TSTP Solution File: ITP353_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 : Mon May 20 23:09:38 EDT 2024
% Result : Theorem 1.57s 0.60s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1462
% Syntax : Number of formulae : 3644 ( 994 unt; 285 typ; 0 def)
% Number of atoms : 8739 (2672 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 8349 (2969 ~;2956 |;1328 &)
% ( 874 <=>; 222 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 6716 (1870 atm; 500 fun;2356 num;1990 var)
% Number of types : 24 ( 21 usr; 2 ari)
% Number of type conns : 500 ( 237 >; 263 *; 0 +; 0 <<)
% Number of predicates : 802 ( 797 usr; 714 prp; 0-3 aty)
% Number of functors : 188 ( 179 usr; 33 con; 0-3 aty)
% Number of variables : 5092 (4760 !; 332 ?;5092 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
'Int_fps_int_fps_fun$': $tType ).
tff(type_def_6,type,
'Int_bool_fun$': $tType ).
tff(type_def_7,type,
'Int_fps$': $tType ).
tff(type_def_8,type,
'Real_ereal_bool_fun_fun$': $tType ).
tff(type_def_9,type,
'Nat_fps$': $tType ).
tff(type_def_10,type,
'Ereal_bool_fun$': $tType ).
tff(type_def_11,type,
'Real_fls$': $tType ).
tff(type_def_12,type,
'Nat_real_real_fun_fun$': $tType ).
tff(type_def_13,type,
'Ereal$': $tType ).
tff(type_def_14,type,
'Nat_nat_fun$': $tType ).
tff(type_def_15,type,
'Nat$': $tType ).
tff(type_def_16,type,
'Real_fps_real_fps_fun$': $tType ).
tff(type_def_17,type,
'Ereal_fps$': $tType ).
tff(type_def_18,type,
'Real_fps$': $tType ).
tff(type_def_19,type,
'Ereal_set$': $tType ).
tff(type_def_20,type,
tlbool: $tType ).
tff(type_def_21,type,
'Real_list$': $tType ).
tff(type_def_22,type,
'Real_real_fun$': $tType ).
tff(type_def_23,type,
'Nat_real_fun$': $tType ).
tff(type_def_24,type,
'Nat_bool_fun$': $tType ).
tff(type_def_25,type,
'Real_bool_fun$': $tType ).
tff(func_def_0,type,
'max$': ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_1,type,
'max$a': $real > 'Real_real_fun$' ).
tff(func_def_2,type,
'zero$b': 'Real_fps$' ).
tff(func_def_3,type,
'fun_app$i': ( 'Real_fps_real_fps_fun$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_4,type,
'times$b': ( 'Ereal_fps$' * 'Ereal_fps$' ) > 'Ereal_fps$' ).
tff(func_def_5,type,
'inverse$c': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_6,type,
'one$e': 'Real_fls$' ).
tff(func_def_7,type,
'fps_nth$a': ( 'Ereal_fps$' * 'Nat$' ) > 'Ereal$' ).
tff(func_def_8,type,
'less$': 'Ereal$' > 'Ereal_bool_fun$' ).
tff(func_def_9,type,
'max$b': ( $int * $int ) > $int ).
tff(func_def_10,type,
'times$g': ( 'Real_fps$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_11,type,
'fun_app$f': ( 'Nat_real_fun$' * 'Nat$' ) > $real ).
tff(func_def_12,type,
'c$a': $real ).
tff(func_def_13,type,
'fun_app$d': ( 'Real_ereal_bool_fun_fun$' * $real ) > 'Ereal_bool_fun$' ).
tff(func_def_14,type,
'size_ereal$': 'Ereal$' > 'Nat$' ).
tff(func_def_15,type,
'uua$': $real > 'Real_bool_fun$' ).
tff(func_def_16,type,
'n$': 'Nat$' ).
tff(func_def_17,type,
'u$': $real ).
tff(func_def_18,type,
'zero$a': 'Real_fls$' ).
tff(func_def_19,type,
'uu$': 'Ereal_set$' > 'Ereal_bool_fun$' ).
tff(func_def_20,type,
'zero$e': 'Nat$' ).
tff(func_def_21,type,
'fps_cutoff$': ( 'Nat$' * 'Ereal_fps$' ) > 'Ereal_fps$' ).
tff(func_def_22,type,
'fps_XD$': 'Int_fps_int_fps_fun$' ).
tff(func_def_23,type,
'fps_tan$': $real > 'Real_fps$' ).
tff(func_def_24,type,
'one$d': 'Int_fps$' ).
tff(func_def_25,type,
'ereal$': $real > 'Ereal$' ).
tff(func_def_26,type,
'of_nat$': 'Nat$' > $int ).
tff(func_def_27,type,
'times$f': 'Nat$' > 'Nat_nat_fun$' ).
tff(func_def_28,type,
'c$': $real ).
tff(func_def_29,type,
'zero$d': 'Int_fps$' ).
tff(func_def_30,type,
'less_eq$': 'Ereal$' > 'Ereal_bool_fun$' ).
tff(func_def_31,type,
'uminus$': 'Ereal$' > 'Ereal$' ).
tff(func_def_32,type,
'fps_ln$': $real > 'Real_fps$' ).
tff(func_def_33,type,
'times$d': ( $int * $int ) > $int ).
tff(func_def_34,type,
'collect$': 'Ereal_bool_fun$' > 'Ereal_set$' ).
tff(func_def_35,type,
'zero$c': 'Ereal_fps$' ).
tff(func_def_36,type,
'fps_nth$c': ( 'Nat_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_37,type,
tltrue: tlbool ).
tff(func_def_38,type,
'times$c': ( 'Int_fps$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_39,type,
'infinity$': 'Ereal$' ).
tff(func_def_40,type,
'fps_Lambert_W$': 'Real_fps$' ).
tff(func_def_41,type,
'uub$': $int > 'Int_bool_fun$' ).
tff(func_def_42,type,
'one$b': 'Nat$' ).
tff(func_def_43,type,
'inverse$a': 'Ereal$' > 'Ereal$' ).
tff(func_def_44,type,
'times$': ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_45,type,
'fps_cutoff$a': ( 'Nat$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_46,type,
'fps_cutoff$b': ( 'Nat$' * 'Real_fps$' ) > 'Real_fps$' ).
tff(func_def_47,type,
'radical$': ( 'Nat_real_real_fun_fun$' * 'Nat$' * 'Real_fps$' ) > 'Nat_real_fun$' ).
tff(func_def_48,type,
'fps_XDp$': $real > 'Real_fps_real_fps_fun$' ).
tff(func_def_49,type,
'uminus$a': 'Ereal_fps$' > 'Ereal_fps$' ).
tff(func_def_50,type,
'c$b': 'Ereal$' ).
tff(func_def_51,type,
'fps_deriv$': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_52,type,
'fps_XD$a': 'Real_fps_real_fps_fun$' ).
tff(func_def_53,type,
'inverse$d': 'Ereal_fps$' > 'Ereal_fps$' ).
tff(func_def_54,type,
'times$e': ( 'Nat_fps$' * 'Nat_fps$' ) > 'Nat_fps$' ).
tff(func_def_55,type,
'fps_nth$b': ( 'Int_fps$' * 'Nat$' ) > $int ).
tff(func_def_56,type,
'times$a': $real > 'Real_real_fun$' ).
tff(func_def_57,type,
'inverse$': 'Real_real_fun$' ).
tff(func_def_58,type,
'fun_app$h': ( 'Int_fps_int_fps_fun$' * 'Int_fps$' ) > 'Int_fps$' ).
tff(func_def_59,type,
'less_eq$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_60,type,
tlfalse: tlbool ).
tff(func_def_61,type,
'nat$': $int > 'Nat$' ).
tff(func_def_62,type,
'fps_XDp$a': $int > 'Int_fps_int_fps_fun$' ).
tff(func_def_63,type,
'fun_app$c': ( 'Real_real_fun$' * $real ) > $real ).
tff(func_def_64,type,
'fps_nth$': 'Real_fps$' > 'Nat_real_fun$' ).
tff(func_def_65,type,
'less$a': 'Nat$' > 'Nat_bool_fun$' ).
tff(func_def_66,type,
'fun_app$g': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_67,type,
'l$': $real ).
tff(func_def_68,type,
'inverse$b': 'Real_fls$' > 'Real_fls$' ).
tff(func_def_69,type,
'uminus$b': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_70,type,
'fps_hypergeo$': ( 'Real_list$' * 'Real_list$' * $real ) > 'Real_fps$' ).
tff(func_def_71,type,
'one$c': 'Ereal_fps$' ).
tff(func_def_72,type,
'fps_inv$': 'Real_fps$' > 'Real_fps$' ).
tff(func_def_73,type,
'one$': 'Real_fps$' ).
tff(func_def_74,type,
'one$a': 'Ereal$' ).
tff(func_def_75,type,
'zero$': 'Ereal$' ).
tff(func_def_86,type,
sK80: $real ).
tff(func_def_87,type,
sK81: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_88,type,
sK82: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_89,type,
sK83: 'Ereal$' > $real ).
tff(func_def_90,type,
sK84: 'Ereal$' > $real ).
tff(func_def_91,type,
sK85: 'Ereal$' > $real ).
tff(func_def_92,type,
sK86: 'Ereal$' > $real ).
tff(func_def_93,type,
sK87: 'Ereal_fps$' > 'Nat$' ).
tff(func_def_94,type,
sK88: 'Int_fps$' > 'Nat$' ).
tff(func_def_95,type,
sK89: ( 'Ereal_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_96,type,
sK90: 'Ereal_fps$' > 'Nat$' ).
tff(func_def_97,type,
sK91: ( 'Int_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_98,type,
sK92: 'Int_fps$' > 'Nat$' ).
tff(func_def_99,type,
sK93: 'Real_fps$' > 'Nat$' ).
tff(func_def_100,type,
sK94: ( 'Real_fps$' * 'Nat$' ) > 'Nat$' ).
tff(func_def_101,type,
sK95: 'Real_fps$' > 'Nat$' ).
tff(func_def_102,type,
sK96: 'Ereal_bool_fun$' > $real ).
tff(func_def_103,type,
sK97: 'Ereal_bool_fun$' > 'Ereal$' ).
tff(func_def_104,type,
sK98: 'Ereal_bool_fun$' > 'Ereal$' ).
tff(func_def_105,type,
sK99: 'Ereal_bool_fun$' > $real ).
tff(func_def_106,type,
sK100: 'Int_fps$' > 'Int_fps$' ).
tff(func_def_107,type,
sK101: 'Int_fps$' > $int ).
tff(func_def_108,type,
sK102: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_109,type,
sK103: 'Real_fps$' > $real ).
tff(func_def_110,type,
sK104: 'Int_fps$' > 'Int_fps$' ).
tff(func_def_111,type,
sK105: 'Int_fps$' > $int ).
tff(func_def_112,type,
sK106: 'Real_fps$' > 'Real_fps$' ).
tff(func_def_113,type,
sK107: 'Real_fps$' > $real ).
tff(func_def_114,type,
sK108: $real > $real ).
tff(func_def_115,type,
sK109: $real > $real ).
tff(func_def_116,type,
sK110: 'Ereal_set$' > 'Ereal$' ).
tff(func_def_117,type,
sK111: ( 'Ereal_set$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_118,type,
sK112: 'Ereal_set$' > 'Ereal$' ).
tff(func_def_119,type,
sK113: ( 'Ereal_set$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_120,type,
sK114: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_121,type,
sK115: ( $real * $real ) > $real ).
tff(func_def_122,type,
sK116: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_123,type,
sK117: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_124,type,
sK118: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_125,type,
sK119: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_126,type,
sK120: ( 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_127,type,
sK121: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_128,type,
sK122: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_129,type,
sK123: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_130,type,
sK124: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_131,type,
sK125: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_132,type,
sK126: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_133,type,
sK127: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_134,type,
sK128: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_135,type,
sK129: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_136,type,
sK130: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_137,type,
sK131: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_138,type,
sK132: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_139,type,
sK133: ( 'Real_fps$' * 'Real_fps$' ) > 'Nat$' ).
tff(func_def_140,type,
sK134: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_141,type,
sK135: ( 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_142,type,
sK136: 'Nat_bool_fun$' > 'Nat$' ).
tff(func_def_143,type,
sK137: ( 'Real_fps$' * 'Real_fps$' ) > 'Nat$' ).
tff(func_def_144,type,
sK138: ( 'Ereal$' * $real ) > $real ).
tff(func_def_145,type,
sK139: ( 'Real_ereal_bool_fun_fun$' * 'Ereal_set$' ) > 'Ereal$' ).
tff(func_def_146,type,
sK140: ( 'Real_ereal_bool_fun_fun$' * 'Ereal$' ) > $real ).
tff(func_def_147,type,
sK141: ( 'Ereal_set$' * 'Real_ereal_bool_fun_fun$' ) > 'Ereal$' ).
tff(func_def_148,type,
sK142: ( 'Ereal_set$' * 'Real_ereal_bool_fun_fun$' * 'Ereal$' ) > $real ).
tff(func_def_149,type,
sK143: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_150,type,
sK144: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_151,type,
sK145: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_152,type,
sK146: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_153,type,
sK147: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_154,type,
sK148: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_155,type,
sK149: ( tlbool * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_156,type,
sK150: ( tlbool * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_157,type,
sK151: ( tlbool * 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_158,type,
sK152: ( tlbool * 'Ereal$' * 'Ereal$' ) > 'Ereal$' ).
tff(func_def_159,type,
sK153: ( tlbool * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_160,type,
sK154: ( tlbool * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_161,type,
sK155: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_162,type,
sK156: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_163,type,
sK157: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_164,type,
sK158: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_165,type,
sK159: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_166,type,
sK160: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_167,type,
sK161: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_168,type,
sK162: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_169,type,
sK163: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_170,type,
sK164: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_171,type,
sK165: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_172,type,
sK166: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_173,type,
sK167: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_174,type,
sK168: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_175,type,
sK169: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_176,type,
sK170: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_177,type,
sK171: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_178,type,
sK172: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_179,type,
sK173: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_180,type,
sK174: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_181,type,
sK175: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_182,type,
sK176: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_183,type,
sK177: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_184,type,
sK178: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_185,type,
sK179: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_186,type,
sK180: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_187,type,
sK181: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $real ).
tff(func_def_188,type,
sK182: $real ).
tff(pred_def_1,type,
'fun_app$e': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).
tff(pred_def_2,type,
'fun_app$a': ( 'Int_bool_fun$' * $int ) > $o ).
tff(pred_def_3,type,
'fun_app$': ( 'Real_bool_fun$' * $real ) > $o ).
tff(pred_def_4,type,
'member$': ( 'Ereal$' * 'Ereal_set$' ) > $o ).
tff(pred_def_5,type,
'fun_app$b': ( 'Ereal_bool_fun$' * 'Ereal$' ) > $o ).
tff(pred_def_10,type,
sP0: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_11,type,
sP1: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_12,type,
sP2: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_13,type,
sP3: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_14,type,
sP4: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_15,type,
sP5: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_16,type,
sP6: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_17,type,
sP7: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_18,type,
sP8: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_19,type,
sP9: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_20,type,
sP10: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_21,type,
sP11: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_22,type,
sP12: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_23,type,
sP13: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_24,type,
sP14: ( $int * $int ) > $o ).
tff(pred_def_25,type,
sP15: ( $int * $int ) > $o ).
tff(pred_def_26,type,
sP16: ( $int * $int ) > $o ).
tff(pred_def_27,type,
sP17: ( $int * $int ) > $o ).
tff(pred_def_28,type,
sP18: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_29,type,
sP19: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_30,type,
sP20: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_31,type,
sP21: ( $real * $real ) > $o ).
tff(pred_def_32,type,
sP22: ( $real * $real ) > $o ).
tff(pred_def_33,type,
sP23: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_34,type,
sP24: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_35,type,
sP25: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_36,type,
sP26: ( 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_37,type,
sP27: ( $real * $real ) > $o ).
tff(pred_def_38,type,
sP28: ( $real * $real ) > $o ).
tff(pred_def_39,type,
sP29: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_40,type,
sP30: ( 'Nat$' * 'Nat$' ) > $o ).
tff(pred_def_41,type,
sP31: ( 'Real_ereal_bool_fun_fun$' * 'Ereal_set$' ) > $o ).
tff(pred_def_42,type,
sP32: ( 'Ereal$' * $real ) > $o ).
tff(pred_def_43,type,
sP33: ( 'Ereal$' * $real ) > $o ).
tff(pred_def_44,type,
sP34: ( 'Ereal$' * $real ) > $o ).
tff(pred_def_45,type,
sP35: ( 'Ereal$' * $real ) > $o ).
tff(pred_def_46,type,
sP36: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_47,type,
sP37: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_48,type,
sP38: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_49,type,
sP39: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_50,type,
sP40: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_51,type,
sP41: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_52,type,
sP42: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_53,type,
sP43: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_54,type,
sP44: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_55,type,
sP45: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_56,type,
sP46: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_57,type,
sP47: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_58,type,
sP48: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_59,type,
sP49: ( tlbool * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_60,type,
sP50: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_61,type,
sP51: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_62,type,
sP52: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_63,type,
sP53: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_64,type,
sP54: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_65,type,
sP55: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_66,type,
sP56: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_67,type,
sP57: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_68,type,
sP58: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_69,type,
sP59: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_70,type,
sP60: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_71,type,
sP61: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_72,type,
sP62: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_73,type,
sP63: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_74,type,
sP64: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_75,type,
sP65: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_76,type,
sP66: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_77,type,
sP67: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_78,type,
sP68: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_79,type,
sP69: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_80,type,
sP70: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_81,type,
sP71: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_82,type,
sP72: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_83,type,
sP73: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_84,type,
sP74: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_85,type,
sP75: ( 'Ereal$' * 'Ereal$' * 'Ereal$' ) > $o ).
tff(pred_def_86,type,
sP76: ( $int * $int * $int ) > $o ).
tff(pred_def_87,type,
sP77: ( $int * $int * $int ) > $o ).
tff(pred_def_88,type,
sP78: ( $real * $real * $real ) > $o ).
tff(pred_def_89,type,
sP79: ( $real * $real * $real ) > $o ).
