inference(avatar_split_clause,[],[f2944,f8243]) ).
tff(f8243,plain,
( spl272_486
<=> ! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
| ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_486])]) ).
tff(f2944,plain,
! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
| ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0)) ),
inference(cnf_transformation,[],[f1902]) ).
tff(f1902,plain,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ( ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
& 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0)) )
| ( ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0))
& ~ $less(sK97(X0),sK96(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95,sK96,sK97])],[f1324,f1901,f1900]) ).
tff(f1900,plain,
! [X0: 'Real_real_bool_fun_fun$'] :
( ? [X3: $real,X4: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X3),X4)
& 'fun_app$'('fun_app$s'(X0,X4),X3) )
=> ( ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
& 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1901,plain,
! [X0: 'Real_real_bool_fun_fun$'] :
( ? [X5: $real,X6: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X5),X6)
& ~ $less(X6,X5) )
=> ( ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0))
& ~ $less(sK97(X0),sK96(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1324,plain,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ? [X3: $real,X4: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X3),X4)
& 'fun_app$'('fun_app$s'(X0,X4),X3) )
| ? [X5: $real,X6: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X5),X6)
& ~ $less(X6,X5) ) ),
inference(flattening,[],[f1323]) ).
tff(f1323,plain,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ? [X3: $real,X4: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X3),X4)
& 'fun_app$'('fun_app$s'(X0,X4),X3) )
| ? [X5: $real,X6: $real] :
( ~ 'fun_app$'('fun_app$s'(X0,X5),X6)
& ~ $less(X6,X5) ) ),
inference(ennf_transformation,[],[f992]) ).
tff(f992,plain,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( ( ! [X3: $real,X4: $real] :
( 'fun_app$'('fun_app$s'(X0,X4),X3)
=> 'fun_app$'('fun_app$s'(X0,X3),X4) )
& ! [X5: $real,X6: $real] :
( ~ $less(X6,X5)
=> 'fun_app$'('fun_app$s'(X0,X5),X6) ) )
=> 'fun_app$'('fun_app$s'(X0,X1),X2) ),
inference(rectify,[],[f801]) ).
tff(f801,plain,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( ( ! [X3: $real,X4: $real] :
( 'fun_app$'('fun_app$s'(X0,X4),X3)
=> 'fun_app$'('fun_app$s'(X0,X3),X4) )
& ! [X3: $real,X4: $real] :
( ~ $less(X4,X3)
=> 'fun_app$'('fun_app$s'(X0,X3),X4) ) )
=> 'fun_app$'('fun_app$s'(X0,X1),X2) ),
inference(theory_normalization,[],[f237]) ).
tff(f237,axiom,
! [X0: 'Real_real_bool_fun_fun$',X1: $real,X2: $real] :
( ( ! [X3: $real,X4: $real] :
( 'fun_app$'('fun_app$s'(X0,X4),X3)
=> 'fun_app$'('fun_app$s'(X0,X3),X4) )
& ! [X3: $real,X4: $real] :
( $lesseq(X3,X4)
=> 'fun_app$'('fun_app$s'(X0,X3),X4) ) )
=> 'fun_app$'('fun_app$s'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
tff(f8241,plain,
spl272_485,
inference(avatar_split_clause,[],[f2942,f8239]) ).
tff(f8239,plain,
( spl272_485
<=> ! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0))
| ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_485])]) ).
tff(f2942,plain,
! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0))
| ~ 'fun_app$'('fun_app$s'(X0,sK96(X0)),sK97(X0)) ),
inference(cnf_transformation,[],[f1902]) ).
tff(f8237,plain,
spl272_484,
inference(avatar_split_clause,[],[f2872,f8235]) ).
tff(f8235,plain,
( spl272_484
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| ~ 'fun_app$n'(X2,sK76(X0,X1,X2))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_484])]) ).
tff(f2872,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| ~ 'fun_app$n'(X2,sK76(X0,X1,X2))
| ~ 'fun_app$n'(X2,X1)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f8233,plain,
spl272_483,
inference(avatar_split_clause,[],[f2867,f8231]) ).
tff(f8231,plain,
( spl272_483
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| 'fun_app$n'(X2,sK75(X0,X1,X2))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_483])]) ).
tff(f2867,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| 'fun_app$n'(X2,sK75(X0,X1,X2))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1843]) ).
tff(f8229,plain,
spl272_482,
inference(avatar_split_clause,[],[f2816,f8227]) ).
tff(f8227,plain,
( spl272_482
<=> ! [X4: 'Nat$',X0: 'Nat_bool_fun$',X2: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4)
| 'fun_app$n'(X0,sK67(X0,X2))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_482])]) ).
tff(f2816,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$',X4: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',sK66(X0)),'fun_app$a'('of_nat$',X4))
| ~ 'fun_app$n'(X0,X4)
| 'fun_app$n'(X0,sK67(X0,X2))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1823]) ).
tff(f8224,plain,
spl272_481,
inference(avatar_split_clause,[],[f2468,f8222]) ).
tff(f2468,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1615]) ).
tff(f1615,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( 'fun_app$n'(X0,sK42(X0,X1))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1))) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1))) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f1098,f1614]) ).
tff(f1614,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
=> ( 'fun_app$n'(X0,sK42(X0,X1))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK42(X0,X1))) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1098,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(flattening,[],[f1097]) ).
tff(f1097,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(ennf_transformation,[],[f717]) ).
tff(f717,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,'nat$'(0))
& 'fun_app$n'(X0,X1) )
=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
=> ~ 'fun_app$n'(X0,X3) )
& ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) ) ),
inference(theory_normalization,[],[f586]) ).
tff(f586,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,'nat$'(0))
& 'fun_app$n'(X0,X1) )
=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
=> ~ 'fun_app$n'(X0,X3) )
& $lesseq('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).
tff(f8219,plain,
spl272_480,
inference(avatar_split_clause,[],[f2465,f8217]) ).
tff(f2465,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1613]) ).
tff(f1613,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK41(X0,X1)),1)))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3)) )
& $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1)) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f1096,f1612]) ).
tff(f1612,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3)) )
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) )
=> ( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK41(X0,X1)),1)))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X3)) )
& $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1096,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3)) )
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(flattening,[],[f1095]) ).
tff(f1095,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3)) )
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) )
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(ennf_transformation,[],[f716]) ).
tff(f716,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,'nat$'(0))
& 'fun_app$n'(X0,X1) )
=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ! [X3: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
=> ~ 'fun_app$n'(X0,X3) )
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
inference(theory_normalization,[],[f599]) ).
tff(f599,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,'nat$'(0))
& 'fun_app$n'(X0,X1) )
=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ! [X3: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
=> ~ 'fun_app$n'(X0,X3) )
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom597) ).
tff(f8215,plain,
spl272_479,
inference(avatar_split_clause,[],[f2358,f8213]) ).
tff(f8213,plain,
( spl272_479
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$d'('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_479])]) ).
tff(f2358,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$d'('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ),
inference(cnf_transformation,[],[f393]) ).
tff(f393,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$d'('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
tff(f8197,plain,
spl272_478,
inference(avatar_split_clause,[],[f2357,f8195]) ).
tff(f8195,plain,
( spl272_478
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$l'('of_nat$c','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$c'('fun_app$l'('of_nat$c',X0),'fun_app$l'('of_nat$c',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_478])]) ).
tff(f2357,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$l'('of_nat$c','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$c'('fun_app$l'('of_nat$c',X0),'fun_app$l'('of_nat$c',X1)) ),
inference(cnf_transformation,[],[f391]) ).
tff(f391,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$l'('of_nat$c','nat$'('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))) = 'times$c'('fun_app$l'('of_nat$c',X0),'fun_app$l'('of_nat$c',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom389) ).
tff(f8075,plain,
( spl272_477
| ~ spl272_109
| ~ spl272_420 ),
inference(avatar_split_clause,[],[f7708,f7507,f4112,f8073]) ).
tff(f7507,plain,
( spl272_420
<=> ! [X0: $real] : ~ $less($sum(4.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_420])]) ).
tff(f7708,plain,
( ! [X0: $real] : $less(X0,$sum(5.0,X0))
| ~ spl272_109
| ~ spl272_420 ),
inference(evaluation,[],[f7702]) ).
tff(f7702,plain,
( ! [X0: $real] : $less(X0,$sum(4.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_420 ),
inference(resolution,[],[f7508,f4113]) ).
tff(f7508,plain,
( ! [X0: $real] : ~ $less($sum(4.0,X0),X0)
| ~ spl272_420 ),
inference(avatar_component_clause,[],[f7507]) ).
tff(f7970,plain,
( spl272_476
| ~ spl272_58
| ~ spl272_420 ),
inference(avatar_split_clause,[],[f7706,f7507,f3865,f7968]) ).
tff(f7968,plain,
( spl272_476
<=> ! [X0: $real] : ~ $less($sum(X0,4.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_476])]) ).
tff(f7706,plain,
( ! [X0: $real] : ~ $less($sum(X0,4.0),X0)
| ~ spl272_58
| ~ spl272_420 ),
inference(superposition,[],[f7508,f3866]) ).
tff(f7909,plain,
( spl272_475
| ~ spl272_55
| ~ spl272_448 ),
inference(avatar_split_clause,[],[f7745,f7742,f3851,f7907]) ).
tff(f7907,plain,
( spl272_475
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_475])]) ).
tff(f7742,plain,
( spl272_448
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_448])]) ).
tff(f7745,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0))) )
| ~ spl272_55
| ~ spl272_448 ),
inference(forward_demodulation,[],[f7743,f3853]) ).
tff(f7743,plain,
( ! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_448 ),
inference(avatar_component_clause,[],[f7742]) ).
tff(f7859,plain,
( spl272_301
| spl272_474 ),
inference(avatar_split_clause,[],[f3607,f7857,f5655]) ).
tff(f5655,plain,
( spl272_301
<=> ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_301])]) ).
tff(f7857,plain,
( spl272_474
<=> ! [X2: 'Nat$',X1: 'Nat$'] : ( 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_474])]) ).
tff(f3607,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(inner_rewriting,[],[f3036]) ).
tff(f3036,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X2)) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1953]) ).
tff(f7855,plain,
( spl272_473
| ~ spl272_107
| ~ spl272_413 ),
inference(avatar_split_clause,[],[f7609,f7290,f4104,f7853]) ).
tff(f7290,plain,
( spl272_413
<=> ! [X0: $int] : ~ $less($sum(4,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_413])]) ).
tff(f7609,plain,
( ! [X0: $int] : $less(X0,$sum(5,X0))
| ~ spl272_107
| ~ spl272_413 ),
inference(evaluation,[],[f7597]) ).
tff(f7597,plain,
( ! [X0: $int] : $less(X0,$sum(4,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_413 ),
inference(resolution,[],[f7291,f4105]) ).
tff(f7291,plain,
( ! [X0: $int] : ~ $less($sum(4,X0),X0)
| ~ spl272_413 ),
inference(avatar_component_clause,[],[f7290]) ).
tff(f7851,plain,
spl272_472,
inference(avatar_split_clause,[],[f3545,f7849]) ).
tff(f7849,plain,
( spl272_472
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',X2))))
| sP5(X1,X0)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_472])]) ).
tff(f3545,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',X2))))
| sP5(X1,X0)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2786,f848]) ).
tff(f2786,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP5(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1815]) ).
tff(f1815,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP5(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,'nat$'(0)) ) )
& ( ( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK65(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f1813,f1814]) ).
tff(f1814,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> ( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK65(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1813,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP5(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
inference(rectify,[],[f1812]) ).
tff(f1812,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP5(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
inference(flattening,[],[f1811]) ).
tff(f1811,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP5(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,'nat$'(0)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f1508]) ).
tff(f1508,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP5(X1,X0)
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0)) ) ),
inference(definition_folding,[],[f978,f1507]) ).
tff(f1507,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP5(X1,X0)
<=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f978,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0)) ) ),
inference(rectify,[],[f570]) ).
tff(f570,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,'nat$'(0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).
tff(f7847,plain,
spl272_471,
inference(avatar_split_clause,[],[f3540,f7845]) ).
tff(f7845,plain,
( spl272_471
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',X3))))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_471])]) ).
tff(f3540,plain,
! [X3: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',X3))))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
| ~ sP3(X1,X0) ),
inference(forward_demodulation,[],[f2770,f848]) ).
tff(f2770,plain,
! [X3: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
| ~ sP3(X1,X0) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f1797,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP3(X1,X0)
| ( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK61(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) )
| ~ sP3(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f1795,f1796]) ).
tff(f1796,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
=> ( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK61(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1795,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP3(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) )
| ~ sP3(X1,X0) ) ),
inference(rectify,[],[f1794]) ).
tff(f1794,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP3(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f1793]) ).
tff(f1793,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP3(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,'nat$'(0)) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f1504]) ).
tff(f1504,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP3(X1,X0)
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) ) ),
inference(definition_folding,[],[f1184,f1503]) ).
tff(f1503,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP3(X1,X0)
<=> ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f1184,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,'nat$'(0)) ) ),
inference(ennf_transformation,[],[f976]) ).
tff(f976,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1))
=> 'fun_app$n'(X1,X2) )
<=> ( ! [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
=> 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X3),1))) )
& 'fun_app$n'(X1,'nat$'(0)) ) ),
inference(rectify,[],[f572]) ).
tff(f572,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1))
=> 'fun_app$n'(X1,X2) )
<=> ( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0))
=> 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',X2),1))) )
& 'fun_app$n'(X1,'nat$'(0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom570) ).
tff(f7843,plain,
spl272_470,
inference(avatar_split_clause,[],[f3518,f7841]) ).
tff(f7841,plain,
( spl272_470
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X1)) )
| ~ $less($sum(1,'fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_470])]) ).
tff(f3518,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X1)) )
| ~ $less($sum(1,'fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f3517,f848]) ).
tff(f3517,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) ),
inference(forward_demodulation,[],[f2725,f848]) ).
tff(f2725,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) ),
inference(cnf_transformation,[],[f1759]) ).
tff(f1759,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
| ( ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) )
& $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0)) ) ),
inference(flattening,[],[f1758]) ).
tff(f1758,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
| ( ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) )
& $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0)) ) ),
inference(nnf_transformation,[],[f758]) ).
tff(f758,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
<=> ( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
inference(theory_normalization,[],[f48]) ).
tff(f48,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
<=> ( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
tff(f7839,plain,
spl272_469,
inference(avatar_split_clause,[],[f3514,f7837]) ).
tff(f7837,plain,
( spl272_469
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK57(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_469])]) ).
tff(f3514,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK57(X0,X1))) ),
inference(forward_demodulation,[],[f2717,f848]) ).
tff(f2717,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK57(X0,X1)))
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1755]) ).
tff(f7835,plain,
spl272_468,
inference(avatar_split_clause,[],[f3498,f7833]) ).
tff(f7833,plain,
( spl272_468
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_468])]) ).
tff(f3498,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2686,f2346]) ).
tff(f2346,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)) = 'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1) ),
inference(cnf_transformation,[],[f122]) ).
tff(f122,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)) = 'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).
tff(f2686,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1)) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f1733,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1)) ) ),
inference(flattening,[],[f1732]) ).
tff(f1732,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1)) ) ),
inference(nnf_transformation,[],[f415]) ).
tff(f415,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1))
<=> ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom413) ).
tff(f7831,plain,
spl272_467,
inference(avatar_split_clause,[],[f3492,f7829]) ).
tff(f7829,plain,
( spl272_467
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK51(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_467])]) ).
tff(f3492,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK51(X0,X1))) ),
inference(forward_demodulation,[],[f2518,f848]) ).
tff(f2518,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',sK51(X0,X1)))
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1636]) ).
tff(f7827,plain,
spl272_466,
inference(avatar_split_clause,[],[f3476,f7825]) ).
tff(f7825,plain,
( spl272_466
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),$sum(1,'fun_app$a'('of_nat$',X1)))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_466])]) ).
tff(f3476,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X0)),$sum(1,'fun_app$a'('of_nat$',X1)))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f3475,f848]) ).
tff(f3475,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum('fun_app$a'('of_nat$',X0),1),$sum(1,'fun_app$a'('of_nat$',X1)))
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(forward_demodulation,[],[f2448,f848]) ).
tff(f2448,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1079]) ).
tff(f1079,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less($sum('fun_app$a'('of_nat$',X0),1),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(ennf_transformation,[],[f557]) ).
tff(f557,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum('fun_app$a'('of_nat$',X0),1),$sum('fun_app$a'('of_nat$',X1),1))
=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
tff(f7823,plain,
spl272_465,
inference(avatar_split_clause,[],[f3414,f7821]) ).
tff(f7821,plain,
( spl272_465
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 1 != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_465])]) ).
tff(f3414,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 1 != 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) ) ),
inference(evaluation,[],[f2731]) ).
tff(f2731,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) != $sum(0,1) ) ),
inference(cnf_transformation,[],[f1764]) ).
tff(f1764,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = $sum(0,1) )
| ( ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) )
& ( 'fun_app$a'('of_nat$',X1) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) != $sum(0,1) ) ) ),
inference(flattening,[],[f1763]) ).
tff(f1763,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = $sum(0,1) )
| ( ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) )
& ( 'fun_app$a'('of_nat$',X1) != 0 ) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X1) = 0 )
| ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) != $sum(0,1) ) ) ),
inference(nnf_transformation,[],[f100]) ).
tff(f100,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = $sum(0,1) )
<=> ( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X1) = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).
tff(f7819,plain,
spl272_464,
inference(avatar_split_clause,[],[f3194,f7817]) ).
tff(f7817,plain,
( spl272_464
<=> ! [X0: $int,X3: $int,X2: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ~ $less(sK245(X1),sK244(X1))
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_464])]) ).
tff(f3194,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ~ $less(sK245(X1),sK244(X1))
| $less(X3,X2)
| $less('fun_app$p'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2102]) ).
tff(f7815,plain,
spl272_463,
inference(avatar_split_clause,[],[f3190,f7813]) ).
tff(f7813,plain,
( spl272_463
<=> ! [X0: $int,X3: $real,X2: $real,X1: 'Real_int_fun$'] :
( ~ $less('fun_app$u'(X1,X3),X0)
| ~ $less(sK241(X1),sK240(X1))
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_463])]) ).
tff(f3190,plain,
! [X2: $real,X3: $real,X0: $int,X1: 'Real_int_fun$'] :
( ~ $less('fun_app$u'(X1,X3),X0)
| ~ $less(sK241(X1),sK240(X1))
| $less(X3,X2)
| $less('fun_app$u'(X1,X2),X0) ),
inference(cnf_transformation,[],[f2098]) ).
tff(f7811,plain,
( spl272_462
| ~ spl272_56
| ~ spl272_413 ),
inference(avatar_split_clause,[],[f7604,f7290,f3857,f7809]) ).
tff(f7809,plain,
( spl272_462
<=> ! [X0: $int] : ~ $less($sum(X0,4),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_462])]) ).
tff(f7604,plain,
( ! [X0: $int] : ~ $less($sum(X0,4),X0)
| ~ spl272_56
| ~ spl272_413 ),
inference(superposition,[],[f7291,f3858]) ).
tff(f7807,plain,
spl272_461,
inference(avatar_split_clause,[],[f3186,f7805]) ).
tff(f7805,plain,
( spl272_461
<=> ! [X0: $int,X3: $int,X2: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| $less(sK236(X1),sK237(X1))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_461])]) ).
tff(f3186,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| $less(sK236(X1),sK237(X1))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$p'(X1,X2)) ),
inference(cnf_transformation,[],[f2094]) ).
tff(f7803,plain,
spl272_460,
inference(avatar_split_clause,[],[f3182,f7801]) ).
tff(f7801,plain,
( spl272_460
<=> ! [X0: $int,X3: $real,X2: $real,X1: 'Real_int_fun$'] :
( $less(X0,'fun_app$u'(X1,X3))
| $less(sK232(X1),sK233(X1))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_460])]) ).
tff(f3182,plain,
! [X2: $real,X3: $real,X0: $int,X1: 'Real_int_fun$'] :
( $less(X0,'fun_app$u'(X1,X3))
| $less(sK232(X1),sK233(X1))
| ~ $less(X2,X3)
| ~ $less(X0,'fun_app$u'(X1,X2)) ),
inference(cnf_transformation,[],[f2090]) ).
tff(f7799,plain,
spl272_459,
inference(avatar_split_clause,[],[f3088,f7797]) ).
tff(f7797,plain,
( spl272_459
<=> ! [X0: $int,X3: $int,X2: 'Int_int_fun$',X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ~ $less(sK139(X2),sK138(X2))
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_459])]) ).
tff(f3088,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ~ $less(sK139(X2),sK138(X2))
| $less(X3,'fun_app$p'(X2,X1))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1996]) ).
tff(f7795,plain,
spl272_458,
inference(avatar_split_clause,[],[f3086,f7793]) ).
tff(f7793,plain,
( spl272_458
<=> ! [X0: $int,X3: $real,X2: 'Int_real_fun$',X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ~ $less(sK137(X2),sK136(X2))
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_458])]) ).
tff(f3086,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ~ $less(sK137(X2),sK136(X2))
| $less(X3,'fun_app$z'(X2,X1))
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1994]) ).
tff(f7791,plain,
spl272_457,
inference(avatar_split_clause,[],[f3072,f7789]) ).
tff(f7789,plain,
( spl272_457
<=> ! [X0: $int,X3: $int,X2: 'Int_int_fun$',X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| $less(sK122(X2),sK123(X2))
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_457])]) ).
tff(f3072,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| $less(sK122(X2),sK123(X2))
| ~ $less('fun_app$p'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1980]) ).
tff(f7787,plain,
spl272_456,
inference(avatar_split_clause,[],[f3070,f7785]) ).
tff(f7785,plain,
( spl272_456
<=> ! [X0: $int,X3: $real,X2: 'Int_real_fun$',X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| $less(sK120(X2),sK121(X2))
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_456])]) ).
tff(f3070,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| $less(sK120(X2),sK121(X2))
| ~ $less('fun_app$z'(X2,X1),X3)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1978]) ).
tff(f7783,plain,
spl272_455,
inference(avatar_split_clause,[],[f2863,f7781]) ).
tff(f7781,plain,
( spl272_455
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| 'fun_app$n'(X2,sK74(X0,X2))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_455])]) ).
tff(f2863,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X1)
| 'fun_app$n'(X2,sK74(X0,X2))
| ~ 'fun_app$n'(X2,X0)
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f7779,plain,
spl272_454,
inference(avatar_split_clause,[],[f2861,f7777]) ).
tff(f7777,plain,
( spl272_454
<=> ! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ~ 'fun_app$n'(X2,sK73(X1,X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_454])]) ).
tff(f2861,plain,
! [X2: 'Nat_bool_fun$',X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'(X2,X0)
| sP7(X2,X1)
| ~ 'fun_app$n'(X2,sK73(X1,X2))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1839]) ).
tff(f7775,plain,
spl272_453,
inference(avatar_split_clause,[],[f2789,f7773]) ).
tff(f7773,plain,
( spl272_453
<=> ! [X2: 'Nat$',X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'fun_app$b'('times$'('numeral$c'(X1)),X2)) = 'fun_app$b'('times$'('numeral$c'('fun_app$c'('times$a'(X0),X1))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_453])]) ).
tff(f2789,plain,
! [X2: 'Nat$',X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'fun_app$b'('times$'('numeral$c'(X1)),X2)) = 'fun_app$b'('times$'('numeral$c'('fun_app$c'('times$a'(X0),X1))),X2) ),
inference(cnf_transformation,[],[f368]) ).
tff(f368,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Nat$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'fun_app$b'('times$'('numeral$c'(X1)),X2)) = 'fun_app$b'('times$'('numeral$c'('fun_app$c'('times$a'(X0),X1))),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom366) ).
tff(f7771,plain,
spl272_452,
inference(avatar_split_clause,[],[f2788,f7769]) ).
tff(f7769,plain,
( spl272_452
<=> ! [X2: $real,X0: 'Num$',X1: 'Num$'] : ( 'times$d'('fun_app$j'('numeral$b',X0),'times$d'('fun_app$j'('numeral$b',X1),X2)) = 'times$d'('fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_452])]) ).
tff(f2788,plain,
! [X2: $real,X0: 'Num$',X1: 'Num$'] : ( 'times$d'('fun_app$j'('numeral$b',X0),'times$d'('fun_app$j'('numeral$b',X1),X2)) = 'times$d'('fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)),X2) ),
inference(cnf_transformation,[],[f371]) ).
tff(f371,axiom,
! [X0: 'Num$',X1: 'Num$',X2: $real] : ( 'times$d'('fun_app$j'('numeral$b',X0),'times$d'('fun_app$j'('numeral$b',X1),X2)) = 'times$d'('fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom369) ).
tff(f7757,plain,
spl272_451,
inference(avatar_split_clause,[],[f2787,f7755]) ).
tff(f7755,plain,
( spl272_451
<=> ! [X2: 'Enat$',X0: 'Num$',X1: 'Num$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'times$c'('fun_app$i'('numeral$a',X1),X2)) = 'times$c'('fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_451])]) ).
tff(f2787,plain,
! [X2: 'Enat$',X0: 'Num$',X1: 'Num$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'times$c'('fun_app$i'('numeral$a',X1),X2)) = 'times$c'('fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)),X2) ),
inference(cnf_transformation,[],[f370]) ).
tff(f370,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Enat$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'times$c'('fun_app$i'('numeral$a',X1),X2)) = 'times$c'('fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom368) ).
tff(f7753,plain,
spl272_450,
inference(avatar_split_clause,[],[f2741,f7751]) ).
tff(f7751,plain,
( spl272_450
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum('fun_app$a'('of_nat$',X0),1) = $sum('fun_app$a'('of_nat$',X1),1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_450])]) ).
tff(f2741,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum('fun_app$a'('of_nat$',X0),1) = $sum('fun_app$a'('of_nat$',X1),1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(cnf_transformation,[],[f1769]) ).
tff(f1769,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $sum('fun_app$a'('of_nat$',X0),1) = $sum('fun_app$a'('of_nat$',X1),1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( $sum('fun_app$a'('of_nat$',X0),1) != $sum('fun_app$a'('of_nat$',X1),1) ) ) ),
inference(nnf_transformation,[],[f22]) ).
tff(f22,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum('fun_app$a'('of_nat$',X0),1) = $sum('fun_app$a'('of_nat$',X1),1) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
tff(f7749,plain,
spl272_449,
inference(avatar_split_clause,[],[f2689,f7747]) ).
tff(f7747,plain,
( spl272_449
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_449])]) ).
tff(f2689,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
inference(cnf_transformation,[],[f1735]) ).
tff(f1735,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ) ),
inference(flattening,[],[f1734]) ).
tff(f1734,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ( ( 'fun_app$a'('of_nat$',X1) != 0 )
& ~ $less(0,'fun_app$a'('of_nat$',X0)) ) )
& ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ) ),
inference(nnf_transformation,[],[f385]) ).
tff(f385,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
<=> ( ( 'fun_app$a'('of_nat$',X1) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom383) ).
tff(f7744,plain,
spl272_448,
inference(avatar_split_clause,[],[f2489,f7742]) ).
tff(f2489,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1627]) ).
tff(f1627,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0))) )
& ~ 'fun_app$n'(X0,sK47(X0))
& $less(0,'fun_app$a'('of_nat$',sK47(X0))) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f1120,f1626]) ).
tff(f1626,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ 'fun_app$n'(X0,X2)
& $less(0,'fun_app$a'('of_nat$',X2)) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK47(X0))) )
& ~ 'fun_app$n'(X0,sK47(X0))
& $less(0,'fun_app$a'('of_nat$',sK47(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1120,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ 'fun_app$n'(X0,X2)
& $less(0,'fun_app$a'('of_nat$',X2)) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(flattening,[],[f1119]) ).
tff(f1119,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ 'fun_app$n'(X0,X2)
& $less(0,'fun_app$a'('of_nat$',X2)) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f445]) ).
tff(f445,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,X2)
& $less(0,'fun_app$a'('of_nat$',X2)) )
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) ) )
& 'fun_app$n'(X0,'nat$'(0)) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
tff(f7740,plain,
spl272_447,
inference(avatar_split_clause,[],[f2459,f7738]) ).
tff(f7738,plain,
( spl272_447
<=> ! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| $less(X1,'times$d'('fun_app$m'('of_nat$b',sK40(X0,X1)),X0))
| $less(X1,0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_447])]) ).
tff(f2459,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| $less(X1,'times$d'('fun_app$m'('of_nat$b',sK40(X0,X1)),X0))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f1610,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ( $less(X1,'times$d'('fun_app$m'('of_nat$b',sK40(X0,X1)),X0))
& $less(0,'fun_app$a'('of_nat$',sK40(X0,X1))) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f1090,f1609]) ).
tff(f1609,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'Nat$'] :
( $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0))
& $less(0,'fun_app$a'('of_nat$',X2)) )
=> ( $less(X1,'times$d'('fun_app$m'('of_nat$b',sK40(X0,X1)),X0))
& $less(0,'fun_app$a'('of_nat$',sK40(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1090,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ? [X2: 'Nat$'] :
( $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0))
& $less(0,'fun_app$a'('of_nat$',X2)) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(flattening,[],[f1089]) ).
tff(f1089,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ? [X2: 'Nat$'] :
( $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0))
& $less(0,'fun_app$a'('of_nat$',X2)) )
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(ennf_transformation,[],[f714]) ).
tff(f714,plain,
! [X0: $real,X1: $real] :
( ( ! [X2: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X2))
=> ~ $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0)) )
& ~ $less(X1,0.0)
& ~ $less(X0,0.0) )
=> ( 0.0 = X0 ) ),
inference(theory_normalization,[],[f630]) ).
tff(f630,axiom,
! [X0: $real,X1: $real] :
( ( ! [X2: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X2))
=> $lesseq('times$d'('fun_app$m'('of_nat$b',X2),X0),X1) )
& $lesseq(0.0,X1)
& $lesseq(0.0,X0) )
=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).
tff(f7736,plain,
spl272_446,
inference(avatar_split_clause,[],[f2449,f7734]) ).
tff(f7734,plain,
( spl272_446
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_446])]) ).
tff(f2449,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ),
inference(cnf_transformation,[],[f1080]) ).
tff(f1080,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2)))) ),
inference(ennf_transformation,[],[f710]) ).
tff(f710,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))))
=> ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f7]) ).
tff(f7,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),'nat$'(2))),'fun_app$a'('of_nat$',X1))
=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f7732,plain,
spl272_445,
inference(avatar_split_clause,[],[f2447,f7730]) ).
tff(f7730,plain,
( spl272_445
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( $sum('fun_app$a'('of_nat$',X0),1) != $sum('fun_app$a'('of_nat$',X1),1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_445])]) ).
tff(f2447,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( $sum('fun_app$a'('of_nat$',X0),1) != $sum('fun_app$a'('of_nat$',X1),1) ) ),
inference(cnf_transformation,[],[f1078]) ).
tff(f1078,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( $sum('fun_app$a'('of_nat$',X0),1) != $sum('fun_app$a'('of_nat$',X1),1) ) ),
inference(ennf_transformation,[],[f34]) ).
tff(f34,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum('fun_app$a'('of_nat$',X0),1) = $sum('fun_app$a'('of_nat$',X1),1) )
=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom32) ).
tff(f7701,plain,
( spl272_444
| ~ spl272_55
| ~ spl272_441 ),
inference(avatar_split_clause,[],[f7596,f7593,f3851,f7699]) ).
tff(f7699,plain,
( spl272_444
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK65(X0,X1)))))
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_444])]) ).
tff(f7593,plain,
( spl272_441
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK65(X0,X1)))))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_441])]) ).
tff(f7596,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK65(X0,X1)))))
| ~ sP5(X1,X0) )
| ~ spl272_55
| ~ spl272_441 ),
inference(forward_demodulation,[],[f7594,f3853]) ).
tff(f7594,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK65(X0,X1)))))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) )
| ~ spl272_441 ),
inference(avatar_component_clause,[],[f7593]) ).
tff(f7697,plain,
( spl272_443
| ~ spl272_55
| ~ spl272_440 ),
inference(avatar_split_clause,[],[f7591,f7588,f3851,f7695]) ).
tff(f7695,plain,
( spl272_443
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK61(X0,X1)))))
| sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_443])]) ).
tff(f7588,plain,
( spl272_440
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK61(X0,X1)))))
| sP3(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_440])]) ).
tff(f7591,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK61(X0,X1)))))
| sP3(X1,X0) )
| ~ spl272_55
| ~ spl272_440 ),
inference(forward_demodulation,[],[f7589,f3853]) ).
tff(f7589,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK61(X0,X1)))))
| sP3(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) )
| ~ spl272_440 ),
inference(avatar_component_clause,[],[f7588]) ).
tff(f7693,plain,
( spl272_442
| ~ spl272_55
| ~ spl272_439 ),
inference(avatar_split_clause,[],[f7586,f7583,f3851,f7691]) ).
tff(f7691,plain,
( spl272_442
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK41(X0,X1)))))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_442])]) ).
tff(f7583,plain,
( spl272_439
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK41(X0,X1)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_439])]) ).
tff(f7586,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK41(X0,X1)))))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_439 ),
inference(forward_demodulation,[],[f7584,f3853]) ).
tff(f7584,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK41(X0,X1)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_439 ),
inference(avatar_component_clause,[],[f7583]) ).
tff(f7595,plain,
spl272_441,
inference(avatar_split_clause,[],[f3546,f7593]) ).
tff(f3546,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK65(X0,X1)))))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ),
inference(forward_demodulation,[],[f2784,f848]) ).
tff(f2784,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK65(X0,X1)),1)))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f1815]) ).
tff(f7590,plain,
spl272_440,
inference(avatar_split_clause,[],[f3539,f7588]) ).
tff(f3539,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'nat$'($sum(1,'fun_app$a'('of_nat$',sK61(X0,X1)))))
| sP3(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) ),
inference(forward_demodulation,[],[f2772,f848]) ).
tff(f2772,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP3(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'($sum('fun_app$a'('of_nat$',sK61(X0,X1)),1)))
| ~ 'fun_app$n'(X1,'nat$'(0)) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f7585,plain,
spl272_439,
inference(avatar_split_clause,[],[f3479,f7583]) ).
tff(f3479,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK41(X0,X1)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(forward_demodulation,[],[f2466,f848]) ).
tff(f2466,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK41(X0,X1)),1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1613]) ).
tff(f7581,plain,
spl272_438,
inference(avatar_split_clause,[],[f3347,f7579]) ).
tff(f7579,plain,
( spl272_438
<=> ! [X2: $int,X1: 'Int_num_fun$',X3: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ $less(sK155(X1),sK154(X1))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_438])]) ).
tff(f3347,plain,
! [X2: $int,X3: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| ~ $less(sK155(X1),sK154(X1))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3104]) ).
tff(f3104,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'fun_app$v'(X1,X3))
| ~ $less(sK155(X1),sK154(X1))
| $less(X3,X2)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2012]) ).
tff(f7577,plain,
spl272_437,
inference(avatar_split_clause,[],[f3345,f7575]) ).
tff(f7575,plain,
( spl272_437
<=> ! [X2: $int,X1: 'Int_enat_fun$',X3: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ $less(sK153(X1),sK152(X1))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_437])]) ).
tff(f3345,plain,
! [X2: $int,X3: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| ~ $less(sK153(X1),sK152(X1))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3102]) ).
tff(f3102,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'fun_app$y'(X1,X3))
| ~ $less(sK153(X1),sK152(X1))
| $less(X3,X2)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2010]) ).
tff(f7573,plain,
spl272_436,
inference(avatar_split_clause,[],[f3343,f7571]) ).