tff(f9024,plain,
$false,
inference(avatar_sat_refutation,[],[f3779,f3783,f3787,f3792,f3797,f3802,f3807,f3812,f3817,f3822,f3827,f3832,f3837,f3842,f3847,f3852,f3857,f3862,f3867,f3872,f3877,f3882,f3887,f3892,f3897,f3902,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3947,f3953,f3957,f3961,f3965,f3969,f3973,f3977,f3981,f3986,f3991,f3996,f4001,f4006,f4011,f4016,f4021,f4026,f4031,f4036,f4041,f4046,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4132,f4143,f4147,f4152,f4157,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4255,f4260,f4265,f4269,f4273,f4277,f4282,f4286,f4290,f4294,f4298,f4303,f4308,f4313,f4327,f4332,f4351,f4355,f4359,f4363,f4368,f4373,f4378,f4385,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4417,f4421,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4556,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4601,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4653,f4657,f4661,f4665,f4669,f4673,f4677,f4681,f4687,f4691,f4695,f4699,f4703,f4707,f4711,f4715,f4719,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4792,f4797,f4802,f4808,f4813,f4850,f4946,f4955,f4959,f4964,f4968,f4972,f4977,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5189,f5193,f5197,f5201,f5205,f5209,f5213,f5217,f5221,f5225,f5232,f5236,f5252,f5256,f5275,f5315,f5365,f5554,f5592,f5596,f5601,f5605,f5609,f5614,f5619,f5624,f5629,f5635,f5640,f5644,f5648,f5652,f5656,f5660,f5664,f5668,f5672,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5805,f5809,f5813,f5817,f5821,f5825,f5829,f5833,f5837,f5841,f5845,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5880,f5884,f5888,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5936,f5940,f5944,f5948,f5952,f5956,f5960,f5964,f5968,f5972,f5976,f5981,f5985,f5989,f5993,f5997,f6001,f6005,f6009,f6013,f6017,f6021,f6025,f6029,f6033,f6037,f6041,f6045,f6049,f6053,f6057,f6061,f6065,f6069,f6073,f6077,f6081,f6085,f6089,f6093,f6097,f6101,f6105,f6109,f6113,f6117,f6121,f6125,f6129,f6133,f6137,f6199,f6254,f6305,f6413,f6575,f6581,f6601,f6640,f6674,f6827,f6869,f7051,f7055,f7059,f7063,f7067,f7072,f7076,f7080,f7084,f7088,f7095,f7099,f7103,f7107,f7112,f7116,f7120,f7124,f7128,f7133,f7143,f7147,f7151,f7155,f7159,f7163,f7167,f7171,f7175,f7179,f7184,f7188,f7192,f7196,f7200,f7204,f7208,f7212,f7216,f7220,f7224,f7229,f7233,f7237,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7274,f7278,f7282,f7286,f7290,f7294,f7299,f7303,f7307,f7311,f7315,f7319,f7323,f7327,f7331,f7335,f7339,f7343,f7347,f7351,f7355,f7359,f7363,f7367,f7371,f7375,f7379,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7456,f7460,f7464,f7468,f7472,f7530,f7587,f7616,f7718,f7735,f7806,f7810,f7814,f7818,f7822,f7827,f7831,f7835,f7839,f7857,f7861,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7910,f7914,f7918,f7922,f7926,f7930,f7934,f7938,f7942,f7946,f7958,f7962,f7966,f7970,f7974,f7978,f7982,f7986,f7991,f7995,f8000,f8004,f8008,f8012,f8016,f8020,f8024,f8028,f8032,f8036,f8040,f8048,f8052,f8056,f8060,f8064,f8068,f8072,f8076,f8080,f8084,f8088,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8171,f8177,f8181,f8185,f8189,f8193,f8197,f8201,f8205,f8209,f8213,f8217,f8237,f8241,f8245,f8249,f8253,f8257,f8261,f8265,f8269,f8273,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8335,f8339,f8343,f8347,f8351,f8355,f8359,f8363,f8367,f8371,f8376,f8380,f8384,f8388,f8392,f8396,f8400,f8404,f8408,f8412,f8416,f8421,f8425,f8429,f8433,f8437,f8441,f8445,f8449,f8453,f8457,f8461,f8466,f8471,f8476,f8481,f8485,f8489,f8493,f8585,f8589,f8669,f8682,f8705,f9019]) ).
tff(f9019,plain,
( ~ spl183_10
| ~ spl183_712 ),
inference(avatar_contradiction_clause,[],[f9018]) ).
tff(f9018,plain,
( $false
| ~ spl183_10
| ~ spl183_712 ),
inference(evaluation,[],[f9014]) ).
tff(f9014,plain,
( $less(0.0,0.0)
| ~ spl183_10
| ~ spl183_712 ),
inference(superposition,[],[f3821,f8704]) ).
tff(f8704,plain,
( ( 'c$' = 0.0 )
| ~ spl183_712 ),
inference(avatar_component_clause,[],[f8702]) ).
tff(f8702,plain,
( spl183_712
<=> ( 'c$' = 0.0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_712])]) ).
tff(f3821,plain,
( $less(0.0,'c$')
| ~ spl183_10 ),
inference(avatar_component_clause,[],[f3819]) ).
tff(f3819,plain,
( spl183_10
<=> $less(0.0,'c$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_10])]) ).
tff(f8705,plain,
( spl183_712
| spl183_1
| ~ spl183_561 ),
inference(avatar_split_clause,[],[f8621,f7825,f3776,f8702]) ).
tff(f3776,plain,
( spl183_1
<=> ( 'ereal$'('fun_app$c'('inverse$','c$')) = 'inverse$a'('ereal$'('c$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_1])]) ).
tff(f7825,plain,
( spl183_561
<=> ! [X0: $real] :
( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_561])]) ).
tff(f8621,plain,
( ( 'c$' = 0.0 )
| spl183_1
| ~ spl183_561 ),
inference(trivial_inequality_removal,[],[f8594]) ).
tff(f8594,plain,
( ( 'inverse$a'('ereal$'('c$')) != 'inverse$a'('ereal$'('c$')) )
| ( 'c$' = 0.0 )
| spl183_1
| ~ spl183_561 ),
inference(superposition,[],[f3778,f7826]) ).
tff(f7826,plain,
( ! [X0: $real] :
( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) )
| ~ spl183_561 ),
inference(avatar_component_clause,[],[f7825]) ).
tff(f3778,plain,
( ( 'ereal$'('fun_app$c'('inverse$','c$')) != 'inverse$a'('ereal$'('c$')) )
| spl183_1 ),
inference(avatar_component_clause,[],[f3776]) ).
tff(f8682,plain,
( spl183_711
| ~ spl183_140
| ~ spl183_566 ),
inference(avatar_split_clause,[],[f7862,f7859,f4423,f8680]) ).
tff(f8680,plain,
( spl183_711
<=> ! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'size_ereal$'('one$a')) )
| ( 'zero$b' != 'inverse$c'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_711])]) ).
tff(f4423,plain,
( spl183_140
<=> ( 'nat$'(0) = 'size_ereal$'('one$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_140])]) ).
tff(f7859,plain,
( spl183_566
<=> ! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) )
| ( 'zero$b' != 'inverse$c'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_566])]) ).
tff(f7862,plain,
( ! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'size_ereal$'('one$a')) )
| ( 'zero$b' != 'inverse$c'(X0) ) )
| ~ spl183_140
| ~ spl183_566 ),
inference(forward_demodulation,[],[f7860,f4425]) ).
tff(f4425,plain,
( ( 'nat$'(0) = 'size_ereal$'('one$a') )
| ~ spl183_140 ),
inference(avatar_component_clause,[],[f4423]) ).
tff(f7860,plain,
( ! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) )
| ( 'zero$b' != 'inverse$c'(X0) ) )
| ~ spl183_566 ),
inference(avatar_component_clause,[],[f7859]) ).
tff(f8669,plain,
( spl183_710
| ~ spl183_140
| ~ spl183_564 ),
inference(avatar_split_clause,[],[f7840,f7837,f4423,f8667]) ).
tff(f8667,plain,
( spl183_710
<=> ! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'size_ereal$'('one$a')) )
| ( 'zero$b' = 'inverse$c'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_710])]) ).
tff(f7837,plain,
( spl183_564
<=> ! [X0: 'Real_fps$'] :
( ( 'zero$b' = 'inverse$c'(X0) )
| ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_564])]) ).
tff(f7840,plain,
( ! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'size_ereal$'('one$a')) )
| ( 'zero$b' = 'inverse$c'(X0) ) )
| ~ spl183_140
| ~ spl183_564 ),
inference(forward_demodulation,[],[f7838,f4425]) ).
tff(f7838,plain,
( ! [X0: 'Real_fps$'] :
( ( 'zero$b' = 'inverse$c'(X0) )
| ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) )
| ~ spl183_564 ),
inference(avatar_component_clause,[],[f7837]) ).
tff(f8589,plain,
( spl183_709
| ~ spl183_140
| ~ spl183_560 ),
inference(avatar_split_clause,[],[f7823,f7820,f4423,f8587]) ).
tff(f8587,plain,
( spl183_709
<=> ! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'size_ereal$'('one$a')) = 'inverse$a'('fps_nth$a'(X0,'size_ereal$'('one$a'))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_709])]) ).
tff(f7820,plain,
( spl183_560
<=> ! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'nat$'(0)) = 'inverse$a'('fps_nth$a'(X0,'nat$'(0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_560])]) ).
tff(f7823,plain,
( ! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'size_ereal$'('one$a')) = 'inverse$a'('fps_nth$a'(X0,'size_ereal$'('one$a'))) )
| ~ spl183_140
| ~ spl183_560 ),
inference(forward_demodulation,[],[f7821,f4425]) ).
tff(f7821,plain,
( ! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'nat$'(0)) = 'inverse$a'('fps_nth$a'(X0,'nat$'(0))) )
| ~ spl183_560 ),
inference(avatar_component_clause,[],[f7820]) ).
tff(f8585,plain,
( spl183_708
| ~ spl183_107
| ~ spl183_277 ),
inference(avatar_split_clause,[],[f5436,f5121,f4252,f8582]) ).
tff(f8582,plain,
( spl183_708
<=> 'fun_app$b'('less_eq$'('ereal$'(sK182)),'ereal$'('c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_708])]) ).
tff(f4252,plain,
( spl183_107
<=> 'fun_app$b'('less$'('ereal$'(sK182)),'ereal$'('c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_107])]) ).
tff(f5121,plain,
( spl183_277
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_277])]) ).
tff(f5436,plain,
( 'fun_app$b'('less_eq$'('ereal$'(sK182)),'ereal$'('c$a'))
| ~ spl183_107
| ~ spl183_277 ),
inference(resolution,[],[f5122,f4254]) ).
tff(f4254,plain,
( 'fun_app$b'('less$'('ereal$'(sK182)),'ereal$'('c$a'))
| ~ spl183_107 ),
inference(avatar_component_clause,[],[f4252]) ).
tff(f5122,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less$'(X0),X1)
| 'fun_app$b'('less_eq$'(X0),X1) )
| ~ spl183_277 ),
inference(avatar_component_clause,[],[f5121]) ).
tff(f8493,plain,
spl183_707,
inference(avatar_split_clause,[],[f3757,f8491]) ).
tff(f8491,plain,
( spl183_707
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
| $less(0,'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_707])]) ).
tff(f3757,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
| $less(0,'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ),
inference(inner_rewriting,[],[f2812]) ).
tff(f2812,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
| $less('of_nat$'(X1),'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ),
inference(cnf_transformation,[],[f1671]) ).
tff(f1671,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP30(X0,X1)
| ( ( 0 != 'of_nat$'(X0) )
& $less('of_nat$'(X1),'of_nat$'(X0)) )
| ( ( 0 != 'of_nat$'(X1) )
& ~ $less('of_nat$'(X1),'of_nat$'(X0)) ) )
& ( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
| ~ sP30(X0,X1) ) ),
inference(flattening,[],[f1670]) ).
tff(f1670,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP30(X0,X1)
| ( ( 0 != 'of_nat$'(X0) )
& $less('of_nat$'(X1),'of_nat$'(X0)) )
| ( ( 0 != 'of_nat$'(X1) )
& ~ $less('of_nat$'(X1),'of_nat$'(X0)) ) )
& ( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
| ~ sP30(X0,X1) ) ),
inference(nnf_transformation,[],[f1237]) ).
tff(f1237,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
<=> ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
tff(f8489,plain,
spl183_706,
inference(avatar_split_clause,[],[f3755,f8487]) ).
tff(f8487,plain,
( spl183_706
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
| $less(0,'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_706])]) ).
tff(f3755,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
| $less(0,'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ),
inference(inner_rewriting,[],[f2803]) ).
tff(f2803,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
| $less('of_nat$'(X1),'of_nat$'(X0))
| ( 0 != 'of_nat$'(X1) ) ),
inference(cnf_transformation,[],[f1667]) ).
tff(f1667,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP29(X0,X1)
| ( ( 0 != 'of_nat$'(X0) )
& $less('of_nat$'(X1),'of_nat$'(X0)) )
| ( ( 0 != 'of_nat$'(X1) )
& ~ $less('of_nat$'(X1),'of_nat$'(X0)) ) )
& ( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
| ~ sP29(X0,X1) ) ),
inference(flattening,[],[f1666]) ).
tff(f1666,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP29(X0,X1)
| ( ( 0 != 'of_nat$'(X0) )
& $less('of_nat$'(X1),'of_nat$'(X0)) )
| ( ( 0 != 'of_nat$'(X1) )
& ~ $less('of_nat$'(X1),'of_nat$'(X0)) ) )
& ( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
| ~ sP29(X0,X1) ) ),
inference(nnf_transformation,[],[f1235]) ).
tff(f1235,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
<=> ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
tff(f8485,plain,
spl183_705,
inference(avatar_split_clause,[],[f3744,f8483]) ).
tff(f8483,plain,
( spl183_705
<=> ! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'($uminus(X0)),X1) = 'fun_app$c'('times$a'(X0),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_705])]) ).
tff(f3744,plain,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'($uminus(X0)),X1) = 'fun_app$c'('times$a'(X0),$uminus(X1)) ),
inference(forward_demodulation,[],[f2351,f2347]) ).
tff(f2347,plain,
! [X0: $real,X1: $real] : ( $uminus('fun_app$c'('times$a'(X0),X1)) = 'fun_app$c'('times$a'(X0),$uminus(X1)) ),
inference(cnf_transformation,[],[f335]) ).
tff(f335,axiom,
! [X0: $real,X1: $real] : ( $uminus('fun_app$c'('times$a'(X0),X1)) = 'fun_app$c'('times$a'(X0),$uminus(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom333) ).
tff(f2351,plain,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'($uminus(X0)),X1) = $uminus('fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f310]) ).
tff(f310,axiom,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'($uminus(X0)),X1) = $uminus('fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom308) ).
tff(f8481,plain,
spl183_704,
inference(avatar_split_clause,[],[f3720,f8478]) ).
tff(f8478,plain,
( spl183_704
<=> ( 'infinity$' = 'times$'('times$'('infinity$','ereal$'(-1.0)),'times$'('infinity$','ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_704])]) ).
tff(f3720,plain,
'infinity$' = 'times$'('times$'('infinity$','ereal$'(-1.0)),'times$'('infinity$','ereal$'(-1.0))),
inference(evaluation,[],[f3220]) ).
tff(f3220,plain,
'infinity$' = 'times$'('times$'('infinity$','ereal$'($uminus(1.0))),'times$'('infinity$','ereal$'($uminus(1.0)))),
inference(definition_unfolding,[],[f1983,f2063,f2063]) ).
tff(f2063,plain,
! [X0: 'Ereal$'] : ( 'uminus$'(X0) = 'times$'(X0,'ereal$'($uminus(1.0))) ),
inference(cnf_transformation,[],[f526]) ).
tff(f526,axiom,
! [X0: 'Ereal$'] : ( 'uminus$'(X0) = 'times$'(X0,'ereal$'($uminus(1.0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom524) ).
tff(f1983,plain,
'infinity$' = 'times$'('uminus$'('infinity$'),'uminus$'('infinity$')),
inference(cnf_transformation,[],[f294]) ).
tff(f294,axiom,
'infinity$' = 'times$'('uminus$'('infinity$'),'uminus$'('infinity$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom292) ).
tff(f8476,plain,
spl183_703,
inference(avatar_split_clause,[],[f3719,f8473]) ).
tff(f8473,plain,
( spl183_703
<=> ( 'times$'('infinity$','ereal$'(-1.0)) = 'times$'('infinity$','times$'('infinity$','ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_703])]) ).
tff(f3719,plain,
'times$'('infinity$','ereal$'(-1.0)) = 'times$'('infinity$','times$'('infinity$','ereal$'(-1.0))),
inference(evaluation,[],[f3221]) ).
tff(f3221,plain,
'times$'('infinity$','ereal$'($uminus(1.0))) = 'times$'('infinity$','times$'('infinity$','ereal$'($uminus(1.0)))),
inference(definition_unfolding,[],[f1985,f2063,f2063]) ).
tff(f1985,plain,
'uminus$'('infinity$') = 'times$'('infinity$','uminus$'('infinity$')),
inference(cnf_transformation,[],[f293]) ).
tff(f293,axiom,
'uminus$'('infinity$') = 'times$'('infinity$','uminus$'('infinity$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom291) ).
tff(f8471,plain,
spl183_702,
inference(avatar_split_clause,[],[f3718,f8468]) ).
tff(f8468,plain,
( spl183_702
<=> ( 'times$'('infinity$','ereal$'(-1.0)) = 'times$'('times$'('infinity$','ereal$'(-1.0)),'infinity$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_702])]) ).
tff(f3718,plain,
'times$'('infinity$','ereal$'(-1.0)) = 'times$'('times$'('infinity$','ereal$'(-1.0)),'infinity$'),
inference(evaluation,[],[f3222]) ).
tff(f3222,plain,
'times$'('infinity$','ereal$'($uminus(1.0))) = 'times$'('times$'('infinity$','ereal$'($uminus(1.0))),'infinity$'),
inference(definition_unfolding,[],[f1986,f2063,f2063]) ).
tff(f1986,plain,
'uminus$'('infinity$') = 'times$'('uminus$'('infinity$'),'infinity$'),
inference(cnf_transformation,[],[f292]) ).
tff(f292,axiom,
'uminus$'('infinity$') = 'times$'('uminus$'('infinity$'),'infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom290) ).
tff(f8466,plain,
( spl183_701
| ~ spl183_51
| ~ spl183_266 ),
inference(avatar_split_clause,[],[f5348,f5074,f4008,f8463]) ).
tff(f8463,plain,
( spl183_701
<=> 'fun_app$b'('less$'('c$b'),sK98('less$'('c$b'))) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_701])]) ).
tff(f4008,plain,
( spl183_51
<=> 'fun_app$b'('less$'('c$b'),'ereal$'('c$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_51])]) ).
tff(f5074,plain,
( spl183_266
<=> ! [X2: $real,X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'ereal$'(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_266])]) ).
tff(f5348,plain,
( 'fun_app$b'('less$'('c$b'),sK98('less$'('c$b')))
| ~ spl183_51
| ~ spl183_266 ),
inference(resolution,[],[f5075,f4010]) ).
tff(f4010,plain,
( 'fun_app$b'('less$'('c$b'),'ereal$'('c$'))
| ~ spl183_51 ),
inference(avatar_component_clause,[],[f4008]) ).
tff(f5075,plain,
( ! [X2: $real,X0: 'Ereal_bool_fun$'] :
( ~ 'fun_app$b'(X0,'ereal$'(X2))
| 'fun_app$b'(X0,sK98(X0)) )
| ~ spl183_266 ),
inference(avatar_component_clause,[],[f5074]) ).
tff(f8461,plain,
spl183_700,
inference(avatar_split_clause,[],[f3692,f8459]) ).
tff(f8459,plain,
( spl183_700
<=> ! [X0: 'Ereal$'] :
( ( 'inverse$a'('inverse$a'(X0)) = X0 )
| ( 'times$'('infinity$','ereal$'(-1.0)) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_700])]) ).
tff(f3692,plain,
! [X0: 'Ereal$'] :
( ( 'inverse$a'('inverse$a'(X0)) = X0 )
| ( 'times$'('infinity$','ereal$'(-1.0)) = X0 ) ),
inference(evaluation,[],[f3244]) ).
tff(f3244,plain,
! [X0: 'Ereal$'] :
( ( 'inverse$a'('inverse$a'(X0)) = X0 )
| ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 ) ),
inference(definition_unfolding,[],[f2094,f2063]) ).
tff(f2094,plain,
! [X0: 'Ereal$'] :
( ( 'inverse$a'('inverse$a'(X0)) = X0 )
| ( 'uminus$'('infinity$') = X0 ) ),
inference(cnf_transformation,[],[f825]) ).
tff(f825,plain,
! [X0: 'Ereal$'] :
( ( ( 'infinity$' = 'inverse$a'('inverse$a'(X0)) )
| ( 'uminus$'('infinity$') != X0 ) )
& ( ( 'inverse$a'('inverse$a'(X0)) = X0 )
| ( 'uminus$'('infinity$') = X0 ) ) ),
inference(ennf_transformation,[],[f181]) ).
tff(f181,axiom,
! [X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
=> ( 'infinity$' = 'inverse$a'('inverse$a'(X0)) ) )
& ( ( 'uminus$'('infinity$') != X0 )
=> ( 'inverse$a'('inverse$a'(X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom179) ).
tff(f8457,plain,
spl183_699,
inference(avatar_split_clause,[],[f3682,f8455]) ).
tff(f8455,plain,
( spl183_699
<=> ! [X0: $int] :
( ( -1 = X0 )
| ( 1 = X0 )
| ( 'times$d'(X0,X0) != 1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_699])]) ).
tff(f3682,plain,
! [X0: $int] :
( ( -1 = X0 )
| ( 1 = X0 )
| ( 'times$d'(X0,X0) != 1 ) ),
inference(evaluation,[],[f2261]) ).
tff(f2261,plain,
! [X0: $int] :
( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ( 'times$d'(X0,X0) != 1 ) ),
inference(cnf_transformation,[],[f1386]) ).
tff(f1386,plain,
! [X0: $int] :
( ( ( 'times$d'(X0,X0) = 1 )
| ( ( $uminus(1) != X0 )
& ( 1 != X0 ) ) )
& ( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ( 'times$d'(X0,X0) != 1 ) ) ),
inference(flattening,[],[f1385]) ).
tff(f1385,plain,
! [X0: $int] :
( ( ( 'times$d'(X0,X0) = 1 )
| ( ( $uminus(1) != X0 )
& ( 1 != X0 ) ) )
& ( ( $uminus(1) = X0 )
| ( 1 = X0 )
| ( 'times$d'(X0,X0) != 1 ) ) ),
inference(nnf_transformation,[],[f488]) ).
tff(f488,axiom,
! [X0: $int] :
( ( 'times$d'(X0,X0) = 1 )
<=> ( ( $uminus(1) = X0 )
| ( 1 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom486) ).
tff(f8453,plain,
spl183_698,
inference(avatar_split_clause,[],[f3681,f8451]) ).
tff(f8451,plain,
( spl183_698
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'(-1.0)))
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_698])]) ).
tff(f3681,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'(-1.0)))
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') ),
inference(evaluation,[],[f3253]) ).
tff(f3253,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'($uminus(1.0))))
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') ),
inference(definition_unfolding,[],[f2269,f2063]) ).
tff(f2269,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'uminus$'(X0))
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') ),
inference(cnf_transformation,[],[f1389]) ).
tff(f1389,plain,
! [X0: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('zero$'),'uminus$'(X0))
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') )
& ( 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),'uminus$'(X0)) ) ),
inference(nnf_transformation,[],[f565]) ).
tff(f565,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'uminus$'(X0))
<=> 'fun_app$b'('less_eq$'(X0),'zero$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom563) ).
tff(f8449,plain,
spl183_697,
inference(avatar_split_clause,[],[f3680,f8447]) ).
tff(f8447,plain,
( spl183_697
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_697])]) ).
tff(f3680,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'(-1.0))) ),
inference(evaluation,[],[f3254]) ).
tff(f3254,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,'ereal$'($uminus(1.0)))) ),
inference(definition_unfolding,[],[f2268,f2063]) ).
tff(f2268,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),'uminus$'(X0)) ),
inference(cnf_transformation,[],[f1389]) ).
tff(f8445,plain,
spl183_696,
inference(avatar_split_clause,[],[f3679,f8443]) ).
tff(f8443,plain,
( spl183_696
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'(X0),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_696])]) ).
tff(f3679,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(evaluation,[],[f3255]) ).
tff(f3255,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'($uminus(1.0))))
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(definition_unfolding,[],[f2275,f2063]) ).
tff(f2275,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'uminus$'(X0))
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(cnf_transformation,[],[f1392]) ).
tff(f1392,plain,
! [X0: 'Ereal$'] :
( ( 'fun_app$b'('less$'('zero$'),'uminus$'(X0))
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),'uminus$'(X0)) ) ),
inference(nnf_transformation,[],[f180]) ).
tff(f180,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'uminus$'(X0))
<=> 'fun_app$b'('less$'(X0),'zero$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom178) ).
tff(f8441,plain,
spl183_695,
inference(avatar_split_clause,[],[f3678,f8439]) ).
tff(f8439,plain,
( spl183_695
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_695])]) ).
tff(f3678,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'(-1.0))) ),
inference(evaluation,[],[f3256]) ).
tff(f3256,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,'ereal$'($uminus(1.0)))) ),
inference(definition_unfolding,[],[f2274,f2063]) ).
tff(f2274,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),'uminus$'(X0)) ),
inference(cnf_transformation,[],[f1392]) ).
tff(f8437,plain,
spl183_694,
inference(avatar_split_clause,[],[f3672,f8435]) ).
tff(f8435,plain,
( spl183_694
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'(-1.0))),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_694])]) ).
tff(f3672,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'(-1.0))),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ),
inference(evaluation,[],[f3262]) ).
tff(f3262,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'($uminus(1.0)))),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ),
inference(definition_unfolding,[],[f2282,f2063]) ).
tff(f2282,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('uminus$'(X0)),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ),
inference(cnf_transformation,[],[f1395]) ).
tff(f1395,plain,
! [X0: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('uminus$'(X0)),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) )
& ( 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('uminus$'(X0)),'zero$') ) ),
inference(nnf_transformation,[],[f566]) ).
tff(f566,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('uminus$'(X0)),'zero$')
<=> 'fun_app$b'('less_eq$'('zero$'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom564) ).
tff(f8433,plain,
spl183_693,
inference(avatar_split_clause,[],[f3671,f8431]) ).
tff(f8431,plain,
( spl183_693
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'(-1.0))),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_693])]) ).
tff(f3671,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'(-1.0))),'zero$') ),
inference(evaluation,[],[f3263]) ).
tff(f3263,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,'ereal$'($uminus(1.0)))),'zero$') ),
inference(definition_unfolding,[],[f2281,f2063]) ).
tff(f2281,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('uminus$'(X0)),'zero$') ),
inference(cnf_transformation,[],[f1395]) ).
tff(f8429,plain,
spl183_692,
inference(avatar_split_clause,[],[f3662,f8427]) ).
tff(f8427,plain,
( spl183_692
<=> ! [X0: 'Ereal_fps$',X1: 'Nat$'] : ( 'fps_nth$a'('uminus$a'(X0),X1) = 'times$'('fps_nth$a'(X0,X1),'ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_692])]) ).
tff(f3662,plain,
! [X0: 'Ereal_fps$',X1: 'Nat$'] : ( 'fps_nth$a'('uminus$a'(X0),X1) = 'times$'('fps_nth$a'(X0,X1),'ereal$'(-1.0)) ),
inference(evaluation,[],[f3270]) ).
tff(f3270,plain,
! [X0: 'Ereal_fps$',X1: 'Nat$'] : ( 'fps_nth$a'('uminus$a'(X0),X1) = 'times$'('fps_nth$a'(X0,X1),'ereal$'($uminus(1.0))) ),
inference(definition_unfolding,[],[f2339,f2063]) ).
tff(f2339,plain,
! [X0: 'Ereal_fps$',X1: 'Nat$'] : ( 'fps_nth$a'('uminus$a'(X0),X1) = 'uminus$'('fps_nth$a'(X0,X1)) ),
inference(cnf_transformation,[],[f162]) ).
tff(f162,axiom,
! [X0: 'Ereal_fps$',X1: 'Nat$'] : ( 'fps_nth$a'('uminus$a'(X0),X1) = 'uminus$'('fps_nth$a'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom160) ).
tff(f8425,plain,
spl183_691,
inference(avatar_split_clause,[],[f3611,f8423]) ).
tff(f8423,plain,
( spl183_691
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'(X0,X1) = 'times$'('infinity$','ereal$'(-1.0)) )
| ~ sP20(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_691])]) ).
tff(f3611,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'(X0,X1) = 'times$'('infinity$','ereal$'(-1.0)) )
| ~ sP20(X1,X0) ),
inference(evaluation,[],[f3313]) ).
tff(f3313,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'(X0,X1) = 'times$'('infinity$','ereal$'($uminus(1.0))) )
| ~ sP20(X1,X0) ),
inference(definition_unfolding,[],[f2697,f2063]) ).
tff(f2697,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = 'times$'(X0,X1) )
| ~ sP20(X1,X0) ),
inference(cnf_transformation,[],[f1609]) ).
tff(f1609,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = 'times$'(X0,X1) )
| ~ sP20(X1,X0) )
& ( sP20(X1,X0)
| ( 'uminus$'('infinity$') != 'times$'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1218]) ).
tff(f1218,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = 'times$'(X0,X1) )
<=> sP20(X1,X0) ),
inference(definition_folding,[],[f263,f1217,f1216,f1215]) ).
tff(f1215,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP18(X1,X0)
<=> ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'infinity$' = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
tff(f1216,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP19(X1,X0)
<=> ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'(X0),'zero$') ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
tff(f1217,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP20(X1,X0)
<=> ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'uminus$'('infinity$') = X0 ) )
| sP19(X1,X0)
| sP18(X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
tff(f263,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = 'times$'(X0,X1) )
<=> ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'uminus$'('infinity$') = X0 ) )
| ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'infinity$' = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom261) ).
tff(f8421,plain,
( spl183_690
| ~ spl183_224
| ~ spl183_231 ),
inference(avatar_split_clause,[],[f4949,f4794,f4765,f8418]) ).
tff(f8418,plain,
( spl183_690
<=> sP19('infinity$','times$'('infinity$','ereal$'(-1.0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_690])]) ).
tff(f4765,plain,
( spl183_224
<=> ! [X1: 'Ereal$'] :
( sP19('infinity$',X1)
| ~ 'fun_app$b'('less$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_224])]) ).
tff(f4794,plain,
( spl183_231
<=> 'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_231])]) ).
tff(f4949,plain,
( sP19('infinity$','times$'('infinity$','ereal$'(-1.0)))
| ~ spl183_224
| ~ spl183_231 ),
inference(resolution,[],[f4796,f4766]) ).
tff(f4766,plain,
( ! [X1: 'Ereal$'] :
( ~ 'fun_app$b'('less$'(X1),'zero$')
| sP19('infinity$',X1) )
| ~ spl183_224 ),
inference(avatar_component_clause,[],[f4765]) ).
tff(f4796,plain,
( 'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'zero$')
| ~ spl183_231 ),
inference(avatar_component_clause,[],[f4794]) ).
tff(f8416,plain,
spl183_689,
inference(avatar_split_clause,[],[f3610,f8414]) ).
tff(f8414,plain,
( spl183_689
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X1,X0)
| ( 'times$'(X0,X1) != 'times$'('infinity$','ereal$'(-1.0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_689])]) ).
tff(f3610,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X1,X0)
| ( 'times$'(X0,X1) != 'times$'('infinity$','ereal$'(-1.0)) ) ),
inference(evaluation,[],[f3314]) ).
tff(f3314,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X1,X0)
| ( 'times$'(X0,X1) != 'times$'('infinity$','ereal$'($uminus(1.0))) ) ),
inference(definition_unfolding,[],[f2696,f2063]) ).
tff(f2696,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X1,X0)
| ( 'uminus$'('infinity$') != 'times$'(X0,X1) ) ),
inference(cnf_transformation,[],[f1609]) ).
tff(f8412,plain,
spl183_688,
inference(avatar_split_clause,[],[f3144,f8410]) ).
tff(f8410,plain,
( spl183_688
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less('times$d'(X0,X1),'times$d'(X0,X2))
| ~ sP77(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_688])]) ).
tff(f3144,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less('times$d'(X0,X1),'times$d'(X0,X2))
| ~ sP77(X1,X2,X0) ),
inference(cnf_transformation,[],[f1875]) ).
tff(f1875,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less('times$d'(X0,X1),'times$d'(X0,X2))
| ~ sP77(X1,X2,X0) )
& ( sP77(X1,X2,X0)
| ~ $less('times$d'(X0,X1),'times$d'(X0,X2)) ) ),
inference(nnf_transformation,[],[f1291]) ).
tff(f1291,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less('times$d'(X0,X1),'times$d'(X0,X2))
<=> sP77(X1,X2,X0) ),
inference(definition_folding,[],[f381,f1290]) ).
tff(f1290,plain,
! [X1: $int,X2: $int,X0: $int] :
( sP77(X1,X2,X0)
<=> ( ( $less(X2,X1)
& $less(X0,0) )
| ( $less(X1,X2)
& $less(0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP77])]) ).
tff(f381,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less('times$d'(X0,X1),'times$d'(X0,X2))
<=> ( ( $less(X2,X1)
& $less(X0,0) )
| ( $less(X1,X2)
& $less(0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom379) ).
tff(f8408,plain,
spl183_687,
inference(avatar_split_clause,[],[f3143,f8406]) ).
tff(f8406,plain,
( spl183_687
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP77(X1,X2,X0)
| ~ $less('times$d'(X0,X1),'times$d'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_687])]) ).
tff(f3143,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP77(X1,X2,X0)
| ~ $less('times$d'(X0,X1),'times$d'(X0,X2)) ),
inference(cnf_transformation,[],[f1875]) ).
tff(f8404,plain,
spl183_686,
inference(avatar_split_clause,[],[f3136,f8402]) ).
tff(f8402,plain,
( spl183_686
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less('times$d'(X0,X1),'times$d'(X2,X1))
| ~ sP76(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_686])]) ).
tff(f3136,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less('times$d'(X0,X1),'times$d'(X2,X1))
| ~ sP76(X0,X2,X1) ),
inference(cnf_transformation,[],[f1871]) ).
tff(f1871,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less('times$d'(X0,X1),'times$d'(X2,X1))
| ~ sP76(X0,X2,X1) )
& ( sP76(X0,X2,X1)
| ~ $less('times$d'(X0,X1),'times$d'(X2,X1)) ) ),
inference(nnf_transformation,[],[f1289]) ).
tff(f1289,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less('times$d'(X0,X1),'times$d'(X2,X1))
<=> sP76(X0,X2,X1) ),
inference(definition_folding,[],[f374,f1288]) ).
tff(f1288,plain,
! [X0: $int,X2: $int,X1: $int] :
( sP76(X0,X2,X1)
<=> ( ( $less(X2,X0)
& $less(X1,0) )
| ( $less(X0,X2)
& $less(0,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP76])]) ).
tff(f374,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less('times$d'(X0,X1),'times$d'(X2,X1))
<=> ( ( $less(X2,X0)
& $less(X1,0) )
| ( $less(X0,X2)
& $less(0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom372) ).
tff(f8400,plain,
spl183_685,
inference(avatar_split_clause,[],[f3135,f8398]) ).
tff(f8398,plain,
( spl183_685
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X2,X1)
| ~ $less('times$d'(X0,X1),'times$d'(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_685])]) ).
tff(f3135,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X2,X1)
| ~ $less('times$d'(X0,X1),'times$d'(X2,X1)) ),
inference(cnf_transformation,[],[f1871]) ).
tff(f8396,plain,
spl183_684,
inference(avatar_split_clause,[],[f3104,f8394]) ).
tff(f8394,plain,
( spl183_684
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less('max$b'(X0,X1),X2)
| ~ $less(X1,X2)
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_684])]) ).
tff(f3104,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less('max$b'(X0,X1),X2)
| ~ $less(X1,X2)
| ~ $less(X0,X2) ),
inference(cnf_transformation,[],[f1851]) ).
tff(f1851,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less('max$b'(X0,X1),X2)
| ~ $less(X1,X2)
| ~ $less(X0,X2) )
& ( ( $less(X1,X2)
& $less(X0,X2) )
| ~ $less('max$b'(X0,X1),X2) ) ),
inference(flattening,[],[f1850]) ).
tff(f1850,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less('max$b'(X0,X1),X2)
| ~ $less(X1,X2)
| ~ $less(X0,X2) )
& ( ( $less(X1,X2)
& $less(X0,X2) )
| ~ $less('max$b'(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f80]) ).
tff(f80,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less('max$b'(X0,X1),X2)
<=> ( $less(X1,X2)
& $less(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom78) ).
tff(f8392,plain,
spl183_683,
inference(avatar_split_clause,[],[f3098,f8390]) ).
tff(f8390,plain,
( spl183_683
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,'max$b'(X0,X1))
| $less(X2,X1)
| $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_683])]) ).
tff(f3098,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X2,'max$b'(X0,X1))
| $less(X2,X1)
| $less(X2,X0) ),
inference(cnf_transformation,[],[f1847]) ).
tff(f1847,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X2,'max$b'(X0,X1))
| $less(X2,X1)
| $less(X2,X0) )
& ( ( ~ $less(X2,X1)
& ~ $less(X2,X0) )
| $less(X2,'max$b'(X0,X1)) ) ),
inference(flattening,[],[f1846]) ).
tff(f1846,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( ~ $less(X2,'max$b'(X0,X1))
| $less(X2,X1)
| $less(X2,X0) )
& ( ( ~ $less(X2,X1)
& ~ $less(X2,X0) )
| $less(X2,'max$b'(X0,X1)) ) ),
inference(nnf_transformation,[],[f705]) ).
tff(f705,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X2,'max$b'(X0,X1))
<=> ( ~ $less(X2,X1)
& ~ $less(X2,X0) ) ),
inference(theory_normalization,[],[f550]) ).
tff(f550,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $lesseq('max$b'(X0,X1),X2)
<=> ( $lesseq(X1,X2)
& $lesseq(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom548) ).
tff(f8388,plain,
spl183_682,
inference(avatar_split_clause,[],[f3092,f8386]) ).
tff(f8386,plain,
( spl183_682
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK181(X0,X1,X2)) = X0 )
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_682])]) ).
tff(f3092,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK181(X0,X1,X2)) = X0 )
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f1845,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK181(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK180(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK179(X0,X1,X2)) = X2 ) )
| ~ sP50(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK179,sK180,sK181])],[f1843,f1844]) ).
tff(f1844,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real,X5: $real] :
( ( 'ereal$'(X5) = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'ereal$'(sK181(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK180(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK179(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1843,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real,X5: $real] :
( ( 'ereal$'(X5) = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP50(X0,X1,X2) ),
inference(rectify,[],[f1842]) ).
tff(f1842,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X27: $real,X28: $real,X29: $real] :
( ( 'ereal$'(X29) = X2 )
& ( 'ereal$'(X28) = X1 )
& ( 'ereal$'(X27) = X0 ) )
| ~ sP50(X2,X1,X0) ),
inference(nnf_transformation,[],[f1261]) ).
tff(f1261,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X27: $real,X28: $real,X29: $real] :
( ( 'ereal$'(X29) = X2 )
& ( 'ereal$'(X28) = X1 )
& ( 'ereal$'(X27) = X0 ) )
| ~ sP50(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP50])]) ).
tff(f8384,plain,
spl183_681,
inference(avatar_split_clause,[],[f3091,f8382]) ).
tff(f8382,plain,
( spl183_681
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK180(X0,X1,X2)) = X1 )
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_681])]) ).
tff(f3091,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK180(X0,X1,X2)) = X1 )
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f8380,plain,
spl183_680,
inference(avatar_split_clause,[],[f3090,f8378]) ).