tff(f7571,plain,
( spl272_436
<=> ! [X2: $int,X1: 'Int_num_fun$',X3: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| $less(sK150(X1),sK151(X1))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_436])]) ).
tff(f3343,plain,
! [X2: $int,X3: $int,X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X1,X2)),'fun_app$v'(X1,X3))
| $less(sK150(X1),sK151(X1))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3100]) ).
tff(f3100,plain,
! [X2: $int,X3: $int,X0: 'Num$',X1: 'Int_num_fun$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'fun_app$v'(X1,X3))
| $less(sK150(X1),sK151(X1))
| ~ $less(X2,X3)
| ( 'fun_app$v'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2008]) ).
tff(f7569,plain,
spl272_435,
inference(avatar_split_clause,[],[f3341,f7567]) ).
tff(f7567,plain,
( spl272_435
<=> ! [X2: $int,X1: 'Int_enat_fun$',X3: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| $less(sK148(X1),sK149(X1))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_435])]) ).
tff(f3341,plain,
! [X2: $int,X3: $int,X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X1,X2)),'fun_app$y'(X1,X3))
| $less(sK148(X1),sK149(X1))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3098]) ).
tff(f3098,plain,
! [X2: $int,X3: $int,X0: 'Enat$',X1: 'Int_enat_fun$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),'fun_app$y'(X1,X3))
| $less(sK148(X1),sK149(X1))
| ~ $less(X2,X3)
| ( 'fun_app$y'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2006]) ).
tff(f7565,plain,
spl272_434,
inference(avatar_split_clause,[],[f3333,f7563]) ).
tff(f7563,plain,
( spl272_434
<=> ! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ $less(sK133(X2),sK132(X2))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_434])]) ).
tff(f3333,plain,
! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| ~ $less(sK133(X2),sK132(X2))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3082]) ).
tff(f3082,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$v'(X2,X0)),X3)
| ~ $less(sK133(X2),sK132(X2))
| ( 'fun_app$v'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1990]) ).
tff(f7561,plain,
spl272_433,
inference(avatar_split_clause,[],[f3331,f7559]) ).
tff(f7559,plain,
( spl272_433
<=> ! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ $less(sK131(X2),sK130(X2))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_433])]) ).
tff(f3331,plain,
! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| ~ $less(sK131(X2),sK130(X2))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3080]) ).
tff(f3080,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$y'(X2,X0)),X3)
| ~ $less(sK131(X2),sK130(X2))
| ( 'fun_app$y'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1988]) ).
tff(f7557,plain,
spl272_432,
inference(avatar_split_clause,[],[f3325,f7555]) ).
tff(f7555,plain,
( spl272_432
<=> ! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| $less(sK116(X2),sK117(X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_432])]) ).
tff(f3325,plain,
! [X2: 'Int_num_fun$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),'fun_app$v'(X2,X1))
| $less(sK116(X2),sK117(X2))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3066]) ).
tff(f3066,plain,
! [X2: 'Int_num_fun$',X3: 'Num$',X0: $int,X1: $int] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$v'(X2,X0)),X3)
| $less(sK116(X2),sK117(X2))
| ( 'fun_app$v'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1974]) ).
tff(f7553,plain,
( spl272_431
| ~ spl272_58
| ~ spl272_380 ),
inference(avatar_split_clause,[],[f7197,f6898,f3865,f7551]) ).
tff(f7551,plain,
( spl272_431
<=> ! [X0: $real] : $less(X0,$sum(X0,4.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_431])]) ).
tff(f6898,plain,
( spl272_380
<=> ! [X0: $real] : $less(X0,$sum(4.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_380])]) ).
tff(f7197,plain,
( ! [X0: $real] : $less(X0,$sum(X0,4.0))
| ~ spl272_58
| ~ spl272_380 ),
inference(superposition,[],[f6899,f3866]) ).
tff(f6899,plain,
( ! [X0: $real] : $less(X0,$sum(4.0,X0))
| ~ spl272_380 ),
inference(avatar_component_clause,[],[f6898]) ).
tff(f7549,plain,
spl272_430,
inference(avatar_split_clause,[],[f3323,f7547]) ).
tff(f7547,plain,
( spl272_430
<=> ! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| $less(sK114(X2),sK115(X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_430])]) ).
tff(f3323,plain,
! [X2: 'Int_enat_fun$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),'fun_app$y'(X2,X1))
| $less(sK114(X2),sK115(X2))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3064]) ).
tff(f3064,plain,
! [X2: 'Int_enat_fun$',X3: 'Enat$',X0: $int,X1: $int] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$y'(X2,X0)),X3)
| $less(sK114(X2),sK115(X2))
| ( 'fun_app$y'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1972]) ).
tff(f7545,plain,
spl272_429,
inference(avatar_split_clause,[],[f2947,f7543]) ).
tff(f7543,plain,
( spl272_429
<=> ! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
| ~ $less(sK101(X0),sK100(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_429])]) ).
tff(f2947,plain,
! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| ~ 'fun_app$q'('fun_app$r'(X0,sK98(X0)),sK99(X0))
| ~ $less(sK101(X0),sK100(X0)) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f7541,plain,
spl272_428,
inference(avatar_split_clause,[],[f2945,f7539]) ).
tff(f7539,plain,
( spl272_428
<=> ! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0))
| ~ $less(sK101(X0),sK100(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_428])]) ).
tff(f2945,plain,
! [X2: $int,X0: 'Int_int_bool_fun_fun$',X1: $int] :
( 'fun_app$q'('fun_app$r'(X0,X1),X2)
| 'fun_app$q'('fun_app$r'(X0,sK99(X0)),sK98(X0))
| ~ $less(sK101(X0),sK100(X0)) ),
inference(cnf_transformation,[],[f1905]) ).
tff(f7537,plain,
spl272_427,
inference(avatar_split_clause,[],[f2943,f7535]) ).
tff(f7535,plain,
( spl272_427
<=> ! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
| ~ $less(sK97(X0),sK96(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_427])]) ).
tff(f2943,plain,
! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| ~ 'fun_app$'('fun_app$s'(X0,sK94(X0)),sK95(X0))
| ~ $less(sK97(X0),sK96(X0)) ),
inference(cnf_transformation,[],[f1902]) ).
tff(f7533,plain,
spl272_426,
inference(avatar_split_clause,[],[f2941,f7531]) ).
tff(f7531,plain,
( spl272_426
<=> ! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0))
| ~ $less(sK97(X0),sK96(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_426])]) ).
tff(f2941,plain,
! [X2: $real,X0: 'Real_real_bool_fun_fun$',X1: $real] :
( 'fun_app$'('fun_app$s'(X0,X1),X2)
| 'fun_app$'('fun_app$s'(X0,sK95(X0)),sK94(X0))
| ~ $less(sK97(X0),sK96(X0)) ),
inference(cnf_transformation,[],[f1902]) ).
tff(f7529,plain,
spl272_425,
inference(avatar_split_clause,[],[f2663,f7527]) ).
tff(f7527,plain,
( spl272_425
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_425])]) ).
tff(f2663,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f1719,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) )
& ( ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
& 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) )
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ) ),
inference(flattening,[],[f1718]) ).
tff(f1718,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) )
& ( ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
& 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) )
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ) ),
inference(nnf_transformation,[],[f627]) ).
tff(f627,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1))
<=> ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
& 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom625) ).
tff(f7525,plain,
spl272_424,
inference(avatar_split_clause,[],[f2525,f7523]) ).
tff(f7523,plain,
( spl272_424
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,0)
| $less('fun_app$a'('power$a'(X1),'nat$'(2)),'fun_app$a'('power$a'(X0),'nat$'(2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_424])]) ).
tff(f2525,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,0)
| $less('fun_app$a'('power$a'(X1),'nat$'(2)),'fun_app$a'('power$a'(X0),'nat$'(2))) ),
inference(cnf_transformation,[],[f1171]) ).
tff(f1171,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,0)
| $less('fun_app$a'('power$a'(X1),'nat$'(2)),'fun_app$a'('power$a'(X0),'nat$'(2))) ),
inference(flattening,[],[f1170]) ).
tff(f1170,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| $less(X1,0)
| $less('fun_app$a'('power$a'(X1),'nat$'(2)),'fun_app$a'('power$a'(X0),'nat$'(2))) ),
inference(ennf_transformation,[],[f730]) ).
tff(f730,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less('fun_app$a'('power$a'(X1),'nat$'(2)),'fun_app$a'('power$a'(X0),'nat$'(2))) )
=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f337]) ).
tff(f337,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(0,X1)
& $lesseq('fun_app$a'('power$a'(X0),'nat$'(2)),'fun_app$a'('power$a'(X1),'nat$'(2))) )
=> $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom335) ).
tff(f7521,plain,
spl272_423,
inference(avatar_split_clause,[],[f2524,f7519]) ).
tff(f7519,plain,
( spl272_423
<=> ! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less(X1,0.0)
| $less('fun_app$m'('power$c'(X1),'nat$'(2)),'fun_app$m'('power$c'(X0),'nat$'(2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_423])]) ).
tff(f2524,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less(X1,0.0)
| $less('fun_app$m'('power$c'(X1),'nat$'(2)),'fun_app$m'('power$c'(X0),'nat$'(2))) ),
inference(cnf_transformation,[],[f1169]) ).
tff(f1169,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less(X1,0.0)
| $less('fun_app$m'('power$c'(X1),'nat$'(2)),'fun_app$m'('power$c'(X0),'nat$'(2))) ),
inference(flattening,[],[f1168]) ).
tff(f1168,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
| $less(X1,0.0)
| $less('fun_app$m'('power$c'(X1),'nat$'(2)),'fun_app$m'('power$c'(X0),'nat$'(2))) ),
inference(ennf_transformation,[],[f729]) ).
tff(f729,plain,
! [X0: $real,X1: $real] :
( ( ~ $less(X1,0.0)
& ~ $less('fun_app$m'('power$c'(X1),'nat$'(2)),'fun_app$m'('power$c'(X0),'nat$'(2))) )
=> ~ $less(X1,X0) ),
inference(theory_normalization,[],[f338]) ).
tff(f338,axiom,
! [X0: $real,X1: $real] :
( ( $lesseq(0.0,X1)
& $lesseq('fun_app$m'('power$c'(X0),'nat$'(2)),'fun_app$m'('power$c'(X1),'nat$'(2))) )
=> $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom336) ).
tff(f7517,plain,
spl272_422,
inference(avatar_split_clause,[],[f2356,f7515]) ).
tff(f7515,plain,
( spl272_422
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$c'('times$a'('fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) = 'fun_app$c'('bit0$','fun_app$c'('bit0$','fun_app$c'('times$a'(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_422])]) ).
tff(f2356,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$c'('times$a'('fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) = 'fun_app$c'('bit0$','fun_app$c'('bit0$','fun_app$c'('times$a'(X0),X1))) ),
inference(cnf_transformation,[],[f609]) ).
tff(f609,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$c'('times$a'('fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) = 'fun_app$c'('bit0$','fun_app$c'('bit0$','fun_app$c'('times$a'(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom607) ).
tff(f7513,plain,
spl272_421,
inference(avatar_split_clause,[],[f2236,f7511]) ).
tff(f7511,plain,
( spl272_421
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_421])]) ).
tff(f2236,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X0)),
inference(cnf_transformation,[],[f668]) ).
tff(f668,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0))),'fun_app$a'('of_nat$',X0)),
inference(theory_normalization,[],[f579]) ).
tff(f579,axiom,
! [X0: 'Nat$'] : $lesseq('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom577) ).
tff(f7509,plain,
( spl272_420
| ~ spl272_50
| ~ spl272_380 ),
inference(avatar_split_clause,[],[f7194,f6898,f3821,f7507]) ).
tff(f7194,plain,
( ! [X0: $real] : ~ $less($sum(4.0,X0),X0)
| ~ spl272_50
| ~ spl272_380 ),
inference(resolution,[],[f6899,f3822]) ).
tff(f7397,plain,
( spl272_419
| ~ spl272_55
| ~ spl272_406 ),
inference(avatar_split_clause,[],[f7125,f7122,f3851,f7395]) ).
tff(f7395,plain,
( spl272_419
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK44(X0)))))
| 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_419])]) ).
tff(f7122,plain,
( spl272_406
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK44(X0)))))
| 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_406])]) ).
tff(f7125,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK44(X0)))))
| 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_406 ),
inference(forward_demodulation,[],[f7123,f3853]) ).
tff(f7123,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK44(X0)))))
| 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_406 ),
inference(avatar_component_clause,[],[f7122]) ).
tff(f7393,plain,
( spl272_418
| ~ spl272_56
| ~ spl272_378 ),
inference(avatar_split_clause,[],[f7065,f6684,f3857,f7391]) ).
tff(f7391,plain,
( spl272_418
<=> ! [X0: $int] : $less(X0,$sum(X0,4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_418])]) ).
tff(f6684,plain,
( spl272_378
<=> ! [X0: $int] : $less(X0,$sum(4,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_378])]) ).
tff(f7065,plain,
( ! [X0: $int] : $less(X0,$sum(X0,4))
| ~ spl272_56
| ~ spl272_378 ),
inference(superposition,[],[f6685,f3858]) ).
tff(f6685,plain,
( ! [X0: $int] : $less(X0,$sum(4,X0))
| ~ spl272_378 ),
inference(avatar_component_clause,[],[f6684]) ).
tff(f7389,plain,
( spl272_417
| ~ spl272_55
| ~ spl272_405 ),
inference(avatar_split_clause,[],[f7112,f7109,f3851,f7387]) ).
tff(f7387,plain,
( spl272_417
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK43(X0)))))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_417])]) ).
tff(f7109,plain,
( spl272_405
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK43(X0)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_405])]) ).
tff(f7112,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK43(X0)))))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_405 ),
inference(forward_demodulation,[],[f7110,f3853]) ).
tff(f7110,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK43(X0)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_405 ),
inference(avatar_component_clause,[],[f7109]) ).
tff(f7318,plain,
( spl272_416
| ~ spl272_55
| ~ spl272_400 ),
inference(avatar_split_clause,[],[f7091,f7088,f3851,f7316]) ).
tff(f7316,plain,
( spl272_416
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK31(X0)))))
| ~ 'fun_app$n'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_416])]) ).
tff(f7088,plain,
( spl272_400
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK31(X0)))))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_400])]) ).
tff(f7091,plain,
( ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK31(X0)))))
| ~ 'fun_app$n'(X0,X2) )
| ~ spl272_55
| ~ spl272_400 ),
inference(forward_demodulation,[],[f7089,f3853]) ).
tff(f7089,plain,
( ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK31(X0)))))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_400 ),
inference(avatar_component_clause,[],[f7088]) ).
tff(f7304,plain,
( spl272_415
| ~ spl272_55
| ~ spl272_398 ),
inference(avatar_split_clause,[],[f7082,f7079,f3851,f7302]) ).
tff(f7302,plain,
( spl272_415
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_415])]) ).
tff(f7079,plain,
( spl272_398
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_398])]) ).
tff(f7082,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ sP5(X1,X0) )
| ~ spl272_55
| ~ spl272_398 ),
inference(forward_demodulation,[],[f7080,f3853]) ).
tff(f7080,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) )
| ~ spl272_398 ),
inference(avatar_component_clause,[],[f7079]) ).
tff(f7300,plain,
( spl272_414
| ~ spl272_55
| ~ spl272_397 ),
inference(avatar_split_clause,[],[f7077,f7074,f3851,f7298]) ).
tff(f7298,plain,
( spl272_414
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| sP3(X1,X0)
| $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_414])]) ).
tff(f7074,plain,
( spl272_397
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP3(X1,X0)
| $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X1,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_397])]) ).
tff(f7077,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| sP3(X1,X0)
| $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0)) )
| ~ spl272_55
| ~ spl272_397 ),
inference(forward_demodulation,[],[f7075,f3853]) ).
tff(f7075,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP3(X1,X0)
| $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X1,'nat$'(0)) )
| ~ spl272_397 ),
inference(avatar_component_clause,[],[f7074]) ).
tff(f7292,plain,
( spl272_413
| ~ spl272_51
| ~ spl272_378 ),
inference(avatar_split_clause,[],[f7061,f6684,f3825,f7290]) ).
tff(f7061,plain,
( ! [X0: $int] : ~ $less($sum(4,X0),X0)
| ~ spl272_51
| ~ spl272_378 ),
inference(resolution,[],[f6685,f3826]) ).
tff(f7232,plain,
( spl272_412
| ~ spl272_55
| ~ spl272_389 ),
inference(avatar_split_clause,[],[f7033,f7030,f3851,f7230]) ).
tff(f7230,plain,
( spl272_412
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1)))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_412])]) ).
tff(f7030,plain,
( spl272_389
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_389])]) ).
tff(f7033,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1)))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_389 ),
inference(forward_demodulation,[],[f7031,f3853]) ).
tff(f7031,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_389 ),
inference(avatar_component_clause,[],[f7030]) ).
tff(f7228,plain,
( spl272_411
| ~ spl272_55
| ~ spl272_388 ),
inference(avatar_split_clause,[],[f7028,f7025,f3851,f7226]) ).
tff(f7226,plain,
( spl272_411
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_411])]) ).
tff(f7025,plain,
( spl272_388
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_388])]) ).
tff(f7028,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_388 ),
inference(forward_demodulation,[],[f7026,f3853]) ).
tff(f7026,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_388 ),
inference(avatar_component_clause,[],[f7025]) ).
tff(f7141,plain,
( spl272_409
| spl272_409
| spl272_410 ),
inference(avatar_split_clause,[],[f3532,f7138,f7135,f7135]) ).
tff(f7135,plain,
( spl272_409
<=> ! [X0: 'Nat$'] : ( 1 != 'fun_app$a'('of_nat$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_409])]) ).
tff(f7138,plain,
( spl272_410
<=> ( 1 = 'fun_app$p'('times$b'(1),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_410])]) ).
tff(f3532,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$p'('times$b'(1),1) )
| ( 1 != 'fun_app$a'('of_nat$',X1) )
| ( 1 != 'fun_app$a'('of_nat$',X0) ) ),
inference(inner_rewriting,[],[f3531]) ).
tff(f3531,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),1) )
| ( 1 != 'fun_app$a'('of_nat$',X1) )
| ( 1 != 'fun_app$a'('of_nat$',X0) ) ),
inference(inner_rewriting,[],[f3413]) ).
tff(f3413,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 1 != 'fun_app$a'('of_nat$',X1) )
| ( 1 != 'fun_app$a'('of_nat$',X0) ) ),
inference(evaluation,[],[f2750]) ).
tff(f2750,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum(0,1) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X1) != $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) ) ),
inference(cnf_transformation,[],[f1774]) ).
tff(f1774,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $sum(0,1) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X1) != $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) ) )
& ( ( ( 'fun_app$a'('of_nat$',X1) = $sum(0,1) )
& ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) ) )
| ( $sum(0,1) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(flattening,[],[f1773]) ).
tff(f1773,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $sum(0,1) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X1) != $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) ) )
& ( ( ( 'fun_app$a'('of_nat$',X1) = $sum(0,1) )
& ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) ) )
| ( $sum(0,1) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
inference(nnf_transformation,[],[f395]) ).
tff(f395,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $sum(0,1) = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
<=> ( ( 'fun_app$a'('of_nat$',X1) = $sum(0,1) )
& ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom393) ).
tff(f7133,plain,
spl272_408,
inference(avatar_split_clause,[],[f3509,f7131]) ).
tff(f7131,plain,
( spl272_408
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_408])]) ).
tff(f3509,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum(1,'fun_app$a'('of_nat$',X1)))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(forward_demodulation,[],[f2715,f848]) ).
tff(f2715,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(cnf_transformation,[],[f1751]) ).
tff(f1751,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) )
& ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(flattening,[],[f1750]) ).
tff(f1750,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
| ( ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) )
& ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
inference(nnf_transformation,[],[f562]) ).
tff(f562,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1))
<=> ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).
tff(f7129,plain,
spl272_407,
inference(avatar_split_clause,[],[f3495,f7127]) ).
tff(f7127,plain,
( spl272_407
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK55(X0)),$sum(1,'fun_app$a'('of_nat$',X3)))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_407])]) ).
tff(f3495,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK55(X0)),$sum(1,'fun_app$a'('of_nat$',X3)))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3) ),
inference(forward_demodulation,[],[f2539,f848]) ).
tff(f2539,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK55(X0)),$sum('fun_app$a'('of_nat$',X3),1)) ),
inference(cnf_transformation,[],[f1644]) ).
tff(f1644,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ~ 'fun_app$n'(X0,sK55(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK55(X0)),$sum('fun_app$a'('of_nat$',X3),1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55])],[f1182,f1643]) ).
tff(f1643,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X3),1)) ) )
=> ( ~ 'fun_app$n'(X0,sK55(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',sK55(X0)),$sum('fun_app$a'('of_nat$',X3),1)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1182,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X3),1)) ) ) ),
inference(ennf_transformation,[],[f734]) ).
tff(f734,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X3),1))
=> 'fun_app$n'(X0,X3) )
=> 'fun_app$n'(X0,X2) )
=> 'fun_app$n'(X0,X1) ),
inference(theory_normalization,[],[f45]) ).
tff(f45,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( $lesseq($sum('fun_app$a'('of_nat$',X3),1),'fun_app$a'('of_nat$',X2))
=> 'fun_app$n'(X0,X3) )
=> 'fun_app$n'(X0,X2) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
tff(f7124,plain,
spl272_406,
inference(avatar_split_clause,[],[f3481,f7122]) ).
tff(f3481,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK44(X0)))))
| 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(forward_demodulation,[],[f2481,f848]) ).
tff(f2481,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK44(X0)),1)))
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1619]) ).
tff(f1619,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK44(X0)),1)))
& 'fun_app$n'(X0,sK44(X0)) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1116,f1618]) ).
tff(f1618,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& 'fun_app$n'(X0,X2) )
=> ( ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK44(X0)),1)))
& 'fun_app$n'(X0,sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1116,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& 'fun_app$n'(X0,X2) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(flattening,[],[f1115]) ).
tff(f1115,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& 'fun_app$n'(X0,X2) )
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f171]) ).
tff(f171,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X0,X2)
=> 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1))) )
& 'fun_app$n'(X0,'nat$'(0)) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom169) ).
tff(f7111,plain,
spl272_405,
inference(avatar_split_clause,[],[f3480,f7109]) ).
tff(f3480,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK43(X0)))))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(forward_demodulation,[],[f2470,f848]) ).
tff(f2470,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK43(X0)),1)))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1617]) ).
tff(f1617,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ( ~ 'fun_app$n'(X0,sK43(X0))
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK43(X0)),1))) )
| ~ 'fun_app$n'(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f1100,f1616]) ).
tff(f1616,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1))) )
=> ( ~ 'fun_app$n'(X0,sK43(X0))
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK43(X0)),1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1100,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1))) )
| ~ 'fun_app$n'(X0,X1) ),
inference(flattening,[],[f1099]) ).
tff(f1099,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1))) )
| ~ 'fun_app$n'(X0,X1) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
=> 'fun_app$n'(X0,X2) )
& 'fun_app$n'(X0,X1) )
=> 'fun_app$n'(X0,'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom171) ).
tff(f7107,plain,
spl272_404,
inference(avatar_split_clause,[],[f3478,f7105]) ).
tff(f7105,plain,
( spl272_404
<=> ! [X0: $int,X1: 'Nat$'] :
( $less('fun_app$a'('power$a'(X0),'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',X1))))),0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_404])]) ).
tff(f3478,plain,
! [X0: $int,X1: 'Nat$'] :
( $less('fun_app$a'('power$a'(X0),'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',X1))))),0)
| ~ $less(X0,0) ),
inference(forward_demodulation,[],[f2451,f848]) ).
tff(f2451,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less(X0,0)
| $less('fun_app$a'('power$a'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0) ),
inference(cnf_transformation,[],[f1082]) ).
tff(f1082,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less(X0,0)
| $less('fun_app$a'('power$a'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0) ),
inference(ennf_transformation,[],[f712]) ).
tff(f712,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0)
=> ~ $less(X0,0) ),
inference(theory_normalization,[],[f342]) ).
tff(f342,axiom,
! [X0: $int,X1: 'Nat$'] :
( $lesseq(0,'fun_app$a'('power$a'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))))
=> $lesseq(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom340) ).
tff(f7103,plain,
spl272_403,
inference(avatar_split_clause,[],[f3477,f7101]) ).
tff(f7101,plain,
( spl272_403
<=> ! [X0: $real,X1: 'Nat$'] :
( $less('fun_app$m'('power$c'(X0),'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',X1))))),0.0)
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_403])]) ).
tff(f3477,plain,
! [X0: $real,X1: 'Nat$'] :
( $less('fun_app$m'('power$c'(X0),'nat$'($sum(1,$product(2,'fun_app$a'('of_nat$',X1))))),0.0)
| ~ $less(X0,0.0) ),
inference(forward_demodulation,[],[f2450,f848]) ).
tff(f2450,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less(X0,0.0)
| $less('fun_app$m'('power$c'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0.0) ),
inference(cnf_transformation,[],[f1081]) ).
tff(f1081,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less(X0,0.0)
| $less('fun_app$m'('power$c'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0.0) ),
inference(ennf_transformation,[],[f711]) ).
tff(f711,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))),0.0)
=> ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f343]) ).
tff(f343,axiom,
! [X0: $real,X1: 'Nat$'] :
( $lesseq(0.0,'fun_app$m'('power$c'(X0),'nat$'($sum($product(2,'fun_app$a'('of_nat$',X1)),1))))
=> $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
tff(f7099,plain,
spl272_402,
inference(avatar_split_clause,[],[f3467,f7097]) ).
tff(f7097,plain,
( spl272_402
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_402])]) ).
tff(f3467,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum(1,'fun_app$a'('of_nat$',X1)),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2436,f848]) ).
tff(f2436,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1068]) ).
tff(f1068,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f705]) ).
tff(f705,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
=> ~ $less($sum('fun_app$a'('of_nat$',X1),1),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f50]) ).
tff(f50,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> $lesseq('fun_app$a'('of_nat$',X0),$sum('fun_app$a'('of_nat$',X1),1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
tff(f7095,plain,
spl272_401,
inference(avatar_split_clause,[],[f3462,f7093]) ).
tff(f7093,plain,
( spl272_401
<=> ! [X0: $real,X1: 'Nat$'] :
( ( 'fun_app$m'('power$c'(sK38(X0,X1)),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) = X0 )
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_401])]) ).
tff(f3462,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 'fun_app$m'('power$c'(sK38(X0,X1)),'nat$'($sum(1,'fun_app$a'('of_nat$',X1)))) = X0 )
| ~ $less(0.0,X0) ),
inference(forward_demodulation,[],[f2384,f848]) ).
tff(f2384,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 'fun_app$m'('power$c'(sK38(X0,X1)),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1599]) ).
tff(f1599,plain,
! [X0: $real,X1: 'Nat$'] :
( ( ( 'fun_app$m'('power$c'(sK38(X0,X1)),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
& $less(0.0,sK38(X0,X1)) )
| ~ $less(0.0,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f1021,f1598]) ).
tff(f1598,plain,
! [X0: $real,X1: 'Nat$'] :
( ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
& $less(0.0,X2) )
=> ( ( 'fun_app$m'('power$c'(sK38(X0,X1)),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
& $less(0.0,sK38(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1021,plain,
! [X0: $real,X1: 'Nat$'] :
( ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
& $less(0.0,X2) )
| ~ $less(0.0,X0) ),
inference(ennf_transformation,[],[f634]) ).
tff(f634,axiom,
! [X0: $real,X1: 'Nat$'] :
( $less(0.0,X0)
=> ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),'nat$'($sum('fun_app$a'('of_nat$',X1),1))) = X0 )
& $less(0.0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom632) ).
tff(f7090,plain,
spl272_400,
inference(avatar_split_clause,[],[f3446,f7088]) ).
tff(f3446,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK31(X0)))))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(forward_demodulation,[],[f2256,f848]) ).
tff(f2256,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK31(X0)),1)))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1549]) ).
tff(f1549,plain,
! [X0: 'Nat_bool_fun$'] :
( ( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK31(X0)),1)))
& ~ 'fun_app$n'(X0,sK31(X0)) )
| ! [X2: 'Nat$'] : ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f1547,f1548]) ).
tff(f1548,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X1),1)))
& ~ 'fun_app$n'(X0,X1) )
=> ( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK31(X0)),1)))
& ~ 'fun_app$n'(X0,sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1547,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X1),1)))
& ~ 'fun_app$n'(X0,X1) )
| ! [X2: 'Nat$'] : ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(rectify,[],[f1008]) ).
tff(f1008,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ~ 'fun_app$n'(X0,X2) )
| ! [X1: 'Nat$'] : ~ 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(flattening,[],[f1007]) ).
tff(f1007,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ~ 'fun_app$n'(X0,X2) )
| ! [X1: 'Nat$'] : ~ 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f900]) ).
tff(f900,plain,
! [X0: 'Nat_bool_fun$'] :
( ( ? [X1: 'Nat$'] : 'fun_app$n'(X0,X1)
& ~ 'fun_app$n'(X0,'nat$'(0)) )
=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& ~ 'fun_app$n'(X0,X2) ) ),
inference(rectify,[],[f602]) ).
tff(f602,axiom,
! [X0: 'Nat_bool_fun$'] :
( ( ? [X1: 'Nat$'] : 'fun_app$n'(X0,X1)
& ~ 'fun_app$n'(X0,'nat$'(0)) )
=> ? [X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X1),1)))
& ~ 'fun_app$n'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom600) ).
tff(f7086,plain,
spl272_399,
inference(avatar_split_clause,[],[f2815,f7084]) ).
tff(f7084,plain,
( spl272_399
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK66(X0))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_399])]) ).
tff(f2815,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK66(X0))
| $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',sK67(X0,X2)))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1823]) ).
tff(f7081,plain,
spl272_398,
inference(avatar_split_clause,[],[f2783,f7079]) ).
tff(f2783,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( $less('fun_app$a'('of_nat$',sK65(X0,X1)),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'(X1,'nat$'(0))
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f1815]) ).
tff(f7076,plain,
spl272_397,
inference(avatar_split_clause,[],[f2771,f7074]) ).
tff(f2771,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP3(X1,X0)
| $less('fun_app$a'('of_nat$',sK61(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X1,'nat$'(0)) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f7072,plain,
spl272_396,
inference(avatar_split_clause,[],[f2706,f7070]) ).
tff(f7070,plain,
( spl272_396
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_396])]) ).
tff(f2706,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ),
inference(cnf_transformation,[],[f1743]) ).
tff(f1743,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) )
& ( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
inference(nnf_transformation,[],[f756]) ).
tff(f756,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
<=> ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ),
inference(theory_normalization,[],[f53]) ).
tff(f53,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
<=> $lesseq('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
tff(f7057,plain,
spl272_395,
inference(avatar_split_clause,[],[f2705,f7055]) ).
tff(f7055,plain,
( spl272_395
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_395])]) ).
tff(f2705,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ),
inference(cnf_transformation,[],[f1743]) ).
tff(f7053,plain,
spl272_394,
inference(avatar_split_clause,[],[f2701,f7051]) ).
tff(f7051,plain,
( spl272_394
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_394])]) ).
tff(f2701,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
inference(cnf_transformation,[],[f1741]) ).
tff(f1741,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) )
& ( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ) ),
inference(nnf_transformation,[],[f755]) ).
tff(f755,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
<=> ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f115]) ).
tff(f115,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
<=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom113) ).
tff(f7049,plain,
spl272_393,
inference(avatar_split_clause,[],[f2700,f7047]) ).
tff(f7047,plain,
( spl272_393
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_393])]) ).
tff(f2700,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ),
inference(cnf_transformation,[],[f1740]) ).
tff(f1740,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) )
& ( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
inference(nnf_transformation,[],[f386]) ).
tff(f386,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
<=> $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom384) ).
tff(f7045,plain,
spl272_392,
inference(avatar_split_clause,[],[f2699,f7043]) ).
tff(f7043,plain,
( spl272_392
<=> ! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_392])]) ).
tff(f2699,plain,
! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ),
inference(cnf_transformation,[],[f1740]) ).
tff(f7041,plain,
spl272_391,
inference(avatar_split_clause,[],[f2495,f7039]) ).
tff(f7039,plain,
( spl272_391
<=> ! [X0: 'Nat$',X1: $real] :
( ( 'fun_app$m'('power$c'(sK49(X0,X1)),X0) = X1 )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_391])]) ).
tff(f2495,plain,
! [X0: 'Nat$',X1: $real] :
( ( 'fun_app$m'('power$c'(sK49(X0,X1)),X0) = X1 )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f7037,plain,
spl272_390,
inference(avatar_split_clause,[],[f2493,f7035]) ).
tff(f7035,plain,
( spl272_390
<=> ! [X0: 'Nat$',X1: $real] :
( ( 'fun_app$m'('power$c'(sK48(X0,X1)),X0) = X1 )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_390])]) ).
tff(f2493,plain,
! [X0: 'Nat$',X1: $real] :
( ( 'fun_app$m'('power$c'(sK48(X0,X1)),X0) = X1 )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1630]) ).
tff(f1630,plain,
! [X0: 'Nat$',X1: $real] :
( ( ( 'fun_app$m'('power$c'(sK48(X0,X1)),X0) = X1 )
& $less(0.0,sK48(X0,X1)) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f1124,f1629]) ).
tff(f1629,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
=> ( ( 'fun_app$m'('power$c'(sK48(X0,X1)),X0) = X1 )
& $less(0.0,sK48(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1124,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(flattening,[],[f1123]) ).
tff(f1123,plain,
! [X0: 'Nat$',X1: $real] :
( ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f636]) ).
tff(f636,axiom,
! [X0: 'Nat$',X1: $real] :
( ( $less(0.0,X1)
& $less(0,'fun_app$a'('of_nat$',X0)) )
=> ? [X2: $real] :
( ( 'fun_app$m'('power$c'(X2),X0) = X1 )
& $less(0.0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).
tff(f7032,plain,
spl272_389,
inference(avatar_split_clause,[],[f2467,f7030]) ).
tff(f2467,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',sK42(X0,X1)))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1615]) ).
tff(f7027,plain,
spl272_388,
inference(avatar_split_clause,[],[f2464,f7025]) ).
tff(f2464,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK41(X0,X1)),'fun_app$a'('of_nat$',X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1613]) ).
tff(f7023,plain,
spl272_387,
inference(avatar_split_clause,[],[f2458,f7021]) ).
tff(f7021,plain,
( spl272_387
<=> ! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| $less(0,'fun_app$a'('of_nat$',sK40(X0,X1)))
| $less(X1,0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_387])]) ).
tff(f2458,plain,
! [X0: $real,X1: $real] :
( ( 0.0 = X0 )
| $less(0,'fun_app$a'('of_nat$',sK40(X0,X1)))
| $less(X1,0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1610]) ).
tff(f7019,plain,
spl272_386,
inference(avatar_split_clause,[],[f2442,f7017]) ).
tff(f7017,plain,
( spl272_386
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_386])]) ).
tff(f2442,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
inference(cnf_transformation,[],[f1073]) ).
tff(f1073,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
inference(ennf_transformation,[],[f429]) ).
tff(f429,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom427) ).
tff(f7001,plain,
spl272_385,
inference(avatar_split_clause,[],[f2434,f6999]) ).
tff(f6999,plain,
( spl272_385
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_385])]) ).
tff(f2434,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1066]) ).
tff(f1066,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f703]) ).
tff(f703,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
inference(theory_normalization,[],[f183]) ).
tff(f183,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).
tff(f6997,plain,
spl272_384,
inference(avatar_split_clause,[],[f2428,f6995]) ).