tff(f8378,plain,
( spl183_680
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK179(X0,X1,X2)) = X2 )
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_680])]) ).
tff(f3090,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK179(X0,X1,X2)) = X2 )
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f1845]) ).
tff(f8376,plain,
( spl183_679
| ~ spl183_225
| ~ spl183_231 ),
inference(avatar_split_clause,[],[f4948,f4794,f4769,f8373]) ).
tff(f8373,plain,
( spl183_679
<=> sP18('times$'('infinity$','ereal$'(-1.0)),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_679])]) ).
tff(f4769,plain,
( spl183_225
<=> ! [X0: 'Ereal$'] :
( sP18(X0,'infinity$')
| ~ 'fun_app$b'('less$'(X0),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_225])]) ).
tff(f4948,plain,
( sP18('times$'('infinity$','ereal$'(-1.0)),'infinity$')
| ~ spl183_225
| ~ spl183_231 ),
inference(resolution,[],[f4796,f4770]) ).
tff(f4770,plain,
( ! [X0: 'Ereal$'] :
( ~ 'fun_app$b'('less$'(X0),'zero$')
| sP18(X0,'infinity$') )
| ~ spl183_225 ),
inference(avatar_component_clause,[],[f4769]) ).
tff(f8371,plain,
spl183_678,
inference(avatar_split_clause,[],[f3088,f8369]) ).
tff(f8369,plain,
( spl183_678
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK178(X0,X1,X2)) = X1 )
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_678])]) ).
tff(f3088,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK178(X0,X1,X2)) = X1 )
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f1841,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK178(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK177(X0,X1,X2)) = X2 ) )
| ~ sP51(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177,sK178])],[f1839,f1840]) ).
tff(f1840,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK178(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK177(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1839,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP51(X0,X1,X2) ),
inference(rectify,[],[f1838]) ).
tff(f1838,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X25: $real,X26: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X26) = X1 )
& ( 'ereal$'(X25) = X0 ) )
| ~ sP51(X2,X1,X0) ),
inference(nnf_transformation,[],[f1262]) ).
tff(f1262,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X25: $real,X26: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X26) = X1 )
& ( 'ereal$'(X25) = X0 ) )
| ~ sP51(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP51])]) ).
tff(f8367,plain,
spl183_677,
inference(avatar_split_clause,[],[f3087,f8365]) ).
tff(f8365,plain,
( spl183_677
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK177(X0,X1,X2)) = X2 )
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_677])]) ).
tff(f3087,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK177(X0,X1,X2)) = X2 )
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f8363,plain,
spl183_676,
inference(avatar_split_clause,[],[f3085,f8361]) ).
tff(f8361,plain,
( spl183_676
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK176(X0,X1,X2)) = X1 )
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_676])]) ).
tff(f3085,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK176(X0,X1,X2)) = X1 )
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1837]) ).
tff(f1837,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK176(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK175(X0,X1,X2)) = X2 ) )
| ~ sP52(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK175,sK176])],[f1835,f1836]) ).
tff(f1836,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK176(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK175(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1835,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP52(X0,X1,X2) ),
inference(rectify,[],[f1834]) ).
tff(f1834,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X23: $real,X24: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X24) = X1 )
& ( 'ereal$'(X23) = X0 ) )
| ~ sP52(X2,X1,X0) ),
inference(nnf_transformation,[],[f1263]) ).
tff(f1263,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X23: $real,X24: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X24) = X1 )
& ( 'ereal$'(X23) = X0 ) )
| ~ sP52(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP52])]) ).
tff(f8359,plain,
spl183_675,
inference(avatar_split_clause,[],[f3084,f8357]) ).
tff(f8357,plain,
( spl183_675
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK175(X0,X1,X2)) = X2 )
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_675])]) ).
tff(f3084,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK175(X0,X1,X2)) = X2 )
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1837]) ).
tff(f8355,plain,
spl183_674,
inference(avatar_split_clause,[],[f3083,f8353]) ).
tff(f8353,plain,
( spl183_674
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK174(X0,X1,X2)) = X0 )
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_674])]) ).
tff(f3083,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK174(X0,X1,X2)) = X0 )
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1833]) ).
tff(f1833,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK174(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK173(X0,X1,X2)) = X2 ) )
| ~ sP53(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173,sK174])],[f1831,f1832]) ).
tff(f1832,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'ereal$'(sK174(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK173(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1831,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP53(X0,X1,X2) ),
inference(rectify,[],[f1830]) ).
tff(f1830,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X21: $real,X22: $real] :
( ( 'ereal$'(X22) = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X21) = X0 ) )
| ~ sP53(X2,X1,X0) ),
inference(nnf_transformation,[],[f1264]) ).
tff(f1264,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X21: $real,X22: $real] :
( ( 'ereal$'(X22) = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X21) = X0 ) )
| ~ sP53(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP53])]) ).
tff(f8351,plain,
spl183_673,
inference(avatar_split_clause,[],[f3081,f8349]) ).
tff(f8349,plain,
( spl183_673
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK173(X0,X1,X2)) = X2 )
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_673])]) ).
tff(f3081,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK173(X0,X1,X2)) = X2 )
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1833]) ).
tff(f8347,plain,
spl183_672,
inference(avatar_split_clause,[],[f3078,f8345]) ).
tff(f8345,plain,
( spl183_672
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK172(X0,X1,X2)) = X2 )
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_672])]) ).
tff(f3078,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK172(X0,X1,X2)) = X2 )
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f1829,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK172(X0,X1,X2)) = X2 ) )
| ~ sP54(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK172])],[f1827,f1828]) ).
tff(f1828,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK172(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1827,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP54(X0,X1,X2) ),
inference(rectify,[],[f1826]) ).
tff(f1826,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X20: $real] :
( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X20) = X0 ) )
| ~ sP54(X2,X1,X0) ),
inference(nnf_transformation,[],[f1265]) ).
tff(f1265,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X20: $real] :
( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X20) = X0 ) )
| ~ sP54(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP54])]) ).
tff(f8343,plain,
spl183_671,
inference(avatar_split_clause,[],[f3075,f8341]) ).
tff(f8341,plain,
( spl183_671
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK171(X0,X1,X2)) = X2 )
| ~ sP55(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_671])]) ).
tff(f3075,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK171(X0,X1,X2)) = X2 )
| ~ sP55(X0,X1,X2) ),
inference(cnf_transformation,[],[f1825]) ).
tff(f1825,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK171(X0,X1,X2)) = X2 ) )
| ~ sP55(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f1823,f1824]) ).
tff(f1824,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK171(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1823,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP55(X0,X1,X2) ),
inference(rectify,[],[f1822]) ).
tff(f1822,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X19: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X19) = X0 ) )
| ~ sP55(X2,X1,X0) ),
inference(nnf_transformation,[],[f1266]) ).
tff(f1266,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X19: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X19) = X0 ) )
| ~ sP55(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP55])]) ).
tff(f8339,plain,
spl183_670,
inference(avatar_split_clause,[],[f3074,f8337]) ).
tff(f8337,plain,
( spl183_670
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK170(X0,X1,X2)) = X0 )
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_670])]) ).
tff(f3074,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK170(X0,X1,X2)) = X0 )
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
tff(f1821,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK170(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK169(X0,X1,X2)) = X2 ) )
| ~ sP56(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170])],[f1819,f1820]) ).
tff(f1820,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'ereal$'(sK170(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK169(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1819,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP56(X0,X1,X2) ),
inference(rectify,[],[f1818]) ).
tff(f1818,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X17: $real,X18: $real] :
( ( 'ereal$'(X18) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X17) = X0 ) )
| ~ sP56(X2,X1,X0) ),
inference(nnf_transformation,[],[f1267]) ).
tff(f1267,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X17: $real,X18: $real] :
( ( 'ereal$'(X18) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X17) = X0 ) )
| ~ sP56(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP56])]) ).
tff(f8335,plain,
spl183_669,
inference(avatar_split_clause,[],[f3072,f8333]) ).
tff(f8333,plain,
( spl183_669
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK169(X0,X1,X2)) = X2 )
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_669])]) ).
tff(f3072,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK169(X0,X1,X2)) = X2 )
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
tff(f8328,plain,
spl183_668,
inference(avatar_split_clause,[],[f3069,f8326]) ).
tff(f8326,plain,
( spl183_668
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK168(X0,X1,X2)) = X2 )
| ~ sP57(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_668])]) ).
tff(f3069,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK168(X0,X1,X2)) = X2 )
| ~ sP57(X0,X1,X2) ),
inference(cnf_transformation,[],[f1817]) ).
tff(f1817,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK168(X0,X1,X2)) = X2 ) )
| ~ sP57(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f1815,f1816]) ).
tff(f1816,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK168(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1815,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP57(X0,X1,X2) ),
inference(rectify,[],[f1814]) ).
tff(f1814,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X16: $real] :
( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X16) = X0 ) )
| ~ sP57(X2,X1,X0) ),
inference(nnf_transformation,[],[f1268]) ).
tff(f1268,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X16: $real] :
( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X16) = X0 ) )
| ~ sP57(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP57])]) ).
tff(f8324,plain,
spl183_667,
inference(avatar_split_clause,[],[f3066,f8322]) ).
tff(f8322,plain,
( spl183_667
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK167(X0,X1,X2)) = X2 )
| ~ sP58(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_667])]) ).
tff(f3066,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK167(X0,X1,X2)) = X2 )
| ~ sP58(X0,X1,X2) ),
inference(cnf_transformation,[],[f1813]) ).
tff(f1813,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK167(X0,X1,X2)) = X2 ) )
| ~ sP58(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK167])],[f1811,f1812]) ).
tff(f1812,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK167(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1811,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP58(X0,X1,X2) ),
inference(rectify,[],[f1810]) ).
tff(f1810,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X15: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X15) = X0 ) )
| ~ sP58(X2,X1,X0) ),
inference(nnf_transformation,[],[f1269]) ).
tff(f1269,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X15: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X15) = X0 ) )
| ~ sP58(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP58])]) ).
tff(f8320,plain,
spl183_666,
inference(avatar_split_clause,[],[f3065,f8318]) ).
tff(f8318,plain,
( spl183_666
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK166(X0,X1,X2)) = X0 )
| ~ sP59(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_666])]) ).
tff(f3065,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK166(X0,X1,X2)) = X0 )
| ~ sP59(X0,X1,X2) ),
inference(cnf_transformation,[],[f1809]) ).
tff(f1809,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK166(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK165(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP59(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165,sK166])],[f1807,f1808]) ).
tff(f1808,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
=> ( ( 'ereal$'(sK166(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK165(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1807,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP59(X0,X1,X2) ),
inference(rectify,[],[f1806]) ).
tff(f1806,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X13: $real,X14: $real] :
( ( 'ereal$'(X14) = X2 )
& ( 'ereal$'(X13) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP59(X2,X1,X0) ),
inference(nnf_transformation,[],[f1270]) ).
tff(f1270,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X13: $real,X14: $real] :
( ( 'ereal$'(X14) = X2 )
& ( 'ereal$'(X13) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP59(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP59])]) ).
tff(f8316,plain,
spl183_665,
inference(avatar_split_clause,[],[f3064,f8314]) ).
tff(f8314,plain,
( spl183_665
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK165(X0,X1,X2)) = X1 )
| ~ sP59(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_665])]) ).
tff(f3064,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK165(X0,X1,X2)) = X1 )
| ~ sP59(X0,X1,X2) ),
inference(cnf_transformation,[],[f1809]) ).
tff(f8312,plain,
spl183_664,
inference(avatar_split_clause,[],[f3061,f8310]) ).
tff(f8310,plain,
( spl183_664
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK164(X0,X1,X2)) = X1 )
| ~ sP60(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_664])]) ).
tff(f3061,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK164(X0,X1,X2)) = X1 )
| ~ sP60(X0,X1,X2) ),
inference(cnf_transformation,[],[f1805]) ).
tff(f1805,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK164(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP60(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f1803,f1804]) ).
tff(f1804,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
=> ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK164(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1803,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP60(X0,X1,X2) ),
inference(rectify,[],[f1802]) ).
tff(f1802,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X12: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X12) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP60(X2,X1,X0) ),
inference(nnf_transformation,[],[f1271]) ).
tff(f1271,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X12: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X12) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP60(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP60])]) ).
tff(f8308,plain,
spl183_663,
inference(avatar_split_clause,[],[f3058,f8306]) ).
tff(f8306,plain,
( spl183_663
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK163(X0,X1,X2)) = X1 )
| ~ sP61(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_663])]) ).
tff(f3058,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK163(X0,X1,X2)) = X1 )
| ~ sP61(X0,X1,X2) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f1801,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK163(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP61(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f1799,f1800]) ).
tff(f1800,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK163(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1799,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP61(X0,X1,X2) ),
inference(rectify,[],[f1798]) ).
tff(f1798,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X11: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X11) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP61(X2,X1,X0) ),
inference(nnf_transformation,[],[f1272]) ).
tff(f1272,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X11: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X11) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP61(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP61])]) ).
tff(f8304,plain,
spl183_662,
inference(avatar_split_clause,[],[f3056,f8302]) ).
tff(f8302,plain,
( spl183_662
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK162(X0,X1,X2)) = X0 )
| ~ sP62(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_662])]) ).
tff(f3056,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK162(X0,X1,X2)) = X0 )
| ~ sP62(X0,X1,X2) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f1797,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK162(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP62(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f1795,f1796]) ).
tff(f1796,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
=> ( ( 'ereal$'(sK162(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1795,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP62(X0,X1,X2) ),
inference(rectify,[],[f1794]) ).
tff(f1794,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X10: $real] :
( ( 'ereal$'(X10) = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP62(X2,X1,X0) ),
inference(nnf_transformation,[],[f1273]) ).
tff(f1273,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X10: $real] :
( ( 'ereal$'(X10) = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP62(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP62])]) ).
tff(f8300,plain,
spl183_661,
inference(avatar_split_clause,[],[f3047,f8298]) ).
tff(f8298,plain,
( spl183_661
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK161(X0,X1,X2)) = X0 )
| ~ sP65(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_661])]) ).
tff(f3047,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK161(X0,X1,X2)) = X0 )
| ~ sP65(X0,X1,X2) ),
inference(cnf_transformation,[],[f1789]) ).
tff(f1789,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK161(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP65(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK161])],[f1787,f1788]) ).
tff(f1788,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
=> ( ( 'ereal$'(sK161(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1787,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP65(X0,X1,X2) ),
inference(rectify,[],[f1786]) ).
tff(f1786,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X9: $real] :
( ( 'ereal$'(X9) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP65(X2,X1,X0) ),
inference(nnf_transformation,[],[f1276]) ).
tff(f1276,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X9: $real] :
( ( 'ereal$'(X9) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP65(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP65])]) ).
tff(f8296,plain,
spl183_660,
inference(avatar_split_clause,[],[f3038,f8294]) ).
tff(f8294,plain,
( spl183_660
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK160(X0,X1,X2)) = X0 )
| ~ sP68(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_660])]) ).
tff(f3038,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK160(X0,X1,X2)) = X0 )
| ~ sP68(X0,X1,X2) ),
inference(cnf_transformation,[],[f1781]) ).
tff(f1781,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK160(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK159(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP68(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK159,sK160])],[f1779,f1780]) ).
tff(f1780,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( 'ereal$'(sK160(X0,X1,X2)) = X0 )
& ( 'ereal$'(sK159(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1779,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'(X4) = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP68(X0,X1,X2) ),
inference(rectify,[],[f1778]) ).
tff(f1778,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( 'ereal$'(X8) = X2 )
& ( 'ereal$'(X7) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP68(X2,X1,X0) ),
inference(nnf_transformation,[],[f1279]) ).
tff(f1279,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( 'ereal$'(X8) = X2 )
& ( 'ereal$'(X7) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP68(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP68])]) ).
tff(f8292,plain,
spl183_659,
inference(avatar_split_clause,[],[f3037,f8290]) ).
tff(f8290,plain,
( spl183_659
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK159(X0,X1,X2)) = X1 )
| ~ sP68(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_659])]) ).
tff(f3037,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK159(X0,X1,X2)) = X1 )
| ~ sP68(X0,X1,X2) ),
inference(cnf_transformation,[],[f1781]) ).
tff(f8273,plain,
spl183_658,
inference(avatar_split_clause,[],[f3034,f8271]) ).
tff(f8271,plain,
( spl183_658
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK158(X0,X1,X2)) = X1 )
| ~ sP69(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_658])]) ).
tff(f3034,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK158(X0,X1,X2)) = X1 )
| ~ sP69(X0,X1,X2) ),
inference(cnf_transformation,[],[f1777]) ).
tff(f1777,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK158(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP69(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK158])],[f1775,f1776]) ).
tff(f1776,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK158(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1775,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP69(X0,X1,X2) ),
inference(rectify,[],[f1774]) ).
tff(f1774,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X6) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP69(X2,X1,X0) ),
inference(nnf_transformation,[],[f1280]) ).
tff(f1280,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real] :
( ( 'infinity$' = X2 )
& ( 'ereal$'(X6) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP69(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP69])]) ).
tff(f8269,plain,
spl183_657,
inference(avatar_split_clause,[],[f3031,f8267]) ).
tff(f8267,plain,
( spl183_657
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK157(X0,X1,X2)) = X1 )
| ~ sP70(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_657])]) ).
tff(f3031,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK157(X0,X1,X2)) = X1 )
| ~ sP70(X0,X1,X2) ),
inference(cnf_transformation,[],[f1773]) ).
tff(f1773,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK157(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP70(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f1771,f1772]) ).
tff(f1772,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK157(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1771,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP70(X0,X1,X2) ),
inference(rectify,[],[f1770]) ).
tff(f1770,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X5) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP70(X2,X1,X0) ),
inference(nnf_transformation,[],[f1281]) ).
tff(f1281,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( ( 'uminus$'('infinity$') = X2 )
& ( 'ereal$'(X5) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP70(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP70])]) ).
tff(f8265,plain,
spl183_656,
inference(avatar_split_clause,[],[f3029,f8263]) ).
tff(f8263,plain,
( spl183_656
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK156(X0,X1,X2)) = X0 )
| ~ sP71(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_656])]) ).
tff(f3029,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK156(X0,X1,X2)) = X0 )
| ~ sP71(X0,X1,X2) ),
inference(cnf_transformation,[],[f1769]) ).
tff(f1769,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK156(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP71(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK156])],[f1767,f1768]) ).
tff(f1768,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( 'ereal$'(sK156(X0,X1,X2)) = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1767,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP71(X0,X1,X2) ),
inference(rectify,[],[f1766]) ).
tff(f1766,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( 'ereal$'(X4) = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP71(X2,X1,X0) ),
inference(nnf_transformation,[],[f1282]) ).
tff(f1282,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( 'ereal$'(X4) = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP71(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP71])]) ).
tff(f8261,plain,
spl183_655,
inference(avatar_split_clause,[],[f3020,f8259]) ).
tff(f8259,plain,
( spl183_655
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK155(X0,X1,X2)) = X0 )
| ~ sP74(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_655])]) ).
tff(f3020,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK155(X0,X1,X2)) = X0 )
| ~ sP74(X0,X1,X2) ),
inference(cnf_transformation,[],[f1761]) ).
tff(f1761,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'(sK155(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP74(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK155])],[f1759,f1760]) ).
tff(f1760,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( 'ereal$'(sK155(X0,X1,X2)) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1759,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP74(X0,X1,X2) ),
inference(rectify,[],[f1758]) ).