tff(f6995,plain,
( spl272_384
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_384])]) ).
tff(f2428,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1060]) ).
tff(f1060,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f426]) ).
tff(f426,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> 'fun_app$g'('fun_app$h'('less$a','fun_app$l'('of_nat$c',X0)),'fun_app$l'('of_nat$c',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom424) ).
tff(f6993,plain,
spl272_383,
inference(avatar_split_clause,[],[f2355,f6991]) ).
tff(f6991,plain,
( spl272_383
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$d'('numeral$','fun_app$c'('pow$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_383])]) ).
tff(f2355,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$d'('numeral$','fun_app$c'('pow$'(X0),X1)) ),
inference(cnf_transformation,[],[f55]) ).
tff(f55,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$a'('power$a'('fun_app$d'('numeral$',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$d'('numeral$','fun_app$c'('pow$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom53) ).
tff(f6989,plain,
spl272_382,
inference(avatar_split_clause,[],[f2354,f6987]) ).
tff(f6987,plain,
( spl272_382
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$j'('numeral$b','fun_app$c'('pow$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_382])]) ).
tff(f2354,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$j'('numeral$b','fun_app$c'('pow$'(X0),X1)) ),
inference(cnf_transformation,[],[f57]) ).
tff(f57,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$m'('power$c'('fun_app$j'('numeral$b',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$j'('numeral$b','fun_app$c'('pow$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom55) ).
tff(f6985,plain,
spl272_381,
inference(avatar_split_clause,[],[f2353,f6983]) ).
tff(f6983,plain,
( spl272_381
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$i'('numeral$a','fun_app$c'('pow$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_381])]) ).
tff(f2353,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$i'('numeral$a','fun_app$c'('pow$'(X0),X1)) ),
inference(cnf_transformation,[],[f56]) ).
tff(f56,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$l'('power$b'('fun_app$i'('numeral$a',X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'fun_app$i'('numeral$a','fun_app$c'('pow$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom54) ).
tff(f6900,plain,
( spl272_380
| ~ spl272_109
| ~ spl272_337 ),
inference(avatar_split_clause,[],[f6454,f6238,f4112,f6898]) ).
tff(f6238,plain,
( spl272_337
<=> ! [X0: $real] : ~ $less($sum(3.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_337])]) ).
tff(f6454,plain,
( ! [X0: $real] : $less(X0,$sum(4.0,X0))
| ~ spl272_109
| ~ spl272_337 ),
inference(evaluation,[],[f6448]) ).
tff(f6448,plain,
( ! [X0: $real] : $less(X0,$sum(3.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_337 ),
inference(resolution,[],[f6239,f4113]) ).
tff(f6239,plain,
( ! [X0: $real] : ~ $less($sum(3.0,X0),X0)
| ~ spl272_337 ),
inference(avatar_component_clause,[],[f6238]) ).
tff(f6765,plain,
( spl272_379
| ~ spl272_58
| ~ spl272_337 ),
inference(avatar_split_clause,[],[f6452,f6238,f3865,f6763]) ).
tff(f6763,plain,
( spl272_379
<=> ! [X0: $real] : ~ $less($sum(X0,3.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_379])]) ).
tff(f6452,plain,
( ! [X0: $real] : ~ $less($sum(X0,3.0),X0)
| ~ spl272_58
| ~ spl272_337 ),
inference(superposition,[],[f6239,f3866]) ).
tff(f6686,plain,
( spl272_378
| ~ spl272_107
| ~ spl272_323 ),
inference(avatar_split_clause,[],[f6357,f6113,f4104,f6684]) ).
tff(f6113,plain,
( spl272_323
<=> ! [X0: $int] : ~ $less($sum(3,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_323])]) ).
tff(f6357,plain,
( ! [X0: $int] : $less(X0,$sum(4,X0))
| ~ spl272_107
| ~ spl272_323 ),
inference(evaluation,[],[f6345]) ).
tff(f6345,plain,
( ! [X0: $int] : $less(X0,$sum(3,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_323 ),
inference(resolution,[],[f6114,f4105]) ).
tff(f6114,plain,
( ! [X0: $int] : ~ $less($sum(3,X0),X0)
| ~ spl272_323 ),
inference(avatar_component_clause,[],[f6113]) ).
tff(f6569,plain,
( spl272_377
| ~ spl272_56
| ~ spl272_323 ),
inference(avatar_split_clause,[],[f6352,f6113,f3857,f6567]) ).
tff(f6567,plain,
( spl272_377
<=> ! [X0: $int] : ~ $less($sum(X0,3),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_377])]) ).
tff(f6352,plain,
( ! [X0: $int] : ~ $less($sum(X0,3),X0)
| ~ spl272_56
| ~ spl272_323 ),
inference(superposition,[],[f6114,f3858]) ).
tff(f6530,plain,
spl272_376,
inference(avatar_split_clause,[],[f3543,f6528]) ).
tff(f6528,plain,
( spl272_376
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP5(X0,X1)
| ~ 'fun_app$n'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_376])]) ).
tff(f3543,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP5(X0,X1)
| ~ 'fun_app$n'(X0,X2) ),
inference(forward_demodulation,[],[f2782,f848]) ).
tff(f2782,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP5(X0,X1)
| ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1810]) ).
tff(f1810,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP5(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ( 'fun_app$n'(X0,sK64(X0,X1))
& $less('fun_app$a'('of_nat$',sK64(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP5(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f1808,f1809]) ).
tff(f1809,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
=> ( 'fun_app$n'(X0,sK64(X0,X1))
& $less('fun_app$a'('of_nat$',sK64(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1808,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP5(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f1807]) ).
tff(f1807,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP5(X1,X0)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) )
& ( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f1507]) ).
tff(f6526,plain,
spl272_375,
inference(avatar_split_clause,[],[f3541,f6524]) ).
tff(f6524,plain,
( spl272_375
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP4(X0,X1)
| ~ 'fun_app$n'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_375])]) ).
tff(f3541,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X2),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP4(X0,X1)
| ~ 'fun_app$n'(X0,X2) ),
inference(forward_demodulation,[],[f2775,f848]) ).
tff(f2775,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP4(X0,X1)
| ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f1801,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP4(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ( 'fun_app$n'(X0,sK62(X0,X1))
& $less('fun_app$a'('of_nat$',sK62(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f1799,f1800]) ).
tff(f1800,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
=> ( 'fun_app$n'(X0,sK62(X0,X1))
& $less('fun_app$a'('of_nat$',sK62(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1799,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP4(X0,X1)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f1798]) ).
tff(f1798,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP4(X1,X0)
| ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) )
& ( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f1505]) ).
tff(f1505,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP4(X1,X0)
<=> ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f6522,plain,
spl272_374,
inference(avatar_split_clause,[],[f3538,f6520]) ).
tff(f6520,plain,
( spl272_374
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),$sum(1,'fun_app$a'('of_nat$',X1)))
| 'fun_app$n'(X0,X3)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_374])]) ).
tff(f3538,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),$sum(1,'fun_app$a'('of_nat$',X1)))
| 'fun_app$n'(X0,X3)
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f2766,f848]) ).
tff(f2766,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f1792,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP3(X0,X1)
| ( ~ 'fun_app$n'(X0,sK60(X0,X1))
& $less('fun_app$a'('of_nat$',sK60(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP3(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f1790,f1791]) ).
tff(f1791,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) )
=> ( ~ 'fun_app$n'(X0,sK60(X0,X1))
& $less('fun_app$a'('of_nat$',sK60(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1790,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP3(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f1789]) ).
tff(f1789,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP3(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) )
& ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f1503]) ).
tff(f6518,plain,
spl272_373,
inference(avatar_split_clause,[],[f3536,f6516]) ).
tff(f6516,plain,
( spl272_373
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),$sum(1,'fun_app$a'('of_nat$',X1)))
| 'fun_app$n'(X0,X3)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_373])]) ).
tff(f3536,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X3),$sum(1,'fun_app$a'('of_nat$',X1)))
| 'fun_app$n'(X0,X3)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f2759,f848]) ).
tff(f2759,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f1783,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP2(X0,X1)
| ( ~ 'fun_app$n'(X0,sK58(X0,X1))
& $less('fun_app$a'('of_nat$',sK58(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP2(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f1781,f1782]) ).
tff(f1782,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) )
=> ( ~ 'fun_app$n'(X0,sK58(X0,X1))
& $less('fun_app$a'('of_nat$',sK58(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1781,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( sP2(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X1),1)) ) )
& ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),$sum('fun_app$a'('of_nat$',X1),1)) )
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f1780]) ).
tff(f1780,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( ( sP2(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) )
& ( ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f1501]) ).
tff(f1501,plain,
! [X1: 'Nat_bool_fun$',X0: 'Nat$'] :
( sP2(X1,X0)
<=> ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f6514,plain,
spl272_372,
inference(avatar_split_clause,[],[f3525,f6512]) ).
tff(f6512,plain,
( spl272_372
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_372])]) ).
tff(f3525,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2735,f2347]) ).
tff(f2735,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1766]) ).
tff(f6510,plain,
spl272_371,
inference(avatar_split_clause,[],[f3524,f6508]) ).
tff(f6508,plain,
( spl272_371
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_371])]) ).
tff(f3524,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(forward_demodulation,[],[f2736,f2347]) ).
tff(f2736,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less$b','zero$'),'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(cnf_transformation,[],[f1766]) ).
tff(f6506,plain,
spl272_370,
inference(avatar_split_clause,[],[f3451,f6504]) ).
tff(f6504,plain,
( spl272_370
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK36(X0))) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_370])]) ).
tff(f3451,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK36(X0))) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2301,f848]) ).
tff(f2301,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK36(X0)),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1579]) ).
tff(f1579,plain,
! [X0: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X0))
| ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK36(X0)),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36])],[f1577,f1578]) ).
tff(f1578,plain,
! [X0: 'Nat$'] :
( ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X2),1) )
=> ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK36(X0)),1) ) ),
introduced(choice_axiom,[]) ).
tff(f1577,plain,
! [X0: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X0))
| ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) )
& ( ? [X2: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X2),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
inference(rectify,[],[f1576]) ).
tff(f1576,plain,
! [X0: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X0))
| ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) )
& ( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
inference(nnf_transformation,[],[f571]) ).
tff(f571,axiom,
! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
<=> ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom569) ).
tff(f6494,plain,
spl272_369,
inference(avatar_split_clause,[],[f3445,f6492]) ).
tff(f6492,plain,
( spl272_369
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK28(X0))) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_369])]) ).
tff(f3445,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(1,'fun_app$a'('of_nat$',sK28(X0))) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2245,f848]) ).
tff(f2245,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK28(X0)),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1542]) ).
tff(f1542,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK28(X0)),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f1001,f1541]) ).
tff(f1541,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
=> ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK28(X0)),1) ) ),
introduced(choice_axiom,[]) ).
tff(f1001,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f573]) ).
tff(f573,axiom,
! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
=> ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom571) ).
tff(f6490,plain,
spl272_368,
inference(avatar_split_clause,[],[f3429,f6488]) ).
tff(f6488,plain,
( spl272_368
<=> ! [X0: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_368])]) ).
tff(f3429,plain,
! [X0: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),2) ),
inference(evaluation,[],[f2246]) ).
tff(f2246,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),2) ),
inference(cnf_transformation,[],[f1003]) ).
tff(f1003,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),2) ),
inference(flattening,[],[f1002]) ).
tff(f1002,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),2) ),
inference(ennf_transformation,[],[f605]) ).
tff(f605,axiom,
! [X0: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),2)
=> ( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom603) ).
tff(f6486,plain,
spl272_367,
inference(avatar_split_clause,[],[f3424,f6484]) ).
tff(f6484,plain,
( spl272_367
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less(1,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_367])]) ).
tff(f3424,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less(1,'fun_app$a'('of_nat$',X0)) ),
inference(evaluation,[],[f2418]) ).
tff(f2418,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1050]) ).
tff(f1050,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less($sum(0,1),'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f600]) ).
tff(f600,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less($sum(0,1),'fun_app$a'('of_nat$',X0))
=> $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom598) ).
tff(f6482,plain,
spl272_366,
inference(avatar_split_clause,[],[f3412,f6480]) ).
tff(f6480,plain,
( spl272_366
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X1) )
| ( 1 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_366])]) ).
tff(f3412,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X1) )
| ( 1 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ),
inference(evaluation,[],[f2749]) ).
tff(f2749,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = $sum(0,1) )
| ( $sum(0,1) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ),
inference(cnf_transformation,[],[f1774]) ).
tff(f6478,plain,
spl272_365,
inference(avatar_split_clause,[],[f3411,f6476]) ).
tff(f6476,plain,
( spl272_365
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 1 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_365])]) ).
tff(f3411,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$',X0) )
| ( 1 != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ),
inference(evaluation,[],[f2748]) ).
tff(f2748,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum(0,1) )
| ( $sum(0,1) != 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) ) ),
inference(cnf_transformation,[],[f1774]) ).
tff(f6474,plain,
spl272_364,
inference(avatar_split_clause,[],[f3406,f6472]) ).
tff(f6472,plain,
( spl272_364
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),1)
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_364])]) ).
tff(f3406,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),1)
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1) ),
inference(evaluation,[],[f2755]) ).
tff(f2755,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),$sum(0,1))
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1)) ),
inference(cnf_transformation,[],[f1778]) ).
tff(f6470,plain,
spl272_363,
inference(avatar_split_clause,[],[f3405,f6468]) ).
tff(f6468,plain,
( spl272_363
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),1)
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_363])]) ).
tff(f3405,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),1)
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),1) ),
inference(evaluation,[],[f2754]) ).
tff(f2754,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1))
| $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)),$sum(0,1)) ),
inference(cnf_transformation,[],[f1778]) ).
tff(f6466,plain,
spl272_362,
inference(avatar_split_clause,[],[f3371,f6464]) ).
tff(f6464,plain,
( spl272_362
<=> ! [X2: $int,X1: 'Int_int_fun$',X3: $int] :
( ~ $less('fun_app$p'(X1,X3),'fun_app$p'(X1,X2))
| ~ $less(sK179(X1),sK178(X1))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_362])]) ).
tff(f3371,plain,
! [X2: $int,X3: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),'fun_app$p'(X1,X2))
| ~ $less(sK179(X1),sK178(X1))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3128]) ).
tff(f3128,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( ~ $less('fun_app$p'(X1,X3),X0)
| ~ $less(sK179(X1),sK178(X1))
| $less(X3,X2)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2036]) ).
tff(f6462,plain,
spl272_361,
inference(avatar_split_clause,[],[f3369,f6460]) ).
tff(f6460,plain,
( spl272_361
<=> ! [X2: $int,X1: 'Int_int_fun$',X3: $int] :
( $less('fun_app$p'(X1,X2),'fun_app$p'(X1,X3))
| $less(sK176(X1),sK177(X1))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_361])]) ).
tff(f3369,plain,
! [X2: $int,X3: $int,X1: 'Int_int_fun$'] :
( $less('fun_app$p'(X1,X2),'fun_app$p'(X1,X3))
| $less(sK176(X1),sK177(X1))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3126]) ).
tff(f3126,plain,
! [X2: $int,X3: $int,X0: $int,X1: 'Int_int_fun$'] :
( $less(X0,'fun_app$p'(X1,X3))
| $less(sK176(X1),sK177(X1))
| ~ $less(X2,X3)
| ( 'fun_app$p'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2034]) ).
tff(f6458,plain,
spl272_360,
inference(avatar_split_clause,[],[f3339,f6456]) ).
tff(f6456,plain,
( spl272_360
<=> ! [X2: $int,X1: 'Int_real_fun$',X3: $int] :
( ~ $less('fun_app$z'(X1,X3),'fun_app$z'(X1,X2))
| ~ $less(sK147(X1),sK146(X1))
| $less(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_360])]) ).
tff(f3339,plain,
! [X2: $int,X3: $int,X1: 'Int_real_fun$'] :
( ~ $less('fun_app$z'(X1,X3),'fun_app$z'(X1,X2))
| ~ $less(sK147(X1),sK146(X1))
| $less(X3,X2) ),
inference(equality_resolution,[],[f3096]) ).
tff(f3096,plain,
! [X2: $int,X3: $int,X0: $real,X1: 'Int_real_fun$'] :
( ~ $less('fun_app$z'(X1,X3),X0)
| ~ $less(sK147(X1),sK146(X1))
| $less(X3,X2)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2004]) ).
tff(f6447,plain,
spl272_359,
inference(avatar_split_clause,[],[f3337,f6445]) ).
tff(f6445,plain,
( spl272_359
<=> ! [X2: $int,X1: 'Int_real_fun$',X3: $int] :
( $less('fun_app$z'(X1,X2),'fun_app$z'(X1,X3))
| $less(sK144(X1),sK145(X1))
| ~ $less(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_359])]) ).
tff(f3337,plain,
! [X2: $int,X3: $int,X1: 'Int_real_fun$'] :
( $less('fun_app$z'(X1,X2),'fun_app$z'(X1,X3))
| $less(sK144(X1),sK145(X1))
| ~ $less(X2,X3) ),
inference(equality_resolution,[],[f3094]) ).
tff(f3094,plain,
! [X2: $int,X3: $int,X0: $real,X1: 'Int_real_fun$'] :
( $less(X0,'fun_app$z'(X1,X3))
| $less(sK144(X1),sK145(X1))
| ~ $less(X2,X3)
| ( 'fun_app$z'(X1,X2) != X0 ) ),
inference(cnf_transformation,[],[f2002]) ).
tff(f6443,plain,
spl272_358,
inference(avatar_split_clause,[],[f3335,f6441]) ).
tff(f6441,plain,
( spl272_358
<=> ! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$p'(X2,X1),'fun_app$p'(X2,X0))
| ~ $less(sK135(X2),sK134(X2))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_358])]) ).
tff(f3335,plain,
! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$p'(X2,X1),'fun_app$p'(X2,X0))
| ~ $less(sK135(X2),sK134(X2))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3084]) ).
tff(f3084,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$p'(X2,X0))
| ~ $less(sK135(X2),sK134(X2))
| ( 'fun_app$p'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1992]) ).
tff(f6439,plain,
spl272_357,
inference(avatar_split_clause,[],[f3329,f6437]) ).
tff(f6437,plain,
( spl272_357
<=> ! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$z'(X2,X1),'fun_app$z'(X2,X0))
| ~ $less(sK129(X2),sK128(X2))
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_357])]) ).
tff(f3329,plain,
! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( ~ $less('fun_app$z'(X2,X1),'fun_app$z'(X2,X0))
| ~ $less(sK129(X2),sK128(X2))
| $less(X1,X0) ),
inference(equality_resolution,[],[f3078]) ).
tff(f3078,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( ~ $less(X3,'fun_app$z'(X2,X0))
| ~ $less(sK129(X2),sK128(X2))
| ( 'fun_app$z'(X2,X1) != X3 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1986]) ).
tff(f6435,plain,
spl272_356,
inference(avatar_split_clause,[],[f3327,f6433]) ).
tff(f6433,plain,
( spl272_356
<=> ! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),'fun_app$p'(X2,X1))
| $less(sK118(X2),sK119(X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_356])]) ).
tff(f3327,plain,
! [X2: 'Int_int_fun$',X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),'fun_app$p'(X2,X1))
| $less(sK118(X2),sK119(X2))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3068]) ).
tff(f3068,plain,
! [X2: 'Int_int_fun$',X3: $int,X0: $int,X1: $int] :
( $less('fun_app$p'(X2,X0),X3)
| $less(sK118(X2),sK119(X2))
| ( 'fun_app$p'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1976]) ).
tff(f6431,plain,
spl272_355,
inference(avatar_split_clause,[],[f3321,f6429]) ).
tff(f6429,plain,
( spl272_355
<=> ! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),'fun_app$z'(X2,X1))
| $less(sK112(X2),sK113(X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_355])]) ).
tff(f3321,plain,
! [X2: 'Int_real_fun$',X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),'fun_app$z'(X2,X1))
| $less(sK112(X2),sK113(X2))
| ~ $less(X0,X1) ),
inference(equality_resolution,[],[f3062]) ).
tff(f3062,plain,
! [X2: 'Int_real_fun$',X3: $real,X0: $int,X1: $int] :
( $less('fun_app$z'(X2,X0),X3)
| $less(sK112(X2),sK113(X2))
| ( 'fun_app$z'(X2,X1) != X3 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1970]) ).
tff(f6427,plain,
spl272_354,
inference(avatar_split_clause,[],[f2845,f6425]) ).
tff(f6425,plain,
( spl272_354
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_354])]) ).
tff(f2845,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1264]) ).
tff(f1264,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(flattening,[],[f1263]) ).
tff(f1263,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(ennf_transformation,[],[f227]) ).
tff(f227,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom225) ).
tff(f6423,plain,
spl272_353,
inference(avatar_split_clause,[],[f2843,f6421]) ).
tff(f6421,plain,
( spl272_353
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_353])]) ).
tff(f2843,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1260]) ).
tff(f1260,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(flattening,[],[f1259]) ).
tff(f1259,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X1),X2)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f520]) ).
tff(f520,axiom,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less$',X1),X2)
& 'fun_app$e'('fun_app$f'('less$',X0),X1) )
=> 'fun_app$e'('fun_app$f'('less$',X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
tff(f6419,plain,
spl272_352,
inference(avatar_split_clause,[],[f2840,f6417]) ).
tff(f6417,plain,
( spl272_352
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_352])]) ).
tff(f2840,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f1254]) ).
tff(f1254,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(flattening,[],[f1253]) ).
tff(f1253,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(ennf_transformation,[],[f248]) ).
tff(f248,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom246) ).
tff(f6415,plain,
spl272_351,
inference(avatar_split_clause,[],[f2838,f6413]) ).
tff(f6413,plain,
( spl272_351
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X1),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_351])]) ).
tff(f2838,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X1),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f1250]) ).
tff(f1250,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X1),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(flattening,[],[f1249]) ).
tff(f1249,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X1),X2)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f522]) ).
tff(f522,axiom,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less$a',X0),X1) )
=> 'fun_app$g'('fun_app$h'('less$a',X0),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom520) ).
tff(f6411,plain,
spl272_350,
inference(avatar_split_clause,[],[f2832,f6409]) ).
tff(f6409,plain,
( spl272_350
<=> ! [X2: 'Nat$',X0: $int,X1: $int] :
( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| $less(X0,0)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_350])]) ).
tff(f2832,plain,
! [X2: 'Nat$',X0: $int,X1: $int] :
( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| $less(X0,0)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1240]) ).
tff(f1240,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| $less(X0,0)
| $less(X1,X0) ),
inference(flattening,[],[f1239]) ).
tff(f1239,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2))
| $less(X0,0)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f780]) ).
tff(f780,plain,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( ~ $less(X0,0)
& ~ $less(X1,X0) )
=> ~ $less('fun_app$a'('power$a'(X1),X2),'fun_app$a'('power$a'(X0),X2)) ),
inference(theory_normalization,[],[f192]) ).
tff(f192,axiom,
! [X0: $int,X1: $int,X2: 'Nat$'] :
( ( $lesseq(0,X0)
& $lesseq(X0,X1) )
=> $lesseq('fun_app$a'('power$a'(X0),X2),'fun_app$a'('power$a'(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom190) ).
tff(f6397,plain,
spl272_349,
inference(avatar_split_clause,[],[f2826,f6395]) ).
tff(f6395,plain,
( spl272_349
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less('fun_app$p'('times$b'(X2),X0),'fun_app$p'('times$b'(X2),X1))
| ~ $less(0,X2)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_349])]) ).
tff(f2826,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less('fun_app$p'('times$b'(X2),X0),'fun_app$p'('times$b'(X2),X1))
| ~ $less(0,X2)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1228]) ).
tff(f1228,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less('fun_app$p'('times$b'(X2),X0),'fun_app$p'('times$b'(X2),X1))
| ~ $less(0,X2)
| ~ $less(X0,X1) ),
inference(flattening,[],[f1227]) ).
tff(f1227,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less('fun_app$p'('times$b'(X2),X0),'fun_app$p'('times$b'(X2),X1))
| ~ $less(0,X2)
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f624]) ).
tff(f624,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( $less(0,X2)
& $less(X0,X1) )
=> $less('fun_app$p'('times$b'(X2),X0),'fun_app$p'('times$b'(X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom622) ).
tff(f6393,plain,
spl272_348,
inference(avatar_split_clause,[],[f2822,f6391]) ).
tff(f6391,plain,
( spl272_348
<=> ! [X2: 'Nat$',X0: $real,X1: $real] :
( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| $less(X0,0.0)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_348])]) ).
tff(f2822,plain,
! [X2: 'Nat$',X0: $real,X1: $real] :
( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| $less(X0,0.0)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1222]) ).
tff(f1222,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| $less(X0,0.0)
| $less(X1,X0) ),
inference(flattening,[],[f1221]) ).
tff(f1221,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2))
| $less(X0,0.0)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f774]) ).
tff(f774,plain,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( ~ $less(X0,0.0)
& ~ $less(X1,X0) )
=> ~ $less('fun_app$m'('power$c'(X1),X2),'fun_app$m'('power$c'(X0),X2)) ),
inference(theory_normalization,[],[f193]) ).
tff(f193,axiom,
! [X0: $real,X1: $real,X2: 'Nat$'] :
( ( $lesseq(0.0,X0)
& $lesseq(X0,X1) )
=> $lesseq('fun_app$m'('power$c'(X0),X2),'fun_app$m'('power$c'(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
tff(f6389,plain,
spl272_347,
inference(avatar_split_clause,[],[f2776,f6387]) ).
tff(f6387,plain,
( spl272_347
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( $less('fun_app$a'('of_nat$',sK63(X0,X1)),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_347])]) ).
tff(f2776,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( $less('fun_app$a'('of_nat$',sK63(X0,X1)),'fun_app$a'('of_nat$',X0))
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f1806,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP4(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,X0) ) )
& ( ( 'fun_app$n'(X1,sK63(X0,X1))
& $less('fun_app$a'('of_nat$',sK63(X0,X1)),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f1804,f1805]) ).
tff(f1805,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
=> ( 'fun_app$n'(X1,sK63(X0,X1))
& $less('fun_app$a'('of_nat$',sK63(X0,X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1804,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP4(X1,X0)
| ( ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
inference(rectify,[],[f1803]) ).
tff(f1803,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP4(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
inference(flattening,[],[f1802]) ).
tff(f1802,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP4(X1,X0)
| ( ! [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& ~ 'fun_app$n'(X1,X0) ) )
& ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f1506]) ).
tff(f1506,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP4(X1,X0)
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0) ) ),
inference(definition_folding,[],[f977,f1505]) ).
tff(f977,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ? [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0) ) ),
inference(rectify,[],[f563]) ).
tff(f563,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ? [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
| 'fun_app$n'(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
tff(f6385,plain,
spl272_346,
inference(avatar_split_clause,[],[f2764,f6383]) ).
tff(f6383,plain,
( spl272_346
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP2(X1,X0)
| $less('fun_app$a'('of_nat$',sK59(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_346])]) ).
tff(f2764,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP2(X1,X0)
| $less('fun_app$a'('of_nat$',sK59(X0,X1)),'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$n'(X1,X0) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f1788,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP2(X1,X0)
| ( ~ 'fun_app$n'(X1,sK59(X0,X1))
& $less('fun_app$a'('of_nat$',sK59(X0,X1)),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) )
| ~ sP2(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1786,f1787]) ).
tff(f1787,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
=> ( ~ 'fun_app$n'(X1,sK59(X0,X1))
& $less('fun_app$a'('of_nat$',sK59(X0,X1)),'fun_app$a'('of_nat$',X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1786,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP2(X1,X0)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X1,X2)
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) )
| ~ sP2(X1,X0) ) ),
inference(rectify,[],[f1785]) ).
tff(f1785,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP2(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) )
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f1784]) ).
tff(f1784,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ( sP2(X1,X0)
| ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X1,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
| ~ 'fun_app$n'(X1,X0) )
& ( ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) )
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f1502]) ).
tff(f1502,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP2(X1,X0)
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) ) ),
inference(definition_folding,[],[f1183,f1501]) ).
tff(f1183,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1)) )
<=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0)) )
& 'fun_app$n'(X1,X0) ) ),
inference(ennf_transformation,[],[f975]) ).
tff(f975,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1))
=> 'fun_app$n'(X1,X2) )
<=> ( ! [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
=> 'fun_app$n'(X1,X3) )
& 'fun_app$n'(X1,X0) ) ),
inference(rectify,[],[f560]) ).
tff(f560,axiom,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),$sum('fun_app$a'('of_nat$',X0),1))
=> 'fun_app$n'(X1,X2) )
<=> ( ! [X2: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0))
=> 'fun_app$n'(X1,X2) )
& 'fun_app$n'(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom558) ).
tff(f6381,plain,
spl272_345,
inference(avatar_split_clause,[],[f2738,f6379]) ).
tff(f6379,plain,
( spl272_345
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_345])]) ).
tff(f2738,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ),
inference(cnf_transformation,[],[f1768]) ).
tff(f1768,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ) ),
inference(flattening,[],[f1767]) ).
tff(f1767,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) )
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ) ),
inference(nnf_transformation,[],[f383]) ).
tff(f383,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)))
<=> ( $less(0,'fun_app$a'('of_nat$',X1))
& $less(0,'fun_app$a'('of_nat$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom381) ).
tff(f6377,plain,
spl272_344,
inference(avatar_split_clause,[],[f2737,f6375]) ).
tff(f6375,plain,
( spl272_344
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_344])]) ).
tff(f2737,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0,'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1))) ),
inference(cnf_transformation,[],[f1768]) ).
tff(f6373,plain,
spl272_343,
inference(avatar_split_clause,[],[f2401,f6371]) ).
tff(f6371,plain,
( spl272_343
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_343])]) ).
tff(f2401,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),2) ),
inference(cnf_transformation,[],[f1036]) ).
tff(f1036,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X1))
| $less('fun_app$a'('of_nat$',X0),2) ),
inference(ennf_transformation,[],[f696]) ).
tff(f696,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),2)
=> ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),'fun_app$a'('of_nat$',X1)) ),
inference(theory_normalization,[],[f5]) ).
tff(f5,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq(2,'fun_app$a'('of_nat$',X0))
=> $lesseq('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3) ).
tff(f6369,plain,
spl272_342,
inference(avatar_split_clause,[],[f2352,f6367]) ).
tff(f6367,plain,
( spl272_342
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$d'('numeral$',X1)) = 'fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_342])]) ).
tff(f2352,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$d'('numeral$',X1)) = 'fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f365]) ).
tff(f365,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$p'('times$b'('fun_app$d'('numeral$',X0)),'fun_app$d'('numeral$',X1)) = 'fun_app$d'('numeral$','fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom363) ).
tff(f6365,plain,
spl272_341,
inference(avatar_split_clause,[],[f2258,f6363]) ).
tff(f6363,plain,
( spl272_341
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK32(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_341])]) ).
tff(f2258,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK32(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(cnf_transformation,[],[f1551]) ).
tff(f1551,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK32(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f1010,f1550]) ).
tff(f1550,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
=> ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK32(X0)),1) ) ),
introduced(choice_axiom,[]) ).
tff(f1010,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(ennf_transformation,[],[f904]) ).
tff(f904,plain,
! [X0: 'Nat$'] :
~ ( ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) )
& ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(flattening,[],[f903]) ).
tff(f903,plain,
! [X0: 'Nat$'] :
~ ( ! [X1: 'Nat$'] :
( ~ 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
& ( ~ 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(true_and_false_elimination,[],[f170]) ).
tff(f170,axiom,
! [X0: 'Nat$'] :
( ( ! [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
=> $false )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
=> $false ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom168) ).
tff(f6361,plain,
spl272_340,
inference(avatar_split_clause,[],[f2244,f6359]) ).
tff(f6359,plain,
( spl272_340
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK27(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_340])]) ).
tff(f2244,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK27(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(cnf_transformation,[],[f1540]) ).
tff(f1540,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK27(X0)),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f1000,f1539]) ).
tff(f1539,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
=> ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',sK27(X0)),1) ) ),
introduced(choice_axiom,[]) ).
tff(f1000,plain,
! [X0: 'Nat$'] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) )
| ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(ennf_transformation,[],[f177]) ).
tff(f177,axiom,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != 0 )
=> ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) = $sum('fun_app$a'('of_nat$',X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).
tff(f6344,plain,
spl272_339,
inference(avatar_split_clause,[],[f2235,f6342]) ).
tff(f6342,plain,
( spl272_339
<=> ! [X0: $real] : ( $product(4.0,'fun_app$m'('power$c'(X0),'nat$'(2))) = 'fun_app$m'('power$c'($product(2.0,X0)),'nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_339])]) ).
tff(f2235,plain,
! [X0: $real] : ( $product(4.0,'fun_app$m'('power$c'(X0),'nat$'(2))) = 'fun_app$m'('power$c'($product(2.0,X0)),'nat$'(2)) ),
inference(cnf_transformation,[],[f632]) ).
tff(f632,axiom,
! [X0: $real] : ( $product(4.0,'fun_app$m'('power$c'(X0),'nat$'(2))) = 'fun_app$m'('power$c'($product(2.0,X0)),'nat$'(2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).
tff(f6307,plain,
( spl272_338
| ~ spl272_58
| ~ spl272_304 ),
inference(avatar_split_clause,[],[f6070,f5684,f3865,f6305]) ).
tff(f6305,plain,
( spl272_338
<=> ! [X0: $real] : $less(X0,$sum(X0,3.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_338])]) ).
tff(f5684,plain,
( spl272_304
<=> ! [X0: $real] : $less(X0,$sum(3.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_304])]) ).
tff(f6070,plain,
( ! [X0: $real] : $less(X0,$sum(X0,3.0))
| ~ spl272_58
| ~ spl272_304 ),
inference(superposition,[],[f5685,f3866]) ).
tff(f5685,plain,
( ! [X0: $real] : $less(X0,$sum(3.0,X0))
| ~ spl272_304 ),
inference(avatar_component_clause,[],[f5684]) ).
tff(f6240,plain,
( spl272_337
| ~ spl272_50
| ~ spl272_304 ),
inference(avatar_split_clause,[],[f6067,f5684,f3821,f6238]) ).
tff(f6067,plain,
( ! [X0: $real] : ~ $less($sum(3.0,X0),X0)
| ~ spl272_50
| ~ spl272_304 ),
inference(resolution,[],[f5685,f3822]) ).
tff(f6167,plain,
spl272_336,
inference(avatar_split_clause,[],[f3544,f6165]) ).
tff(f6165,plain,
( spl272_336
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK64(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_336])]) ).
tff(f3544,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK64(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f2780,f848]) ).
tff(f2780,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK64(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f1810]) ).
tff(f6163,plain,
spl272_335,
inference(avatar_split_clause,[],[f3542,f6161]) ).
tff(f6161,plain,
( spl272_335
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK62(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_335])]) ).
tff(f3542,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK62(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| ~ sP4(X0,X1) ),
inference(forward_demodulation,[],[f2773,f848]) ).
tff(f2773,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK62(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f6159,plain,
( spl272_334
| ~ spl272_56
| ~ spl272_284 ),
inference(avatar_split_clause,[],[f5906,f5585,f3857,f6157]) ).
tff(f6157,plain,
( spl272_334
<=> ! [X0: $int] : $less(X0,$sum(X0,3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_334])]) ).
tff(f5585,plain,
( spl272_284
<=> ! [X0: $int] : $less(X0,$sum(3,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_284])]) ).
tff(f5906,plain,
( ! [X0: $int] : $less(X0,$sum(X0,3))
| ~ spl272_56
| ~ spl272_284 ),
inference(superposition,[],[f5586,f3858]) ).
tff(f5586,plain,
( ! [X0: $int] : $less(X0,$sum(3,X0))
| ~ spl272_284 ),
inference(avatar_component_clause,[],[f5585]) ).
tff(f6155,plain,
spl272_333,
inference(avatar_split_clause,[],[f3537,f6153]) ).
tff(f6153,plain,
( spl272_333
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK60(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_333])]) ).
tff(f3537,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK60(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP3(X0,X1) ),
inference(forward_demodulation,[],[f2767,f848]) ).
tff(f2767,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP3(X0,X1)
| $less('fun_app$a'('of_nat$',sK60(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f6151,plain,
spl272_332,
inference(avatar_split_clause,[],[f3535,f6149]) ).
tff(f6149,plain,
( spl272_332
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK58(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_332])]) ).
tff(f3535,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK58(X0,X1)),$sum(1,'fun_app$a'('of_nat$',X1)))
| sP2(X0,X1) ),
inference(forward_demodulation,[],[f2760,f848]) ).
tff(f2760,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP2(X0,X1)
| $less('fun_app$a'('of_nat$',sK58(X0,X1)),$sum('fun_app$a'('of_nat$',X1),1)) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f6147,plain,
spl272_331,
inference(avatar_split_clause,[],[f3450,f6145]) ).
tff(f6145,plain,
( spl272_331
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X1)) )
| $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_331])]) ).
tff(f3450,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) != $sum(1,'fun_app$a'('of_nat$',X1)) )
| $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2302,f848]) ).
tff(f2302,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X1),1) ) ),
inference(cnf_transformation,[],[f1579]) ).
tff(f6143,plain,
spl272_330,
inference(avatar_split_clause,[],[f2722,f6141]) ).
tff(f6141,plain,
( spl272_330
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_330])]) ).
tff(f2722,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1757]) ).
tff(f1757,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ) ),
inference(nnf_transformation,[],[f28]) ).
tff(f28,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom26) ).
tff(f6139,plain,
spl272_329,
inference(avatar_split_clause,[],[f2721,f6137]) ).
tff(f6137,plain,
( spl272_329
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_329])]) ).
tff(f2721,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ),
inference(cnf_transformation,[],[f1757]) ).
tff(f6135,plain,
spl272_328,
inference(avatar_split_clause,[],[f2720,f6133]) ).
tff(f6133,plain,
( spl272_328
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_328])]) ).
tff(f2720,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1756]) ).
tff(f1756,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ) ),
inference(nnf_transformation,[],[f351]) ).
tff(f351,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1))
<=> 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom349) ).
tff(f6131,plain,
spl272_327,
inference(avatar_split_clause,[],[f2719,f6129]) ).
tff(f6129,plain,
( spl272_327
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_327])]) ).
tff(f2719,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$e'('fun_app$f'('less$','fun_app$c'('bit0$',X0)),'fun_app$c'('bit0$',X1)) ),
inference(cnf_transformation,[],[f1756]) ).
tff(f6127,plain,
spl272_326,
inference(avatar_split_clause,[],[f2704,f6125]) ).
tff(f6125,plain,
( spl272_326
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_326])]) ).
tff(f2704,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1742]) ).
tff(f1742,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
inference(nnf_transformation,[],[f12]) ).
tff(f12,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom10) ).
tff(f6123,plain,
spl272_325,
inference(avatar_split_clause,[],[f2703,f6121]) ).
tff(f6121,plain,
( spl272_325
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_325])]) ).
tff(f2703,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ),
inference(cnf_transformation,[],[f1742]) ).
tff(f6119,plain,
spl272_324,
inference(avatar_split_clause,[],[f2698,f6117]) ).
tff(f6117,plain,
( spl272_324
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_324])]) ).
tff(f2698,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1739]) ).
tff(f1739,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
inference(nnf_transformation,[],[f362]) ).
tff(f362,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1))
<=> 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
tff(f6115,plain,
( spl272_323
| ~ spl272_51
| ~ spl272_284 ),
inference(avatar_split_clause,[],[f5902,f5585,f3825,f6113]) ).
tff(f5902,plain,
( ! [X0: $int] : ~ $less($sum(3,X0),X0)
| ~ spl272_51
| ~ spl272_284 ),
inference(resolution,[],[f5586,f3826]) ).
tff(f6111,plain,
spl272_322,
inference(avatar_split_clause,[],[f2697,f6109]) ).
tff(f6109,plain,
( spl272_322
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_322])]) ).
tff(f2697,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','fun_app$i'('numeral$a',X0)),'fun_app$i'('numeral$a',X1)) ),
inference(cnf_transformation,[],[f1739]) ).
tff(f6107,plain,
spl272_321,
inference(avatar_split_clause,[],[f2652,f6105]) ).
tff(f6105,plain,
( spl272_321
<=> ! [X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_321])]) ).
tff(f2652,plain,
! [X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1)) ),
inference(cnf_transformation,[],[f1713]) ).
tff(f1713,plain,
! [X0: 'Nat$',X1: 'Num$'] :
( ( $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1)) )
& ( $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1)) ) ),
inference(nnf_transformation,[],[f399]) ).
tff(f399,axiom,
! [X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1))
<=> $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom397) ).
tff(f6103,plain,
spl272_320,
inference(avatar_split_clause,[],[f2651,f6101]) ).
tff(f6101,plain,
( spl272_320
<=> ! [X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_320])]) ).
tff(f2651,plain,
! [X0: 'Nat$',X1: 'Num$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$d'('numeral$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$j'('numeral$b',X1)) ),
inference(cnf_transformation,[],[f1713]) ).
tff(f6099,plain,
spl272_319,
inference(avatar_split_clause,[],[f2650,f6097]) ).
tff(f6097,plain,
( spl272_319
<=> ! [X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_319])]) ).
tff(f2650,plain,
! [X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1712]) ).
tff(f1712,plain,
! [X0: 'Num$',X1: 'Nat$'] :
( ( $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1)) )
& ( $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1)) ) ),
inference(nnf_transformation,[],[f398]) ).
tff(f398,axiom,
! [X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1))
<=> $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
tff(f6095,plain,
spl272_318,
inference(avatar_split_clause,[],[f2649,f6093]) ).
tff(f6093,plain,
( spl272_318
<=> ! [X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_318])]) ).
tff(f2649,plain,
! [X0: 'Num$',X1: 'Nat$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$m'('of_nat$b',X1)) ),
inference(cnf_transformation,[],[f1712]) ).
tff(f6091,plain,
spl272_317,
inference(avatar_split_clause,[],[f2638,f6089]) ).
tff(f6089,plain,
( spl272_317
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('of_nat$b',X1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_317])]) ).
tff(f2638,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('of_nat$b',X1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(cnf_transformation,[],[f1706]) ).
tff(f1706,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('of_nat$b',X1) )
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('of_nat$b',X1) ) ) ),
inference(nnf_transformation,[],[f86]) ).
tff(f86,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 'fun_app$m'('of_nat$b',X1) )
<=> ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
tff(f6087,plain,
spl272_316,
inference(avatar_split_clause,[],[f2637,f6085]) ).
tff(f6085,plain,
( spl272_316
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('of_nat$b',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_316])]) ).
tff(f2637,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
| ( 'fun_app$m'('of_nat$b',X0) != 'fun_app$m'('of_nat$b',X1) ) ),
inference(cnf_transformation,[],[f1706]) ).
tff(f6083,plain,
spl272_315,
inference(avatar_split_clause,[],[f2537,f6081]) ).
tff(f6081,plain,
( spl272_315
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK54(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_315])]) ).
tff(f2537,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK54(X0))) ),
inference(cnf_transformation,[],[f1642]) ).
tff(f1642,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ~ 'fun_app$n'(X0,sK54(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK54(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54])],[f1181,f1641]) ).
tff(f1641,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) ) )
=> ( ~ 'fun_app$n'(X0,sK54(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK54(X0))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1181,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) ) ) ),
inference(ennf_transformation,[],[f616]) ).
tff(f616,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2))
=> 'fun_app$n'(X0,X3) )
=> 'fun_app$n'(X0,X2) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom614) ).
tff(f6079,plain,
spl272_314,
inference(avatar_split_clause,[],[f2534,f6077]) ).
tff(f6077,plain,
( spl272_314
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$',X3: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK52(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_314])]) ).
tff(f2534,plain,
! [X3: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK52(X0))) ),
inference(cnf_transformation,[],[f1638]) ).
tff(f1638,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK52(X0))) )
& ~ 'fun_app$n'(X0,sK52(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f1179,f1637]) ).
tff(f1637,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ 'fun_app$n'(X0,X2) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',sK52(X0))) )
& ~ 'fun_app$n'(X0,sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1179,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$n'(X0,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) )
& ~ 'fun_app$n'(X0,X2) ) ),
inference(ennf_transformation,[],[f615]) ).
tff(f615,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,X3)
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X2)) ) )
=> 'fun_app$n'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom613) ).
tff(f6075,plain,
spl272_313,
inference(avatar_split_clause,[],[f2424,f6073]) ).
tff(f6073,plain,
( spl272_313
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_313])]) ).
tff(f2424,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(cnf_transformation,[],[f1056]) ).
tff(f1056,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1))
| ~ $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
inference(ennf_transformation,[],[f428]) ).
tff(f428,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
=> $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
tff(f6064,plain,
spl272_312,
inference(avatar_split_clause,[],[f2420,f6062]) ).
tff(f6062,plain,
( spl272_312
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_312])]) ).
tff(f2420,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ),
inference(cnf_transformation,[],[f1052]) ).
tff(f1052,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1))
| ~ $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1)) ),
inference(ennf_transformation,[],[f431]) ).
tff(f431,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('fun_app$m'('of_nat$b',X0),'fun_app$m'('of_nat$b',X1))
=> $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
tff(f6060,plain,
spl272_311,
inference(avatar_split_clause,[],[f2417,f6058]) ).
tff(f6058,plain,
( spl272_311
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_311])]) ).
tff(f2417,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(cnf_transformation,[],[f1049]) ).
tff(f1049,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0))
| ( 'fun_app$a'('of_nat$',X0) != 'fun_app$a'('of_nat$',X1) ) ),
inference(ennf_transformation,[],[f697]) ).
tff(f697,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
=> ~ $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X0)) ),
inference(theory_normalization,[],[f38]) ).
tff(f38,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 'fun_app$a'('of_nat$',X1) )
=> $lesseq('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$',X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
tff(f6056,plain,
spl272_310,
inference(avatar_split_clause,[],[f2351,f6054]) ).
tff(f6054,plain,
( spl272_310
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('power$'('numeral$c'(X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'numeral$c'('fun_app$c'('pow$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_310])]) ).
tff(f2351,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('power$'('numeral$c'(X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'numeral$c'('fun_app$c'('pow$'(X0),X1)) ),
inference(cnf_transformation,[],[f54]) ).
tff(f54,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('power$'('numeral$c'(X0)),'nat$'('fun_app$d'('numeral$',X1))) = 'numeral$c'('fun_app$c'('pow$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom52) ).
tff(f6052,plain,
spl272_309,
inference(avatar_split_clause,[],[f2350,f6050]) ).
tff(f6050,plain,
( spl272_309
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'times$d'('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) = 'fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_309])]) ).
tff(f2350,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'times$d'('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) = 'fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f367]) ).
tff(f367,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'times$d'('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) = 'fun_app$j'('numeral$b','fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom365) ).
tff(f6048,plain,
spl272_308,
inference(avatar_split_clause,[],[f2349,f6046]) ).
tff(f6046,plain,
( spl272_308
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'fun_app$i'('numeral$a',X1)) = 'fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_308])]) ).
tff(f2349,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'fun_app$i'('numeral$a',X1)) = 'fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f366]) ).
tff(f366,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'times$c'('fun_app$i'('numeral$a',X0),'fun_app$i'('numeral$a',X1)) = 'fun_app$i'('numeral$a','fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom364) ).
tff(f5887,plain,
( spl272_307
| ~ spl272_55
| ~ spl272_286 ),
inference(avatar_split_clause,[],[f5597,f5594,f3851,f5885]) ).
tff(f5885,plain,
( spl272_307
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| $less(0,'fun_app$a'('of_nat$',sK47(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_307])]) ).
tff(f5594,plain,
( spl272_286
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| $less(0,'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_286])]) ).
tff(f5597,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| $less(0,'fun_app$a'('of_nat$',sK47(X0))) )
| ~ spl272_55
| ~ spl272_286 ),
inference(forward_demodulation,[],[f5595,f3853]) ).
tff(f5595,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| $less(0,'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_286 ),
inference(avatar_component_clause,[],[f5594]) ).
tff(f5883,plain,
( spl272_306
| ~ spl272_55
| ~ spl272_285 ),
inference(avatar_split_clause,[],[f5592,f5589,f3851,f5881]) ).
tff(f5881,plain,
( spl272_306
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK46(X0))
| sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_306])]) ).
tff(f5589,plain,
( spl272_285
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK46(X0))
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_285])]) ).
tff(f5592,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK46(X0))
| sP1(X0) )
| ~ spl272_55
| ~ spl272_285 ),
inference(forward_demodulation,[],[f5590,f3853]) ).
tff(f5590,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK46(X0))
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_285 ),
inference(avatar_component_clause,[],[f5589]) ).
tff(f5728,plain,
spl272_305,
inference(avatar_split_clause,[],[f3549,f5726]) ).
tff(f5726,plain,
( spl272_305
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK72(X0,X1)))))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_305])]) ).
tff(f3549,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum(1,'fun_app$a'('of_nat$',sK72(X0,X1)))))
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f2858,f848]) ).
tff(f2858,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK72(X0,X1)),1)))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f1836,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ~ 'fun_app$n'(X0,sK72(X0,X1))
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK72(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK72(X0,X1)),'fun_app$a'('of_nat$',X1)) )
| ~ sP7(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f1834,f1835]) ).
tff(f1835,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) )
=> ( ~ 'fun_app$n'(X0,sK72(X0,X1))
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',sK72(X0,X1)),1)))
& $less('fun_app$a'('of_nat$',sK72(X0,X1)),'fun_app$a'('of_nat$',X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1834,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$n'(X0,X2)
& 'fun_app$n'(X0,'nat$'($sum('fun_app$a'('of_nat$',X2),1)))
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X1)) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f1833]) ).
tff(f1833,plain,
! [X2: 'Nat_bool_fun$',X1: 'Nat$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X2,X3)
& 'fun_app$n'(X2,'nat$'($sum('fun_app$a'('of_nat$',X3),1)))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X1)) )
| ~ sP7(X2,X1) ),
inference(nnf_transformation,[],[f1511]) ).
tff(f5686,plain,
( spl272_304
| ~ spl272_109
| ~ spl272_248 ),
inference(avatar_split_clause,[],[f5467,f5250,f4112,f5684]) ).
tff(f5250,plain,
( spl272_248
<=> ! [X0: $real] : ~ $less($sum(2.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_248])]) ).
tff(f5467,plain,
( ! [X0: $real] : $less(X0,$sum(3.0,X0))
| ~ spl272_109
| ~ spl272_248 ),
inference(evaluation,[],[f5461]) ).
tff(f5461,plain,
( ! [X0: $real] : $less(X0,$sum(2.0,$sum(X0,1.0)))
| ~ spl272_109
| ~ spl272_248 ),
inference(resolution,[],[f5251,f4113]) ).
tff(f5251,plain,
( ! [X0: $real] : ~ $less($sum(2.0,X0),X0)
| ~ spl272_248 ),
inference(avatar_component_clause,[],[f5250]) ).
tff(f5676,plain,
( ~ spl272_40
| ~ spl272_301 ),
inference(avatar_contradiction_clause,[],[f5675]) ).
tff(f5675,plain,
( $false
| ~ spl272_40
| ~ spl272_301 ),
inference(trivial_inequality_removal,[],[f5669]) ).
tff(f5669,plain,
( ( 0 != 0 )
| ~ spl272_40
| ~ spl272_301 ),
inference(superposition,[],[f5656,f3780]) ).
tff(f5656,plain,
( ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) != 0 )
| ~ spl272_301 ),
inference(avatar_component_clause,[],[f5655]) ).
tff(f5674,plain,
( ~ spl272_41
| ~ spl272_301 ),
inference(avatar_contradiction_clause,[],[f5673]) ).
tff(f5673,plain,
( $false
| ~ spl272_41
| ~ spl272_301 ),
inference(trivial_inequality_removal,[],[f5670]) ).
tff(f5670,plain,
( ( 0 != 0 )
| ~ spl272_41
| ~ spl272_301 ),
inference(superposition,[],[f5656,f3785]) ).
tff(f3785,plain,
( ( 0 = 'fun_app$a'('of_nat$','nat$'(0)) )
| ~ spl272_41 ),
inference(avatar_component_clause,[],[f3783]) ).
tff(f3783,plain,
( spl272_41
<=> ( 0 = 'fun_app$a'('of_nat$','nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_41])]) ).
tff(f5668,plain,
( spl272_301
| spl272_303 ),
inference(avatar_split_clause,[],[f3523,f5666,f5655]) ).
tff(f3523,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'fun_app$p'('times$b'(0),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(inner_rewriting,[],[f2729]) ).
tff(f2729,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1762]) ).
tff(f5660,plain,
( spl272_301
| spl272_302 ),
inference(avatar_split_clause,[],[f3522,f5658,f5655]) ).
tff(f3522,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),0) )
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(inner_rewriting,[],[f2730]) ).
tff(f2730,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X1)) )
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(cnf_transformation,[],[f1762]) ).
tff(f5653,plain,
spl272_300,
inference(avatar_split_clause,[],[f3497,f5651]) ).
tff(f5651,plain,
( spl272_300
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_300])]) ).
tff(f3497,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(forward_demodulation,[],[f2687,f2346]) ).
tff(f2687,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f5649,plain,
spl272_299,
inference(avatar_split_clause,[],[f3496,f5647]) ).
tff(f5647,plain,
( spl272_299
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_299])]) ).
tff(f3496,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(forward_demodulation,[],[f2688,f2346]) ).
tff(f2688,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0.0,'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f5645,plain,
spl272_298,
inference(avatar_split_clause,[],[f3423,f5643]) ).
tff(f5643,plain,
( spl272_298
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),1)
| $less('fun_app$a'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_298])]) ).
tff(f3423,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),1)
| $less('fun_app$a'('of_nat$',X0),1) ),
inference(evaluation,[],[f2419]) ).
tff(f2419,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),$sum(0,1))
| $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ),
inference(cnf_transformation,[],[f1051]) ).
tff(f1051,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),$sum(0,1))
| $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ),
inference(ennf_transformation,[],[f698]) ).
tff(f698,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1))
=> ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)),$sum(0,1)) ),
inference(theory_normalization,[],[f325]) ).
tff(f325,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $lesseq($sum(0,1),'fun_app$a'('of_nat$',X0))
=> $lesseq($sum(0,1),'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom323) ).
tff(f5641,plain,
spl272_297,
inference(avatar_split_clause,[],[f3416,f5639]) ).
tff(f5639,plain,
( spl272_297
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) )
| ( 1 != 'fun_app$a'('of_nat$',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_297])]) ).
tff(f3416,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) )
| ( 1 != 'fun_app$a'('of_nat$',X0) ) ),
inference(evaluation,[],[f2733]) ).
tff(f2733,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X0) != $sum(0,1) ) ),
inference(cnf_transformation,[],[f1764]) ).
tff(f5637,plain,
spl272_296,
inference(avatar_split_clause,[],[f3415,f5635]) ).
tff(f5635,plain,
( spl272_296
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) )
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_296])]) ).
tff(f3415,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) )
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(evaluation,[],[f2732]) ).
tff(f2732,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = $sum(0,1) )
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(cnf_transformation,[],[f1764]) ).
tff(f5633,plain,
( spl272_295
| ~ spl272_58
| ~ spl272_248 ),
inference(avatar_split_clause,[],[f5465,f5250,f3865,f5631]) ).
tff(f5631,plain,
( spl272_295
<=> ! [X0: $real] : ~ $less($sum(X0,2.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_295])]) ).
tff(f5465,plain,
( ! [X0: $real] : ~ $less($sum(X0,2.0),X0)
| ~ spl272_58
| ~ spl272_248 ),
inference(superposition,[],[f5251,f3866]) ).
tff(f5629,plain,
spl272_294,
inference(avatar_split_clause,[],[f3224,f5627]) ).
tff(f5627,plain,
( spl272_294
<=> ! [X2: $int,X0: $int,X3: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_294])]) ).
tff(f3224,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f864]) ).
tff(f864,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_151,[]) ).
tff(f5625,plain,
spl272_293,
inference(avatar_split_clause,[],[f3223,f5623]) ).
tff(f5623,plain,
( spl272_293
<=> ! [X2: $real,X0: $real,X3: $real] :
( ( 0.0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_293])]) ).
tff(f3223,plain,
! [X2: $real,X3: $real,X0: $real] :
( ( 0.0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f882]) ).
tff(f882,plain,
! [X2: $real,X3: $real,X0: $real,X1: $real] :
( ( 0.0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_151,[]) ).
tff(f5621,plain,
spl272_292,
inference(avatar_split_clause,[],[f2779,f5619]) ).
tff(f5619,plain,
( spl272_292
<=> ! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP4(X1,X0)
| ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_292])]) ).
tff(f2779,plain,
! [X2: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP4(X1,X0)
| ~ 'fun_app$n'(X1,X2)
| ~ $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f5617,plain,
spl272_291,
inference(avatar_split_clause,[],[f2763,f5615]) ).
tff(f5615,plain,
( spl272_291
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$',X3: 'Nat$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
| ~ sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_291])]) ).
tff(f2763,plain,
! [X3: 'Nat$',X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,X3)
| ~ $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X0))
| ~ sP2(X1,X0) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f5613,plain,
spl272_290,
inference(avatar_split_clause,[],[f2691,f5611]) ).
tff(f5611,plain,
( spl272_290
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_290])]) ).
tff(f2691,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ( 'fun_app$a'('of_nat$',X1) != 0 ) ),
inference(cnf_transformation,[],[f1735]) ).
tff(f5609,plain,
spl272_289,
inference(avatar_split_clause,[],[f2690,f5607]) ).
tff(f2690,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1735]) ).
tff(f5605,plain,
spl272_288,
inference(avatar_split_clause,[],[f2494,f5603]) ).
tff(f5603,plain,
( spl272_288
<=> ! [X0: 'Nat$',X1: $real] :
( $less(0.0,sK49(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_288])]) ).
tff(f2494,plain,
! [X0: 'Nat$',X1: $real] :
( $less(0.0,sK49(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f5601,plain,
spl272_287,
inference(avatar_split_clause,[],[f2492,f5599]) ).
tff(f5599,plain,
( spl272_287
<=> ! [X0: 'Nat$',X1: $real] :
( $less(0.0,sK48(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_287])]) ).
tff(f2492,plain,
! [X0: 'Nat$',X1: $real] :
( $less(0.0,sK48(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1630]) ).
tff(f5596,plain,
spl272_286,
inference(avatar_split_clause,[],[f2487,f5594]) ).
tff(f2487,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| $less(0,'fun_app$a'('of_nat$',sK47(X0)))
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1627]) ).
tff(f5591,plain,
spl272_285,
inference(avatar_split_clause,[],[f2485,f5589]) ).
tff(f2485,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK46(X0))
| sP1(X0)
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1625]) ).
tff(f5587,plain,
( spl272_284
| ~ spl272_107
| ~ spl272_240 ),
inference(avatar_split_clause,[],[f5365,f5087,f4104,f5585]) ).
tff(f5365,plain,
( ! [X0: $int] : $less(X0,$sum(3,X0))
| ~ spl272_107
| ~ spl272_240 ),
inference(evaluation,[],[f5353]) ).
tff(f5353,plain,
( ! [X0: $int] : $less(X0,$sum(2,$sum(X0,1)))
| ~ spl272_107
| ~ spl272_240 ),
inference(resolution,[],[f5088,f4105]) ).
tff(f5583,plain,
spl272_283,
inference(avatar_split_clause,[],[f2400,f5581]) ).
tff(f5581,plain,
( spl272_283
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),'fun_app$b'('power$'(X0),X1))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_283])]) ).
tff(f2400,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),'fun_app$b'('power$'(X0),X1))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(cnf_transformation,[],[f1035]) ).
tff(f1035,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),'fun_app$b'('power$'(X0),X1))
| ~ 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0) ),
inference(ennf_transformation,[],[f194]) ).
tff(f194,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),X0)
=> 'fun_app$n'('fun_app$o'('less_eq$b','zero$'),'fun_app$b'('power$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom192) ).
tff(f5579,plain,
spl272_282,
inference(avatar_split_clause,[],[f2373,f5577]) ).
tff(f5577,plain,
( spl272_282
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ( X0 = X1 )
| 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_282])]) ).
tff(f2373,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ( X0 = X1 )
| 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f464]) ).
tff(f464,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ( X0 = X1 )
| 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
tff(f5575,plain,
spl272_281,
inference(avatar_split_clause,[],[f2371,f5573]) ).
tff(f5573,plain,
( spl272_281
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ( X0 = X1 )
| 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_281])]) ).
tff(f2371,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ( X0 = X1 )
| 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f466]) ).
tff(f466,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ( X0 = X1 )
| 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom464) ).
tff(f5571,plain,
spl272_280,
inference(avatar_split_clause,[],[f2365,f5569]) ).
tff(f5569,plain,
( spl272_280
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_280])]) ).
tff(f2365,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f283]) ).
tff(f283,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom281) ).
tff(f5567,plain,
spl272_279,
inference(avatar_split_clause,[],[f2364,f5565]) ).
tff(f5565,plain,
( spl272_279
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_279])]) ).
tff(f2364,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f284]) ).
tff(f284,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1)
| ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom282) ).
tff(f5563,plain,
spl272_278,
inference(avatar_split_clause,[],[f2348,f5561]) ).
tff(f2348,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X0)),X1) ),
inference(cnf_transformation,[],[f121]) ).
tff(f121,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$a'('of_nat$','fun_app$b'('power$'(X0),X1)) = 'fun_app$a'('power$a'('fun_app$a'('of_nat$',X0)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom119) ).
tff(f5559,plain,
spl272_277,
inference(avatar_split_clause,[],[f2347,f5557]) ).
tff(f5557,plain,
( spl272_277
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$b'('of_nat$a','fun_app$b'('power$'(X0),X1)) = 'fun_app$b'('power$'('fun_app$b'('of_nat$a',X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_277])]) ).
tff(f5555,plain,
spl272_276,
inference(avatar_split_clause,[],[f2346,f5553]) ).
tff(f5553,plain,
( spl272_276
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$m'('of_nat$b','fun_app$b'('power$'(X0),X1)) = 'fun_app$m'('power$c'('fun_app$m'('of_nat$b',X0)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_276])]) ).
tff(f5551,plain,
spl272_275,
inference(avatar_split_clause,[],[f2344,f5549]) ).
tff(f5549,plain,
( spl272_275
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( $product(2,'fun_app$a'('of_nat$',X1)) != $sum($product(2,'fun_app$a'('of_nat$',X0)),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_275])]) ).
tff(f2344,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( $product(2,'fun_app$a'('of_nat$',X1)) != $sum($product(2,'fun_app$a'('of_nat$',X0)),1) ),
inference(cnf_transformation,[],[f608]) ).
tff(f608,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( $product(2,'fun_app$a'('of_nat$',X1)) != $sum($product(2,'fun_app$a'('of_nat$',X0)),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom606) ).
tff(f5547,plain,
spl272_274,
inference(avatar_split_clause,[],[f881,f5545]) ).
tff(f5545,plain,
( spl272_274
<=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_274])]) ).
tff(f881,plain,
! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f5543,plain,
( spl272_273
| ~ spl272_56
| ~ spl272_240 ),
inference(avatar_split_clause,[],[f5360,f5087,f3857,f5541]) ).
tff(f5541,plain,
( spl272_273
<=> ! [X0: $int] : ~ $less($sum(X0,2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_273])]) ).
tff(f5360,plain,
( ! [X0: $int] : ~ $less($sum(X0,2),X0)
| ~ spl272_56
| ~ spl272_240 ),
inference(superposition,[],[f5088,f3858]) ).
tff(f5539,plain,
spl272_272,
inference(avatar_split_clause,[],[f863,f5537]) ).
tff(f5537,plain,
( spl272_272
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_272])]) ).
tff(f863,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f5492,plain,
( spl272_271
| ~ spl272_55
| ~ spl272_257 ),
inference(avatar_split_clause,[],[f5382,f5379,f3851,f5490]) ).
tff(f5490,plain,
( spl272_271
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,sK42(X0,X1))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_271])]) ).
tff(f5379,plain,
( spl272_257
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK42(X0,X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_257])]) ).
tff(f5382,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,sK42(X0,X1))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_257 ),
inference(forward_demodulation,[],[f5380,f3853]) ).
tff(f5380,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK42(X0,X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_257 ),
inference(avatar_component_clause,[],[f5379]) ).
tff(f5444,plain,
spl272_270,
inference(avatar_split_clause,[],[f2857,f5442]) ).
tff(f5442,plain,
( spl272_270
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK72(X0,X1)),'fun_app$a'('of_nat$',X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_270])]) ).
tff(f2857,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( $less('fun_app$a'('of_nat$',sK72(X0,X1)),'fun_app$a'('of_nat$',X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f5440,plain,
spl272_269,
inference(avatar_split_clause,[],[f2814,f5438]) ).
tff(f5438,plain,
( spl272_269
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK66(X0))
| 'fun_app$n'(X0,sK67(X0,X2))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_269])]) ).
tff(f2814,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK66(X0))
| 'fun_app$n'(X0,sK67(X0,X2))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1823]) ).
tff(f5436,plain,
spl272_268,
inference(avatar_split_clause,[],[f2676,f5434]) ).
tff(f5434,plain,
( spl272_268
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_268])]) ).
tff(f2676,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1726]) ).
tff(f1726,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ) ),
inference(nnf_transformation,[],[f750]) ).
tff(f750,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(theory_normalization,[],[f11]) ).
tff(f11,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $lesseq('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom9) ).
tff(f5432,plain,
spl272_267,
inference(avatar_split_clause,[],[f2675,f5430]) ).
tff(f5430,plain,
( spl272_267
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_267])]) ).
tff(f2675,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$d'('numeral$',X1),'fun_app$d'('numeral$',X0)) ),
inference(cnf_transformation,[],[f1726]) ).
tff(f5428,plain,
spl272_266,
inference(avatar_split_clause,[],[f2665,f5426]) ).
tff(f5426,plain,
( spl272_266
<=> ! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_266])]) ).
tff(f2665,plain,
! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1720]) ).
tff(f1720,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ) ),
inference(nnf_transformation,[],[f361]) ).
tff(f361,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1))
<=> 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom359) ).
tff(f5424,plain,
spl272_265,
inference(avatar_split_clause,[],[f2664,f5422]) ).
tff(f5422,plain,
( spl272_265
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_265])]) ).
tff(f2664,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$d'('numeral$',X0),'fun_app$d'('numeral$',X1)) ),
inference(cnf_transformation,[],[f1720]) ).
tff(f5420,plain,
spl272_264,
inference(avatar_split_clause,[],[f2662,f5418]) ).
tff(f5418,plain,
( spl272_264
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_264])]) ).
tff(f2662,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X1)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f5406,plain,
spl272_263,
inference(avatar_split_clause,[],[f2661,f5404]) ).
tff(f5404,plain,
( spl272_263
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_263])]) ).
tff(f2661,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0)
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'times$c'(X0,X1)) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f5402,plain,
spl272_262,
inference(avatar_split_clause,[],[f2656,f5400]) ).
tff(f5400,plain,
( spl272_262
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_262])]) ).
tff(f2656,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f1715]) ).
tff(f1715,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ~ $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0))
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0)) ) ),
inference(nnf_transformation,[],[f745]) ).
tff(f745,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(theory_normalization,[],[f13]) ).
tff(f13,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $lesseq('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1))
<=> 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
tff(f5398,plain,
spl272_261,
inference(avatar_split_clause,[],[f2655,f5396]) ).
tff(f5396,plain,
( spl272_261
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_261])]) ).
tff(f2655,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),X1)
| $less('fun_app$j'('numeral$b',X1),'fun_app$j'('numeral$b',X0)) ),
inference(cnf_transformation,[],[f1715]) ).
tff(f5394,plain,
spl272_260,
inference(avatar_split_clause,[],[f2648,f5392]) ).
tff(f5392,plain,
( spl272_260
<=> ! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_260])]) ).
tff(f2648,plain,
! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f1711,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1))
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) )
& ( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) ) ),
inference(nnf_transformation,[],[f363]) ).
tff(f363,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1))
<=> 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom361) ).
tff(f5390,plain,
spl272_259,
inference(avatar_split_clause,[],[f2647,f5388]) ).
tff(f5388,plain,
( spl272_259
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_259])]) ).
tff(f2647,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
| ~ $less('fun_app$j'('numeral$b',X0),'fun_app$j'('numeral$b',X1)) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f5386,plain,
spl272_258,
inference(avatar_split_clause,[],[f2535,f5384]) ).
tff(f5384,plain,
( spl272_258
<=> ! [X0: 'Enat_bool_fun$',X1: 'Enat$',X3: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),sK53(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_258])]) ).
tff(f2535,plain,
! [X3: 'Enat$',X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),sK53(X0)) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f1640,plain,
! [X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| ( ~ 'fun_app$g'(X0,sK53(X0))
& ! [X3: 'Enat$'] :
( 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),sK53(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1180,f1639]) ).
tff(f1639,plain,
! [X0: 'Enat_bool_fun$'] :
( ? [X2: 'Enat$'] :
( ~ 'fun_app$g'(X0,X2)
& ! [X3: 'Enat$'] :
( 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),X2) ) )
=> ( ~ 'fun_app$g'(X0,sK53(X0))
& ! [X3: 'Enat$'] :
( 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),sK53(X0)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1180,plain,
! [X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| ? [X2: 'Enat$'] :
( ~ 'fun_app$g'(X0,X2)
& ! [X3: 'Enat$'] :
( 'fun_app$g'(X0,X3)
| ~ 'fun_app$g'('fun_app$h'('less$a',X3),X2) ) ) ),
inference(ennf_transformation,[],[f613]) ).
tff(f613,axiom,
! [X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( ! [X2: 'Enat$'] :
( ! [X3: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X3),X2)
=> 'fun_app$g'(X0,X3) )
=> 'fun_app$g'(X0,X2) )
=> 'fun_app$g'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom611) ).
tff(f5381,plain,
spl272_257,
inference(avatar_split_clause,[],[f2469,f5379]) ).
tff(f2469,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK42(X0,X1))
| 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1615]) ).
tff(f5377,plain,
spl272_256,
inference(avatar_split_clause,[],[f2343,f5375]) ).
tff(f5375,plain,
( spl272_256
<=> ! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'numeral$c'(X1)) = 'numeral$c'('fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_256])]) ).
tff(f2343,plain,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'numeral$c'(X1)) = 'numeral$c'('fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f364]) ).
tff(f364,axiom,
! [X0: 'Num$',X1: 'Num$'] : ( 'fun_app$b'('times$'('numeral$c'(X0)),'numeral$c'(X1)) = 'numeral$c'('fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
tff(f5373,plain,
spl272_255,
inference(avatar_split_clause,[],[f2331,f5371]) ).
tff(f5371,plain,
( spl272_255
<=> ! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a')
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_255])]) ).
tff(f2331,plain,
! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a')
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1592]) ).
tff(f1592,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a')
| ( 'fun_app$a'('of_nat$',X0) != 0 ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a') ) ),
inference(nnf_transformation,[],[f104]) ).