tff(f1758,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP74(X2,X1,X0) ),
inference(nnf_transformation,[],[f1285]) ).
tff(f1285,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP74(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP74])]) ).
tff(f8257,plain,
spl183_654,
inference(avatar_split_clause,[],[f3010,f8255]) ).
tff(f8255,plain,
( spl183_654
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK154(X0,X1,X2)) = X1 )
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_654])]) ).
tff(f3010,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK154(X0,X1,X2)) = X1 )
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f1754]) ).
tff(f1754,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( ( tltrue = X0 )
| ~ $less(sK153(X0,X1,X2),sK154(X0,X1,X2)) )
& ( $less(sK153(X0,X1,X2),sK154(X0,X1,X2))
| ( tltrue != X0 ) )
& ( 'ereal$'(sK154(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK153(X0,X1,X2)) = X2 ) )
| ~ sP44(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153,sK154])],[f1752,f1753]) ).
tff(f1753,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( ( tltrue = X0 )
| ~ $less(X3,X4) )
& ( $less(X3,X4)
| ( tltrue != X0 ) )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( ( tltrue = X0 )
| ~ $less(sK153(X0,X1,X2),sK154(X0,X1,X2)) )
& ( $less(sK153(X0,X1,X2),sK154(X0,X1,X2))
| ( tltrue != X0 ) )
& ( 'ereal$'(sK154(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK153(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1752,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( ( tltrue = X0 )
| ~ $less(X3,X4) )
& ( $less(X3,X4)
| ( tltrue != X0 ) )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP44(X0,X1,X2) ),
inference(rectify,[],[f1751]) ).
tff(f1751,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( ( tltrue = X2 )
| ~ $less(X7,X8) )
& ( $less(X7,X8)
| ( tltrue != X2 ) )
& ( 'ereal$'(X8) = X1 )
& ( 'ereal$'(X7) = X0 ) )
| ~ sP44(X2,X1,X0) ),
inference(flattening,[],[f1750]) ).
tff(f1750,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( ( tltrue = X2 )
| ~ $less(X7,X8) )
& ( $less(X7,X8)
| ( tltrue != X2 ) )
& ( 'ereal$'(X8) = X1 )
& ( 'ereal$'(X7) = X0 ) )
| ~ sP44(X2,X1,X0) ),
inference(nnf_transformation,[],[f1254]) ).
tff(f1254,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( ( tltrue = X2 )
<=> $less(X7,X8) )
& ( 'ereal$'(X8) = X1 )
& ( 'ereal$'(X7) = X0 ) )
| ~ sP44(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP44])]) ).
tff(f8253,plain,
spl183_653,
inference(avatar_split_clause,[],[f3009,f8251]) ).
tff(f8251,plain,
( spl183_653
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK153(X0,X1,X2)) = X2 )
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_653])]) ).
tff(f3009,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK153(X0,X1,X2)) = X2 )
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f1754]) ).
tff(f8249,plain,
spl183_652,
inference(avatar_split_clause,[],[f3000,f8247]) ).
tff(f8247,plain,
( spl183_652
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK150(X0,X1,X2)) = X2 )
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_652])]) ).
tff(f3000,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK150(X0,X1,X2)) = X2 )
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1741]) ).
tff(f1741,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( tltrue = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK150(X0,X1,X2)) = X2 ) )
| ~ sP47(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150])],[f1739,f1740]) ).
tff(f1740,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( tltrue = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK150(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1739,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X0 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP47(X0,X1,X2) ),
inference(rectify,[],[f1738]) ).
tff(f1738,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( tltrue = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP47(X2,X1,X0) ),
inference(nnf_transformation,[],[f1257]) ).
tff(f1257,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( tltrue = X2 )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP47(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
tff(f8245,plain,
spl183_651,
inference(avatar_split_clause,[],[f2998,f8243]) ).
tff(f8243,plain,
( spl183_651
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK149(X0,X1,X2)) = X1 )
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_651])]) ).
tff(f2998,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'ereal$'(sK149(X0,X1,X2)) = X1 )
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1737]) ).
tff(f1737,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( tltrue = X0 )
& ( 'ereal$'(sK149(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP48(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f1735,f1736]) ).
tff(f1736,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( ( tltrue = X0 )
& ( 'ereal$'(sK149(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1735,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X0 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP48(X0,X1,X2) ),
inference(rectify,[],[f1734]) ).
tff(f1734,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X2 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP48(X2,X1,X0) ),
inference(nnf_transformation,[],[f1258]) ).
tff(f1258,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( tltrue = X2 )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP48(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP48])]) ).
tff(f8241,plain,
spl183_650,
inference(avatar_split_clause,[],[f2970,f8239]) ).
tff(f8239,plain,
( spl183_650
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK148(X0,X1,X2)) = X2 )
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_650])]) ).
tff(f2970,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK148(X0,X1,X2)) = X2 )
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f1723,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( sP32(X0,sK148(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK148(X0,X1,X2) ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK148(X0,X1,X2)) = X2 ) )
| ~ sP36(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f1721,f1722]) ).
tff(f1722,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP32(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( sP32(X0,sK148(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK148(X0,X1,X2) ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(sK148(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1721,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP32(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP36(X0,X1,X2) ),
inference(rectify,[],[f1720]) ).
tff(f1720,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real] :
( sP32(X2,X6)
& ( ( 'zero$' = X2 )
| ( 0.0 != X6 ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X6) = X0 ) )
| ~ sP36(X2,X1,X0) ),
inference(nnf_transformation,[],[f1245]) ).
tff(f1245,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real] :
( sP32(X2,X6)
& ( ( 'zero$' = X2 )
| ( 0.0 != X6 ) )
& ( 'infinity$' = X1 )
& ( 'ereal$'(X6) = X0 ) )
| ~ sP36(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
tff(f8237,plain,
spl183_649,
inference(avatar_split_clause,[],[f2967,f8235]) ).
tff(f8235,plain,
( spl183_649
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK147(X0,X1,X2)) = X1 )
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_649])]) ).
tff(f2967,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK147(X0,X1,X2)) = X1 )
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f1719,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( sP33(X0,sK147(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK147(X0,X1,X2) ) )
& ( 'ereal$'(sK147(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP37(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147])],[f1717,f1718]) ).
tff(f1718,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP33(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
=> ( sP33(X0,sK147(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK147(X0,X1,X2) ) )
& ( 'ereal$'(sK147(X0,X1,X2)) = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1717,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP33(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP37(X0,X1,X2) ),
inference(rectify,[],[f1716]) ).
tff(f1716,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( sP33(X2,X5)
& ( ( 'zero$' = X2 )
| ( 0.0 != X5 ) )
& ( 'ereal$'(X5) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP37(X2,X1,X0) ),
inference(nnf_transformation,[],[f1246]) ).
tff(f1246,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( sP33(X2,X5)
& ( ( 'zero$' = X2 )
| ( 0.0 != X5 ) )
& ( 'ereal$'(X5) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP37(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
tff(f8217,plain,
spl183_648,
inference(avatar_split_clause,[],[f2962,f8215]) ).
tff(f8215,plain,
( spl183_648
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK146(X0,X1,X2)) = X2 )
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_648])]) ).
tff(f2962,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK146(X0,X1,X2)) = X2 )
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1715]) ).
tff(f1715,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( sP34(X0,sK146(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK146(X0,X1,X2) ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK146(X0,X1,X2)) = X2 ) )
| ~ sP38(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK146])],[f1713,f1714]) ).
tff(f1714,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP34(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( sP34(X0,sK146(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK146(X0,X1,X2) ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(sK146(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1713,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP34(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP38(X0,X1,X2) ),
inference(rectify,[],[f1712]) ).
tff(f1712,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( sP34(X2,X4)
& ( ( 'zero$' = X2 )
| ( 0.0 != X4 ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP38(X2,X1,X0) ),
inference(nnf_transformation,[],[f1247]) ).
tff(f1247,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( sP34(X2,X4)
& ( ( 'zero$' = X2 )
| ( 0.0 != X4 ) )
& ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP38(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
tff(f8213,plain,
spl183_647,
inference(avatar_split_clause,[],[f2959,f8211]) ).
tff(f8211,plain,
( spl183_647
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK145(X0,X1,X2)) = X1 )
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_647])]) ).
tff(f2959,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK145(X0,X1,X2)) = X1 )
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f1711,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( sP35(X0,sK145(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK145(X0,X1,X2) ) )
& ( 'ereal$'(sK145(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP39(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK145])],[f1709,f1710]) ).
tff(f1710,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP35(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
=> ( sP35(X0,sK145(X0,X1,X2))
& ( ( 'zero$' = X0 )
| ( 0.0 != sK145(X0,X1,X2) ) )
& ( 'ereal$'(sK145(X0,X1,X2)) = X1 )
& ( 'uminus$'('infinity$') = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1709,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real] :
( sP35(X0,X3)
& ( ( 'zero$' = X0 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP39(X0,X1,X2) ),
inference(rectify,[],[f1708]) ).
tff(f1708,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( sP35(X2,X3)
& ( ( 'zero$' = X2 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP39(X2,X1,X0) ),
inference(nnf_transformation,[],[f1248]) ).
tff(f1248,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( sP35(X2,X3)
& ( ( 'zero$' = X2 )
| ( 0.0 != X3 ) )
& ( 'ereal$'(X3) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP39(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
tff(f8209,plain,
spl183_646,
inference(avatar_split_clause,[],[f2956,f8207]) ).
tff(f8207,plain,
( spl183_646
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK144(X0,X1,X2)) = X1 )
| ~ sP40(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_646])]) ).
tff(f2956,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK144(X0,X1,X2)) = X1 )
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1707]) ).
tff(f1707,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'ereal$'('fun_app$c'('times$a'(sK143(X0,X1,X2)),sK144(X0,X1,X2))) = X0 )
& ( 'ereal$'(sK144(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK143(X0,X1,X2)) = X2 ) )
| ~ sP40(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143,sK144])],[f1705,f1706]) ).
tff(f1706,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'('fun_app$c'('times$a'(X3),X4)) = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
=> ( ( 'ereal$'('fun_app$c'('times$a'(sK143(X0,X1,X2)),sK144(X0,X1,X2))) = X0 )
& ( 'ereal$'(sK144(X0,X1,X2)) = X1 )
& ( 'ereal$'(sK143(X0,X1,X2)) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1705,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: $real,X4: $real] :
( ( 'ereal$'('fun_app$c'('times$a'(X3),X4)) = X0 )
& ( 'ereal$'(X4) = X1 )
& ( 'ereal$'(X3) = X2 ) )
| ~ sP40(X0,X1,X2) ),
inference(rectify,[],[f1704]) ).
tff(f1704,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( 'ereal$'('fun_app$c'('times$a'(X7),X8)) = X2 )
& ( 'ereal$'(X8) = X1 )
& ( 'ereal$'(X7) = X0 ) )
| ~ sP40(X2,X1,X0) ),
inference(nnf_transformation,[],[f1249]) ).
tff(f1249,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X7: $real,X8: $real] :
( ( 'ereal$'('fun_app$c'('times$a'(X7),X8)) = X2 )
& ( 'ereal$'(X8) = X1 )
& ( 'ereal$'(X7) = X0 ) )
| ~ sP40(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
tff(f8205,plain,
spl183_645,
inference(avatar_split_clause,[],[f2955,f8203]) ).
tff(f8203,plain,
( spl183_645
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK143(X0,X1,X2)) = X2 )
| ~ sP40(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_645])]) ).
tff(f2955,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK143(X0,X1,X2)) = X2 )
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f1707]) ).
tff(f8201,plain,
spl183_644,
inference(avatar_split_clause,[],[f2833,f8199]) ).
tff(f8199,plain,
( spl183_644
<=> ! [X2: $int,X0: $int,X1: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'('times$d'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_644])]) ).
tff(f2833,plain,
! [X2: $int,X0: $int,X1: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'('times$d'(X0,X1),X2) ),
inference(cnf_transformation,[],[f282]) ).
tff(f282,axiom,
! [X0: $int,X1: $int,X2: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'('times$d'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom280) ).
tff(f8197,plain,
spl183_643,
inference(avatar_split_clause,[],[f2832,f8195]) ).
tff(f8195,plain,
( spl183_643
<=> ! [X2: $int,X0: $int,X1: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'(X1,'times$d'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_643])]) ).
tff(f2832,plain,
! [X2: $int,X0: $int,X1: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'(X1,'times$d'(X0,X2)) ),
inference(cnf_transformation,[],[f274]) ).
tff(f274,axiom,
! [X0: $int,X1: $int,X2: $int] : ( 'times$d'(X0,'times$d'(X1,X2)) = 'times$d'(X1,'times$d'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom272) ).
tff(f8193,plain,
spl183_642,
inference(avatar_split_clause,[],[f2830,f8191]) ).
tff(f8191,plain,
( spl183_642
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'('times$'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_642])]) ).
tff(f2830,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'('times$'(X0,X1),X2) ),
inference(cnf_transformation,[],[f285]) ).
tff(f285,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'('times$'(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom283) ).
tff(f8189,plain,
spl183_641,
inference(avatar_split_clause,[],[f2829,f8187]) ).
tff(f8187,plain,
( spl183_641
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'(X1,'times$'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_641])]) ).
tff(f2829,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'(X1,'times$'(X0,X2)) ),
inference(cnf_transformation,[],[f273]) ).
tff(f273,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] : ( 'times$'(X0,'times$'(X1,X2)) = 'times$'(X1,'times$'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom271) ).
tff(f8185,plain,
spl183_640,
inference(avatar_split_clause,[],[f2828,f8183]) ).
tff(f8183,plain,
( spl183_640
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'('max$'(X0,X1),X2) = 'max$'(X0,'max$'(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_640])]) ).
tff(f2828,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'('max$'(X0,X1),X2) = 'max$'(X0,'max$'(X1,X2)) ),
inference(cnf_transformation,[],[f98]) ).
tff(f98,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] : ( 'max$'('max$'(X0,X1),X2) = 'max$'(X0,'max$'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom96) ).
tff(f8181,plain,
spl183_639,
inference(avatar_split_clause,[],[f2827,f8179]) ).
tff(f8179,plain,
( spl183_639
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,'max$'(X1,X2)) = 'max$'(X1,'max$'(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_639])]) ).
tff(f2827,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,'max$'(X1,X2)) = 'max$'(X1,'max$'(X0,X2)) ),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] : ( 'max$'(X0,'max$'(X1,X2)) = 'max$'(X1,'max$'(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom98) ).
tff(f8177,plain,
( spl183_638
| ~ spl183_277
| ~ spl183_595 ),
inference(avatar_split_clause,[],[f8044,f7997,f5121,f8174]) ).
tff(f8174,plain,
( spl183_638
<=> 'fun_app$b'('less_eq$'('c$b'),'ereal$'(sK182)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_638])]) ).
tff(f7997,plain,
( spl183_595
<=> 'fun_app$b'('less$'('c$b'),'ereal$'(sK182)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_595])]) ).
tff(f8044,plain,
( 'fun_app$b'('less_eq$'('c$b'),'ereal$'(sK182))
| ~ spl183_277
| ~ spl183_595 ),
inference(resolution,[],[f7999,f5122]) ).
tff(f7999,plain,
( 'fun_app$b'('less$'('c$b'),'ereal$'(sK182))
| ~ spl183_595 ),
inference(avatar_component_clause,[],[f7997]) ).
tff(f8171,plain,
( spl183_636
| spl183_637 ),
inference(avatar_split_clause,[],[f2824,f8169,f8166]) ).
tff(f8166,plain,
( spl183_636
<=> ! [X3: $real] : ~ $less(0.0,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_636])]) ).
tff(f8169,plain,
( spl183_637
<=> ! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( sP31(X1,X0)
| 'member$'(sK141(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_637])]) ).
tff(f2824,plain,
! [X3: $real,X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( sP31(X1,X0)
| 'member$'(sK141(X0,X1),X0)
| ~ $less(0.0,X3) ),
inference(cnf_transformation,[],[f1683]) ).
tff(f1683,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ( sP31(X1,X0)
| ! [X3: $real] :
( ( ~ 'fun_app$b'('fun_app$d'(X1,X3),sK141(X0,X1))
& 'member$'(sK141(X0,X1),X0) )
| ~ $less(0.0,X3) ) )
& ( ! [X4: 'Ereal$'] :
( ( 'fun_app$b'('fun_app$d'(X1,sK142(X0,X1,X4)),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,sK142(X0,X1,X4)) )
| ~ sP31(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141,sK142])],[f1680,f1682,f1681]) ).
tff(f1681,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ? [X2: 'Ereal$'] :
! [X3: $real] :
( ( ~ 'fun_app$b'('fun_app$d'(X1,X3),X2)
& 'member$'(X2,X0) )
| ~ $less(0.0,X3) )
=> ! [X3: $real] :
( ( ~ 'fun_app$b'('fun_app$d'(X1,X3),sK141(X0,X1))
& 'member$'(sK141(X0,X1),X0) )
| ~ $less(0.0,X3) ) ),
introduced(choice_axiom,[]) ).
tff(f1682,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$',X4: 'Ereal$'] :
( ? [X5: $real] :
( ( 'fun_app$b'('fun_app$d'(X1,X5),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,X5) )
=> ( ( 'fun_app$b'('fun_app$d'(X1,sK142(X0,X1,X4)),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,sK142(X0,X1,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f1680,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ( sP31(X1,X0)
| ? [X2: 'Ereal$'] :
! [X3: $real] :
( ( ~ 'fun_app$b'('fun_app$d'(X1,X3),X2)
& 'member$'(X2,X0) )
| ~ $less(0.0,X3) ) )
& ( ! [X4: 'Ereal$'] :
? [X5: $real] :
( ( 'fun_app$b'('fun_app$d'(X1,X5),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,X5) )
| ~ sP31(X1,X0) ) ),
inference(rectify,[],[f1679]) ).
tff(f1679,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ( sP31(X1,X0)
| ? [X4: 'Ereal$'] :
! [X5: $real] :
( ( ~ 'fun_app$b'('fun_app$d'(X1,X5),X4)
& 'member$'(X4,X0) )
| ~ $less(0.0,X5) ) )
& ( ! [X4: 'Ereal$'] :
? [X5: $real] :
( ( 'fun_app$b'('fun_app$d'(X1,X5),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,X5) )
| ~ sP31(X1,X0) ) ),
inference(nnf_transformation,[],[f1240]) ).
tff(f1240,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( sP31(X1,X0)
<=> ! [X4: 'Ereal$'] :
? [X5: $real] :
( ( 'fun_app$b'('fun_app$d'(X1,X5),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,X5) ) ),
inference(definition_folding,[],[f1051,f1239]) ).
tff(f1239,plain,
! [X1: 'Real_ereal_bool_fun_fun$',X0: 'Ereal_set$'] :
( sP31(X1,X0)
<=> ! [X2: 'Ereal$'] :
( ? [X3: $real] :
( 'fun_app$b'('fun_app$d'(X1,X3),X2)
& $less(0.0,X3) )
| ~ 'member$'(X2,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
tff(f1051,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ! [X2: 'Ereal$'] :
( ? [X3: $real] :
( 'fun_app$b'('fun_app$d'(X1,X3),X2)
& $less(0.0,X3) )
| ~ 'member$'(X2,X0) )
<=> ! [X4: 'Ereal$'] :
? [X5: $real] :
( ( 'fun_app$b'('fun_app$d'(X1,X5),X4)
| ~ 'member$'(X4,X0) )
& $less(0.0,X5) ) ),
inference(ennf_transformation,[],[f800]) ).