tff(f104,axiom,
! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a')
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom102) ).
tff(f5369,plain,
spl272_254,
inference(avatar_split_clause,[],[f2330,f5367]) ).
tff(f5367,plain,
( spl272_254
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_254])]) ).
tff(f2330,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$l'('of_nat$c',X0)),'zero$a') ),
inference(cnf_transformation,[],[f1592]) ).
tff(f5352,plain,
spl272_253,
inference(avatar_split_clause,[],[f2329,f5350]) ).
tff(f5350,plain,
( spl272_253
<=> ! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_253])]) ).
tff(f2329,plain,
! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1591]) ).
tff(f1591,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0)) ) ),
inference(nnf_transformation,[],[f403]) ).
tff(f403,axiom,
! [X0: 'Nat$'] :
( 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0))
<=> $less(0,'fun_app$a'('of_nat$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom401) ).
tff(f5348,plain,
spl272_252,
inference(avatar_split_clause,[],[f2328,f5346]) ).
tff(f5346,plain,
( spl272_252
<=> ! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_252])]) ).
tff(f2328,plain,
! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),'fun_app$l'('of_nat$c',X0)) ),
inference(cnf_transformation,[],[f1591]) ).
tff(f5344,plain,
spl272_251,
inference(avatar_split_clause,[],[f2240,f5342]) ).
tff(f5342,plain,
( spl272_251
<=> ! [X0: $real,X1: $real] :
( $less(X1,'times$d'('fun_app$m'('of_nat$b',sK24(X0,X1)),X0))
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_251])]) ).
tff(f2240,plain,
! [X0: $real,X1: $real] :
( $less(X1,'times$d'('fun_app$m'('of_nat$b',sK24(X0,X1)),X0))
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1534]) ).
tff(f1534,plain,
! [X0: $real] :
( ! [X1: $real] : $less(X1,'times$d'('fun_app$m'('of_nat$b',sK24(X0,X1)),X0))
| ~ $less(0.0,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f997,f1533]) ).
tff(f1533,plain,
! [X0: $real,X1: $real] :
( ? [X2: 'Nat$'] : $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0))
=> $less(X1,'times$d'('fun_app$m'('of_nat$b',sK24(X0,X1)),X0)) ),
introduced(choice_axiom,[]) ).
tff(f997,plain,
! [X0: $real] :
( ! [X1: $real] :
? [X2: 'Nat$'] : $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0))
| ~ $less(0.0,X0) ),
inference(ennf_transformation,[],[f625]) ).
tff(f625,axiom,
! [X0: $real] :
( $less(0.0,X0)
=> ! [X1: $real] :
? [X2: 'Nat$'] : $less(X1,'times$d'('fun_app$m'('of_nat$b',X2),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom623) ).
tff(f5340,plain,
spl272_250,
inference(avatar_split_clause,[],[f2233,f5338]) ).
tff(f2233,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),
inference(cnf_transformation,[],[f667]) ).
tff(f667,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0)),
inference(theory_normalization,[],[f578]) ).
tff(f578,axiom,
! [X0: 'Nat$'] : $lesseq('fun_app$a'('of_nat$',X0),'fun_app$p'('times$b'('fun_app$a'('of_nat$',X0)),'fun_app$a'('of_nat$',X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom576) ).
tff(f5314,plain,
( spl272_249
| ~ spl272_58
| ~ spl272_211 ),
inference(avatar_split_clause,[],[f5044,f4818,f3865,f5312]) ).
tff(f5312,plain,
( spl272_249
<=> ! [X0: $real] : $less(X0,$sum(X0,2.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_249])]) ).
tff(f4818,plain,
( spl272_211
<=> ! [X0: $real] : $less(X0,$sum(2.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_211])]) ).
tff(f5044,plain,
( ! [X0: $real] : $less(X0,$sum(X0,2.0))
| ~ spl272_58
| ~ spl272_211 ),
inference(superposition,[],[f4819,f3866]) ).
tff(f4819,plain,
( ! [X0: $real] : $less(X0,$sum(2.0,X0))
| ~ spl272_211 ),
inference(avatar_component_clause,[],[f4818]) ).
tff(f5252,plain,
( spl272_248
| ~ spl272_50
| ~ spl272_211 ),
inference(avatar_split_clause,[],[f5041,f4818,f3821,f5250]) ).
tff(f5041,plain,
( ! [X0: $real] : ~ $less($sum(2.0,X0),X0)
| ~ spl272_50
| ~ spl272_211 ),
inference(resolution,[],[f4819,f3822]) ).
tff(f5232,plain,
( spl272_247
| ~ spl272_55
| ~ spl272_226 ),
inference(avatar_split_clause,[],[f5026,f5023,f3851,f5230]) ).
tff(f5230,plain,
( spl272_247
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK47(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_247])]) ).
tff(f5023,plain,
( spl272_226
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK47(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_226])]) ).
tff(f5026,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK47(X0)) )
| ~ spl272_55
| ~ spl272_226 ),
inference(forward_demodulation,[],[f5024,f3853]) ).
tff(f5024,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK47(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_226 ),
inference(avatar_component_clause,[],[f5023]) ).
tff(f5228,plain,
( spl272_246
| ~ spl272_55
| ~ spl272_224 ),
inference(avatar_split_clause,[],[f5017,f5014,f3851,f5226]) ).
tff(f5226,plain,
( spl272_246
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK44(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_246])]) ).
tff(f5014,plain,
( spl272_224
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK44(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_224])]) ).
tff(f5017,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'size$a'('one$'))
| 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK44(X0)) )
| ~ spl272_55
| ~ spl272_224 ),
inference(forward_demodulation,[],[f5015,f3853]) ).
tff(f5015,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK44(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_224 ),
inference(avatar_component_clause,[],[f5014]) ).
tff(f5224,plain,
( spl272_245
| ~ spl272_55
| ~ spl272_223 ),
inference(avatar_split_clause,[],[f5012,f5009,f3851,f5222]) ).
tff(f5222,plain,
( spl272_245
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,sK43(X0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_245])]) ).
tff(f5009,plain,
( spl272_223
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,sK43(X0))
| ~ 'fun_app$n'(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_223])]) ).
tff(f5012,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,sK43(X0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_55
| ~ spl272_223 ),
inference(forward_demodulation,[],[f5010,f3853]) ).
tff(f5010,plain,
( ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,sK43(X0))
| ~ 'fun_app$n'(X0,X1) )
| ~ spl272_223 ),
inference(avatar_component_clause,[],[f5009]) ).
tff(f5193,plain,
( spl272_244
| ~ spl272_56
| ~ spl272_201 ),
inference(avatar_split_clause,[],[f4936,f4712,f3857,f5191]) ).
tff(f5191,plain,
( spl272_244
<=> ! [X0: $int] : $less(X0,$sum(X0,2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_244])]) ).
tff(f4712,plain,
( spl272_201
<=> ! [X0: $int] : $less(X0,$sum(2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_201])]) ).
tff(f4936,plain,
( ! [X0: $int] : $less(X0,$sum(X0,2))
| ~ spl272_56
| ~ spl272_201 ),
inference(superposition,[],[f4713,f3858]) ).
tff(f4713,plain,
( ! [X0: $int] : $less(X0,$sum(2,X0))
| ~ spl272_201 ),
inference(avatar_component_clause,[],[f4712]) ).
tff(f5186,plain,
( spl272_243
| ~ spl272_55
| ~ spl272_218 ),
inference(avatar_split_clause,[],[f4984,f4981,f3851,f5184]) ).
tff(f5184,plain,
( spl272_243
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,sK31(X0))
| ~ 'fun_app$n'(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_243])]) ).
tff(f4981,plain,
( spl272_218
<=> ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X0,sK31(X0))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_218])]) ).
tff(f4984,plain,
( ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,'size$a'('one$'))
| ~ 'fun_app$n'(X0,sK31(X0))
| ~ 'fun_app$n'(X0,X2) )
| ~ spl272_55
| ~ spl272_218 ),
inference(forward_demodulation,[],[f4982,f3853]) ).
tff(f4982,plain,
( ! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X0,sK31(X0))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) )
| ~ spl272_218 ),
inference(avatar_component_clause,[],[f4981]) ).
tff(f5097,plain,
spl272_242,
inference(avatar_split_clause,[],[f3444,f5095]) ).
tff(f5095,plain,
( spl272_242
<=> ! [X0: 'Nat$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_242])]) ).
tff(f3444,plain,
! [X0: 'Nat$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2230,f848]) ).
tff(f2230,plain,
! [X0: 'Nat$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f108]) ).
tff(f108,axiom,
! [X0: 'Nat$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom106) ).
tff(f5093,plain,
spl272_241,
inference(avatar_split_clause,[],[f3443,f5091]) ).
tff(f5091,plain,
( spl272_241
<=> ! [X0: 'Nat$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_241])]) ).
tff(f3443,plain,
! [X0: 'Nat$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2229,f848]) ).
tff(f2229,plain,
! [X0: 'Nat$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f109]) ).
tff(f109,axiom,
! [X0: 'Nat$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom107) ).
tff(f5089,plain,
( spl272_240
| ~ spl272_51
| ~ spl272_201 ),
inference(avatar_split_clause,[],[f4932,f4712,f3825,f5087]) ).
tff(f4932,plain,
( ! [X0: $int] : ~ $less($sum(2,X0),X0)
| ~ spl272_51
| ~ spl272_201 ),
inference(resolution,[],[f4713,f3826]) ).
tff(f5085,plain,
spl272_239,
inference(avatar_split_clause,[],[f3442,f5083]) ).
tff(f5083,plain,
( spl272_239
<=> ! [X0: 'Nat$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_239])]) ).
tff(f3442,plain,
! [X0: 'Nat$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2228,f848]) ).
tff(f2228,plain,
! [X0: 'Nat$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
! [X0: 'Nat$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).
tff(f5081,plain,
spl272_238,
inference(avatar_split_clause,[],[f3441,f5079]) ).
tff(f5079,plain,
( spl272_238
<=> ! [X0: 'Nat$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_238])]) ).
tff(f3441,plain,
! [X0: 'Nat$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2227,f848]) ).
tff(f2227,plain,
! [X0: 'Nat$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f107]) ).
tff(f107,axiom,
! [X0: 'Nat$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
tff(f5077,plain,
spl272_237,
inference(avatar_split_clause,[],[f3303,f5075]) ).
tff(f5075,plain,
( spl272_237
<=> ! [X1: 'Nat$'] :
( ( 'zero$' = 'fun_app$b'('power$'('zero$'),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_237])]) ).
tff(f3303,plain,
! [X1: 'Nat$'] :
( ( 'zero$' = 'fun_app$b'('power$'('zero$'),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ),
inference(equality_resolution,[],[f2619]) ).
tff(f2619,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),X1) = 'zero$' )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 'zero$' != X0 ) ),
inference(cnf_transformation,[],[f1696]) ).
tff(f1696,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$b'('power$'(X0),X1) = 'zero$' )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 'zero$' != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'zero$' = X0 ) )
| ( 'fun_app$b'('power$'(X0),X1) != 'zero$' ) ) ),
inference(flattening,[],[f1695]) ).
tff(f1695,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'fun_app$b'('power$'(X0),X1) = 'zero$' )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 'zero$' != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'zero$' = X0 ) )
| ( 'fun_app$b'('power$'(X0),X1) != 'zero$' ) ) ),
inference(nnf_transformation,[],[f387]) ).
tff(f387,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),X1) = 'zero$' )
<=> ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'zero$' = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom385) ).
tff(f5073,plain,
spl272_236,
inference(avatar_split_clause,[],[f3302,f5071]) ).
tff(f5071,plain,
( spl272_236
<=> ! [X1: 'Nat$'] :
( ( 0 = 'fun_app$a'('power$a'(0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_236])]) ).
tff(f3302,plain,
! [X1: 'Nat$'] :
( ( 0 = 'fun_app$a'('power$a'(0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ),
inference(equality_resolution,[],[f2616]) ).
tff(f2616,plain,
! [X0: $int,X1: 'Nat$'] :
( ( 0 = 'fun_app$a'('power$a'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0 != X0 ) ),
inference(cnf_transformation,[],[f1694]) ).
tff(f1694,plain,
! [X0: $int,X1: 'Nat$'] :
( ( ( 0 = 'fun_app$a'('power$a'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0 != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0 = X0 ) )
| ( 0 != 'fun_app$a'('power$a'(X0),X1) ) ) ),
inference(flattening,[],[f1693]) ).
tff(f1693,plain,
! [X0: $int,X1: 'Nat$'] :
( ( ( 0 = 'fun_app$a'('power$a'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0 != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0 = X0 ) )
| ( 0 != 'fun_app$a'('power$a'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f388]) ).
tff(f388,axiom,
! [X0: $int,X1: 'Nat$'] :
( ( 0 = 'fun_app$a'('power$a'(X0),X1) )
<=> ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom386) ).
tff(f5069,plain,
spl272_235,
inference(avatar_split_clause,[],[f3301,f5067]) ).
tff(f5067,plain,
( spl272_235
<=> ! [X1: 'Nat$'] :
( ( 0.0 = 'fun_app$m'('power$c'(0.0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_235])]) ).
tff(f3301,plain,
! [X1: 'Nat$'] :
( ( 0.0 = 'fun_app$m'('power$c'(0.0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1)) ),
inference(equality_resolution,[],[f2613]) ).
tff(f2613,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 0.0 = 'fun_app$m'('power$c'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0.0 != X0 ) ),
inference(cnf_transformation,[],[f1692]) ).
tff(f1692,plain,
! [X0: $real,X1: 'Nat$'] :
( ( ( 0.0 = 'fun_app$m'('power$c'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0.0 != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0.0 = X0 ) )
| ( 0.0 != 'fun_app$m'('power$c'(X0),X1) ) ) ),
inference(flattening,[],[f1691]) ).
tff(f1691,plain,
! [X0: $real,X1: 'Nat$'] :
( ( ( 0.0 = 'fun_app$m'('power$c'(X0),X1) )
| ~ $less(0,'fun_app$a'('of_nat$',X1))
| ( 0.0 != X0 ) )
& ( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0.0 = X0 ) )
| ( 0.0 != 'fun_app$m'('power$c'(X0),X1) ) ) ),
inference(nnf_transformation,[],[f389]) ).
tff(f389,axiom,
! [X0: $real,X1: 'Nat$'] :
( ( 0.0 = 'fun_app$m'('power$c'(X0),X1) )
<=> ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 0.0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom387) ).
tff(f5065,plain,
spl272_234,
inference(avatar_split_clause,[],[f2852,f5063]) ).
tff(f5063,plain,
( spl272_234
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$a'('of_nat$',sK69(X0)),'fun_app$a'('of_nat$',sK70(X0)))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_234])]) ).
tff(f2852,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$a'('of_nat$',sK69(X0)),'fun_app$a'('of_nat$',sK70(X0)))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f1829,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ( ~ 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK70(X0))
& 'fun_app$n'('fun_app$o'(X0,sK69(X0)),sK70(X0))
& 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK69(X0))
& $less('fun_app$a'('of_nat$',sK69(X0)),'fun_app$a'('of_nat$',sK70(X0)))
& $less('fun_app$a'('of_nat$',sK68(X0)),'fun_app$a'('of_nat$',sK69(X0))) )
| ~ sP6(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70])],[f1827,f1828]) ).
tff(f1828,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,X1),X3)
& 'fun_app$n'('fun_app$o'(X0,X2),X3)
& 'fun_app$n'('fun_app$o'(X0,X1),X2)
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
& $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
=> ( ~ 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK70(X0))
& 'fun_app$n'('fun_app$o'(X0,sK69(X0)),sK70(X0))
& 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK69(X0))
& $less('fun_app$a'('of_nat$',sK69(X0)),'fun_app$a'('of_nat$',sK70(X0)))
& $less('fun_app$a'('of_nat$',sK68(X0)),'fun_app$a'('of_nat$',sK69(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f1827,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ? [X1: 'Nat$',X2: 'Nat$',X3: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,X1),X3)
& 'fun_app$n'('fun_app$o'(X0,X2),X3)
& 'fun_app$n'('fun_app$o'(X0,X1),X2)
& $less('fun_app$a'('of_nat$',X2),'fun_app$a'('of_nat$',X3))
& $less('fun_app$a'('of_nat$',X1),'fun_app$a'('of_nat$',X2)) )
| ~ sP6(X0) ),
inference(rectify,[],[f1826]) ).
tff(f1826,plain,
! [X2: 'Nat_nat_bool_fun_fun$'] :
( ? [X3: 'Nat$',X4: 'Nat$',X5: 'Nat$'] :
( ~ 'fun_app$n'('fun_app$o'(X2,X3),X5)
& 'fun_app$n'('fun_app$o'(X2,X4),X5)
& 'fun_app$n'('fun_app$o'(X2,X3),X4)
& $less('fun_app$a'('of_nat$',X4),'fun_app$a'('of_nat$',X5))
& $less('fun_app$a'('of_nat$',X3),'fun_app$a'('of_nat$',X4)) )
| ~ sP6(X2) ),
inference(nnf_transformation,[],[f1509]) ).
tff(f5061,plain,
spl272_233,
inference(avatar_split_clause,[],[f2851,f5059]) ).
tff(f5059,plain,
( spl272_233
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$a'('of_nat$',sK68(X0)),'fun_app$a'('of_nat$',sK69(X0)))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_233])]) ).
tff(f2851,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( $less('fun_app$a'('of_nat$',sK68(X0)),'fun_app$a'('of_nat$',sK69(X0)))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f5057,plain,
spl272_232,
inference(avatar_split_clause,[],[f2777,f5055]) ).
tff(f5055,plain,
( spl272_232
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,sK63(X0,X1))
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_232])]) ).
tff(f2777,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,sK63(X0,X1))
| 'fun_app$n'(X1,X0)
| ~ sP4(X1,X0) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f5053,plain,
spl272_231,
inference(avatar_split_clause,[],[f2765,f5051]) ).
tff(f5051,plain,
( spl272_231
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP2(X1,X0)
| ~ 'fun_app$n'(X1,sK59(X0,X1))
| ~ 'fun_app$n'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_231])]) ).
tff(f2765,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP2(X1,X0)
| ~ 'fun_app$n'(X1,sK59(X0,X1))
| ~ 'fun_app$n'(X1,X0) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f5049,plain,
spl272_230,
inference(avatar_split_clause,[],[f2618,f5047]) ).
tff(f5047,plain,
( spl272_230
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 'fun_app$b'('power$'(X0),X1) != 'zero$' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_230])]) ).
tff(f2618,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 'fun_app$b'('power$'(X0),X1) != 'zero$' ) ),
inference(cnf_transformation,[],[f1696]) ).
tff(f5038,plain,
spl272_229,
inference(avatar_split_clause,[],[f2615,f5036]) ).
tff(f5036,plain,
( spl272_229
<=> ! [X0: $int,X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 0 != 'fun_app$a'('power$a'(X0),X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_229])]) ).
tff(f2615,plain,
! [X0: $int,X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 0 != 'fun_app$a'('power$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f1694]) ).
tff(f5034,plain,
spl272_228,
inference(avatar_split_clause,[],[f2612,f5032]) ).
tff(f2612,plain,
! [X0: $real,X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
| ( 0.0 != 'fun_app$m'('power$c'(X0),X1) ) ),
inference(cnf_transformation,[],[f1692]) ).
tff(f5030,plain,
spl272_227,
inference(avatar_split_clause,[],[f2608,f5028]) ).
tff(f5028,plain,
( spl272_227
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'zero$a' = X1 )
| ( 'zero$a' = X0 )
| ( 'zero$a' != 'times$c'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_227])]) ).
tff(f2608,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'zero$a' = X1 )
| ( 'zero$a' = X0 )
| ( 'zero$a' != 'times$c'(X0,X1) ) ),
inference(cnf_transformation,[],[f1690]) ).
tff(f1690,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( ( 'zero$a' = 'times$c'(X0,X1) )
| ( ( 'zero$a' != X1 )
& ( 'zero$a' != X0 ) ) )
& ( ( 'zero$a' = X1 )
| ( 'zero$a' = X0 )
| ( 'zero$a' != 'times$c'(X0,X1) ) ) ),
inference(flattening,[],[f1689]) ).
tff(f1689,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( ( 'zero$a' = 'times$c'(X0,X1) )
| ( ( 'zero$a' != X1 )
& ( 'zero$a' != X0 ) ) )
& ( ( 'zero$a' = X1 )
| ( 'zero$a' = X0 )
| ( 'zero$a' != 'times$c'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f626]) ).
tff(f626,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'zero$a' = 'times$c'(X0,X1) )
<=> ( ( 'zero$a' = X1 )
| ( 'zero$a' = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom624) ).
tff(f5025,plain,
spl272_226,
inference(avatar_split_clause,[],[f2488,f5023]) ).
tff(f2488,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK47(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1627]) ).
tff(f5021,plain,
spl272_225,
inference(avatar_split_clause,[],[f2484,f5019]) ).
tff(f5019,plain,
( spl272_225
<=> ! [X0: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',sK45(X0)))))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_225])]) ).
tff(f2484,plain,
! [X0: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',sK45(X0)))))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f1623]) ).
tff(f1623,plain,
! [X0: 'Nat_bool_fun$'] :
( ( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',sK45(X0)))))
& $less(0,'fun_app$a'('of_nat$',sK45(X0)))
& 'fun_app$n'(X0,sK45(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1621,f1622]) ).
tff(f1622,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X1))))
& $less(0,'fun_app$a'('of_nat$',X1))
& 'fun_app$n'(X0,X1) )
=> ( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',sK45(X0)))))
& $less(0,'fun_app$a'('of_nat$',sK45(X0)))
& 'fun_app$n'(X0,sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1621,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X1))))
& $less(0,'fun_app$a'('of_nat$',X1))
& 'fun_app$n'(X0,X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f1620]) ).
tff(f1620,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X3: 'Nat$'] :
( ~ 'fun_app$n'(X0,'nat$'($product(2,'fun_app$a'('of_nat$',X3))))
& $less(0,'fun_app$a'('of_nat$',X3))
& 'fun_app$n'(X0,X3) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f1499]) ).
tff(f5016,plain,
spl272_224,
inference(avatar_split_clause,[],[f2480,f5014]) ).
tff(f2480,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| 'fun_app$n'(X0,sK44(X0))
| ~ 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1619]) ).
tff(f5011,plain,
spl272_223,
inference(avatar_split_clause,[],[f2471,f5009]) ).
tff(f2471,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,'nat$'(0))
| ~ 'fun_app$n'(X0,sK43(X0))
| ~ 'fun_app$n'(X0,X1) ),
inference(cnf_transformation,[],[f1617]) ).
tff(f5007,plain,
spl272_222,
inference(avatar_split_clause,[],[f2342,f5005]) ).
tff(f5005,plain,
( spl272_222
<=> ! [X0: $int,X1: 'Nat$'] : ~ $less('fun_app$a'('power$a'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_222])]) ).
tff(f2342,plain,
! [X0: $int,X1: 'Nat$'] : ~ $less('fun_app$a'('power$a'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0),
inference(cnf_transformation,[],[f683]) ).
tff(f683,plain,
! [X0: $int,X1: 'Nat$'] : ~ $less('fun_app$a'('power$a'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0),
inference(theory_normalization,[],[f349]) ).
tff(f349,axiom,
! [X0: $int,X1: 'Nat$'] : $lesseq(0,'fun_app$a'('power$a'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom347) ).
tff(f5003,plain,
spl272_221,
inference(avatar_split_clause,[],[f2341,f5001]) ).
tff(f5001,plain,
( spl272_221
<=> ! [X0: $real,X1: 'Nat$'] : ~ $less('fun_app$m'('power$c'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_221])]) ).
tff(f2341,plain,
! [X0: $real,X1: 'Nat$'] : ~ $less('fun_app$m'('power$c'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0.0),
inference(cnf_transformation,[],[f682]) ).
tff(f682,plain,
! [X0: $real,X1: 'Nat$'] : ~ $less('fun_app$m'('power$c'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1)))),0.0),
inference(theory_normalization,[],[f350]) ).
tff(f350,axiom,
! [X0: $real,X1: 'Nat$'] : $lesseq(0.0,'fun_app$m'('power$c'(X0),'nat$'($product(2,'fun_app$a'('of_nat$',X1))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom348) ).
tff(f4999,plain,
spl272_220,
inference(avatar_split_clause,[],[f2261,f4997]) ).
tff(f4997,plain,
( spl272_220
<=> ! [X2: $real,X0: 'Real_set$'] :
( ~ $less(X2,sK33(X0))
| $less(X2,sK34(X0,X2))
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_220])]) ).
tff(f2261,plain,
! [X2: $real,X0: 'Real_set$'] :
( ~ $less(X2,sK33(X0))
| $less(X2,sK34(X0,X2))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f1556]) ).
tff(f1556,plain,
! [X0: 'Real_set$'] :
( ( ! [X2: $real] :
( ~ $less(X2,sK33(X0))
| ( $less(X2,sK34(X0,X2))
& 'member$'(sK34(X0,X2),X0) ) )
& ! [X4: $real] :
( ~ $less(sK33(X0),X4)
| ~ 'member$'(X4,X0) ) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f1553,f1555,f1554]) ).
tff(f1554,plain,
! [X0: 'Real_set$'] :
( ? [X1: $real] :
( ! [X2: $real] :
( ~ $less(X2,X1)
| ? [X3: $real] :
( $less(X2,X3)
& 'member$'(X3,X0) ) )
& ! [X4: $real] :
( ~ $less(X1,X4)
| ~ 'member$'(X4,X0) ) )
=> ( ! [X2: $real] :
( ~ $less(X2,sK33(X0))
| ? [X3: $real] :
( $less(X2,X3)
& 'member$'(X3,X0) ) )
& ! [X4: $real] :
( ~ $less(sK33(X0),X4)
| ~ 'member$'(X4,X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1555,plain,
! [X0: 'Real_set$',X2: $real] :
( ? [X3: $real] :
( $less(X2,X3)
& 'member$'(X3,X0) )
=> ( $less(X2,sK34(X0,X2))
& 'member$'(sK34(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f1553,plain,
! [X0: 'Real_set$'] :
( ? [X1: $real] :
( ! [X2: $real] :
( ~ $less(X2,X1)
| ? [X3: $real] :
( $less(X2,X3)
& 'member$'(X3,X0) ) )
& ! [X4: $real] :
( ~ $less(X1,X4)
| ~ 'member$'(X4,X0) ) )
| ~ sP0(X0) ),
inference(rectify,[],[f1552]) ).
tff(f1552,plain,
! [X0: 'Real_set$'] :
( ? [X4: $real] :
( ! [X5: $real] :
( ~ $less(X5,X4)
| ? [X6: $real] :
( $less(X5,X6)
& 'member$'(X6,X0) ) )
& ! [X7: $real] :
( ~ $less(X4,X7)
| ~ 'member$'(X7,X0) ) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f1497]) ).
tff(f1497,plain,
! [X0: 'Real_set$'] :
( ? [X4: $real] :
( ! [X5: $real] :
( ~ $less(X5,X4)
| ? [X6: $real] :
( $less(X5,X6)
& 'member$'(X6,X0) ) )
& ! [X7: $real] :
( ~ $less(X4,X7)
| ~ 'member$'(X7,X0) ) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f4988,plain,
spl272_219,
inference(avatar_split_clause,[],[f2260,f4986]) ).
tff(f4986,plain,
( spl272_219
<=> ! [X2: $real,X0: 'Real_set$'] :
( ~ $less(X2,sK33(X0))
| 'member$'(sK34(X0,X2),X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_219])]) ).
tff(f2260,plain,
! [X2: $real,X0: 'Real_set$'] :
( ~ $less(X2,sK33(X0))
| 'member$'(sK34(X0,X2),X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f1556]) ).
tff(f4983,plain,
spl272_218,
inference(avatar_split_clause,[],[f2255,f4981]) ).
tff(f2255,plain,
! [X2: 'Nat$',X0: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X0,sK31(X0))
| ~ 'fun_app$n'(X0,X2)
| 'fun_app$n'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1549]) ).
tff(f4979,plain,
spl272_217,
inference(avatar_split_clause,[],[f2232,f4977]) ).
tff(f2232,plain,
! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0))),
inference(cnf_transformation,[],[f606]) ).
tff(f606,axiom,
! [X0: 'Nat$'] : $less('fun_app$a'('of_nat$',X0),'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(2)),X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom604) ).
tff(f4975,plain,
spl272_216,
inference(avatar_split_clause,[],[f2231,f4973]) ).
tff(f4973,plain,
( spl272_216
<=> ! [X0: 'Num$'] : ( 'fun_app$p'('dbl$','fun_app$d'('numeral$',X0)) = 'fun_app$d'('numeral$','fun_app$c'('bit0$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_216])]) ).
tff(f2231,plain,
! [X0: 'Num$'] : ( 'fun_app$p'('dbl$','fun_app$d'('numeral$',X0)) = 'fun_app$d'('numeral$','fun_app$c'('bit0$',X0)) ),
inference(cnf_transformation,[],[f81]) ).
tff(f81,axiom,
! [X0: 'Num$'] : ( 'fun_app$p'('dbl$','fun_app$d'('numeral$',X0)) = 'fun_app$d'('numeral$','fun_app$c'('bit0$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
tff(f4971,plain,
spl272_215,
inference(avatar_split_clause,[],[f878,f4969]) ).
tff(f4969,plain,
( spl272_215
<=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_215])]) ).
tff(f878,plain,
! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f4967,plain,
spl272_214,
inference(avatar_split_clause,[],[f867,f4965]) ).
tff(f4965,plain,
( spl272_214
<=> ! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_214])]) ).
tff(f867,plain,
! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f4963,plain,
spl272_213,
inference(avatar_split_clause,[],[f860,f4961]) ).
tff(f4961,plain,
( spl272_213
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_213])]) ).
tff(f860,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f4959,plain,
spl272_212,
inference(avatar_split_clause,[],[f849,f4957]) ).
tff(f4957,plain,
( spl272_212
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_212])]) ).
tff(f849,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f4820,plain,
( spl272_211
| ~ spl272_109
| ~ spl272_171 ),
inference(avatar_split_clause,[],[f4581,f4421,f4112,f4818]) ).
tff(f4421,plain,
( spl272_171
<=> ! [X0: $real] : ~ $less($sum(X0,1.0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_171])]) ).
tff(f4581,plain,
( ! [X0: $real] : $less(X0,$sum(2.0,X0))
| ~ spl272_109
| ~ spl272_171 ),
inference(evaluation,[],[f4576]) ).
tff(f4576,plain,
( ! [X0: $real] : $less(X0,$sum($sum(X0,1.0),1.0))
| ~ spl272_109
| ~ spl272_171 ),
inference(resolution,[],[f4422,f4113]) ).
tff(f4422,plain,
( ! [X0: $real] : ~ $less($sum(X0,1.0),X0)
| ~ spl272_171 ),
inference(avatar_component_clause,[],[f4421]) ).
tff(f4774,plain,
( spl272_210
| ~ spl272_58
| ~ spl272_171 ),
inference(avatar_split_clause,[],[f4579,f4421,f3865,f4772]) ).
tff(f4772,plain,
( spl272_210
<=> ! [X0: $real] : ~ $less($sum(1.0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_210])]) ).
tff(f4579,plain,
( ! [X0: $real] : ~ $less($sum(1.0,X0),X0)
| ~ spl272_58
| ~ spl272_171 ),
inference(superposition,[],[f4422,f3866]) ).
tff(f4746,plain,
spl272_209,
inference(avatar_split_clause,[],[f3440,f4744]) ).
tff(f4744,plain,
( spl272_209
<=> ! [X0: 'Nat$'] : ( 0 != 'fun_app$a'('of_nat$','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_209])]) ).
tff(f3440,plain,
! [X0: 'Nat$'] : ( 0 != 'fun_app$a'('of_nat$','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2220,f848]) ).
tff(f2220,plain,
! [X0: 'Nat$'] : ( 0 != 'fun_app$a'('of_nat$','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f152]) ).
tff(f152,axiom,
! [X0: 'Nat$'] : ( 0 != 'fun_app$a'('of_nat$','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom150) ).
tff(f4742,plain,
spl272_208,
inference(avatar_split_clause,[],[f3439,f4740]) ).
tff(f3439,plain,
! [X0: 'Nat$'] : ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2219,f848]) ).
tff(f2219,plain,
! [X0: 'Nat$'] : ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f153]) ).
tff(f153,axiom,
! [X0: 'Nat$'] : ( 0.0 != 'fun_app$m'('of_nat$b','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom151) ).
tff(f4738,plain,
spl272_207,
inference(avatar_split_clause,[],[f3438,f4736]) ).
tff(f3438,plain,
! [X0: 'Nat$'] : ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum(1,'fun_app$a'('of_nat$',X0)))) ),
inference(forward_demodulation,[],[f2218,f848]) ).
tff(f2218,plain,
! [X0: 'Nat$'] : ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,axiom,
! [X0: 'Nat$'] : ( 'zero$a' != 'fun_app$l'('of_nat$c','nat$'($sum('fun_app$a'('of_nat$',X0),1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).
tff(f4734,plain,
spl272_206,
inference(avatar_split_clause,[],[f3425,f4732]) ).
tff(f4732,plain,
( spl272_206
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_206])]) ).
tff(f3425,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),1) ),
inference(evaluation,[],[f2334]) ).
tff(f2334,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ),
inference(cnf_transformation,[],[f1594]) ).
tff(f1594,plain,
! [X0: 'Nat$'] :
( ( $less('fun_app$a'('of_nat$',X0),$sum(0,1))
| ( 'fun_app$a'('of_nat$',X0) != 0 ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ~ $less('fun_app$a'('of_nat$',X0),$sum(0,1)) ) ),
inference(nnf_transformation,[],[f376]) ).
tff(f376,axiom,
! [X0: 'Nat$'] :
( $less('fun_app$a'('of_nat$',X0),$sum(0,1))
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom374) ).
tff(f4730,plain,
spl272_205,
inference(avatar_split_clause,[],[f2635,f4728]) ).
tff(f4728,plain,
( spl272_205
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$d'('numeral$',X0) != 'fun_app$d'('numeral$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_205])]) ).
tff(f2635,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$d'('numeral$',X0) != 'fun_app$d'('numeral$',X1) ) ),
inference(cnf_transformation,[],[f1705]) ).
tff(f1705,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'fun_app$d'('numeral$',X0) = 'fun_app$d'('numeral$',X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$d'('numeral$',X0) != 'fun_app$d'('numeral$',X1) ) ) ),
inference(nnf_transformation,[],[f24]) ).
tff(f24,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$d'('numeral$',X0) = 'fun_app$d'('numeral$',X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
tff(f4726,plain,
spl272_204,
inference(avatar_split_clause,[],[f2631,f4724]) ).
tff(f4724,plain,
( spl272_204
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$c'('bit0$',X0) != 'fun_app$c'('bit0$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_204])]) ).
tff(f2631,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$c'('bit0$',X0) != 'fun_app$c'('bit0$',X1) ) ),
inference(cnf_transformation,[],[f1703]) ).
tff(f1703,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'fun_app$c'('bit0$',X0) = 'fun_app$c'('bit0$',X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$c'('bit0$',X0) != 'fun_app$c'('bit0$',X1) ) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$c'('bit0$',X0) = 'fun_app$c'('bit0$',X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
tff(f4722,plain,
spl272_203,
inference(avatar_split_clause,[],[f2629,f4720]) ).
tff(f4720,plain,
( spl272_203
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$i'('numeral$a',X0) != 'fun_app$i'('numeral$a',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_203])]) ).
tff(f2629,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$i'('numeral$a',X0) != 'fun_app$i'('numeral$a',X1) ) ),
inference(cnf_transformation,[],[f1702]) ).
tff(f1702,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'fun_app$i'('numeral$a',X0) = 'fun_app$i'('numeral$a',X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$i'('numeral$a',X0) != 'fun_app$i'('numeral$a',X1) ) ) ),
inference(nnf_transformation,[],[f25]) ).
tff(f25,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$i'('numeral$a',X0) = 'fun_app$i'('numeral$a',X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
tff(f4718,plain,
spl272_202,
inference(avatar_split_clause,[],[f2627,f4716]) ).
tff(f4716,plain,
( spl272_202
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$j'('numeral$b',X0) != 'fun_app$j'('numeral$b',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_202])]) ).
tff(f2627,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( X0 = X1 )
| ( 'fun_app$j'('numeral$b',X0) != 'fun_app$j'('numeral$b',X1) ) ),
inference(cnf_transformation,[],[f1701]) ).
tff(f1701,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ( ( 'fun_app$j'('numeral$b',X0) = 'fun_app$j'('numeral$b',X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fun_app$j'('numeral$b',X0) != 'fun_app$j'('numeral$b',X1) ) ) ),
inference(nnf_transformation,[],[f26]) ).
tff(f26,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$j'('numeral$b',X0) = 'fun_app$j'('numeral$b',X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom24) ).
tff(f4714,plain,
( spl272_201
| ~ spl272_107
| ~ spl272_152 ),
inference(avatar_split_clause,[],[f4543,f4316,f4104,f4712]) ).
tff(f4316,plain,
( spl272_152
<=> ! [X0: $int] : ~ $less($sum(X0,1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_152])]) ).
tff(f4543,plain,
( ! [X0: $int] : $less(X0,$sum(2,X0))
| ~ spl272_107
| ~ spl272_152 ),
inference(evaluation,[],[f4532]) ).
tff(f4532,plain,
( ! [X0: $int] : $less(X0,$sum($sum(X0,1),1))
| ~ spl272_107
| ~ spl272_152 ),
inference(resolution,[],[f4317,f4105]) ).
tff(f4317,plain,
( ! [X0: $int] : ~ $less($sum(X0,1),X0)
| ~ spl272_152 ),
inference(avatar_component_clause,[],[f4316]) ).
tff(f4710,plain,
spl272_200,
inference(avatar_split_clause,[],[f2409,f4708]) ).
tff(f4708,plain,
( spl272_200
<=> ! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_200])]) ).
tff(f2409,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(cnf_transformation,[],[f1043]) ).
tff(f1043,plain,
! [X0: 'Num$',X1: 'Num$'] :
( ~ 'fun_app$e'('fun_app$f'('less$',X1),X0)
| ~ 'fun_app$e'('fun_app$f'('less$',X0),X1) ),
inference(ennf_transformation,[],[f472]) ).
tff(f472,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),X1)
=> ~ 'fun_app$e'('fun_app$f'('less$',X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom470) ).
tff(f4706,plain,
spl272_199,
inference(avatar_split_clause,[],[f2403,f4704]) ).
tff(f4704,plain,
( spl272_199
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_199])]) ).
tff(f2403,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(cnf_transformation,[],[f1038]) ).
tff(f1038,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a',X1),X0)
| ~ 'fun_app$g'('fun_app$h'('less$a',X0),X1) ),
inference(ennf_transformation,[],[f474]) ).
tff(f474,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less$a',X0),X1)
=> ~ 'fun_app$g'('fun_app$h'('less$a',X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom472) ).
tff(f4702,plain,
spl272_198,
inference(avatar_split_clause,[],[f2374,f4700]) ).
tff(f4700,plain,
( spl272_198
<=> ! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_198])]) ).
tff(f2374,plain,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
inference(cnf_transformation,[],[f287]) ).
tff(f287,axiom,
! [X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom285) ).
tff(f4698,plain,
spl272_197,
inference(avatar_split_clause,[],[f2372,f4696]) ).
tff(f4696,plain,
( spl272_197
<=> ! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_197])]) ).
tff(f2372,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
inference(cnf_transformation,[],[f288]) ).
tff(f288,axiom,
! [X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom286) ).
tff(f4694,plain,
spl272_196,
inference(avatar_split_clause,[],[f2333,f4692]) ).
tff(f4692,plain,
( spl272_196
<=> ! [X0: $int] :
( $less(0,'fun_app$a'('power$a'(X0),'nat$'(2)))
| ( 0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_196])]) ).
tff(f2333,plain,
! [X0: $int] :
( $less(0,'fun_app$a'('power$a'(X0),'nat$'(2)))
| ( 0 = X0 ) ),
inference(cnf_transformation,[],[f1593]) ).
tff(f1593,plain,
! [X0: $int] :
( ( $less(0,'fun_app$a'('power$a'(X0),'nat$'(2)))
| ( 0 = X0 ) )
& ( ( 0 != X0 )
| ~ $less(0,'fun_app$a'('power$a'(X0),'nat$'(2))) ) ),
inference(nnf_transformation,[],[f347]) ).
tff(f347,axiom,
! [X0: $int] :
( $less(0,'fun_app$a'('power$a'(X0),'nat$'(2)))
<=> ( 0 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom345) ).
tff(f4690,plain,
spl272_195,
inference(avatar_split_clause,[],[f2325,f4688]) ).
tff(f4688,plain,
( spl272_195
<=> ! [X0: $real] :
( $less(0.0,'fun_app$m'('power$c'(X0),'nat$'(2)))
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_195])]) ).
tff(f2325,plain,
! [X0: $real] :
( $less(0.0,'fun_app$m'('power$c'(X0),'nat$'(2)))
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f1589]) ).
tff(f1589,plain,
! [X0: $real] :
( ( $less(0.0,'fun_app$m'('power$c'(X0),'nat$'(2)))
| ( 0.0 = X0 ) )
& ( ( 0.0 != X0 )
| ~ $less(0.0,'fun_app$m'('power$c'(X0),'nat$'(2))) ) ),
inference(nnf_transformation,[],[f348]) ).
tff(f348,axiom,
! [X0: $real] :
( $less(0.0,'fun_app$m'('power$c'(X0),'nat$'(2)))
<=> ( 0.0 != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom346) ).
tff(f4686,plain,
spl272_194,
inference(avatar_split_clause,[],[f2292,f4684]) ).
tff(f4684,plain,
( spl272_194
<=> ! [X0: 'Nat$'] :
( ~ $less(0.0,'fun_app$m'('of_nat$b',X0))
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_194])]) ).
tff(f2292,plain,
! [X0: 'Nat$'] :
( ~ $less(0.0,'fun_app$m'('of_nat$b',X0))
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1571]) ).
tff(f1571,plain,
! [X0: 'Nat$'] :
( ( ~ $less(0.0,'fun_app$m'('of_nat$b',X0))
| ( 'fun_app$a'('of_nat$',X0) != 0 ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0.0,'fun_app$m'('of_nat$b',X0)) ) ),
inference(nnf_transformation,[],[f674]) ).
tff(f674,plain,
! [X0: 'Nat$'] :
( ~ $less(0.0,'fun_app$m'('of_nat$b',X0))
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(theory_normalization,[],[f105]) ).
tff(f105,axiom,
! [X0: 'Nat$'] :
( $lesseq('fun_app$m'('of_nat$b',X0),0.0)
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
tff(f4682,plain,
spl272_193,
inference(avatar_split_clause,[],[f2291,f4680]) ).
tff(f4680,plain,
( spl272_193
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0.0,'fun_app$m'('of_nat$b',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_193])]) ).
tff(f2291,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0.0,'fun_app$m'('of_nat$b',X0)) ),
inference(cnf_transformation,[],[f1571]) ).
tff(f4678,plain,
spl272_192,
inference(avatar_split_clause,[],[f2290,f4676]) ).
tff(f2290,plain,
! [X0: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f1570,plain,
! [X0: 'Nat$'] :
( ( $less(0.0,'fun_app$m'('of_nat$b',X0))
| ~ $less(0,'fun_app$a'('of_nat$',X0)) )
& ( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('of_nat$b',X0)) ) ),
inference(nnf_transformation,[],[f405]) ).
tff(f405,axiom,
! [X0: 'Nat$'] :
( $less(0.0,'fun_app$m'('of_nat$b',X0))
<=> $less(0,'fun_app$a'('of_nat$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom403) ).
tff(f4674,plain,
spl272_191,
inference(avatar_split_clause,[],[f2289,f4672]) ).
tff(f4672,plain,
( spl272_191
<=> ! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('of_nat$b',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_191])]) ).
tff(f2289,plain,
! [X0: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X0))
| ~ $less(0.0,'fun_app$m'('of_nat$b',X0)) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f4670,plain,
( spl272_190
| ~ spl272_56
| ~ spl272_152 ),
inference(avatar_split_clause,[],[f4538,f4316,f3857,f4668]) ).
tff(f4668,plain,
( spl272_190
<=> ! [X0: $int] : ~ $less($sum(1,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_190])]) ).
tff(f4538,plain,
( ! [X0: $int] : ~ $less($sum(1,X0),X0)
| ~ spl272_56
| ~ spl272_152 ),
inference(superposition,[],[f4317,f3858]) ).
tff(f4666,plain,
spl272_189,
inference(avatar_split_clause,[],[f2282,f4664]) ).
tff(f4664,plain,
( spl272_189
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 0.0 )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_189])]) ).
tff(f2282,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 0.0 )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f1566,plain,
! [X0: 'Nat$'] :
( ( ( 'fun_app$m'('of_nat$b',X0) = 0.0 )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$m'('of_nat$b',X0) != 0.0 ) ) ),
inference(nnf_transformation,[],[f95]) ).
tff(f95,axiom,
! [X0: 'Nat$'] :
( ( 'fun_app$m'('of_nat$b',X0) = 0.0 )
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).
tff(f4662,plain,
spl272_188,
inference(avatar_split_clause,[],[f2281,f4660]) ).
tff(f4660,plain,
( spl272_188
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$m'('of_nat$b',X0) != 0.0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_188])]) ).
tff(f2281,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'fun_app$m'('of_nat$b',X0) != 0.0 ) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f4658,plain,
spl272_187,
inference(avatar_split_clause,[],[f2276,f4656]) ).
tff(f4656,plain,
( spl272_187
<=> ! [X0: 'Nat$'] :
( ( 'zero$a' = 'fun_app$l'('of_nat$c',X0) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_187])]) ).
tff(f2276,plain,
! [X0: 'Nat$'] :
( ( 'zero$a' = 'fun_app$l'('of_nat$c',X0) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) ),
inference(cnf_transformation,[],[f1564]) ).
tff(f1564,plain,
! [X0: 'Nat$'] :
( ( ( 'zero$a' = 'fun_app$l'('of_nat$c',X0) )
| ( 'fun_app$a'('of_nat$',X0) != 0 ) )
& ( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'zero$a' != 'fun_app$l'('of_nat$c',X0) ) ) ),
inference(nnf_transformation,[],[f90]) ).
tff(f90,axiom,
! [X0: 'Nat$'] :
( ( 'zero$a' = 'fun_app$l'('of_nat$c',X0) )
<=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
tff(f4654,plain,
spl272_186,
inference(avatar_split_clause,[],[f2275,f4652]) ).
tff(f4652,plain,
( spl272_186
<=> ! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'zero$a' != 'fun_app$l'('of_nat$c',X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_186])]) ).
tff(f2275,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| ( 'zero$a' != 'fun_app$l'('of_nat$c',X0) ) ),
inference(cnf_transformation,[],[f1564]) ).
tff(f4650,plain,
spl272_185,
inference(avatar_split_clause,[],[f2263,f4648]) ).
tff(f4648,plain,
( spl272_185
<=> ! [X0: 'Real_set$',X1: $real,X3: $real] :
( sP0(X0)
| $less(X1,sK35(X0,X1))
| ~ 'member$'(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_185])]) ).
tff(f2263,plain,
! [X3: $real,X0: 'Real_set$',X1: $real] :
( sP0(X0)
| $less(X1,sK35(X0,X1))
| ~ 'member$'(X3,X0) ),
inference(cnf_transformation,[],[f1558]) ).
tff(f1558,plain,
! [X0: 'Real_set$'] :
( sP0(X0)
| ! [X1: $real] :
( $less(X1,sK35(X0,X1))
& 'member$'(sK35(X0,X1),X0) )
| ! [X3: $real] : ~ 'member$'(X3,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f1498,f1557]) ).
tff(f1557,plain,
! [X0: 'Real_set$',X1: $real] :
( ? [X2: $real] :
( $less(X1,X2)
& 'member$'(X2,X0) )
=> ( $less(X1,sK35(X0,X1))
& 'member$'(sK35(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f1498,plain,
! [X0: 'Real_set$'] :
( sP0(X0)
| ! [X1: $real] :
? [X2: $real] :
( $less(X1,X2)
& 'member$'(X2,X0) )
| ! [X3: $real] : ~ 'member$'(X3,X0) ),
inference(definition_folding,[],[f1012,f1497]) ).
tff(f1012,plain,
! [X0: 'Real_set$'] :
( ? [X4: $real] :
( ! [X5: $real] :
( ~ $less(X5,X4)
| ? [X6: $real] :
( $less(X5,X6)
& 'member$'(X6,X0) ) )
& ! [X7: $real] :
( ~ $less(X4,X7)
| ~ 'member$'(X7,X0) ) )
| ! [X1: $real] :
? [X2: $real] :
( $less(X1,X2)
& 'member$'(X2,X0) )
| ! [X3: $real] : ~ 'member$'(X3,X0) ),
inference(flattening,[],[f1011]) ).
tff(f1011,plain,
! [X0: 'Real_set$'] :
( ? [X4: $real] :
( ! [X5: $real] :
( ~ $less(X5,X4)
| ? [X6: $real] :
( $less(X5,X6)
& 'member$'(X6,X0) ) )
& ! [X7: $real] :
( ~ $less(X4,X7)
| ~ 'member$'(X7,X0) ) )
| ! [X1: $real] :
? [X2: $real] :
( $less(X1,X2)
& 'member$'(X2,X0) )
| ! [X3: $real] : ~ 'member$'(X3,X0) ),
inference(ennf_transformation,[],[f905]) ).
tff(f905,plain,
! [X0: 'Real_set$'] :
( ( ? [X1: $real] :
! [X2: $real] :
( 'member$'(X2,X0)
=> ~ $less(X1,X2) )
& ? [X3: $real] : 'member$'(X3,X0) )
=> ? [X4: $real] :
( ! [X5: $real] :
( ! [X6: $real] :
( 'member$'(X6,X0)
=> ~ $less(X5,X6) )
=> ~ $less(X5,X4) )
& ! [X7: $real] :
( 'member$'(X7,X0)
=> ~ $less(X4,X7) ) ) ),
inference(rectify,[],[f673]) ).
tff(f673,plain,
! [X0: 'Real_set$'] :
( ( ? [X1: $real] :
! [X2: $real] :
( 'member$'(X2,X0)
=> ~ $less(X1,X2) )
& ? [X1: $real] : 'member$'(X1,X0) )
=> ? [X1: $real] :
( ! [X2: $real] :
( ! [X3: $real] :
( 'member$'(X3,X0)
=> ~ $less(X2,X3) )
=> ~ $less(X2,X1) )
& ! [X2: $real] :
( 'member$'(X2,X0)
=> ~ $less(X1,X2) ) ) ),
inference(theory_normalization,[],[f437]) ).
tff(f437,axiom,
! [X0: 'Real_set$'] :
( ( ? [X1: $real] :
! [X2: $real] :
( 'member$'(X2,X0)
=> $lesseq(X2,X1) )
& ? [X1: $real] : 'member$'(X1,X0) )
=> ? [X1: $real] :
( ! [X2: $real] :
( ! [X3: $real] :
( 'member$'(X3,X0)
=> $lesseq(X3,X2) )
=> $lesseq(X1,X2) )
& ! [X2: $real] :
( 'member$'(X2,X0)
=> $lesseq(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom435) ).
tff(f4646,plain,
spl272_184,
inference(avatar_split_clause,[],[f2262,f4644]) ).
tff(f4644,plain,
( spl272_184
<=> ! [X0: 'Real_set$',X1: $real,X3: $real] :
( sP0(X0)
| 'member$'(sK35(X0,X1),X0)
| ~ 'member$'(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_184])]) ).
tff(f2262,plain,
! [X3: $real,X0: 'Real_set$',X1: $real] :
( sP0(X0)
| 'member$'(sK35(X0,X1),X0)
| ~ 'member$'(X3,X0) ),
inference(cnf_transformation,[],[f1558]) ).
tff(f4642,plain,
spl272_183,
inference(avatar_split_clause,[],[f2248,f4640]) ).
tff(f2248,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(cnf_transformation,[],[f1004]) ).
tff(f1004,plain,
! [X0: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X0) = 0 )
| $less(0,'fun_app$a'('of_nat$',X0)) ),
inference(ennf_transformation,[],[f671]) ).
tff(f671,plain,
! [X0: 'Nat$'] :
( ~ $less(0,'fun_app$a'('of_nat$',X0))
=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
inference(theory_normalization,[],[f180]) ).
tff(f180,axiom,
! [X0: 'Nat$'] :
( $lesseq('fun_app$a'('of_nat$',X0),0)
=> ( 'fun_app$a'('of_nat$',X0) = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
tff(f4638,plain,
spl272_182,
inference(avatar_split_clause,[],[f2226,f4636]) ).
tff(f2226,plain,
! [X0: 'Num$'] : ( 'dbl$a'('fun_app$j'('numeral$b',X0)) = 'fun_app$j'('numeral$b','fun_app$c'('bit0$',X0)) ),
inference(cnf_transformation,[],[f82]) ).
tff(f82,axiom,
! [X0: 'Num$'] : ( 'dbl$a'('fun_app$j'('numeral$b',X0)) = 'fun_app$j'('numeral$b','fun_app$c'('bit0$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
tff(f4634,plain,
spl272_181,
inference(avatar_split_clause,[],[f2224,f4632]) ).
tff(f2224,plain,
! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) = 'fun_app$a'('of_nat$','nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,axiom,
! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) = 'fun_app$a'('of_nat$','nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom116) ).
tff(f4630,plain,
spl272_180,
inference(avatar_split_clause,[],[f2223,f4628]) ).
tff(f4628,plain,
( spl272_180
<=> ! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) = 'fun_app$c'('times$a'('fun_app$c'('bit0$','one$')),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_180])]) ).
tff(f2223,plain,
! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) = 'fun_app$c'('times$a'('fun_app$c'('bit0$','one$')),X0) ),
inference(cnf_transformation,[],[f612]) ).
tff(f612,axiom,
! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) = 'fun_app$c'('times$a'('fun_app$c'('bit0$','one$')),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom610) ).
tff(f4619,plain,
spl272_179,
inference(avatar_split_clause,[],[f2222,f4617]) ).
tff(f4617,plain,
( spl272_179
<=> ! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) = 'fun_app$l'('of_nat$c','nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_179])]) ).
tff(f2222,plain,
! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) = 'fun_app$l'('of_nat$c','nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f117]) ).
tff(f117,axiom,
! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) = 'fun_app$l'('of_nat$c','nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom115) ).
tff(f4615,plain,
spl272_178,
inference(avatar_split_clause,[],[f2221,f4613]) ).
tff(f4613,plain,
( spl272_178
<=> ! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) = 'fun_app$m'('of_nat$b','nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_178])]) ).
tff(f2221,plain,
! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) = 'fun_app$m'('of_nat$b','nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f119]) ).
tff(f119,axiom,
! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) = 'fun_app$m'('of_nat$b','nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
tff(f4611,plain,
spl272_177,
inference(avatar_split_clause,[],[f874,f4609]) ).
tff(f4609,plain,
( spl272_177
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_177])]) ).
tff(f874,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f4607,plain,
spl272_176,
inference(avatar_split_clause,[],[f869,f4605]) ).
tff(f4605,plain,
( spl272_176
<=> ! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_176])]) ).
tff(f869,plain,
! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f4603,plain,
spl272_175,
inference(avatar_split_clause,[],[f856,f4601]) ).
tff(f4601,plain,
( spl272_175
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_175])]) ).
tff(f856,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f4599,plain,
spl272_174,
inference(avatar_split_clause,[],[f851,f4597]) ).
tff(f4597,plain,
( spl272_174
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_174])]) ).
tff(f851,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f4592,plain,
spl272_173,
inference(avatar_split_clause,[],[f3434,f4589]) ).
tff(f3434,plain,
$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum(1,'fun_app$a'('of_nat$','n$')))))),'size$'('ys$')))),
inference(forward_demodulation,[],[f2129,f848]) ).
tff(f2129,plain,
$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(cnf_transformation,[],[f883]) ).
tff(f883,plain,
$less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(flattening,[],[f642]) ).
tff(f642,plain,
~ ~ $less('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$')),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$')))),
inference(theory_normalization,[],[f3]) ).
tff(f3,negated_conjecture,
~ $lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$'))),
inference(negated_conjecture,[],[f2]) ).
tff(f2,conjecture,
$lesseq('fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'size$'('ys$'))),'fun_app$a'('of_nat$','fun_app$b'('power$'('fun_app$b'('power$'('nat$'(2)),'fun_app$b'('power$'('nat$'(2)),'nat$'($sum('fun_app$a'('of_nat$','n$'),1))))),'n$'))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture1) ).
tff(f4470,plain,
( spl272_172
| ~ spl272_58
| ~ spl272_123 ),
inference(avatar_split_clause,[],[f4273,f4192,f3865,f4468]) ).
tff(f4468,plain,
( spl272_172
<=> ! [X0: $real] : $less(X0,$sum(1.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_172])]) ).
tff(f4192,plain,
( spl272_123
<=> ! [X0: $real] : $less(X0,$sum(X0,1.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_123])]) ).
tff(f4273,plain,
( ! [X0: $real] : $less(X0,$sum(1.0,X0))
| ~ spl272_58
| ~ spl272_123 ),
inference(superposition,[],[f4193,f3866]) ).
tff(f4193,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl272_123 ),
inference(avatar_component_clause,[],[f4192]) ).
tff(f4423,plain,
( spl272_171
| ~ spl272_50
| ~ spl272_123 ),
inference(avatar_split_clause,[],[f4272,f4192,f3821,f4421]) ).
tff(f4272,plain,
( ! [X0: $real] : ~ $less($sum(X0,1.0),X0)
| ~ spl272_50
| ~ spl272_123 ),
inference(resolution,[],[f4193,f3822]) ).
tff(f4390,plain,
spl272_170,
inference(avatar_split_clause,[],[f3430,f4388]) ).
tff(f3430,plain,
! [X0: 'Nat$'] : ( 1 = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'(1)),X0)) ),
inference(evaluation,[],[f2234]) ).
tff(f2234,plain,
! [X0: 'Nat$'] : ( $sum(0,1) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'($sum(0,1))),X0)) ),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
! [X0: 'Nat$'] : ( $sum(0,1) = 'fun_app$a'('of_nat$','fun_app$b'('power$'('nat$'($sum(0,1))),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
tff(f4386,plain,
spl272_169,
inference(avatar_split_clause,[],[f2926,f4384]) ).
tff(f4384,plain,
( spl272_169
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_169])]) ).
tff(f2926,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f1879]) ).
tff(f1879,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ~ sP20(X0,X1,X2) ),
inference(rectify,[],[f1878]) ).
tff(f1878,plain,
! [X2: 'Num$',X1: 'Num$',X0: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X1) )
| ~ sP20(X2,X1,X0) ),
inference(nnf_transformation,[],[f1528]) ).
tff(f4382,plain,
spl272_168,
inference(avatar_split_clause,[],[f2925,f4380]) ).
tff(f4380,plain,
( spl272_168
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_168])]) ).
tff(f2925,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f1879]) ).
tff(f4378,plain,
spl272_167,
inference(avatar_split_clause,[],[f2924,f4376]) ).
tff(f4376,plain,
( spl272_167
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_167])]) ).
tff(f2924,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f1877,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ~ sP21(X0,X1,X2) ),
inference(rectify,[],[f1876]) ).
tff(f1876,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),X2)
& 'fun_app$e'('fun_app$f'('less_eq$',X1),X0) )
| ~ sP21(X2,X0,X1) ),
inference(nnf_transformation,[],[f1529]) ).
tff(f4374,plain,
spl272_166,
inference(avatar_split_clause,[],[f2923,f4372]) ).
tff(f4372,plain,
( spl272_166
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_166])]) ).
tff(f2923,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f1877]) ).
tff(f4370,plain,
spl272_165,
inference(avatar_split_clause,[],[f2922,f4368]) ).
tff(f4368,plain,
( spl272_165
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_165])]) ).
tff(f2922,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1875]) ).
tff(f1875,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ~ sP22(X0,X1,X2) ),
inference(rectify,[],[f1874]) ).
tff(f1874,plain,
! [X1: 'Num$',X2: 'Num$',X0: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
& 'fun_app$e'('fun_app$f'('less_eq$',X0),X2) )
| ~ sP22(X1,X2,X0) ),
inference(nnf_transformation,[],[f1530]) ).
tff(f4366,plain,
spl272_164,
inference(avatar_split_clause,[],[f2921,f4364]) ).
tff(f4364,plain,
( spl272_164
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_164])]) ).
tff(f2921,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f1875]) ).
tff(f4362,plain,
( spl272_163
| ~ spl272_56
| ~ spl272_122 ),
inference(avatar_split_clause,[],[f4230,f4177,f3857,f4360]) ).
tff(f4360,plain,
( spl272_163
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_163])]) ).
tff(f4177,plain,
( spl272_122
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_122])]) ).
tff(f4230,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl272_56
| ~ spl272_122 ),
inference(superposition,[],[f4178,f3858]) ).
tff(f4178,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl272_122 ),
inference(avatar_component_clause,[],[f4177]) ).
tff(f4358,plain,
spl272_162,
inference(avatar_split_clause,[],[f2920,f4356]) ).
tff(f4356,plain,
( spl272_162
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_162])]) ).
tff(f2920,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f1873,plain,
! [X0: 'Num$',X1: 'Num$',X2: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X1),X0)
& 'fun_app$e'('fun_app$f'('less_eq$',X2),X1) )
| ~ sP23(X0,X1,X2) ),
inference(nnf_transformation,[],[f1531]) ).
tff(f4354,plain,
spl272_161,
inference(avatar_split_clause,[],[f2919,f4352]) ).
tff(f4352,plain,
( spl272_161
<=> ! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_161])]) ).
tff(f2919,plain,
! [X2: 'Num$',X0: 'Num$',X1: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X2),X1)
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f1873]) ).
tff(f4350,plain,
spl272_160,
inference(avatar_split_clause,[],[f2914,f4348]) ).
tff(f4348,plain,
( spl272_160
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_160])]) ).
tff(f2914,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f1872]) ).
tff(f1872,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ~ sP16(X0,X1,X2) ),
inference(rectify,[],[f1871]) ).
tff(f1871,plain,
! [X2: 'Enat$',X1: 'Enat$',X0: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X1) )
| ~ sP16(X2,X1,X0) ),
inference(nnf_transformation,[],[f1523]) ).
tff(f4346,plain,
spl272_159,
inference(avatar_split_clause,[],[f2913,f4344]) ).
tff(f4344,plain,
( spl272_159
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_159])]) ).
tff(f2913,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f1872]) ).
tff(f4342,plain,
spl272_158,
inference(avatar_split_clause,[],[f2912,f4340]) ).
tff(f4340,plain,
( spl272_158
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_158])]) ).
tff(f2912,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f1870,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ~ sP17(X0,X1,X2) ),
inference(rectify,[],[f1869]) ).
tff(f1869,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2)
& 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0) )
| ~ sP17(X2,X0,X1) ),
inference(nnf_transformation,[],[f1524]) ).
tff(f4338,plain,
spl272_157,
inference(avatar_split_clause,[],[f2911,f4336]) ).
tff(f4336,plain,
( spl272_157
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_157])]) ).
tff(f2911,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f4334,plain,
spl272_156,
inference(avatar_split_clause,[],[f2910,f4332]) ).
tff(f4332,plain,
( spl272_156
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_156])]) ).
tff(f2910,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f1868]) ).
tff(f1868,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ~ sP18(X0,X1,X2) ),
inference(rectify,[],[f1867]) ).
tff(f1867,plain,
! [X1: 'Enat$',X2: 'Enat$',X0: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
& 'fun_app$g'('fun_app$h'('less_eq$a',X0),X2) )
| ~ sP18(X1,X2,X0) ),
inference(nnf_transformation,[],[f1525]) ).
tff(f4330,plain,
spl272_155,
inference(avatar_split_clause,[],[f2909,f4328]) ).
tff(f4328,plain,
( spl272_155
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_155])]) ).
tff(f2909,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f1868]) ).
tff(f4326,plain,
spl272_154,
inference(avatar_split_clause,[],[f2908,f4324]) ).
tff(f4324,plain,
( spl272_154
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP19(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_154])]) ).
tff(f2908,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f1866]) ).
tff(f1866,plain,
! [X0: 'Enat$',X1: 'Enat$',X2: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X1),X0)
& 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1) )
| ~ sP19(X0,X1,X2) ),
inference(nnf_transformation,[],[f1526]) ).
tff(f4322,plain,
spl272_153,
inference(avatar_split_clause,[],[f2907,f4320]) ).
tff(f4320,plain,
( spl272_153
<=> ! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP19(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_153])]) ).
tff(f2907,plain,
! [X2: 'Enat$',X0: 'Enat$',X1: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X2),X1)
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f1866]) ).
tff(f4318,plain,
( spl272_152
| ~ spl272_51
| ~ spl272_122 ),
inference(avatar_split_clause,[],[f4229,f4177,f3825,f4316]) ).
tff(f4229,plain,
( ! [X0: $int] : ~ $less($sum(X0,1),X0)
| ~ spl272_51
| ~ spl272_122 ),
inference(resolution,[],[f4178,f3826]) ).
tff(f4314,plain,
spl272_151,
inference(avatar_split_clause,[],[f2855,f4312]) ).
tff(f4312,plain,
( spl272_151
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK70(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_151])]) ).
tff(f2855,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( ~ 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK70(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f4310,plain,
spl272_150,
inference(avatar_split_clause,[],[f2854,f4308]) ).
tff(f4308,plain,
( spl272_150
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X0,sK69(X0)),sK70(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_150])]) ).
tff(f2854,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X0,sK69(X0)),sK70(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f4306,plain,
spl272_149,
inference(avatar_split_clause,[],[f2853,f4304]) ).
tff(f4304,plain,
( spl272_149
<=> ! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK69(X0))
| ~ sP6(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_149])]) ).
tff(f2853,plain,
! [X0: 'Nat_nat_bool_fun_fun$'] :
( 'fun_app$n'('fun_app$o'(X0,sK68(X0)),sK69(X0))
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f4302,plain,
spl272_148,
inference(avatar_split_clause,[],[f2829,f4300]) ).
tff(f4300,plain,
( spl272_148
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| $less(X2,X1)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_148])]) ).
tff(f2829,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,X0)
| $less(X2,X1)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1234]) ).
tff(f1234,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,X0)
| $less(X2,X1)
| $less(X1,X0) ),
inference(flattening,[],[f1233]) ).
tff(f1233,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,X0)
| $less(X2,X1)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f777]) ).
tff(f777,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
=> ~ $less(X2,X0) ),
inference(theory_normalization,[],[f230]) ).
tff(f230,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( $lesseq(X1,X2)
& $lesseq(X0,X1) )
=> $lesseq(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
tff(f4298,plain,
spl272_147,
inference(avatar_split_clause,[],[f2819,f4296]) ).
tff(f4296,plain,
( spl272_147
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X2)
| $less(X0,X2)
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_147])]) ).
tff(f2819,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X2)
| $less(X0,X2)
| $less(X1,X0) ),
inference(cnf_transformation,[],[f1216]) ).
tff(f1216,plain,
! [X0: $real,X1: $real,X2: $real] :
( ~ $less(X1,X2)
| $less(X0,X2)
| $less(X1,X0) ),
inference(flattening,[],[f1215]) ).
tff(f1215,plain,
! [X0: $real,X1: $real,X2: $real] :
( ~ $less(X1,X2)
| $less(X0,X2)
| $less(X1,X0) ),
inference(ennf_transformation,[],[f771]) ).
tff(f771,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X0,X2)
& ~ $less(X1,X0) )
=> ~ $less(X1,X2) ),
inference(theory_normalization,[],[f249]) ).
tff(f249,axiom,
! [X0: $real,X1: $real,X2: $real] :
( ( $lesseq(X2,X0)
& $lesseq(X0,X1) )
=> $lesseq(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom247) ).
tff(f4294,plain,
spl272_146,
inference(avatar_split_clause,[],[f2388,f4292]) ).
tff(f4292,plain,
( spl272_146
<=> ! [X0: $int,X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X0),X1),0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_146])]) ).
tff(f2388,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X0),X1),0)
| $less(X0,0) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f1024,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less('fun_app$a'('power$a'(X0),X1),0)
| $less(X0,0) ),
inference(ennf_transformation,[],[f694]) ).
tff(f694,plain,
! [X0: $int,X1: 'Nat$'] :
( ~ $less(X0,0)
=> ~ $less('fun_app$a'('power$a'(X0),X1),0) ),
inference(theory_normalization,[],[f195]) ).
tff(f195,axiom,
! [X0: $int,X1: 'Nat$'] :
( $lesseq(0,X0)
=> $lesseq(0,'fun_app$a'('power$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).
tff(f4290,plain,
spl272_145,
inference(avatar_split_clause,[],[f2385,f4288]) ).
tff(f4288,plain,
( spl272_145
<=> ! [X0: $real,X1: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X0),X1),0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_145])]) ).
tff(f2385,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X0),X1),0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1022]) ).
tff(f1022,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less('fun_app$m'('power$c'(X0),X1),0.0)
| $less(X0,0.0) ),
inference(ennf_transformation,[],[f692]) ).
tff(f692,plain,
! [X0: $real,X1: 'Nat$'] :
( ~ $less(X0,0.0)
=> ~ $less('fun_app$m'('power$c'(X0),X1),0.0) ),
inference(theory_normalization,[],[f196]) ).
tff(f196,axiom,
! [X0: $real,X1: 'Nat$'] :
( $lesseq(0.0,X0)
=> $lesseq(0.0,'fun_app$m'('power$c'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
tff(f4286,plain,
spl272_144,
inference(avatar_split_clause,[],[f2378,f4284]) ).
tff(f4284,plain,
( spl272_144
<=> ! [X0: $int,X1: 'Nat$'] :
( ( 0 != 'fun_app$a'('power$a'(X0),X1) )
| ( 0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_144])]) ).
tff(f2378,plain,
! [X0: $int,X1: 'Nat$'] :
( ( 0 != 'fun_app$a'('power$a'(X0),X1) )
| ( 0 = X0 ) ),
inference(cnf_transformation,[],[f1016]) ).
tff(f1016,plain,
! [X0: $int,X1: 'Nat$'] :
( ( 0 != 'fun_app$a'('power$a'(X0),X1) )
| ( 0 = X0 ) ),
inference(ennf_transformation,[],[f164]) ).
tff(f164,axiom,
! [X0: $int,X1: 'Nat$'] :
( ( 0 != X0 )
=> ( 0 != 'fun_app$a'('power$a'(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
tff(f4282,plain,
spl272_143,
inference(avatar_split_clause,[],[f2377,f4280]) ).
tff(f4280,plain,
( spl272_143
<=> ! [X0: $real,X1: 'Nat$'] :
( ( 0.0 != 'fun_app$m'('power$c'(X0),X1) )
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_143])]) ).