tff(f800,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ! [X2: 'Ereal$'] :
( 'member$'(X2,X0)
=> ? [X3: $real] :
( 'fun_app$b'('fun_app$d'(X1,X3),X2)
& $less(0.0,X3) ) )
<=> ! [X4: 'Ereal$'] :
? [X5: $real] :
( ( 'member$'(X4,X0)
=> 'fun_app$b'('fun_app$d'(X1,X5),X4) )
& $less(0.0,X5) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( ! [X2: 'Ereal$'] :
( 'member$'(X2,X0)
=> ? [X3: $real] :
( 'fun_app$b'('fun_app$d'(X1,X3),X2)
& $less(0.0,X3) ) )
<=> ! [X2: 'Ereal$'] :
? [X3: $real] :
( ( 'member$'(X2,X0)
=> 'fun_app$b'('fun_app$d'(X1,X3),X2) )
& $less(0.0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom67) ).
tff(f8164,plain,
spl183_635,
inference(avatar_split_clause,[],[f2818,f8162]) ).
tff(f8162,plain,
( spl183_635
<=> ! [X4: 'Ereal$',X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( $less(0.0,sK140(X0,X4))
| ~ 'member$'(X4,X1)
| ~ sP31(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_635])]) ).
tff(f2818,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$',X4: 'Ereal$'] :
( $less(0.0,sK140(X0,X4))
| ~ 'member$'(X4,X1)
| ~ sP31(X0,X1) ),
inference(cnf_transformation,[],[f1678]) ).
tff(f1678,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( ( sP31(X0,X1)
| ( ! [X3: $real] :
( ~ 'fun_app$b'('fun_app$d'(X0,X3),sK139(X0,X1))
| ~ $less(0.0,X3) )
& 'member$'(sK139(X0,X1),X1) ) )
& ( ! [X4: 'Ereal$'] :
( ( 'fun_app$b'('fun_app$d'(X0,sK140(X0,X4)),X4)
& $less(0.0,sK140(X0,X4)) )
| ~ 'member$'(X4,X1) )
| ~ sP31(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK139,sK140])],[f1675,f1677,f1676]) ).
tff(f1676,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( ? [X2: 'Ereal$'] :
( ! [X3: $real] :
( ~ 'fun_app$b'('fun_app$d'(X0,X3),X2)
| ~ $less(0.0,X3) )
& 'member$'(X2,X1) )
=> ( ! [X3: $real] :
( ~ 'fun_app$b'('fun_app$d'(X0,X3),sK139(X0,X1))
| ~ $less(0.0,X3) )
& 'member$'(sK139(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f1677,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X4: 'Ereal$'] :
( ? [X5: $real] :
( 'fun_app$b'('fun_app$d'(X0,X5),X4)
& $less(0.0,X5) )
=> ( 'fun_app$b'('fun_app$d'(X0,sK140(X0,X4)),X4)
& $less(0.0,sK140(X0,X4)) ) ),
introduced(choice_axiom,[]) ).
tff(f1675,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( ( sP31(X0,X1)
| ? [X2: 'Ereal$'] :
( ! [X3: $real] :
( ~ 'fun_app$b'('fun_app$d'(X0,X3),X2)
| ~ $less(0.0,X3) )
& 'member$'(X2,X1) ) )
& ( ! [X4: 'Ereal$'] :
( ? [X5: $real] :
( 'fun_app$b'('fun_app$d'(X0,X5),X4)
& $less(0.0,X5) )
| ~ 'member$'(X4,X1) )
| ~ sP31(X0,X1) ) ),
inference(rectify,[],[f1674]) ).
tff(f1674,plain,
! [X1: 'Real_ereal_bool_fun_fun$',X0: 'Ereal_set$'] :
( ( sP31(X1,X0)
| ? [X2: 'Ereal$'] :
( ! [X3: $real] :
( ~ 'fun_app$b'('fun_app$d'(X1,X3),X2)
| ~ $less(0.0,X3) )
& 'member$'(X2,X0) ) )
& ( ! [X2: 'Ereal$'] :
( ? [X3: $real] :
( 'fun_app$b'('fun_app$d'(X1,X3),X2)
& $less(0.0,X3) )
| ~ 'member$'(X2,X0) )
| ~ sP31(X1,X0) ) ),
inference(nnf_transformation,[],[f1239]) ).
tff(f8160,plain,
spl183_634,
inference(avatar_split_clause,[],[f2814,f8158]) ).
tff(f8158,plain,
( spl183_634
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
| ( 0 != 'of_nat$'(X0) )
| ( 0 != 'of_nat$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_634])]) ).
tff(f2814,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
| ( 0 != 'of_nat$'(X0) )
| ( 0 != 'of_nat$'(X1) ) ),
inference(cnf_transformation,[],[f1671]) ).
tff(f8156,plain,
spl183_633,
inference(avatar_split_clause,[],[f2805,f8154]) ).
tff(f8154,plain,
( spl183_633
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
| ( 0 != 'of_nat$'(X0) )
| ( 0 != 'of_nat$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_633])]) ).
tff(f2805,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
| ( 0 != 'of_nat$'(X0) )
| ( 0 != 'of_nat$'(X1) ) ),
inference(cnf_transformation,[],[f1667]) ).
tff(f8152,plain,
spl183_632,
inference(avatar_split_clause,[],[f2795,f8150]) ).
tff(f8150,plain,
( spl183_632
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'of_nat$'(X1))
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_632])]) ).
tff(f2795,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'of_nat$'(X1))
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ),
inference(cnf_transformation,[],[f1663]) ).
tff(f1663,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1)))
| ~ $less(0,'of_nat$'(X1))
| ~ $less(0,'of_nat$'(X0)) )
& ( ( $less(0,'of_nat$'(X1))
& $less(0,'of_nat$'(X0)) )
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ) ),
inference(flattening,[],[f1662]) ).
tff(f1662,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1)))
| ~ $less(0,'of_nat$'(X1))
| ~ $less(0,'of_nat$'(X0)) )
& ( ( $less(0,'of_nat$'(X1))
& $less(0,'of_nat$'(X0)) )
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ) ),
inference(nnf_transformation,[],[f336]) ).
tff(f336,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1)))
<=> ( $less(0,'of_nat$'(X1))
& $less(0,'of_nat$'(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom334) ).
tff(f8148,plain,
spl183_631,
inference(avatar_split_clause,[],[f2794,f8146]) ).
tff(f8146,plain,
( spl183_631
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'of_nat$'(X0))
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_631])]) ).
tff(f2794,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less(0,'of_nat$'(X0))
| ~ $less(0,'times$d'('of_nat$'(X0),'of_nat$'(X1))) ),
inference(cnf_transformation,[],[f1663]) ).
tff(f8144,plain,
spl183_630,
inference(avatar_split_clause,[],[f2789,f8142]) ).
tff(f8142,plain,
( spl183_630
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X1) = 1 )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_630])]) ).
tff(f2789,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X1) = 1 )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ),
inference(cnf_transformation,[],[f1659]) ).
tff(f1659,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) = 1 )
| ( 'of_nat$'(X1) != 1 )
| ( 'of_nat$'(X0) != 1 ) )
& ( ( ( 'of_nat$'(X1) = 1 )
& ( 'of_nat$'(X0) = 1 ) )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ) ),
inference(flattening,[],[f1658]) ).
tff(f1658,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) = 1 )
| ( 'of_nat$'(X1) != 1 )
| ( 'of_nat$'(X0) != 1 ) )
& ( ( ( 'of_nat$'(X1) = 1 )
& ( 'of_nat$'(X0) = 1 ) )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ) ),
inference(nnf_transformation,[],[f517]) ).
tff(f517,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) = 1 )
<=> ( ( 'of_nat$'(X1) = 1 )
& ( 'of_nat$'(X0) = 1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom515) ).
tff(f8140,plain,
spl183_629,
inference(avatar_split_clause,[],[f2788,f8138]) ).
tff(f8138,plain,
( spl183_629
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X0) = 1 )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_629])]) ).
tff(f2788,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X0) = 1 )
| ( 'times$d'('of_nat$'(X0),'of_nat$'(X1)) != 1 ) ),
inference(cnf_transformation,[],[f1659]) ).
tff(f8136,plain,
spl183_628,
inference(avatar_split_clause,[],[f2761,f8134]) ).
tff(f8134,plain,
( spl183_628
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_628])]) ).
tff(f2761,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1643]) ).
tff(f1643,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP26(X0,X1)
| ( ( ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'(X1),'zero$') )
& ( ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ) )
& ( ( 'fun_app$b'('less$'('zero$'),X0)
& 'fun_app$b'('less$'(X1),'zero$') )
| ( 'fun_app$b'('less$'(X0),'zero$')
& 'fun_app$b'('less$'('zero$'),X1) )
| ~ sP26(X0,X1) ) ),
inference(rectify,[],[f1642]) ).
tff(f1642,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP26(X1,X0)
| ( ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP26(X1,X0) ) ),
inference(flattening,[],[f1641]) ).
tff(f1641,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP26(X1,X0)
| ( ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP26(X1,X0) ) ),
inference(nnf_transformation,[],[f1229]) ).
tff(f1229,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP26(X1,X0)
<=> ( ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'('zero$'),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
tff(f8132,plain,
( spl183_627
| ~ spl183_125
| ~ spl183_442 ),
inference(avatar_split_clause,[],[f7445,f6197,f4357,f8130]) ).
tff(f8130,plain,
( spl183_627
<=> ! [X0: $real] : $less(X0,$sum(1.0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_627])]) ).
tff(f4357,plain,
( spl183_125
<=> ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_125])]) ).
tff(f6197,plain,
( spl183_442
<=> ! [X0: $real] : $less(X0,$sum(X0,1.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_442])]) ).
tff(f7445,plain,
( ! [X0: $real] : $less(X0,$sum(1.0,X0))
| ~ spl183_125
| ~ spl183_442 ),
inference(superposition,[],[f6198,f4358]) ).
tff(f4358,plain,
( ! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl183_125 ),
inference(avatar_component_clause,[],[f4357]) ).
tff(f6198,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl183_442 ),
inference(avatar_component_clause,[],[f6197]) ).
tff(f8128,plain,
spl183_626,
inference(avatar_split_clause,[],[f2760,f8126]) ).
tff(f8126,plain,
( spl183_626
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_626])]) ).
tff(f2760,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1643]) ).
tff(f8124,plain,
spl183_625,
inference(avatar_split_clause,[],[f2759,f8122]) ).
tff(f8122,plain,
( spl183_625
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| 'fun_app$b'('less$'(X0),'zero$')
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_625])]) ).
tff(f2759,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| 'fun_app$b'('less$'(X0),'zero$')
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
tff(f8120,plain,
spl183_624,
inference(avatar_split_clause,[],[f2758,f8118]) ).
tff(f8118,plain,
( spl183_624
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_624])]) ).
tff(f2758,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
tff(f8116,plain,
spl183_623,
inference(avatar_split_clause,[],[f2757,f8114]) ).
tff(f8114,plain,
( spl183_623
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'(X0),'zero$')
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_623])]) ).
tff(f2757,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'(X0),'zero$')
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
tff(f8112,plain,
spl183_622,
inference(avatar_split_clause,[],[f2756,f8110]) ).
tff(f8110,plain,
( spl183_622
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_622])]) ).
tff(f2756,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f1643]) ).
tff(f8108,plain,
spl183_621,
inference(avatar_split_clause,[],[f2753,f8106]) ).
tff(f8106,plain,
( spl183_621
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X0,X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_621])]) ).
tff(f2753,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X0,X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1639]) ).
tff(f1639,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP25(X0,X1)
| ( ( ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ) ) )
& ( ( 'fun_app$b'('less_eq$'('zero$'),X0)
& 'fun_app$b'('less_eq$'(X1),'zero$') )
| ( 'fun_app$b'('less_eq$'(X0),'zero$')
& 'fun_app$b'('less_eq$'('zero$'),X1) )
| ~ sP25(X0,X1) ) ),
inference(rectify,[],[f1638]) ).
tff(f1638,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP25(X1,X0)
| ( ( ~ 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'(X1),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'('zero$'),X0) )
| ~ sP25(X1,X0) ) ),
inference(flattening,[],[f1637]) ).
tff(f1637,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP25(X1,X0)
| ( ( ~ 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'(X1),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'('zero$'),X0) )
| ~ sP25(X1,X0) ) ),
inference(nnf_transformation,[],[f1227]) ).
tff(f1227,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP25(X1,X0)
<=> ( ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'('zero$'),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
tff(f8104,plain,
spl183_620,
inference(avatar_split_clause,[],[f2752,f8102]) ).
tff(f8102,plain,
( spl183_620
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X0,X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_620])]) ).
tff(f2752,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X0,X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1639]) ).
tff(f8100,plain,
spl183_619,
inference(avatar_split_clause,[],[f2751,f8098]) ).
tff(f8098,plain,
( spl183_619
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_619])]) ).
tff(f2751,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f1639]) ).
tff(f8096,plain,
spl183_618,
inference(avatar_split_clause,[],[f2750,f8094]) ).
tff(f8094,plain,
( spl183_618
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_618])]) ).
tff(f2750,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f1639]) ).
tff(f8092,plain,
spl183_617,
inference(avatar_split_clause,[],[f2749,f8090]) ).
tff(f8090,plain,
( spl183_617
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_617])]) ).
tff(f2749,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f1639]) ).
tff(f8088,plain,
( spl183_616
| ~ spl183_123
| ~ spl183_433 ),
inference(avatar_split_clause,[],[f6716,f6103,f4349,f8086]) ).
tff(f8086,plain,
( spl183_616
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_616])]) ).
tff(f4349,plain,
( spl183_123
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_123])]) ).
tff(f6103,plain,
( spl183_433
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_433])]) ).
tff(f6716,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl183_123
| ~ spl183_433 ),
inference(superposition,[],[f6104,f4350]) ).
tff(f4350,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl183_123 ),
inference(avatar_component_clause,[],[f4349]) ).
tff(f6104,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl183_433 ),
inference(avatar_component_clause,[],[f6103]) ).
tff(f8084,plain,
spl183_615,
inference(avatar_split_clause,[],[f2748,f8082]) ).
tff(f8082,plain,
( spl183_615
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_615])]) ).
tff(f2748,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f1639]) ).
tff(f8080,plain,
spl183_614,
inference(avatar_split_clause,[],[f2739,f8078]) ).
tff(f8078,plain,
( spl183_614
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_614])]) ).
tff(f2739,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1632]) ).
tff(f1632,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP24(X0,X1)
| ( ( ~ 'fun_app$b'('less$'(X0),'zero$')
| ~ 'fun_app$b'('less$'(X1),'zero$') )
& ( ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ) )
& ( ( 'fun_app$b'('less$'(X0),'zero$')
& 'fun_app$b'('less$'(X1),'zero$') )
| ( 'fun_app$b'('less$'('zero$'),X0)
& 'fun_app$b'('less$'('zero$'),X1) )
| ~ sP24(X0,X1) ) ),
inference(rectify,[],[f1631]) ).
tff(f1631,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP24(X1,X0)
| ( ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP24(X1,X0) ) ),
inference(flattening,[],[f1630]) ).
tff(f1630,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP24(X1,X0)
| ( ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP24(X1,X0) ) ),
inference(nnf_transformation,[],[f1225]) ).
tff(f1225,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP24(X1,X0)
<=> ( ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'('zero$'),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
tff(f8076,plain,
spl183_613,
inference(avatar_split_clause,[],[f2738,f8074]) ).
tff(f8074,plain,
( spl183_613
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_613])]) ).
tff(f2738,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f8072,plain,
spl183_612,
inference(avatar_split_clause,[],[f2737,f8070]) ).
tff(f8070,plain,
( spl183_612
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| 'fun_app$b'('less$'('zero$'),X0)
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_612])]) ).
tff(f2737,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| 'fun_app$b'('less$'('zero$'),X0)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f8068,plain,
spl183_611,
inference(avatar_split_clause,[],[f2736,f8066]) ).
tff(f8066,plain,
( spl183_611
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_611])]) ).
tff(f2736,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f8064,plain,
spl183_610,
inference(avatar_split_clause,[],[f2735,f8062]) ).
tff(f8062,plain,
( spl183_610
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X0)
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_610])]) ).
tff(f2735,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X0)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f8060,plain,
spl183_609,
inference(avatar_split_clause,[],[f2734,f8058]) ).
tff(f8058,plain,
( spl183_609
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_609])]) ).
tff(f2734,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| 'fun_app$b'('less$'('zero$'),X1)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f1632]) ).
tff(f8056,plain,
spl183_608,
inference(avatar_split_clause,[],[f2731,f8054]) ).
tff(f8054,plain,
( spl183_608
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X0,X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_608])]) ).
tff(f2731,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X0,X1)
| ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1628]) ).
tff(f1628,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP23(X0,X1)
| ( ( ~ 'fun_app$b'('less_eq$'(X0),'zero$')
| ~ 'fun_app$b'('less_eq$'(X1),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ) ) )
& ( ( 'fun_app$b'('less_eq$'(X0),'zero$')
& 'fun_app$b'('less_eq$'(X1),'zero$') )
| ( 'fun_app$b'('less_eq$'('zero$'),X0)
& 'fun_app$b'('less_eq$'('zero$'),X1) )
| ~ sP23(X0,X1) ) ),
inference(rectify,[],[f1627]) ).
tff(f1627,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP23(X1,X0)
| ( ( ~ 'fun_app$b'('less_eq$'(X1),'zero$')
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'('zero$'),X0) )
| ~ sP23(X1,X0) ) ),
inference(flattening,[],[f1626]) ).
tff(f1626,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP23(X1,X0)
| ( ( ~ 'fun_app$b'('less_eq$'(X1),'zero$')
| ~ 'fun_app$b'('less_eq$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ) )
& ( ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'('zero$'),X0) )
| ~ sP23(X1,X0) ) ),
inference(nnf_transformation,[],[f1223]) ).
tff(f1223,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP23(X1,X0)
<=> ( ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'('zero$'),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
tff(f8052,plain,
spl183_607,
inference(avatar_split_clause,[],[f2730,f8050]) ).
tff(f8050,plain,
( spl183_607
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X0,X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_607])]) ).
tff(f2730,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X0,X1)
| ~ 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f8048,plain,
spl183_606,
inference(avatar_split_clause,[],[f2729,f8046]) ).
tff(f8046,plain,
( spl183_606
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_606])]) ).
tff(f2729,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f8040,plain,
spl183_605,
inference(avatar_split_clause,[],[f2728,f8038]) ).
tff(f8038,plain,
( spl183_605
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_605])]) ).
tff(f2728,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f8036,plain,
spl183_604,
inference(avatar_split_clause,[],[f2727,f8034]) ).
tff(f8034,plain,
( spl183_604
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_604])]) ).
tff(f2727,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X0)
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f8032,plain,
spl183_603,
inference(avatar_split_clause,[],[f2726,f8030]) ).
tff(f8030,plain,
( spl183_603
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP23(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_603])]) ).
tff(f2726,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),'zero$')
| 'fun_app$b'('less_eq$'('zero$'),X1)
| ~ sP23(X0,X1) ),
inference(cnf_transformation,[],[f1628]) ).
tff(f8028,plain,
spl183_602,
inference(avatar_split_clause,[],[f2617,f8026]) ).
tff(f8026,plain,
( spl183_602
<=> ! [X0: $int,X1: $int] :
( ( 1 = X0 )
| ( 0 = X1 )
| ( 'times$d'(X0,X1) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_602])]) ).