tff(f2377,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 0.0 != 'fun_app$m'('power$c'(X0),X1) )
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f1015]) ).
tff(f1015,plain,
! [X0: $real,X1: 'Nat$'] :
( ( 0.0 != 'fun_app$m'('power$c'(X0),X1) )
| ( 0.0 = X0 ) ),
inference(ennf_transformation,[],[f165]) ).
tff(f165,axiom,
! [X0: $real,X1: 'Nat$'] :
( ( 0.0 != X0 )
=> ( 0.0 != 'fun_app$m'('power$c'(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom163) ).
tff(f4278,plain,
spl272_142,
inference(avatar_split_clause,[],[f2376,f4276]) ).
tff(f4276,plain,
( spl272_142
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),X1) != 'zero$' )
| ( 'zero$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_142])]) ).
tff(f2376,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),X1) != 'zero$' )
| ( 'zero$' = X0 ) ),
inference(cnf_transformation,[],[f1014]) ).
tff(f1014,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'fun_app$b'('power$'(X0),X1) != 'zero$' )
| ( 'zero$' = X0 ) ),
inference(ennf_transformation,[],[f163]) ).
tff(f163,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'zero$' != X0 )
=> ( 'fun_app$b'('power$'(X0),X1) != 'zero$' ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
tff(f4271,plain,
spl272_141,
inference(avatar_split_clause,[],[f2259,f4269]) ).
tff(f4269,plain,
( spl272_141
<=> ! [X4: $real,X0: 'Real_set$'] :
( ~ $less(sK33(X0),X4)
| ~ 'member$'(X4,X0)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_141])]) ).
tff(f2259,plain,
! [X0: 'Real_set$',X4: $real] :
( ~ $less(sK33(X0),X4)
| ~ 'member$'(X4,X0)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f1556]) ).
tff(f4267,plain,
spl272_140,
inference(avatar_split_clause,[],[f2254,f4265]) ).
tff(f2254,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK30(X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f1546]) ).
tff(f1546,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK30(X0)) = X0 )
| $less(X0,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f1006,f1545]) ).
tff(f1545,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 )
=> ( 'fun_app$a'('of_nat$',sK30(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f1006,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 )
| $less(X0,0) ),
inference(ennf_transformation,[],[f899]) ).
tff(f899,plain,
! [X0: $int] :
~ ( ! [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) != X0 )
& ~ $less(X0,0) ),
inference(flattening,[],[f898]) ).
tff(f898,plain,
! [X0: $int] :
~ ( ! [X1: 'Nat$'] :
( ~ 'fun_app$a'('of_nat$',X1) = X0 )
& ~ $less(X0,0) ),
inference(true_and_false_elimination,[],[f672]) ).
tff(f672,plain,
! [X0: $int] :
( ( ! [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = X0 )
=> $false )
& ~ $less(X0,0) )
=> $false ),
inference(theory_normalization,[],[f443]) ).
tff(f443,axiom,
! [X0: $int] :
( ( ! [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = X0 )
=> $false )
& $lesseq(0,X0) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
tff(f4263,plain,
spl272_139,
inference(avatar_split_clause,[],[f2253,f4261]) ).
tff(f4261,plain,
( spl272_139
<=> ! [X0: $int] :
( $less(0,'fun_app$a'('of_nat$',sK29(X0)))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_139])]) ).
tff(f2253,plain,
! [X0: $int] :
( $less(0,'fun_app$a'('of_nat$',sK29(X0)))
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f1544]) ).
tff(f1544,plain,
! [X0: $int] :
( ( $less(0,'fun_app$a'('of_nat$',sK29(X0)))
& ( 'fun_app$a'('of_nat$',sK29(X0)) = X0 ) )
| ~ $less(0,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f1005,f1543]) ).
tff(f1543,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X1) = X0 ) )
=> ( $less(0,'fun_app$a'('of_nat$',sK29(X0)))
& ( 'fun_app$a'('of_nat$',sK29(X0)) = X0 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1005,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] :
( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X1) = X0 ) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f897]) ).
tff(f897,plain,
! [X0: $int] :
~ ( ! [X1: 'Nat$'] :
~ ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X1) = X0 ) )
& $less(0,X0) ),
inference(true_and_false_elimination,[],[f542]) ).
tff(f542,axiom,
! [X0: $int] :
( ( ! [X1: 'Nat$'] :
( ( $less(0,'fun_app$a'('of_nat$',X1))
& ( 'fun_app$a'('of_nat$',X1) = X0 ) )
=> $false )
& $less(0,X0) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
tff(f4259,plain,
spl272_138,
inference(avatar_split_clause,[],[f2252,f4257]) ).
tff(f4257,plain,
( spl272_138
<=> ! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK29(X0)) = X0 )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_138])]) ).
tff(f2252,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK29(X0)) = X0 )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f1544]) ).
tff(f4255,plain,
spl272_137,
inference(avatar_split_clause,[],[f2243,f4253]) ).
tff(f2243,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK26(X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f1538]) ).
tff(f1538,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK26(X0)) = X0 )
| $less(X0,0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f999,f1537]) ).
tff(f1537,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 )
=> ( 'fun_app$a'('of_nat$',sK26(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
tff(f999,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 )
| $less(X0,0) ),
inference(ennf_transformation,[],[f670]) ).
tff(f670,plain,
! [X0: $int] :
( ~ $less(X0,0)
=> ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 ) ),
inference(theory_normalization,[],[f447]) ).
tff(f447,axiom,
! [X0: $int] :
( $lesseq(0,X0)
=> ? [X1: 'Nat$'] : ( 'fun_app$a'('of_nat$',X1) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
tff(f4251,plain,
spl272_136,
inference(avatar_split_clause,[],[f2242,f4249]) ).
tff(f4249,plain,
( spl272_136
<=> ! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK25(X0)) = X0 )
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_136])]) ).
tff(f2242,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$',sK25(X0)) = X0 )
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f1536,plain,
! [X0: $int] :
( ( ( 'fun_app$a'('of_nat$',sK25(X0)) = X0 )
& $less(0,'fun_app$a'('of_nat$',sK25(X0))) )
| ~ $less(0,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f998,f1535]) ).
tff(f1535,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = X0 )
& $less(0,'fun_app$a'('of_nat$',X1)) )
=> ( ( 'fun_app$a'('of_nat$',sK25(X0)) = X0 )
& $less(0,'fun_app$a'('of_nat$',sK25(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f998,plain,
! [X0: $int] :
( ? [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = X0 )
& $less(0,'fun_app$a'('of_nat$',X1)) )
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f536]) ).
tff(f536,axiom,
! [X0: $int] :
( $less(0,X0)
=> ? [X1: 'Nat$'] :
( ( 'fun_app$a'('of_nat$',X1) = X0 )
& $less(0,'fun_app$a'('of_nat$',X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
tff(f4247,plain,
spl272_135,
inference(avatar_split_clause,[],[f2241,f4245]) ).
tff(f4245,plain,
( spl272_135
<=> ! [X0: $int] :
( $less(0,'fun_app$a'('of_nat$',sK25(X0)))
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_135])]) ).
tff(f2241,plain,
! [X0: $int] :
( $less(0,'fun_app$a'('of_nat$',sK25(X0)))
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f4243,plain,
spl272_134,
inference(avatar_split_clause,[],[f2238,f4241]) ).
tff(f4241,plain,
( spl272_134
<=> ! [X0: $int] :
( ( 0 = 'fun_app$a'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_134])]) ).
tff(f2238,plain,
! [X0: $int] :
( ( 0 = 'fun_app$a'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f996]) ).
tff(f996,plain,
! [X0: $int] :
( ( ( 0 = 'fun_app$a'('of_nat$','nat$'(X0)) )
| ~ $less(X0,0) )
& ( ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f669]) ).
tff(f669,plain,
! [X0: $int] :
( ( $less(X0,0)
=> ( 0 = 'fun_app$a'('of_nat$','nat$'(X0)) ) )
& ( ~ $less(X0,0)
=> ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 ) ) ),
inference(theory_normalization,[],[f639]) ).
tff(f639,axiom,
! [X0: $int] :
( ( ~ $lesseq(0,X0)
=> ( 0 = 'fun_app$a'('of_nat$','nat$'(X0)) ) )
& ( $lesseq(0,X0)
=> ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).
tff(f4239,plain,
spl272_133,
inference(avatar_split_clause,[],[f2237,f4237]) ).
tff(f2237,plain,
! [X0: $int] :
( ( 'fun_app$a'('of_nat$','nat$'(X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f996]) ).
tff(f4235,plain,
spl272_132,
inference(avatar_split_clause,[],[f2213,f4233]) ).
tff(f4233,plain,
( spl272_132
<=> ! [X0: 'Num$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_132])]) ).
tff(f2213,plain,
! [X0: 'Num$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f112]) ).
tff(f112,axiom,
! [X0: 'Num$'] : ( 0 = 'fun_app$a'('power$a'(0),'nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom110) ).
tff(f4227,plain,
spl272_131,
inference(avatar_split_clause,[],[f2212,f4225]) ).
tff(f4225,plain,
( spl272_131
<=> ! [X0: 'Num$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_131])]) ).
tff(f2212,plain,
! [X0: 'Num$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f113]) ).
tff(f113,axiom,
! [X0: 'Num$'] : ( 0.0 = 'fun_app$m'('power$c'(0.0),'nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom111) ).
tff(f4223,plain,
spl272_130,
inference(avatar_split_clause,[],[f2211,f4221]) ).
tff(f4221,plain,
( spl272_130
<=> ! [X0: 'Num$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_130])]) ).
tff(f2211,plain,
! [X0: 'Num$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f110]) ).
tff(f110,axiom,
! [X0: 'Num$'] : ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
tff(f4219,plain,
spl272_129,
inference(avatar_split_clause,[],[f2210,f4217]) ).
tff(f4217,plain,
( spl272_129
<=> ! [X0: 'Num$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'('fun_app$d'('numeral$',X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_129])]) ).
tff(f2210,plain,
! [X0: 'Num$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'('fun_app$d'('numeral$',X0))) ),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
! [X0: 'Num$'] : ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'('fun_app$d'('numeral$',X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom109) ).
tff(f4215,plain,
spl272_128,
inference(avatar_split_clause,[],[f2208,f4213]) ).
tff(f4213,plain,
( spl272_128
<=> ! [X0: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_128])]) ).
tff(f2208,plain,
! [X0: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X0),1) ),
inference(cnf_transformation,[],[f33]) ).
tff(f33,axiom,
! [X0: 'Nat$'] : ( 'fun_app$a'('of_nat$',X0) != $sum('fun_app$a'('of_nat$',X0),1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom31) ).
tff(f4211,plain,
spl272_127,
inference(avatar_split_clause,[],[f873,f4209]) ).
tff(f4209,plain,
( spl272_127
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_127])]) ).
tff(f873,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f4207,plain,
spl272_126,
inference(avatar_split_clause,[],[f872,f4205]) ).
tff(f4205,plain,
( spl272_126
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_126])]) ).
tff(f872,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f4203,plain,
spl272_125,
inference(avatar_split_clause,[],[f855,f4201]) ).
tff(f4201,plain,
( spl272_125
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_125])]) ).
tff(f855,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f4199,plain,
spl272_124,
inference(avatar_split_clause,[],[f854,f4197]) ).
tff(f4197,plain,
( spl272_124
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_124])]) ).
tff(f854,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f4194,plain,
( spl272_123
| ~ spl272_2
| ~ spl272_109 ),
inference(avatar_split_clause,[],[f4171,f4112,f3621,f4192]) ).
tff(f3621,plain,
( spl272_2
<=> ! [X0: $real] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_2])]) ).
tff(f4171,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl272_2
| ~ spl272_109 ),
inference(resolution,[],[f4113,f3622]) ).
tff(f3622,plain,
( ! [X0: $real] : ~ $less(X0,X0)
| ~ spl272_2 ),
inference(avatar_component_clause,[],[f3621]) ).
tff(f4179,plain,
( spl272_122
| ~ spl272_1
| ~ spl272_107 ),
inference(avatar_split_clause,[],[f4164,f4104,f3617,f4177]) ).
tff(f4164,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl272_1
| ~ spl272_107 ),
inference(resolution,[],[f4105,f3618]) ).
tff(f4163,plain,
spl272_121,
inference(avatar_split_clause,[],[f2859,f4161]) ).
tff(f4161,plain,
( spl272_121
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,sK72(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_121])]) ).
tff(f2859,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ~ 'fun_app$n'(X0,sK72(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f1836]) ).
tff(f4159,plain,
spl272_120,
inference(avatar_split_clause,[],[f2781,f4157]) ).
tff(f4157,plain,
( spl272_120
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK64(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_120])]) ).
tff(f2781,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK64(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f1810]) ).
tff(f4155,plain,
spl272_119,
inference(avatar_split_clause,[],[f2774,f4153]) ).
tff(f4153,plain,
( spl272_119
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK62(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_119])]) ).
tff(f2774,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,sK62(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f4151,plain,
spl272_118,
inference(avatar_split_clause,[],[f2768,f4149]) ).
tff(f4149,plain,
( spl272_118
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP3(X0,X1)
| ~ 'fun_app$n'(X0,sK60(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_118])]) ).
tff(f2768,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP3(X0,X1)
| ~ 'fun_app$n'(X0,sK60(X0,X1)) ),
inference(cnf_transformation,[],[f1792]) ).
tff(f4147,plain,
spl272_117,
inference(avatar_split_clause,[],[f2761,f4145]) ).
tff(f4145,plain,
( spl272_117
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP2(X0,X1)
| ~ 'fun_app$n'(X0,sK58(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_117])]) ).
tff(f2761,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( sP2(X0,X1)
| ~ 'fun_app$n'(X0,sK58(X0,X1)) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f4143,plain,
spl272_116,
inference(avatar_split_clause,[],[f2483,f4141]) ).
tff(f4141,plain,
( spl272_116
<=> ! [X0: 'Nat_bool_fun$'] :
( $less(0,'fun_app$a'('of_nat$',sK45(X0)))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_116])]) ).
tff(f2483,plain,
! [X0: 'Nat_bool_fun$'] :
( $less(0,'fun_app$a'('of_nat$',sK45(X0)))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f1623]) ).
tff(f4139,plain,
spl272_115,
inference(avatar_split_clause,[],[f2383,f4137]) ).
tff(f4137,plain,
( spl272_115
<=> ! [X0: $real,X1: 'Nat$'] :
( $less(0.0,sK38(X0,X1))
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_115])]) ).
tff(f2383,plain,
! [X0: $real,X1: 'Nat$'] :
( $less(0.0,sK38(X0,X1))
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1599]) ).
tff(f4135,plain,
spl272_114,
inference(avatar_split_clause,[],[f2309,f4133]) ).
tff(f4133,plain,
( spl272_114
<=> ! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_114])]) ).
tff(f2309,plain,
! [X0: 'Num$'] :
( ( 'one$' = X0 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'one$') ),
inference(cnf_transformation,[],[f1582]) ).
tff(f1582,plain,
! [X0: 'Num$'] :
( ( 'fun_app$e'('fun_app$f'('less_eq$',X0),'one$')
| ( 'one$' != X0 ) )
& ( ( 'one$' = X0 )
| ~ 'fun_app$e'('fun_app$f'('less_eq$',X0),'one$') ) ),
inference(nnf_transformation,[],[f31]) ).
tff(f31,axiom,
! [X0: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$',X0),'one$')
<=> ( 'one$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
tff(f4131,plain,
spl272_113,
inference(avatar_split_clause,[],[f2295,f4129]) ).
tff(f4129,plain,
( spl272_113
<=> ! [X0: 'Enat$'] :
( ( 'zero$a' = X0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'zero$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_113])]) ).
tff(f2295,plain,
! [X0: 'Enat$'] :
( ( 'zero$a' = X0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'zero$a') ),
inference(cnf_transformation,[],[f1573]) ).
tff(f1573,plain,
! [X0: 'Enat$'] :
( ( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'zero$a')
| ( 'zero$a' != X0 ) )
& ( ( 'zero$a' = X0 )
| ~ 'fun_app$g'('fun_app$h'('less_eq$a',X0),'zero$a') ) ),
inference(nnf_transformation,[],[f340]) ).
tff(f340,axiom,
! [X0: 'Enat$'] :
( 'fun_app$g'('fun_app$h'('less_eq$a',X0),'zero$a')
<=> ( 'zero$a' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom338) ).
tff(f4127,plain,
spl272_112,
inference(avatar_split_clause,[],[f2273,f4125]) ).
tff(f4125,plain,
( spl272_112
<=> ! [X0: $real] :
( ( 0.0 = X0 )
| $less(0.0,'times$d'(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_112])]) ).
tff(f2273,plain,
! [X0: $real] :
( ( 0.0 = X0 )
| $less(0.0,'times$d'(X0,X0)) ),
inference(cnf_transformation,[],[f1563]) ).
tff(f1563,plain,
! [X0: $real] :
( ( ~ $less(0.0,'times$d'(X0,X0))
| ( 0.0 != X0 ) )
& ( ( 0.0 = X0 )
| $less(0.0,'times$d'(X0,X0)) ) ),
inference(nnf_transformation,[],[f633]) ).
tff(f633,axiom,
! [X0: $real] :
( ~ $less(0.0,'times$d'(X0,X0))
<=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom631) ).
tff(f4123,plain,
spl272_111,
inference(avatar_split_clause,[],[f2269,f4121]) ).
tff(f4121,plain,
( spl272_111
<=> ! [X0: 'Enat$'] :
( ( 'zero$a' = X0 )
| 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_111])]) ).
tff(f2269,plain,
! [X0: 'Enat$'] :
( ( 'zero$a' = X0 )
| 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ),
inference(cnf_transformation,[],[f1561]) ).
tff(f1561,plain,
! [X0: 'Enat$'] :
( ( ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0)
| ( 'zero$a' != X0 ) )
& ( ( 'zero$a' = X0 )
| 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0) ) ),
inference(nnf_transformation,[],[f360]) ).
tff(f360,axiom,
! [X0: 'Enat$'] :
( ~ 'fun_app$g'('fun_app$h'('less$a','zero$a'),X0)
<=> ( 'zero$a' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom358) ).
tff(f4119,plain,
~ spl272_110,
inference(avatar_split_clause,[],[f2148,f4116]) ).
tff(f2148,plain,
~ $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$'))),
inference(cnf_transformation,[],[f645]) ).
tff(f645,plain,
~ $less('fun_app$a'('of_nat$','n$'),'fun_app$a'('of_nat$','size$'('ys$'))),
inference(theory_normalization,[],[f4]) ).
tff(f4,axiom,
$lesseq('fun_app$a'('of_nat$','size$'('ys$')),'fun_app$a'('of_nat$','n$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f4114,plain,
spl272_109,
inference(avatar_split_clause,[],[f875,f4112]) ).
tff(f875,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ),
introduced(theory_axiom_147,[]) ).
tff(f4110,plain,
spl272_108,
inference(avatar_split_clause,[],[f865,f4108]) ).
tff(f4108,plain,
( spl272_108
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_108])]) ).
tff(f865,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f4106,plain,
spl272_107,
inference(avatar_split_clause,[],[f857,f4104]) ).
tff(f857,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f4102,plain,
( spl272_106
| ~ spl272_39
| ~ spl272_55 ),
inference(avatar_split_clause,[],[f3894,f3851,f3773,f4099]) ).
tff(f4099,plain,
( spl272_106
<=> ( 0.0 = 'fun_app$m'('of_nat$b','size$a'('one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_106])]) ).
tff(f3773,plain,
( spl272_39
<=> ( 0.0 = 'fun_app$m'('of_nat$b','nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_39])]) ).
tff(f3894,plain,
( ( 0.0 = 'fun_app$m'('of_nat$b','size$a'('one$')) )
| ~ spl272_39
| ~ spl272_55 ),
inference(superposition,[],[f3775,f3853]) ).
tff(f3775,plain,
( ( 0.0 = 'fun_app$m'('of_nat$b','nat$'(0)) )
| ~ spl272_39 ),
inference(avatar_component_clause,[],[f3773]) ).
tff(f4092,plain,
( spl272_105
| ~ spl272_42
| ~ spl272_55 ),
inference(avatar_split_clause,[],[f3892,f3851,f3788,f4089]) ).
tff(f4089,plain,
( spl272_105
<=> ( 'zero$a' = 'fun_app$l'('of_nat$c','size$a'('one$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_105])]) ).
tff(f3788,plain,
( spl272_42
<=> ( 'fun_app$l'('of_nat$c','nat$'(0)) = 'zero$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_42])]) ).
tff(f3892,plain,
( ( 'zero$a' = 'fun_app$l'('of_nat$c','size$a'('one$')) )
| ~ spl272_42
| ~ spl272_55 ),
inference(superposition,[],[f3790,f3853]) ).
tff(f3790,plain,
( ( 'fun_app$l'('of_nat$c','nat$'(0)) = 'zero$a' )
| ~ spl272_42 ),
inference(avatar_component_clause,[],[f3788]) ).
tff(f4087,plain,
( spl272_104
| ~ spl272_55
| ~ spl272_80 ),
inference(avatar_split_clause,[],[f3964,f3961,f3851,f4085]) ).
tff(f4085,plain,
( spl272_104
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_104])]) ).
tff(f3961,plain,
( spl272_80
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP5(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_80])]) ).
tff(f3964,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,'size$a'('one$'))
| sP5(X1,X0) )
| ~ spl272_55
| ~ spl272_80 ),
inference(forward_demodulation,[],[f3962,f3853]) ).
tff(f3962,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP5(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) )
| ~ spl272_80 ),
inference(avatar_component_clause,[],[f3961]) ).
tff(f4083,plain,
( spl272_103
| ~ spl272_55
| ~ spl272_79 ),
inference(avatar_split_clause,[],[f3959,f3956,f3851,f4081]) ).
tff(f4081,plain,
( spl272_103
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_103])]) ).
tff(f3956,plain,
( spl272_79
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'(0))
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_79])]) ).
tff(f3959,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'size$a'('one$'))
| ~ sP3(X1,X0) )
| ~ spl272_55
| ~ spl272_79 ),
inference(forward_demodulation,[],[f3957,f3853]) ).
tff(f3957,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'(0))
| ~ sP3(X1,X0) )
| ~ spl272_79 ),
inference(avatar_component_clause,[],[f3956]) ).
tff(f4064,plain,
( spl272_102
| ~ spl272_12
| ~ spl272_59 ),
inference(avatar_split_clause,[],[f4057,f3869,f3663,f4062]) ).
tff(f4062,plain,
( spl272_102
<=> ! [X0: $real] : ( 0.0 = $product(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_102])]) ).
tff(f3663,plain,
( spl272_12
<=> ! [X0: $real] : ( 0.0 = $product(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_12])]) ).
tff(f3869,plain,
( spl272_59
<=> ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_59])]) ).
tff(f4057,plain,
( ! [X0: $real] : ( 0.0 = $product(0.0,X0) )
| ~ spl272_12
| ~ spl272_59 ),
inference(superposition,[],[f3870,f3664]) ).
tff(f3664,plain,
( ! [X0: $real] : ( 0.0 = $product(X0,0.0) )
| ~ spl272_12 ),
inference(avatar_component_clause,[],[f3663]) ).
tff(f3870,plain,
( ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl272_59 ),
inference(avatar_component_clause,[],[f3869]) ).
tff(f4048,plain,
spl272_101,
inference(avatar_split_clause,[],[f3435,f4046]) ).
tff(f4046,plain,
( spl272_101
<=> ! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$a'('of_nat$',X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_101])]) ).
tff(f3435,plain,
! [X0: 'Nat$'] : $less(0,$sum(1,'fun_app$a'('of_nat$',X0))),
inference(forward_demodulation,[],[f2205,f848]) ).
tff(f2205,plain,
! [X0: 'Nat$'] : $less(0,$sum('fun_app$a'('of_nat$',X0),1)),
inference(cnf_transformation,[],[f377]) ).
tff(f377,axiom,
! [X0: 'Nat$'] : $less(0,$sum('fun_app$a'('of_nat$',X0),1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom375) ).
tff(f4044,plain,
spl272_100,
inference(avatar_split_clause,[],[f3433,f4042]) ).
tff(f4042,plain,
( spl272_100
<=> ! [X0: $real] : ( 'fun_app$m'('power$c'(X0),'nat$'(1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_100])]) ).
tff(f3433,plain,
! [X0: $real] : ( 'fun_app$m'('power$c'(X0),'nat$'(1)) = X0 ),
inference(evaluation,[],[f2214]) ).
tff(f2214,plain,
! [X0: $real] : ( 'fun_app$m'('power$c'(X0),'nat$'($sum(0,1))) = X0 ),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
! [X0: $real] : ( 'fun_app$m'('power$c'(X0),'nat$'($sum(0,1))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
tff(f4040,plain,
spl272_99,
inference(avatar_split_clause,[],[f3432,f4038]) ).
tff(f3432,plain,
! [X0: 'Nat$'] : ( 'fun_app$b'('power$'(X0),'nat$'(1)) = X0 ),
inference(evaluation,[],[f2215]) ).
tff(f2215,plain,
! [X0: 'Nat$'] : ( 'fun_app$b'('power$'(X0),'nat$'($sum(0,1))) = X0 ),
inference(cnf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: 'Nat$'] : ( 'fun_app$b'('power$'(X0),'nat$'($sum(0,1))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
tff(f4036,plain,
spl272_98,
inference(avatar_split_clause,[],[f3431,f4034]) ).
tff(f4034,plain,
( spl272_98
<=> ! [X0: $int] : ( 'fun_app$a'('power$a'(X0),'nat$'(1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_98])]) ).
tff(f3431,plain,
! [X0: $int] : ( 'fun_app$a'('power$a'(X0),'nat$'(1)) = X0 ),
inference(evaluation,[],[f2216]) ).
tff(f2216,plain,
! [X0: $int] : ( 'fun_app$a'('power$a'(X0),'nat$'($sum(0,1))) = X0 ),
inference(cnf_transformation,[],[f97]) ).
tff(f97,axiom,
! [X0: $int] : ( 'fun_app$a'('power$a'(X0),'nat$'($sum(0,1))) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
tff(f4032,plain,
spl272_97,
inference(avatar_split_clause,[],[f2902,f4030]) ).
tff(f4030,plain,
( spl272_97
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_97])]) ).
tff(f2902,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f1865,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP12(X0,X1,X2) ),
inference(rectify,[],[f1864]) ).
tff(f1864,plain,
! [X1: $int,X2: $int,X0: $int] :
( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
| ~ sP12(X1,X2,X0) ),
inference(nnf_transformation,[],[f1518]) ).
tff(f4028,plain,
spl272_96,
inference(avatar_split_clause,[],[f2901,f4026]) ).
tff(f4026,plain,
( spl272_96
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_96])]) ).
tff(f2901,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f1865]) ).
tff(f4024,plain,
spl272_95,
inference(avatar_split_clause,[],[f2900,f4022]) ).
tff(f4022,plain,
( spl272_95
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_95])]) ).
tff(f2900,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f1863]) ).
tff(f1863,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP13(X0,X1,X2) ),
inference(rectify,[],[f1862]) ).
tff(f1862,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ~ sP13(X0,X2,X1) ),
inference(nnf_transformation,[],[f1519]) ).
tff(f4020,plain,
spl272_94,
inference(avatar_split_clause,[],[f2899,f4018]) ).
tff(f4018,plain,
( spl272_94
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_94])]) ).
tff(f2899,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f1863]) ).
tff(f4016,plain,
spl272_93,
inference(avatar_split_clause,[],[f2898,f4014]) ).
tff(f4014,plain,
( spl272_93
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_93])]) ).
tff(f2898,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f1861]) ).
tff(f1861,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP14(X0,X1,X2) ),
inference(rectify,[],[f1860]) ).
tff(f1860,plain,
! [X2: $int,X1: $int,X0: $int] :
( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ~ sP14(X2,X1,X0) ),
inference(nnf_transformation,[],[f1520]) ).
tff(f4012,plain,
spl272_92,
inference(avatar_split_clause,[],[f2897,f4010]) ).
tff(f4010,plain,
( spl272_92
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_92])]) ).
tff(f2897,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f1861]) ).
tff(f4008,plain,
spl272_91,
inference(avatar_split_clause,[],[f2896,f4006]) ).
tff(f4006,plain,
( spl272_91
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_91])]) ).
tff(f2896,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f1859]) ).
tff(f1859,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP15(X0,X1,X2) ),
inference(rectify,[],[f1858]) ).
tff(f1858,plain,
! [X1: $int,X0: $int,X2: $int] :
( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ~ sP15(X1,X0,X2) ),
inference(nnf_transformation,[],[f1521]) ).
tff(f4004,plain,
spl272_90,
inference(avatar_split_clause,[],[f2895,f4002]) ).
tff(f4002,plain,
( spl272_90
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_90])]) ).
tff(f2895,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f1859]) ).
tff(f4000,plain,
spl272_89,
inference(avatar_split_clause,[],[f2890,f3998]) ).
tff(f3998,plain,
( spl272_89
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_89])]) ).
tff(f2890,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f1857]) ).
tff(f1857,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f1856]) ).
tff(f1856,plain,
! [X1: $real,X2: $real,X0: $real] :
( ( ~ $less(X2,X1)
& ~ $less(X1,X0) )
| ~ sP8(X1,X2,X0) ),
inference(nnf_transformation,[],[f1513]) ).
tff(f3996,plain,
spl272_88,
inference(avatar_split_clause,[],[f2889,f3994]) ).
tff(f3994,plain,
( spl272_88
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_88])]) ).
tff(f2889,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f1857]) ).
tff(f3992,plain,
spl272_87,
inference(avatar_split_clause,[],[f2888,f3990]) ).
tff(f3990,plain,
( spl272_87
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_87])]) ).
tff(f2888,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f1855]) ).
tff(f1855,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP9(X0,X1,X2) ),
inference(rectify,[],[f1854]) ).
tff(f1854,plain,
! [X0: $real,X2: $real,X1: $real] :
( ( ~ $less(X2,X0)
& ~ $less(X0,X1) )
| ~ sP9(X0,X2,X1) ),
inference(nnf_transformation,[],[f1514]) ).
tff(f3988,plain,
spl272_86,
inference(avatar_split_clause,[],[f2887,f3986]) ).
tff(f3986,plain,
( spl272_86
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_86])]) ).
tff(f2887,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f1855]) ).
tff(f3984,plain,
( spl272_85
| ~ spl272_52
| ~ spl272_54 ),
inference(avatar_split_clause,[],[f3855,f3837,f3829,f3982]) ).
tff(f3982,plain,
( spl272_85
<=> ! [X0: 'Nat_bool_fun$'] :
( sP4(X0,sK45(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_85])]) ).
tff(f3829,plain,
( spl272_52
<=> ! [X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,sK45(X0))
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_52])]) ).
tff(f3837,plain,
( spl272_54
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP4(X1,X0)
| ~ 'fun_app$n'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_54])]) ).
tff(f3855,plain,
( ! [X0: 'Nat_bool_fun$'] :
( sP4(X0,sK45(X0))
| ~ sP1(X0) )
| ~ spl272_52
| ~ spl272_54 ),
inference(resolution,[],[f3838,f3830]) ).
tff(f3830,plain,
( ! [X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,sK45(X0))
| ~ sP1(X0) )
| ~ spl272_52 ),
inference(avatar_component_clause,[],[f3829]) ).
tff(f3838,plain,
( ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( ~ 'fun_app$n'(X1,X0)
| sP4(X1,X0) )
| ~ spl272_54 ),
inference(avatar_component_clause,[],[f3837]) ).
tff(f3980,plain,
spl272_84,
inference(avatar_split_clause,[],[f2886,f3978]) ).
tff(f3978,plain,
( spl272_84
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_84])]) ).
tff(f2886,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f1853]) ).
tff(f1853,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP10(X0,X1,X2) ),
inference(rectify,[],[f1852]) ).
tff(f1852,plain,
! [X2: $real,X1: $real,X0: $real] :
( ( ~ $less(X1,X2)
& ~ $less(X2,X0) )
| ~ sP10(X2,X1,X0) ),
inference(nnf_transformation,[],[f1515]) ).
tff(f3976,plain,
spl272_83,
inference(avatar_split_clause,[],[f2885,f3974]) ).
tff(f3974,plain,
( spl272_83
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP10(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_83])]) ).
tff(f2885,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP10(X0,X1,X2) ),
inference(cnf_transformation,[],[f1853]) ).
tff(f3972,plain,
spl272_82,
inference(avatar_split_clause,[],[f2884,f3970]) ).
tff(f3970,plain,
( spl272_82
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_82])]) ).
tff(f2884,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X1,X0)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f1851]) ).
tff(f1851,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( ~ $less(X1,X0)
& ~ $less(X0,X2) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f1850]) ).
tff(f1850,plain,
! [X1: $real,X0: $real,X2: $real] :
( ( ~ $less(X0,X1)
& ~ $less(X1,X2) )
| ~ sP11(X1,X0,X2) ),
inference(nnf_transformation,[],[f1516]) ).
tff(f3968,plain,
spl272_81,
inference(avatar_split_clause,[],[f2883,f3966]) ).
tff(f3966,plain,
( spl272_81
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_81])]) ).
tff(f2883,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f1851]) ).
tff(f3963,plain,
spl272_80,
inference(avatar_split_clause,[],[f2785,f3961]) ).
tff(f2785,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP5(X1,X0)
| ~ 'fun_app$n'(X1,'nat$'(0)) ),
inference(cnf_transformation,[],[f1815]) ).
tff(f3958,plain,
spl272_79,
inference(avatar_split_clause,[],[f2769,f3956]) ).
tff(f2769,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,'nat$'(0))
| ~ sP3(X1,X0) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f3954,plain,
spl272_78,
inference(avatar_split_clause,[],[f2601,f3952]) ).
tff(f3952,plain,
( spl272_78
<=> ! [X0: 'Real_set$',X1: $real] :
( 'fun_app$'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_78])]) ).
tff(f2601,plain,
! [X0: 'Real_set$',X1: $real] :
( 'fun_app$'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f1684,plain,
! [X0: 'Real_set$',X1: $real] :
( ( 'fun_app$'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) )
& ( 'member$'(X1,X0)
| ~ 'fun_app$'('uu$'(X0),X1) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: 'Real_set$',X1: $real] :
( 'fun_app$'('uu$'(X0),X1)
<=> 'member$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
tff(f3950,plain,
spl272_77,
inference(avatar_split_clause,[],[f2600,f3948]) ).
tff(f3948,plain,
( spl272_77
<=> ! [X0: 'Real_set$',X1: $real] :
( 'member$'(X1,X0)
| ~ 'fun_app$'('uu$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_77])]) ).
tff(f2600,plain,
! [X0: 'Real_set$',X1: $real] :
( 'member$'(X1,X0)
| ~ 'fun_app$'('uu$'(X0),X1) ),
inference(cnf_transformation,[],[f1684]) ).
tff(f3946,plain,
spl272_76,
inference(avatar_split_clause,[],[f2599,f3944]) ).
tff(f3944,plain,
( spl272_76
<=> ! [X0: $real,X1: 'Real_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_76])]) ).
tff(f2599,plain,
! [X0: $real,X1: 'Real_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$'(X1,X0) ),
inference(cnf_transformation,[],[f1683]) ).
tff(f1683,plain,
! [X0: $real,X1: 'Real_bool_fun$'] :
( ( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$'(X1,X0) )
& ( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
inference(nnf_transformation,[],[f67]) ).
tff(f67,axiom,
! [X0: $real,X1: 'Real_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
<=> 'fun_app$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom65) ).