tff(f2617,plain,
! [X0: $int,X1: $int] :
( ( 1 = X0 )
| ( 0 = X1 )
| ( 'times$d'(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f1563]) ).
tff(f1563,plain,
! [X0: $int,X1: $int] :
( ( ( 'times$d'(X0,X1) = X1 )
| ( ( 1 != X0 )
& ( 0 != X1 ) ) )
& ( ( 1 = X0 )
| ( 0 = X1 )
| ( 'times$d'(X0,X1) != X1 ) ) ),
inference(flattening,[],[f1562]) ).
tff(f1562,plain,
! [X0: $int,X1: $int] :
( ( ( 'times$d'(X0,X1) = X1 )
| ( ( 1 != X0 )
& ( 0 != X1 ) ) )
& ( ( 1 = X0 )
| ( 0 = X1 )
| ( 'times$d'(X0,X1) != X1 ) ) ),
inference(nnf_transformation,[],[f432]) ).
tff(f432,axiom,
! [X0: $int,X1: $int] :
( ( 'times$d'(X0,X1) = X1 )
<=> ( ( 1 = X0 )
| ( 0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom430) ).
tff(f8024,plain,
spl183_601,
inference(avatar_split_clause,[],[f2611,f8022]) ).
tff(f8022,plain,
( spl183_601
<=> ! [X0: $int,X1: $int] :
( ( 1 = X1 )
| ( 0 = X0 )
| ( 'times$d'(X0,X1) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_601])]) ).
tff(f2611,plain,
! [X0: $int,X1: $int] :
( ( 1 = X1 )
| ( 0 = X0 )
| ( 'times$d'(X0,X1) != X0 ) ),
inference(cnf_transformation,[],[f1559]) ).
tff(f1559,plain,
! [X0: $int,X1: $int] :
( ( ( 'times$d'(X0,X1) = X0 )
| ( ( 1 != X1 )
& ( 0 != X0 ) ) )
& ( ( 1 = X1 )
| ( 0 = X0 )
| ( 'times$d'(X0,X1) != X0 ) ) ),
inference(flattening,[],[f1558]) ).
tff(f1558,plain,
! [X0: $int,X1: $int] :
( ( ( 'times$d'(X0,X1) = X0 )
| ( ( 1 != X1 )
& ( 0 != X0 ) ) )
& ( ( 1 = X1 )
| ( 0 = X0 )
| ( 'times$d'(X0,X1) != X0 ) ) ),
inference(nnf_transformation,[],[f438]) ).
tff(f438,axiom,
! [X0: $int,X1: $int] :
( ( 'times$d'(X0,X1) = X0 )
<=> ( ( 1 = X1 )
| ( 0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom436) ).
tff(f8020,plain,
spl183_600,
inference(avatar_split_clause,[],[f2581,f8018]) ).
tff(f8018,plain,
( spl183_600
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'zero$' = X1 )
| ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_600])]) ).
tff(f2581,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'zero$' = X1 )
| ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,X1) ) ),
inference(cnf_transformation,[],[f1541]) ).
tff(f1541,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'zero$' = 'times$'(X0,X1) )
| ( ( 'zero$' != X1 )
& ( 'zero$' != X0 ) ) )
& ( ( 'zero$' = X1 )
| ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,X1) ) ) ),
inference(flattening,[],[f1540]) ).
tff(f1540,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'zero$' = 'times$'(X0,X1) )
| ( ( 'zero$' != X1 )
& ( 'zero$' != X0 ) ) )
& ( ( 'zero$' = X1 )
| ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f254]) ).
tff(f254,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'zero$' = 'times$'(X0,X1) )
<=> ( ( 'zero$' = X1 )
| ( 'zero$' = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom252) ).
tff(f8016,plain,
spl183_599,
inference(avatar_split_clause,[],[f2568,f8014]) ).
tff(f8014,plain,
( spl183_599
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( X0 = X1 )
| 'fun_app$b'('less$'(X0),X1)
| ~ 'fun_app$b'('less_eq$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_599])]) ).
tff(f2568,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( X0 = X1 )
| 'fun_app$b'('less$'(X0),X1)
| ~ 'fun_app$b'('less_eq$'(X0),X1) ),
inference(cnf_transformation,[],[f1533]) ).
tff(f1533,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'(X0),X1)
| ( ( X0 != X1 )
& ~ 'fun_app$b'('less$'(X0),X1) ) )
& ( ( X0 = X1 )
| 'fun_app$b'('less$'(X0),X1)
| ~ 'fun_app$b'('less_eq$'(X0),X1) ) ),
inference(flattening,[],[f1532]) ).
tff(f1532,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'(X0),X1)
| ( ( X0 != X1 )
& ~ 'fun_app$b'('less$'(X0),X1) ) )
& ( ( X0 = X1 )
| 'fun_app$b'('less$'(X0),X1)
| ~ 'fun_app$b'('less_eq$'(X0),X1) ) ),
inference(nnf_transformation,[],[f628]) ).
tff(f628,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
<=> ( ( X0 = X1 )
| 'fun_app$b'('less$'(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom626) ).
tff(f8012,plain,
spl183_598,
inference(avatar_split_clause,[],[f2546,f8010]) ).
tff(f8010,plain,
( spl183_598
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ( X0 = X1 )
| ( 'max$b'(X1,X0) != X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_598])]) ).
tff(f2546,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| ( X0 = X1 )
| ( 'max$b'(X1,X0) != X1 ) ),
inference(cnf_transformation,[],[f1520]) ).
tff(f1520,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,X1)
| ( X0 = X1 )
| ( 'max$b'(X1,X0) != X1 ) )
& ( ( ( X0 != X1 )
& ( 'max$b'(X1,X0) = X1 ) )
| ~ $less(X0,X1) ) ),
inference(flattening,[],[f1519]) ).
tff(f1519,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,X1)
| ( X0 = X1 )
| ( 'max$b'(X1,X0) != X1 ) )
& ( ( ( X0 != X1 )
& ( 'max$b'(X1,X0) = X1 ) )
| ~ $less(X0,X1) ) ),
inference(nnf_transformation,[],[f110]) ).
tff(f110,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
<=> ( ( X0 != X1 )
& ( 'max$b'(X1,X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom108) ).
tff(f8008,plain,
spl183_597,
inference(avatar_split_clause,[],[f2539,f8006]) ).
tff(f8006,plain,
( spl183_597
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(sK135(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_597])]) ).
tff(f2539,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(sK135(X0,X1))) ),
inference(cnf_transformation,[],[f1512]) ).
tff(f1512,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| ( ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(sK135(X0,X1)))
& 'fun_app$b'('less_eq$'(X0),'ereal$'(sK135(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f1047,f1511]) ).
tff(f1511,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(X2))
& 'fun_app$b'('less_eq$'(X0),'ereal$'(X2)) )
=> ( ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(sK135(X0,X1)))
& 'fun_app$b'('less_eq$'(X0),'ereal$'(sK135(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f1047,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| ? [X2: $real] :
( ~ 'fun_app$b'('less_eq$'(X1),'ereal$'(X2))
& 'fun_app$b'('less_eq$'(X0),'ereal$'(X2)) ) ),
inference(ennf_transformation,[],[f631]) ).
tff(f631,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ! [X2: $real] :
( 'fun_app$b'('less_eq$'(X0),'ereal$'(X2))
=> 'fun_app$b'('less_eq$'(X1),'ereal$'(X2)) )
=> 'fun_app$b'('less_eq$'(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom629) ).
tff(f8004,plain,
spl183_596,
inference(avatar_split_clause,[],[f2538,f8002]) ).
tff(f8002,plain,
( spl183_596
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| 'fun_app$b'('less_eq$'(X0),'ereal$'(sK135(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_596])]) ).
tff(f2538,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X0)
| 'fun_app$b'('less_eq$'(X0),'ereal$'(sK135(X0,X1))) ),
inference(cnf_transformation,[],[f1512]) ).
tff(f8000,plain,
( spl183_595
| ~ spl183_478
| ~ spl183_511 ),
inference(avatar_split_clause,[],[f7757,f7296,f7161,f7997]) ).
tff(f7161,plain,
( spl183_478
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X2)
| ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_478])]) ).
tff(f7296,plain,
( spl183_511
<=> 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(sK182)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_511])]) ).
tff(f7757,plain,
( 'fun_app$b'('less$'('c$b'),'ereal$'(sK182))
| ~ spl183_478
| ~ spl183_511 ),
inference(resolution,[],[f7298,f7162]) ).
tff(f7162,plain,
( ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2)
| 'fun_app$b'('less$'(X0),X2) )
| ~ spl183_478 ),
inference(avatar_component_clause,[],[f7161]) ).
tff(f7298,plain,
( 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(sK182))
| ~ spl183_511 ),
inference(avatar_component_clause,[],[f7296]) ).
tff(f7995,plain,
spl183_594,
inference(avatar_split_clause,[],[f2499,f7993]) ).
tff(f7993,plain,
( spl183_594
<=> ! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(0,X0)
| ~ $less(0,'times$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_594])]) ).
tff(f2499,plain,
! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(0,X0)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(cnf_transformation,[],[f1024]) ).
tff(f1024,plain,
! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(0,X0)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(flattening,[],[f1023]) ).
tff(f1023,plain,
! [X0: $int,X1: $int] :
( $less(0,X1)
| ~ $less(0,X0)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(ennf_transformation,[],[f396]) ).
tff(f396,axiom,
! [X0: $int,X1: $int] :
( ( $less(0,X0)
& $less(0,'times$d'(X0,X1)) )
=> $less(0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom394) ).
tff(f7991,plain,
spl183_593,
inference(avatar_split_clause,[],[f2498,f7989]) ).
tff(f7989,plain,
( spl183_593
<=> ! [X0: $int,X1: $int] :
( $less(0,X0)
| ~ $less(0,X1)
| ~ $less(0,'times$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_593])]) ).
tff(f2498,plain,
! [X0: $int,X1: $int] :
( $less(0,X0)
| ~ $less(0,X1)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(cnf_transformation,[],[f1022]) ).
tff(f1022,plain,
! [X0: $int,X1: $int] :
( $less(0,X0)
| ~ $less(0,X1)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(flattening,[],[f1021]) ).
tff(f1021,plain,
! [X0: $int,X1: $int] :
( $less(0,X0)
| ~ $less(0,X1)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(ennf_transformation,[],[f393]) ).
tff(f393,axiom,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& $less(0,'times$d'(X0,X1)) )
=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom391) ).
tff(f7986,plain,
spl183_592,
inference(avatar_split_clause,[],[f2473,f7984]) ).
tff(f7984,plain,
( spl183_592
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK122(X0))
| ~ 'fun_app$e'(X0,'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_592])]) ).
tff(f2473,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK122(X0))
| ~ 'fun_app$e'(X0,'nat$'(0)) ),
inference(cnf_transformation,[],[f1472]) ).
tff(f1472,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK122(X0))) )
& ~ 'fun_app$e'(X0,sK122(X0))
& $less(0,'of_nat$'(sK122(X0))) )
| ~ 'fun_app$e'(X0,'nat$'(0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122])],[f992,f1471]) ).
tff(f1471,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
& ~ 'fun_app$e'(X0,X2)
& $less(0,'of_nat$'(X2)) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK122(X0))) )
& ~ 'fun_app$e'(X0,sK122(X0))
& $less(0,'of_nat$'(sK122(X0))) ) ),
introduced(choice_axiom,[]) ).
tff(f992,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
& ~ 'fun_app$e'(X0,X2)
& $less(0,'of_nat$'(X2)) )
| ~ 'fun_app$e'(X0,'nat$'(0)) ),
inference(flattening,[],[f991]) ).
tff(f991,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
& ~ 'fun_app$e'(X0,X2)
& $less(0,'of_nat$'(X2)) )
| ~ 'fun_app$e'(X0,'nat$'(0)) ),
inference(ennf_transformation,[],[f129]) ).
tff(f129,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ( ! [X2: 'Nat$'] :
( ( ~ 'fun_app$e'(X0,X2)
& $less(0,'of_nat$'(X2)) )
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$e'(X0,X3)
& $less('of_nat$'(X3),'of_nat$'(X2)) ) )
& 'fun_app$e'(X0,'nat$'(0)) )
=> 'fun_app$e'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom127) ).
tff(f7982,plain,
spl183_591,
inference(avatar_split_clause,[],[f2466,f7980]) ).
tff(f7980,plain,
( spl183_591
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ( 0.0 != sK121(X0,X1) )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_591])]) ).
tff(f2466,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ( 0.0 != sK121(X0,X1) )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
tff(f1470,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( ( 'ereal$'('fun_app$c'('inverse$',sK121(X0,X1))) = X0 )
| ( 0.0 = sK121(X0,X1) ) )
& ( ( 'infinity$' = X0 )
| ( 0.0 != sK121(X0,X1) ) )
& ( 'ereal$'(sK121(X0,X1)) = X1 ) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK121])],[f1468,f1469]) ).
tff(f1469,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( ( 'ereal$'('fun_app$c'('inverse$',X2)) = X0 )
| ( 0.0 = X2 ) )
& ( ( 'infinity$' = X0 )
| ( 0.0 != X2 ) )
& ( 'ereal$'(X2) = X1 ) )
=> ( ( ( 'ereal$'('fun_app$c'('inverse$',sK121(X0,X1))) = X0 )
| ( 0.0 = sK121(X0,X1) ) )
& ( ( 'infinity$' = X0 )
| ( 0.0 != sK121(X0,X1) ) )
& ( 'ereal$'(sK121(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1468,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( ( 'ereal$'('fun_app$c'('inverse$',X2)) = X0 )
| ( 0.0 = X2 ) )
& ( ( 'infinity$' = X0 )
| ( 0.0 != X2 ) )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f1467]) ).
tff(f1467,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X2: $real] :
( ( ( 'ereal$'('fun_app$c'('inverse$',X2)) = X1 )
| ( 0.0 = X2 ) )
& ( ( 'infinity$' = X1 )
| ( 0.0 != X2 ) )
& ( 'ereal$'(X2) = X0 ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f1190]) ).
tff(f1190,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X2: $real] :
( ( ( 'ereal$'('fun_app$c'('inverse$',X2)) = X1 )
| ( 0.0 = X2 ) )
& ( ( 'infinity$' = X1 )
| ( 0.0 != X2 ) )
& ( 'ereal$'(X2) = X0 ) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f7978,plain,
spl183_590,
inference(avatar_split_clause,[],[f2454,f7976]) ).
tff(f7976,plain,
( spl183_590
<=> ! [X0: $real,X1: $real] :
( $less(sK115(X0,X1),X1)
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_590])]) ).
tff(f2454,plain,
! [X0: $real,X1: $real] :
( $less(sK115(X0,X1),X1)
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1457]) ).
tff(f1457,plain,
! [X0: $real,X1: $real] :
( ( $less(sK115(X0,X1),X1)
& $less(sK115(X0,X1),X0)
& $less(0.0,sK115(X0,X1)) )
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK115])],[f986,f1456]) ).
tff(f1456,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( $less(X2,X1)
& $less(X2,X0)
& $less(0.0,X2) )
=> ( $less(sK115(X0,X1),X1)
& $less(sK115(X0,X1),X0)
& $less(0.0,sK115(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f986,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( $less(X2,X1)
& $less(X2,X0)
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(flattening,[],[f985]) ).
tff(f985,plain,
! [X0: $real,X1: $real] :
( ? [X2: $real] :
( $less(X2,X1)
& $less(X2,X0)
& $less(0.0,X2) )
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(ennf_transformation,[],[f137]) ).
tff(f137,axiom,
! [X0: $real,X1: $real] :
( ( $less(0.0,X1)
& $less(0.0,X0) )
=> ? [X2: $real] :
( $less(X2,X1)
& $less(X2,X0)
& $less(0.0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom135) ).
tff(f7974,plain,
spl183_589,
inference(avatar_split_clause,[],[f2453,f7972]) ).
tff(f7972,plain,
( spl183_589
<=> ! [X0: $real,X1: $real] :
( $less(sK115(X0,X1),X0)
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_589])]) ).
tff(f2453,plain,
! [X0: $real,X1: $real] :
( $less(sK115(X0,X1),X0)
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1457]) ).
tff(f7970,plain,
spl183_588,
inference(avatar_split_clause,[],[f2452,f7968]) ).
tff(f7968,plain,
( spl183_588
<=> ! [X0: $real,X1: $real] :
( $less(0.0,sK115(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_588])]) ).
tff(f2452,plain,
! [X0: $real,X1: $real] :
( $less(0.0,sK115(X0,X1))
| ~ $less(0.0,X1)
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1457]) ).
tff(f7966,plain,
spl183_587,
inference(avatar_split_clause,[],[f2435,f7964]) ).
tff(f7964,plain,
( spl183_587
<=> ! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(0,X1)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_587])]) ).
tff(f2435,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(0,X1)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f960]) ).
tff(f960,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(0,X1)
| ~ $less(0,X0) ),
inference(flattening,[],[f959]) ).
tff(f959,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(0,X1)
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f404]) ).
tff(f404,axiom,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& $less(0,X0) )
=> $less(0,'times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom402) ).
tff(f7962,plain,
spl183_586,
inference(avatar_split_clause,[],[f2433,f7960]) ).
tff(f7960,plain,
( spl183_586
<=> ! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_586])]) ).
tff(f2433,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f956]) ).
tff(f956,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(0,X0) ),
inference(flattening,[],[f955]) ).
tff(f955,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(X1,0)
| ~ $less(0,X0) ),
inference(ennf_transformation,[],[f407]) ).
tff(f407,axiom,
! [X0: $int,X1: $int] :
( ( $less(X1,0)
& $less(0,X0) )
=> $less('times$d'(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom405) ).
tff(f7958,plain,
spl183_585,
inference(avatar_split_clause,[],[f2432,f7956]) ).
tff(f7956,plain,
( spl183_585
<=> ! [X0: $int,X1: $int] :
( $less(1,'times$d'(X0,X1))
| ~ $less(1,X1)
| ~ $less(1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_585])]) ).
tff(f2432,plain,
! [X0: $int,X1: $int] :
( $less(1,'times$d'(X0,X1))
| ~ $less(1,X1)
| ~ $less(1,X0) ),
inference(cnf_transformation,[],[f954]) ).
tff(f954,plain,
! [X0: $int,X1: $int] :
( $less(1,'times$d'(X0,X1))
| ~ $less(1,X1)
| ~ $less(1,X0) ),
inference(flattening,[],[f953]) ).
tff(f953,plain,
! [X0: $int,X1: $int] :
( $less(1,'times$d'(X0,X1))
| ~ $less(1,X1)
| ~ $less(1,X0) ),
inference(ennf_transformation,[],[f485]) ).
tff(f485,axiom,
! [X0: $int,X1: $int] :
( ( $less(1,X1)
& $less(1,X0) )
=> $less(1,'times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom483) ).
tff(f7946,plain,
spl183_584,
inference(avatar_split_clause,[],[f2431,f7944]) ).
tff(f7944,plain,
( spl183_584
<=> ! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(0,X1)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_584])]) ).
tff(f2431,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(0,X1)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f952]) ).
tff(f952,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(0,X1)
| ~ $less(X0,0) ),
inference(flattening,[],[f951]) ).
tff(f951,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ $less(0,X1)
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f410]) ).
tff(f410,axiom,
! [X0: $int,X1: $int] :
( ( $less(0,X1)
& $less(X0,0) )
=> $less('times$d'(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom408) ).
tff(f7942,plain,
spl183_583,
inference(avatar_split_clause,[],[f2430,f7940]) ).