tff(f3942,plain,
spl272_75,
inference(avatar_split_clause,[],[f2598,f3940]) ).
tff(f3940,plain,
( spl272_75
<=> ! [X0: $real,X1: 'Real_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_75])]) ).
tff(f2598,plain,
! [X0: $real,X1: 'Real_bool_fun$'] :
( 'fun_app$'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ),
inference(cnf_transformation,[],[f1683]) ).
tff(f3938,plain,
( spl272_74
| ~ spl272_43
| ~ spl272_51 ),
inference(avatar_split_clause,[],[f3849,f3825,f3793,f3936]) ).
tff(f3936,plain,
( spl272_74
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$a'('power$a'(2),X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_74])]) ).
tff(f3793,plain,
( spl272_43
<=> ! [X0: 'Nat$'] : $less(0,'fun_app$a'('power$a'(2),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_43])]) ).
tff(f3849,plain,
( ! [X0: 'Nat$'] : ~ $less('fun_app$a'('power$a'(2),X0),0)
| ~ spl272_43
| ~ spl272_51 ),
inference(resolution,[],[f3826,f3794]) ).
tff(f3794,plain,
( ! [X0: 'Nat$'] : $less(0,'fun_app$a'('power$a'(2),X0))
| ~ spl272_43 ),
inference(avatar_component_clause,[],[f3793]) ).
tff(f3934,plain,
spl272_73,
inference(avatar_split_clause,[],[f2540,f3932]) ).
tff(f3932,plain,
( spl272_73
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK55(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_73])]) ).
tff(f2540,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK55(X0)) ),
inference(cnf_transformation,[],[f1644]) ).
tff(f3930,plain,
spl272_72,
inference(avatar_split_clause,[],[f2538,f3928]) ).
tff(f3928,plain,
( spl272_72
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK54(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_72])]) ).
tff(f2538,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK54(X0)) ),
inference(cnf_transformation,[],[f1642]) ).
tff(f3926,plain,
spl272_71,
inference(avatar_split_clause,[],[f2536,f3924]) ).
tff(f3924,plain,
( spl272_71
<=> ! [X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| ~ 'fun_app$g'(X0,sK53(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_71])]) ).
tff(f2536,plain,
! [X0: 'Enat_bool_fun$',X1: 'Enat$'] :
( 'fun_app$g'(X0,X1)
| ~ 'fun_app$g'(X0,sK53(X0)) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f3922,plain,
spl272_70,
inference(avatar_split_clause,[],[f2533,f3920]) ).
tff(f3920,plain,
( spl272_70
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK52(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_70])]) ).
tff(f2533,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$n'(X0,X1)
| ~ 'fun_app$n'(X0,sK52(X0)) ),
inference(cnf_transformation,[],[f1638]) ).
tff(f3918,plain,
spl272_69,
inference(avatar_split_clause,[],[f2337,f3916]) ).
tff(f3916,plain,
( spl272_69
<=> ! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'one$') ),
introduced(avatar_definition,[new_symbols(naming,[spl272_69])]) ).
tff(f2337,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'one$'),
inference(cnf_transformation,[],[f920]) ).
tff(f920,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'one$'),
inference(flattening,[],[f919]) ).
tff(f919,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'one$'),
inference(true_and_false_elimination,[],[f30]) ).
tff(f30,axiom,
! [X0: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','fun_app$c'('bit0$',X0)),'one$')
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
tff(f3914,plain,
spl272_68,
inference(avatar_split_clause,[],[f2336,f3912]) ).
tff(f3912,plain,
( spl272_68
<=> ! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less$','one$'),'fun_app$c'('bit0$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_68])]) ).
tff(f2336,plain,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less$','one$'),'fun_app$c'('bit0$',X0)),
inference(cnf_transformation,[],[f918]) ).
tff(f918,plain,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less$','one$'),'fun_app$c'('bit0$',X0)),
inference(true_and_false_elimination,[],[f372]) ).
tff(f372,axiom,
! [X0: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$','one$'),'fun_app$c'('bit0$',X0))
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom370) ).
tff(f3910,plain,
spl272_67,
inference(avatar_split_clause,[],[f2206,f3908]) ).
tff(f3908,plain,
( spl272_67
<=> ! [X0: $int] : ~ $less('fun_app$a'('power$a'(X0),'nat$'(2)),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_67])]) ).
tff(f2206,plain,
! [X0: $int] : ~ $less('fun_app$a'('power$a'(X0),'nat$'(2)),0),
inference(cnf_transformation,[],[f664]) ).
tff(f664,plain,
! [X0: $int] : ~ $less('fun_app$a'('power$a'(X0),'nat$'(2)),0),
inference(theory_normalization,[],[f331]) ).
tff(f331,axiom,
! [X0: $int] : $lesseq(0,'fun_app$a'('power$a'(X0),'nat$'(2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom329) ).
tff(f3906,plain,
spl272_66,
inference(avatar_split_clause,[],[f2202,f3904]) ).
tff(f3904,plain,
( spl272_66
<=> ! [X0: $real] : ~ $less('fun_app$m'('power$c'(X0),'nat$'(2)),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_66])]) ).
tff(f2202,plain,
! [X0: $real] : ~ $less('fun_app$m'('power$c'(X0),'nat$'(2)),0.0),
inference(cnf_transformation,[],[f663]) ).
tff(f663,plain,
! [X0: $real] : ~ $less('fun_app$m'('power$c'(X0),'nat$'(2)),0.0),
inference(theory_normalization,[],[f332]) ).
tff(f332,axiom,
! [X0: $real] : $lesseq(0.0,'fun_app$m'('power$c'(X0),'nat$'(2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom330) ).
tff(f3902,plain,
spl272_65,
inference(avatar_split_clause,[],[f2198,f3900]) ).
tff(f3900,plain,
( spl272_65
<=> ! [X0: 'Num$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'zero$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl272_65])]) ).
tff(f2198,plain,
! [X0: 'Num$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'zero$a'),
inference(cnf_transformation,[],[f189]) ).
tff(f189,axiom,
! [X0: 'Num$'] : ~ 'fun_app$g'('fun_app$h'('less_eq$a','fun_app$i'('numeral$a',X0)),'zero$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom187) ).
tff(f3898,plain,
spl272_64,
inference(avatar_split_clause,[],[f2194,f3896]) ).
tff(f3896,plain,
( spl272_64
<=> ! [X0: 'Nat$'] : ( $sum('fun_app$a'('of_nat$',X0),1) != 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_64])]) ).
tff(f2194,plain,
! [X0: 'Nat$'] : ( $sum('fun_app$a'('of_nat$',X0),1) != 0 ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,axiom,
! [X0: 'Nat$'] : ( $sum('fun_app$a'('of_nat$',X0),1) != 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).
tff(f3891,plain,
spl272_63,
inference(avatar_split_clause,[],[f2147,f3888]) ).
tff(f3888,plain,
( spl272_63
<=> ( 0 = 'fun_app$a'('power$a'(0),'nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_63])]) ).
tff(f2147,plain,
0 = 'fun_app$a'('power$a'(0),'nat$'(2)),
inference(cnf_transformation,[],[f328]) ).
tff(f328,axiom,
0 = 'fun_app$a'('power$a'(0),'nat$'(2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom326) ).
tff(f3886,plain,
spl272_62,
inference(avatar_split_clause,[],[f2146,f3883]) ).
tff(f2146,plain,
0.0 = 'fun_app$m'('power$c'(0.0),'nat$'(2)),
inference(cnf_transformation,[],[f329]) ).
tff(f329,axiom,
0.0 = 'fun_app$m'('power$c'(0.0),'nat$'(2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom327) ).
tff(f3881,plain,
spl272_61,
inference(avatar_split_clause,[],[f2144,f3878]) ).
tff(f3878,plain,
( spl272_61
<=> ( 'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_61])]) ).
tff(f2144,plain,
'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'(2)),
inference(cnf_transformation,[],[f326]) ).
tff(f326,axiom,
'zero$a' = 'fun_app$l'('power$b'('zero$a'),'nat$'(2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom324) ).
tff(f3876,plain,
spl272_60,
inference(avatar_split_clause,[],[f2143,f3873]) ).
tff(f3873,plain,
( spl272_60
<=> ( 'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'(2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_60])]) ).
tff(f2143,plain,
'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'(2)),
inference(cnf_transformation,[],[f327]) ).
tff(f327,axiom,
'zero$' = 'fun_app$b'('power$'('zero$'),'nat$'(2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom325) ).
tff(f3871,plain,
spl272_59,
inference(avatar_split_clause,[],[f877,f3869]) ).
tff(f877,plain,
! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f3867,plain,
spl272_58,
inference(avatar_split_clause,[],[f866,f3865]) ).
tff(f866,plain,
! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f3863,plain,
spl272_57,
inference(avatar_split_clause,[],[f859,f3861]) ).
tff(f3861,plain,
( spl272_57
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_57])]) ).
tff(f859,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f3859,plain,
spl272_56,
inference(avatar_split_clause,[],[f848,f3857]) ).
tff(f3854,plain,
( spl272_55
| ~ spl272_40
| ~ spl272_44 ),
inference(avatar_split_clause,[],[f3843,f3797,f3778,f3851]) ).
tff(f3843,plain,
( ( 'nat$'(0) = 'size$a'('one$') )
| ~ spl272_40
| ~ spl272_44 ),
inference(superposition,[],[f3798,f3780]) ).
tff(f3839,plain,
spl272_54,
inference(avatar_split_clause,[],[f2778,f3837]) ).
tff(f2778,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( sP4(X1,X0)
| ~ 'fun_app$n'(X1,X0) ),
inference(cnf_transformation,[],[f1806]) ).
tff(f3835,plain,
spl272_53,
inference(avatar_split_clause,[],[f2762,f3833]) ).
tff(f3833,plain,
( spl272_53
<=> ! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,X0)
| ~ sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_53])]) ).
tff(f2762,plain,
! [X0: 'Nat$',X1: 'Nat_bool_fun$'] :
( 'fun_app$n'(X1,X0)
| ~ sP2(X1,X0) ),
inference(cnf_transformation,[],[f1788]) ).
tff(f3831,plain,
spl272_52,
inference(avatar_split_clause,[],[f2482,f3829]) ).
tff(f2482,plain,
! [X0: 'Nat_bool_fun$'] :
( 'fun_app$n'(X0,sK45(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f1623]) ).
tff(f3827,plain,
spl272_51,
inference(avatar_split_clause,[],[f2370,f3825]) ).
tff(f2370,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(cnf_transformation,[],[f688]) ).
tff(f688,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(theory_normalization,[],[f286]) ).
tff(f286,axiom,
! [X0: $int,X1: $int] :
( $lesseq(X1,X0)
| $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom284) ).
tff(f3823,plain,
spl272_50,
inference(avatar_split_clause,[],[f2367,f3821]) ).
tff(f2367,plain,
! [X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(cnf_transformation,[],[f686]) ).
tff(f686,plain,
! [X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(theory_normalization,[],[f289]) ).
tff(f289,axiom,
! [X0: $real,X1: $real] :
( $lesseq(X1,X0)
| $lesseq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom287) ).
tff(f3819,plain,
spl272_49,
inference(avatar_split_clause,[],[f2340,f3817]) ).
tff(f3817,plain,
( spl272_49
<=> ! [X0: $real] : ~ $less('fun_app$m'('of_nat$b',sK37(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_49])]) ).
tff(f2340,plain,
! [X0: $real] : ~ $less('fun_app$m'('of_nat$b',sK37(X0)),X0),
inference(cnf_transformation,[],[f1597]) ).
tff(f1597,plain,
! [X0: $real] : ~ $less('fun_app$m'('of_nat$b',sK37(X0)),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f681,f1596]) ).
tff(f1596,plain,
! [X0: $real] :
( ? [X1: 'Nat$'] : ~ $less('fun_app$m'('of_nat$b',X1),X0)
=> ~ $less('fun_app$m'('of_nat$b',sK37(X0)),X0) ),
introduced(choice_axiom,[]) ).
tff(f681,plain,
! [X0: $real] :
? [X1: 'Nat$'] : ~ $less('fun_app$m'('of_nat$b',X1),X0),
inference(theory_normalization,[],[f344]) ).
tff(f344,axiom,
! [X0: $real] :
? [X1: 'Nat$'] : $lesseq(X0,'fun_app$m'('of_nat$b',X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom342) ).
tff(f3815,plain,
spl272_48,
inference(avatar_split_clause,[],[f2239,f3813]) ).
tff(f3813,plain,
( spl272_48
<=> ! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_48])]) ).
tff(f2239,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(cnf_transformation,[],[f888]) ).
tff(f888,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(rectify,[],[f640]) ).
tff(f640,axiom,
! [X6: tlbool] :
( ( tlfalse = X6 )
| ( tltrue = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_639) ).
tff(f3811,plain,
spl272_47,
inference(avatar_split_clause,[],[f2193,f3809]) ).
tff(f3809,plain,
( spl272_47
<=> ! [X0: 'Num$'] : ( 'fun_app$c'('times$a'(X0),'one$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_47])]) ).
tff(f2193,plain,
! [X0: 'Num$'] : ( 'fun_app$c'('times$a'(X0),'one$') = X0 ),
inference(cnf_transformation,[],[f611]) ).
tff(f611,axiom,
! [X0: 'Num$'] : ( 'fun_app$c'('times$a'(X0),'one$') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom609) ).
tff(f3807,plain,
spl272_46,
inference(avatar_split_clause,[],[f2192,f3805]) ).
tff(f3805,plain,
( spl272_46
<=> ! [X0: 'Num$'] : ( 'fun_app$c'('pow$'(X0),'one$') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_46])]) ).
tff(f2192,plain,
! [X0: 'Num$'] : ( 'fun_app$c'('pow$'(X0),'one$') = X0 ),
inference(cnf_transformation,[],[f197]) ).
tff(f197,axiom,
! [X0: 'Num$'] : ( 'fun_app$c'('pow$'(X0),'one$') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
tff(f3803,plain,
spl272_45,
inference(avatar_split_clause,[],[f2191,f3801]) ).
tff(f3801,plain,
( spl272_45
<=> ! [X0: 'Num$'] : ( 'fun_app$c'('times$a'('one$'),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_45])]) ).
tff(f2191,plain,
! [X0: 'Num$'] : ( 'fun_app$c'('times$a'('one$'),X0) = X0 ),
inference(cnf_transformation,[],[f610]) ).
tff(f610,axiom,
! [X0: 'Num$'] : ( 'fun_app$c'('times$a'('one$'),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom608) ).
tff(f3799,plain,
spl272_44,
inference(avatar_split_clause,[],[f2190,f3797]) ).
tff(f2190,plain,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$a'('of_nat$',X0)) = X0 ),
inference(cnf_transformation,[],[f638]) ).
tff(f638,axiom,
! [X0: 'Nat$'] : ( 'nat$'('fun_app$a'('of_nat$',X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom636) ).
tff(f3795,plain,
spl272_43,
inference(avatar_split_clause,[],[f2189,f3793]) ).
tff(f2189,plain,
! [X0: 'Nat$'] : $less(0,'fun_app$a'('power$a'(2),X0)),
inference(cnf_transformation,[],[f662]) ).
tff(f662,plain,
! [X0: 'Nat$'] : $less(0,'fun_app$a'('power$a'(2),X0)),
inference(theory_normalization,[],[f345]) ).
tff(f345,axiom,
! [X0: 'Nat$'] : ~ $lesseq('fun_app$a'('power$a'(2),X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom343) ).
tff(f3791,plain,
spl272_42,
inference(avatar_split_clause,[],[f2142,f3788]) ).
tff(f2142,plain,
'fun_app$l'('of_nat$c','nat$'(0)) = 'zero$a',
inference(cnf_transformation,[],[f87]) ).
tff(f87,axiom,
'fun_app$l'('of_nat$c','nat$'(0)) = 'zero$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
tff(f3786,plain,
spl272_41,
inference(avatar_split_clause,[],[f2140,f3783]) ).
tff(f2140,plain,
0 = 'fun_app$a'('of_nat$','nat$'(0)),
inference(cnf_transformation,[],[f550]) ).
tff(f550,axiom,
0 = 'fun_app$a'('of_nat$','nat$'(0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
tff(f3781,plain,
spl272_40,
inference(avatar_split_clause,[],[f2139,f3778]) ).
tff(f2139,plain,
0 = 'fun_app$a'('of_nat$','size$a'('one$')),
inference(cnf_transformation,[],[f156]) ).
tff(f156,axiom,
0 = 'fun_app$a'('of_nat$','size$a'('one$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom154) ).
tff(f3776,plain,
spl272_39,
inference(avatar_split_clause,[],[f2138,f3773]) ).
tff(f2138,plain,
0.0 = 'fun_app$m'('of_nat$b','nat$'(0)),
inference(cnf_transformation,[],[f89]) ).
tff(f89,axiom,
0.0 = 'fun_app$m'('of_nat$b','nat$'(0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).
tff(f3771,plain,
spl272_38,
inference(avatar_split_clause,[],[f870,f3769]) ).
tff(f3769,plain,
( spl272_38
<=> ! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_38])]) ).
tff(f870,plain,
! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f3767,plain,
spl272_37,
inference(avatar_split_clause,[],[f852,f3765]) ).
tff(f3765,plain,
( spl272_37
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_37])]) ).
tff(f852,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f3763,plain,
spl272_36,
inference(avatar_split_clause,[],[f3300,f3761]) ).
tff(f3761,plain,
( spl272_36
<=> ! [X1: 'Enat$'] : ( 'zero$a' = 'times$c'('zero$a',X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_36])]) ).
tff(f3300,plain,
! [X1: 'Enat$'] : ( 'zero$a' = 'times$c'('zero$a',X1) ),
inference(equality_resolution,[],[f2609]) ).
tff(f2609,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'zero$a' = 'times$c'(X0,X1) )
| ( 'zero$a' != X0 ) ),
inference(cnf_transformation,[],[f1690]) ).
tff(f3759,plain,
spl272_35,
inference(avatar_split_clause,[],[f3299,f3757]) ).
tff(f3757,plain,
( spl272_35
<=> ! [X0: 'Enat$'] : ( 'zero$a' = 'times$c'(X0,'zero$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_35])]) ).
tff(f3299,plain,
! [X0: 'Enat$'] : ( 'zero$a' = 'times$c'(X0,'zero$a') ),
inference(equality_resolution,[],[f2610]) ).
tff(f2610,plain,
! [X0: 'Enat$',X1: 'Enat$'] :
( ( 'zero$a' = 'times$c'(X0,X1) )
| ( 'zero$a' != X1 ) ),
inference(cnf_transformation,[],[f1690]) ).
tff(f3755,plain,
~ spl272_34,
inference(avatar_split_clause,[],[f3226,f3752]) ).
tff(f3752,plain,
( spl272_34
<=> $less(0.0,'times$d'(0.0,0.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_34])]) ).
tff(f3226,plain,
~ $less(0.0,'times$d'(0.0,0.0)),
inference(equality_resolution,[],[f2274]) ).
tff(f2274,plain,
! [X0: $real] :
( ~ $less(0.0,'times$d'(X0,X0))
| ( 0.0 != X0 ) ),
inference(cnf_transformation,[],[f1563]) ).
tff(f3750,plain,
spl272_33,
inference(avatar_split_clause,[],[f2308,f3748]) ).
tff(f3748,plain,
( spl272_33
<=> ! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),'one$') ),
introduced(avatar_definition,[new_symbols(naming,[spl272_33])]) ).
tff(f2308,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),'one$'),
inference(cnf_transformation,[],[f916]) ).
tff(f916,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),'one$'),
inference(flattening,[],[f915]) ).
tff(f915,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),'one$'),
inference(true_and_false_elimination,[],[f352]) ).
tff(f352,axiom,
! [X0: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less$',X0),'one$')
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom350) ).
tff(f3746,plain,
spl272_32,
inference(avatar_split_clause,[],[f2307,f3744]) ).
tff(f3744,plain,
( spl272_32
<=> ! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$','one$'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_32])]) ).
tff(f2307,plain,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$','one$'),X0),
inference(cnf_transformation,[],[f914]) ).
tff(f914,plain,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$','one$'),X0),
inference(true_and_false_elimination,[],[f29]) ).
tff(f29,axiom,
! [X0: 'Num$'] :
( 'fun_app$e'('fun_app$f'('less_eq$','one$'),X0)
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
tff(f3742,plain,
spl272_31,
inference(avatar_split_clause,[],[f2186,f3740]) ).
tff(f3740,plain,
( spl272_31
<=> ! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$',X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_31])]) ).
tff(f2186,plain,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$',X0),X0),
inference(cnf_transformation,[],[f199]) ).
tff(f199,axiom,
! [X0: 'Num$'] : 'fun_app$e'('fun_app$f'('less_eq$',X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
tff(f3738,plain,
spl272_30,
inference(avatar_split_clause,[],[f2183,f3736]) ).
tff(f3736,plain,
( spl272_30
<=> ! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a',X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_30])]) ).
tff(f2183,plain,
! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a',X0),X0),
inference(cnf_transformation,[],[f65]) ).
tff(f65,axiom,
! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a',X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
tff(f3734,plain,
spl272_29,
inference(avatar_split_clause,[],[f2178,f3732]) ).
tff(f3732,plain,
( spl272_29
<=> ! [X0: 'Num$'] : ~ $less('fun_app$d'('numeral$',X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_29])]) ).
tff(f2178,plain,
! [X0: 'Num$'] : ~ $less('fun_app$d'('numeral$',X0),0),
inference(cnf_transformation,[],[f657]) ).
tff(f657,plain,
! [X0: 'Num$'] : ~ $less('fun_app$d'('numeral$',X0),0),
inference(theory_normalization,[],[f185]) ).
tff(f185,axiom,
! [X0: 'Num$'] : $lesseq(0,'fun_app$d'('numeral$',X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom183) ).
tff(f3730,plain,
spl272_28,
inference(avatar_split_clause,[],[f2176,f3728]) ).
tff(f3728,plain,
( spl272_28
<=> ! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','zero$a'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_28])]) ).
tff(f2176,plain,
! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','zero$a'),X0),
inference(cnf_transformation,[],[f346]) ).
tff(f346,axiom,
! [X0: 'Enat$'] : 'fun_app$g'('fun_app$h'('less_eq$a','zero$a'),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom344) ).
tff(f3726,plain,
spl272_27,
inference(avatar_split_clause,[],[f2175,f3724]) ).
tff(f3724,plain,
( spl272_27
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$m'('of_nat$b',X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_27])]) ).
tff(f2175,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$m'('of_nat$b',X0),0.0),
inference(cnf_transformation,[],[f656]) ).
tff(f656,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$m'('of_nat$b',X0),0.0),
inference(theory_normalization,[],[f150]) ).
tff(f150,axiom,
! [X0: 'Nat$'] : $lesseq(0.0,'fun_app$m'('of_nat$b',X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom148) ).
tff(f3722,plain,
spl272_26,
inference(avatar_split_clause,[],[f2174,f3720]) ).
tff(f2174,plain,
! [X0: 'Num$'] : ~ $less('fun_app$j'('numeral$b',X0),0.0),
inference(cnf_transformation,[],[f655]) ).
tff(f655,plain,
! [X0: 'Num$'] : ~ $less('fun_app$j'('numeral$b',X0),0.0),
inference(theory_normalization,[],[f187]) ).
tff(f187,axiom,
! [X0: 'Num$'] : $lesseq(0.0,'fun_app$j'('numeral$b',X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom185) ).
tff(f3718,plain,
spl272_25,
inference(avatar_split_clause,[],[f2173,f3716]) ).
tff(f3716,plain,
( spl272_25
<=> ! [X0: 'Real_set$'] : ( 'collect$'('uu$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_25])]) ).
tff(f2173,plain,
! [X0: 'Real_set$'] : ( 'collect$'('uu$'(X0)) = X0 ),
inference(cnf_transformation,[],[f68]) ).
tff(f68,axiom,
! [X0: 'Real_set$'] : ( 'collect$'('uu$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom66) ).
tff(f3714,plain,
spl272_24,
inference(avatar_split_clause,[],[f2172,f3712]) ).
tff(f3712,plain,
( spl272_24
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_24])]) ).
tff(f2172,plain,
! [X0: $int] : ( 0 = $product(0,X0) ),
inference(cnf_transformation,[],[f622]) ).
tff(f622,axiom,
! [X0: $int] : ( 0 = $product(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).
tff(f3710,plain,
spl272_23,
inference(avatar_split_clause,[],[f2170,f3708]) ).
tff(f3708,plain,
( spl272_23
<=> ! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_23])]) ).
tff(f2170,plain,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),X0),
inference(cnf_transformation,[],[f496]) ).
tff(f496,axiom,
! [X0: 'Num$'] : ~ 'fun_app$e'('fun_app$f'('less$',X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom494) ).
tff(f3706,plain,
spl272_22,
inference(avatar_split_clause,[],[f2169,f3704]) ).
tff(f3704,plain,
( spl272_22
<=> ! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),'zero$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl272_22])]) ).
tff(f2169,plain,
! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),'zero$a'),
inference(cnf_transformation,[],[f541]) ).
tff(f541,axiom,
! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),'zero$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
tff(f3702,plain,
spl272_21,
inference(avatar_split_clause,[],[f2168,f3700]) ).
tff(f3700,plain,
( spl272_21
<=> ! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_21])]) ).
tff(f2168,plain,
! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),X0),
inference(cnf_transformation,[],[f498]) ).
tff(f498,axiom,
! [X0: 'Enat$'] : ~ 'fun_app$g'('fun_app$h'('less$a',X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom496) ).
tff(f3698,plain,
spl272_20,
inference(avatar_split_clause,[],[f2167,f3696]) ).
tff(f3696,plain,
( spl272_20
<=> ! [X0: 'Num$'] : $less(0,'fun_app$d'('numeral$',X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_20])]) ).
tff(f2167,plain,
! [X0: 'Num$'] : $less(0,'fun_app$d'('numeral$',X0)),
inference(cnf_transformation,[],[f654]) ).
tff(f654,plain,
! [X0: 'Num$'] : $less(0,'fun_app$d'('numeral$',X0)),
inference(theory_normalization,[],[f188]) ).
tff(f188,axiom,
! [X0: 'Num$'] : ~ $lesseq('fun_app$d'('numeral$',X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom186) ).
tff(f3694,plain,
spl272_19,
inference(avatar_split_clause,[],[f2165,f3692]) ).
tff(f3692,plain,
( spl272_19
<=> ! [X0: 'Nat$'] : ~ $less('fun_app$a'('of_nat$',X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_19])]) ).
tff(f2165,plain,
! [X0: 'Nat$'] : ~ $less('fun_app$a'('of_nat$',X0),0),
inference(cnf_transformation,[],[f425]) ).
tff(f425,axiom,
! [X0: 'Nat$'] : ~ $less('fun_app$a'('of_nat$',X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom423) ).
tff(f3690,plain,
spl272_18,
inference(avatar_split_clause,[],[f2164,f3688]) ).
tff(f2164,plain,
! [X0: 'Num$'] : $less(0.0,'fun_app$j'('numeral$b',X0)),
inference(cnf_transformation,[],[f653]) ).
tff(f653,plain,
! [X0: 'Num$'] : $less(0.0,'fun_app$j'('numeral$b',X0)),
inference(theory_normalization,[],[f190]) ).
tff(f190,axiom,
! [X0: 'Num$'] : ~ $lesseq('fun_app$j'('numeral$b',X0),0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom188) ).
tff(f3686,plain,
spl272_17,
inference(avatar_split_clause,[],[f2163,f3684]) ).
tff(f3684,plain,
( spl272_17
<=> ! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) != 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_17])]) ).
tff(f2163,plain,
! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) != 0 ),
inference(cnf_transformation,[],[f160]) ).
tff(f160,axiom,
! [X0: 'Num$'] : ( 'fun_app$d'('numeral$',X0) != 0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom158) ).
tff(f3682,plain,
spl272_16,
inference(avatar_split_clause,[],[f2162,f3680]) ).
tff(f3680,plain,
( spl272_16
<=> ! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) != 'one$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_16])]) ).
tff(f2162,plain,
! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) != 'one$' ),
inference(cnf_transformation,[],[f75]) ).
tff(f75,axiom,
! [X0: 'Num$'] : ( 'fun_app$c'('bit0$',X0) != 'one$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom73) ).
tff(f3678,plain,
spl272_15,
inference(avatar_split_clause,[],[f2161,f3676]) ).
tff(f3676,plain,
( spl272_15
<=> ! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) != 'zero$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_15])]) ).
tff(f2161,plain,
! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) != 'zero$a' ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,axiom,
! [X0: 'Num$'] : ( 'fun_app$i'('numeral$a',X0) != 'zero$a' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
tff(f3674,plain,
spl272_14,
inference(avatar_split_clause,[],[f2160,f3672]) ).
tff(f2160,plain,
! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) != 0.0 ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,axiom,
! [X0: 'Num$'] : ( 'fun_app$j'('numeral$b',X0) != 0.0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
tff(f3670,plain,
spl272_13,
inference(avatar_split_clause,[],[f2136,f3667]) ).
tff(f3667,plain,
( spl272_13
<=> ( 0 = 'fun_app$p'('dbl$',0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_13])]) ).
tff(f2136,plain,
0 = 'fun_app$p'('dbl$',0),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
0 = 'fun_app$p'('dbl$',0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).
tff(f3665,plain,
spl272_12,
inference(avatar_split_clause,[],[f880,f3663]) ).
tff(f880,plain,
! [X0: $real] : ( 0.0 = $product(X0,0.0) ),
introduced(theory_axiom_149,[]) ).
tff(f3661,plain,
spl272_11,
inference(avatar_split_clause,[],[f879,f3659]) ).
tff(f3659,plain,
( spl272_11
<=> ! [X0: $real] : ( $product(X0,1.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_11])]) ).
tff(f879,plain,
! [X0: $real] : ( $product(X0,1.0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3657,plain,
spl272_10,
inference(avatar_split_clause,[],[f876,f3655]) ).
tff(f3655,plain,
( spl272_10
<=> ! [X0: $real] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_10])]) ).
tff(f876,plain,
! [X0: $real] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f3653,plain,
spl272_9,
inference(avatar_split_clause,[],[f868,f3651]) ).
tff(f3651,plain,
( spl272_9
<=> ! [X0: $real] : ( $sum(X0,0.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_9])]) ).
tff(f868,plain,
! [X0: $real] : ( $sum(X0,0.0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3649,plain,
spl272_8,
inference(avatar_split_clause,[],[f862,f3647]) ).
tff(f3647,plain,
( spl272_8
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_8])]) ).
tff(f862,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f3645,plain,
spl272_7,
inference(avatar_split_clause,[],[f861,f3643]) ).
tff(f3643,plain,
( spl272_7
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_7])]) ).
tff(f861,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3641,plain,
spl272_6,
inference(avatar_split_clause,[],[f858,f3639]) ).
tff(f3639,plain,
( spl272_6
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_6])]) ).
tff(f858,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f3637,plain,
spl272_5,
inference(avatar_split_clause,[],[f850,f3635]) ).
tff(f3635,plain,
( spl272_5
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_5])]) ).
tff(f850,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3633,plain,
spl272_4,
inference(avatar_split_clause,[],[f2134,f3630]) ).
tff(f3630,plain,
( spl272_4
<=> ( 0.0 = 'dbl$a'(0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_4])]) ).
tff(f2134,plain,
0.0 = 'dbl$a'(0.0),
inference(cnf_transformation,[],[f102]) ).
tff(f102,axiom,
0.0 = 'dbl$a'(0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom100) ).
tff(f3628,plain,
~ spl272_3,
inference(avatar_split_clause,[],[f2130,f3625]) ).
tff(f3625,plain,
( spl272_3
<=> ( tltrue = tlfalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl272_3])]) ).
tff(f2130,plain,
tltrue != tlfalse,
inference(cnf_transformation,[],[f641]) ).
tff(f641,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_640) ).
tff(f3623,plain,
spl272_2,
inference(avatar_split_clause,[],[f871,f3621]) ).
tff(f871,plain,
! [X0: $real] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f3619,plain,
spl272_1,
inference(avatar_split_clause,[],[f853,f3617]) ).
tff(f853,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ITP001_1 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n023.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 19:12:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (21715)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.42 % (21718)WARNING: value z3 for option sas not known
% 0.20/0.42 % (21717)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.42 % (21721)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.42 % (21719)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.42 % (21722)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.20/0.42 % (21718)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.20/0.42 % (21720)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.42 % (21716)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.46 % (21717)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.46 % (21717)Terminated due to inappropriate strategy.
% 0.20/0.46 % (21717)------------------------------
% 0.20/0.46 % (21717)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.46 % (21717)Termination reason: Inappropriate
% 0.20/0.46
% 0.20/0.46 % (21717)Memory used [KB]: 2351
% 0.20/0.46 % (21717)Time elapsed: 0.043 s
% 0.20/0.46 % (21717)Instructions burned: 126 (million)
% 0.20/0.46 % (21717)------------------------------
% 0.20/0.46 % (21717)------------------------------
% 0.20/0.47 % (21719)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.47 % (21719)Terminated due to inappropriate strategy.
% 0.20/0.47 % (21719)------------------------------
% 0.20/0.47 % (21719)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.47 % (21719)Termination reason: Inappropriate
% 0.20/0.47
% 0.20/0.47 % (21719)Memory used [KB]: 2334
% 0.20/0.47 % (21719)Time elapsed: 0.050 s
% 0.20/0.47 % (21719)Instructions burned: 120 (million)
% 0.20/0.47 % (21719)------------------------------
% 0.20/0.47 % (21719)------------------------------
% 0.20/0.47 % (21716)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.47 % (21716)Terminated due to inappropriate strategy.
% 0.20/0.47 % (21716)------------------------------
% 0.20/0.47 % (21716)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.47 % (21716)Termination reason: Inappropriate
% 0.20/0.47
% 0.20/0.47 % (21716)Memory used [KB]: 2351
% 0.20/0.47 % (21716)Time elapsed: 0.051 s
% 0.20/0.47 % (21716)Instructions burned: 126 (million)
% 0.20/0.47 % (21723)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.47 % (21716)------------------------------
% 0.20/0.47 % (21716)------------------------------
% 0.20/0.49 % (21724)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.49 % (21723)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.49 % (21723)Terminated due to inappropriate strategy.
% 0.20/0.49 % (21723)------------------------------
% 0.20/0.49 % (21723)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.49 % (21723)Termination reason: Inappropriate
% 0.20/0.49
% 0.20/0.49 % (21723)Memory used [KB]: 2249
% 0.20/0.49 % (21723)Time elapsed: 0.021 s
% 0.20/0.49 % (21723)Instructions burned: 93 (million)
% 0.20/0.49 % (21723)------------------------------
% 0.20/0.49 % (21723)------------------------------
% 0.20/0.49 % (21725)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.50 % (21726)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 3.44/0.89 % (21720)First to succeed.
% 3.92/0.97 % (21720)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21715"
% 3.92/0.97 % (21720)Refutation found. Thanks to Tanya!
% 3.92/0.97 % SZS status Theorem for theBenchmark
% 3.92/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 3.92/1.01 % (21720)------------------------------
% 3.92/1.01 % (21720)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.92/1.01 % (21720)Termination reason: Refutation
% 3.92/1.01
% 3.92/1.01 % (21720)Memory used [KB]: 8027
% 3.92/1.01 % (21720)Time elapsed: 0.550 s
% 3.92/1.01 % (21720)Instructions burned: 1008 (million)
% 3.92/1.01 % (21715)Success in time 0.645 s
%------------------------------------------------------------------------------