tff(f7940,plain,
( spl183_583
<=> ! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(X1,0)
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_583])]) ).
tff(f2430,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f950]) ).
tff(f950,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(flattening,[],[f949]) ).
tff(f949,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ $less(X1,0)
| ~ $less(X0,0) ),
inference(ennf_transformation,[],[f416]) ).
tff(f416,axiom,
! [X0: $int,X1: $int] :
( ( $less(X1,0)
& $less(X0,0) )
=> $less(0,'times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom414) ).
tff(f7938,plain,
spl183_582,
inference(avatar_split_clause,[],[f2429,f7936]) ).
tff(f7936,plain,
( spl183_582
<=> ! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(X1,0)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_582])]) ).
tff(f2429,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(X1,0)
| $less(X0,0) ),
inference(cnf_transformation,[],[f948]) ).
tff(f948,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(X1,0)
| $less(X0,0) ),
inference(flattening,[],[f947]) ).
tff(f947,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(X1,0)
| $less(X0,0) ),
inference(ennf_transformation,[],[f678]) ).
tff(f678,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(X0,0) )
=> ~ $less('times$d'(X0,X1),0) ),
inference(theory_normalization,[],[f589]) ).
tff(f589,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(0,X1)
& $lesseq(0,X0) )
=> $lesseq(0,'times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom587) ).
tff(f7934,plain,
spl183_581,
inference(avatar_split_clause,[],[f2428,f7932]) ).
tff(f7932,plain,
( spl183_581
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(0,X1)
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_581])]) ).
tff(f2428,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(0,X1)
| $less(X0,0) ),
inference(cnf_transformation,[],[f946]) ).
tff(f946,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(0,X1)
| $less(X0,0) ),
inference(flattening,[],[f945]) ).
tff(f945,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(0,X1)
| $less(X0,0) ),
inference(ennf_transformation,[],[f677]) ).
tff(f677,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(0,X1)
& ~ $less(X0,0) )
=> ~ $less(0,'times$d'(X0,X1)) ),
inference(theory_normalization,[],[f586]) ).
tff(f586,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(X1,0)
& $lesseq(0,X0) )
=> $lesseq('times$d'(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom584) ).
tff(f7930,plain,
spl183_580,
inference(avatar_split_clause,[],[f2426,f7928]) ).
tff(f7928,plain,
( spl183_580
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(X1,0)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_580])]) ).
tff(f2426,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(X1,0)
| $less(0,X0) ),
inference(cnf_transformation,[],[f942]) ).
tff(f942,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(X1,0)
| $less(0,X0) ),
inference(flattening,[],[f941]) ).
tff(f941,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| $less(X1,0)
| $less(0,X0) ),
inference(ennf_transformation,[],[f675]) ).
tff(f675,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(X1,0)
& ~ $less(0,X0) )
=> ~ $less(0,'times$d'(X0,X1)) ),
inference(theory_normalization,[],[f583]) ).
tff(f583,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(0,X1)
& $lesseq(X0,0) )
=> $lesseq('times$d'(X0,X1),0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom581) ).
tff(f7926,plain,
spl183_579,
inference(avatar_split_clause,[],[f2425,f7924]) ).
tff(f7924,plain,
( spl183_579
<=> ! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(0,X1)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_579])]) ).
tff(f2425,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(0,X1)
| $less(0,X0) ),
inference(cnf_transformation,[],[f940]) ).
tff(f940,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(0,X1)
| $less(0,X0) ),
inference(flattening,[],[f939]) ).
tff(f939,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| $less(0,X1)
| $less(0,X0) ),
inference(ennf_transformation,[],[f674]) ).
tff(f674,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(0,X1)
& ~ $less(0,X0) )
=> ~ $less('times$d'(X0,X1),0) ),
inference(theory_normalization,[],[f604]) ).
tff(f604,axiom,
! [X0: $int,X1: $int] :
( ( $lesseq(X1,0)
& $lesseq(X0,0) )
=> $lesseq(0,'times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom602) ).
tff(f7922,plain,
spl183_578,
inference(avatar_split_clause,[],[f2408,f7920]) ).
tff(f7920,plain,
( spl183_578
<=> ! [X0: $real,X1: $real] :
( ( 'fun_app$c'('inverse$',X0) = X1 )
| ( 'fun_app$c'('times$a'(X0),X1) != 1.0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_578])]) ).
tff(f2408,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('inverse$',X0) = X1 )
| ( 'fun_app$c'('times$a'(X0),X1) != 1.0 ) ),
inference(cnf_transformation,[],[f910]) ).
tff(f910,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('inverse$',X0) = X1 )
| ( 'fun_app$c'('times$a'(X0),X1) != 1.0 ) ),
inference(ennf_transformation,[],[f494]) ).
tff(f494,axiom,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('times$a'(X0),X1) = 1.0 )
=> ( 'fun_app$c'('inverse$',X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom492) ).
tff(f7918,plain,
spl183_577,
inference(avatar_split_clause,[],[f2395,f7916]) ).
tff(f7916,plain,
( spl183_577
<=> ! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( 0 = X0 )
| ( 0 != 'times$d'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_577])]) ).
tff(f2395,plain,
! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( 0 = X0 )
| ( 0 != 'times$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f897]) ).
tff(f897,plain,
! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( 0 = X0 )
| ( 0 != 'times$d'(X0,X1) ) ),
inference(flattening,[],[f896]) ).
tff(f896,plain,
! [X0: $int,X1: $int] :
( ( 0 = X1 )
| ( 0 = X0 )
| ( 0 != 'times$d'(X0,X1) ) ),
inference(ennf_transformation,[],[f359]) ).
tff(f359,axiom,
! [X0: $int,X1: $int] :
( ( 0 = 'times$d'(X0,X1) )
=> ( ( 0 = X1 )
| ( 0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom357) ).
tff(f7914,plain,
spl183_576,
inference(avatar_split_clause,[],[f2390,f7912]) ).
tff(f7912,plain,
( spl183_576
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('ereal$'(sK114(X0,X1))),X1)
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_576])]) ).
tff(f2390,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('ereal$'(sK114(X0,X1))),X1)
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1451]) ).
tff(f1451,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less$'('ereal$'(sK114(X0,X1))),X1)
& 'fun_app$b'('less$'(X0),'ereal$'(sK114(X0,X1))) )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK114])],[f892,f1450]) ).
tff(f1450,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( 'fun_app$b'('less$'('ereal$'(X2)),X1)
& 'fun_app$b'('less$'(X0),'ereal$'(X2)) )
=> ( 'fun_app$b'('less$'('ereal$'(sK114(X0,X1))),X1)
& 'fun_app$b'('less$'(X0),'ereal$'(sK114(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
tff(f892,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( 'fun_app$b'('less$'('ereal$'(X2)),X1)
& 'fun_app$b'('less$'(X0),'ereal$'(X2)) )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(ennf_transformation,[],[f48]) ).
tff(f48,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X1)
=> ? [X2: $real] :
( 'fun_app$b'('less$'('ereal$'(X2)),X1)
& 'fun_app$b'('less$'(X0),'ereal$'(X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom46) ).
tff(f7910,plain,
spl183_575,
inference(avatar_split_clause,[],[f2389,f7908]) ).
tff(f7908,plain,
( spl183_575
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'ereal$'(sK114(X0,X1)))
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_575])]) ).
tff(f2389,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'ereal$'(sK114(X0,X1)))
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1451]) ).
tff(f7894,plain,
spl183_574,
inference(avatar_split_clause,[],[f2372,f7892]) ).
tff(f7892,plain,
( spl183_574
<=> ! [X0: $real,X1: $real] :
( ( 'ereal$'(X0) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_574])]) ).
tff(f2372,plain,
! [X0: $real,X1: $real] :
( ( 'ereal$'(X0) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| ~ $less(X1,X0) ),
inference(cnf_transformation,[],[f875]) ).
tff(f875,plain,
! [X0: $real,X1: $real] :
( ( ( 'ereal$'(X0) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| ~ $less(X1,X0) )
& ( ( 'ereal$'(X1) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| $less(X1,X0) ) ),
inference(ennf_transformation,[],[f664]) ).
tff(f664,plain,
! [X0: $real,X1: $real] :
( ( $less(X1,X0)
=> ( 'ereal$'(X0) = 'max$'('ereal$'(X0),'ereal$'(X1)) ) )
& ( ~ $less(X1,X0)
=> ( 'ereal$'(X1) = 'max$'('ereal$'(X0),'ereal$'(X1)) ) ) ),
inference(theory_normalization,[],[f97]) ).
tff(f97,axiom,
! [X0: $real,X1: $real] :
( ( ~ $lesseq(X0,X1)
=> ( 'ereal$'(X0) = 'max$'('ereal$'(X0),'ereal$'(X1)) ) )
& ( $lesseq(X0,X1)
=> ( 'ereal$'(X1) = 'max$'('ereal$'(X0),'ereal$'(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom95) ).
tff(f7890,plain,
spl183_573,
inference(avatar_split_clause,[],[f2371,f7888]) ).
tff(f7888,plain,
( spl183_573
<=> ! [X0: $real,X1: $real] :
( ( 'ereal$'(X1) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_573])]) ).
tff(f2371,plain,
! [X0: $real,X1: $real] :
( ( 'ereal$'(X1) = 'max$'('ereal$'(X0),'ereal$'(X1)) )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f875]) ).
tff(f7886,plain,
spl183_572,
inference(avatar_split_clause,[],[f2350,f7884]) ).
tff(f7884,plain,
( spl183_572
<=> ! [X0: $real,X1: $real] : ( 'times$'('ereal$'(X0),'ereal$'(X1)) = 'ereal$'('fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_572])]) ).
tff(f2350,plain,
! [X0: $real,X1: $real] : ( 'times$'('ereal$'(X0),'ereal$'(X1)) = 'ereal$'('fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f343]) ).
tff(f343,axiom,
! [X0: $real,X1: $real] : ( 'times$'('ereal$'(X0),'ereal$'(X1)) = 'ereal$'('fun_app$c'('times$a'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom341) ).
tff(f7882,plain,
spl183_571,
inference(avatar_split_clause,[],[f2349,f7880]) ).
tff(f7880,plain,
( spl183_571
<=> ! [X0: 'Real_fps$',X1: 'Nat$'] : ( 'fun_app$f'('fps_nth$'('uminus$b'(X0)),X1) = $uminus('fun_app$f'('fps_nth$'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_571])]) ).
tff(f2349,plain,
! [X0: 'Real_fps$',X1: 'Nat$'] : ( 'fun_app$f'('fps_nth$'('uminus$b'(X0)),X1) = $uminus('fun_app$f'('fps_nth$'(X0),X1)) ),
inference(cnf_transformation,[],[f163]) ).
tff(f163,axiom,
! [X0: 'Real_fps$',X1: 'Nat$'] : ( 'fun_app$f'('fps_nth$'('uminus$b'(X0)),X1) = $uminus('fun_app$f'('fps_nth$'(X0),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom161) ).
tff(f7878,plain,
spl183_570,
inference(avatar_split_clause,[],[f2347,f7876]) ).
tff(f7876,plain,
( spl183_570
<=> ! [X0: $real,X1: $real] : ( $uminus('fun_app$c'('times$a'(X0),X1)) = 'fun_app$c'('times$a'(X0),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_570])]) ).
tff(f7874,plain,
spl183_569,
inference(avatar_split_clause,[],[f2346,f7872]) ).
tff(f7872,plain,
( spl183_569
<=> ! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'($uminus(X0)),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_569])]) ).
tff(f2346,plain,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'($uminus(X0)),$uminus(X1)) ),
inference(cnf_transformation,[],[f307]) ).
tff(f307,axiom,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'($uminus(X0)),$uminus(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom305) ).
tff(f7870,plain,
spl183_568,
inference(avatar_split_clause,[],[f2330,f7868]) ).
tff(f7868,plain,
( spl183_568
<=> ! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| ~ 'fun_app$b'('less_eq$'(sK113(X0,X2)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_568])]) ).
tff(f2330,plain,
! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| ~ 'fun_app$b'('less_eq$'(sK113(X0,X2)),X2) ),
inference(cnf_transformation,[],[f1449]) ).
tff(f1449,plain,
! [X0: 'Ereal_set$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| ( ~ 'fun_app$b'('less_eq$'(sK113(X0,X2)),X2)
& 'member$'(sK113(X0,X2),X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X4),sK112(X0))
| ~ 'member$'(X4,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK112,sK113])],[f871,f1448,f1447]) ).
tff(f1447,plain,
! [X0: 'Ereal_set$'] :
( ? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X2)
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X3),X2)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X4),X1)
| ~ 'member$'(X4,X0) ) )
=> ( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X3),X2)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X4),sK112(X0))
| ~ 'member$'(X4,X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1448,plain,
! [X0: 'Ereal_set$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X3),X2)
& 'member$'(X3,X0) )
=> ( ~ 'fun_app$b'('less_eq$'(sK113(X0,X2)),X2)
& 'member$'(sK113(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f871,plain,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X2)
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X3),X2)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X4),X1)
| ~ 'member$'(X4,X0) ) ),
inference(ennf_transformation,[],[f786]) ).
tff(f786,plain,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( ! [X3: 'Ereal$'] :
( 'member$'(X3,X0)
=> 'fun_app$b'('less_eq$'(X3),X2) )
=> 'fun_app$b'('less_eq$'(X1),X2) )
& ! [X4: 'Ereal$'] :
( 'member$'(X4,X0)
=> 'fun_app$b'('less_eq$'(X4),X1) ) ),
inference(rectify,[],[f630]) ).
tff(f630,axiom,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( ! [X3: 'Ereal$'] :
( 'member$'(X3,X0)
=> 'fun_app$b'('less_eq$'(X3),X2) )
=> 'fun_app$b'('less_eq$'(X1),X2) )
& ! [X2: 'Ereal$'] :
( 'member$'(X2,X0)
=> 'fun_app$b'('less_eq$'(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom628) ).
tff(f7866,plain,
spl183_567,
inference(avatar_split_clause,[],[f2327,f7864]) ).
tff(f7864,plain,
( spl183_567
<=> ! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| ~ 'fun_app$b'('less_eq$'(X2),sK111(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_567])]) ).
tff(f2327,plain,
! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| ~ 'fun_app$b'('less_eq$'(X2),sK111(X0,X2)) ),
inference(cnf_transformation,[],[f1446]) ).
tff(f1446,plain,
! [X0: 'Ereal_set$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| ( ~ 'fun_app$b'('less_eq$'(X2),sK111(X0,X2))
& 'member$'(sK111(X0,X2),X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(sK110(X0)),X4)
| ~ 'member$'(X4,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK110,sK111])],[f870,f1445,f1444]) ).
tff(f1444,plain,
! [X0: 'Ereal_set$'] :
( ? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X2),X1)
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X2),X3)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X4)
| ~ 'member$'(X4,X0) ) )
=> ( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X2),X3)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(sK110(X0)),X4)
| ~ 'member$'(X4,X0) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1445,plain,
! [X0: 'Ereal_set$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X2),X3)
& 'member$'(X3,X0) )
=> ( ~ 'fun_app$b'('less_eq$'(X2),sK111(X0,X2))
& 'member$'(sK111(X0,X2),X0) ) ),
introduced(choice_axiom,[]) ).
tff(f870,plain,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X2),X1)
| ? [X3: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X2),X3)
& 'member$'(X3,X0) ) )
& ! [X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X4)
| ~ 'member$'(X4,X0) ) ),
inference(ennf_transformation,[],[f785]) ).
tff(f785,plain,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( ! [X3: 'Ereal$'] :
( 'member$'(X3,X0)
=> 'fun_app$b'('less_eq$'(X2),X3) )
=> 'fun_app$b'('less_eq$'(X2),X1) )
& ! [X4: 'Ereal$'] :
( 'member$'(X4,X0)
=> 'fun_app$b'('less_eq$'(X1),X4) ) ),
inference(rectify,[],[f629]) ).
tff(f629,axiom,
! [X0: 'Ereal_set$'] :
? [X1: 'Ereal$'] :
( ! [X2: 'Ereal$'] :
( ! [X3: 'Ereal$'] :
( 'member$'(X3,X0)
=> 'fun_app$b'('less_eq$'(X2),X3) )
=> 'fun_app$b'('less_eq$'(X2),X1) )
& ! [X2: 'Ereal$'] :
( 'member$'(X2,X0)
=> 'fun_app$b'('less_eq$'(X1),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom627) ).
tff(f7861,plain,
spl183_566,
inference(avatar_split_clause,[],[f2181,f7859]) ).
tff(f2181,plain,
! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) )
| ( 'zero$b' != 'inverse$c'(X0) ) ),
inference(cnf_transformation,[],[f1346]) ).
tff(f1346,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' = 'inverse$c'(X0) )
| ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) )
& ( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) )
| ( 'zero$b' != 'inverse$c'(X0) ) ) ),
inference(nnf_transformation,[],[f144]) ).
tff(f144,axiom,
! [X0: 'Real_fps$'] :
( ( 'zero$b' = 'inverse$c'(X0) )
<=> ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom142) ).
tff(f7857,plain,
spl183_565,
inference(avatar_split_clause,[],[f2133,f7855]) ).
tff(f7855,plain,
( spl183_565
<=> ! [X0: $real] :
( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_565])]) ).
tff(f2133,plain,
! [X0: $real] :
( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f854]) ).
tff(f854,plain,
! [X0: $real] :
( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) ),
inference(flattening,[],[f853]) ).
tff(f853,plain,
! [X0: $real] :
( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) ),
inference(ennf_transformation,[],[f503]) ).
tff(f503,axiom,
! [X0: $real] :
( ( $less(X0,1.0)
& $less(0.0,X0) )
=> $less(1.0,'fun_app$c'('inverse$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom501) ).
tff(f7839,plain,
spl183_564,
inference(avatar_split_clause,[],[f2131,f7837]) ).
tff(f2131,plain,
! [X0: 'Real_fps$'] :
( ( 'zero$b' = 'inverse$c'(X0) )
| ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) ),
inference(cnf_transformation,[],[f851]) ).
tff(f851,plain,
! [X0: 'Real_fps$'] :
( ( 'zero$b' = 'inverse$c'(X0) )
| ( 0.0 != 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) ) ),
inference(ennf_transformation,[],[f230]) ).
tff(f230,axiom,
! [X0: 'Real_fps$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),'nat$'(0)) )
=> ( 'zero$b' = 'inverse$c'(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom228) ).
tff(f7835,plain,
spl183_563,
inference(avatar_split_clause,[],[f2115,f7833]) ).
tff(f7833,plain,
( spl183_563
<=> ! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'('fun_app$c'('inverse$',X0)),X0) )
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_563])]) ).
tff(f2115,plain,
! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'('fun_app$c'('inverse$',X0)),X0) )
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f837]) ).
tff(f837,plain,
! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'('fun_app$c'('inverse$',X0)),X0) )
| ( 0.0 = X0 ) ),
inference(ennf_transformation,[],[f501]) ).
tff(f501,axiom,
! [X0: $real] :
( ( 0.0 != X0 )
=> ( 1.0 = 'fun_app$c'('times$a'('fun_app$c'('inverse$',X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom499) ).
tff(f7831,plain,
spl183_562,
inference(avatar_split_clause,[],[f2114,f7829]) ).
tff(f7829,plain,
( spl183_562
<=> ! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'(X0),'fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_562])]) ).
tff(f2114,plain,
! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'(X0),'fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f836]) ).
tff(f836,plain,
! [X0: $real] :
( ( 1.0 = 'fun_app$c'('times$a'(X0),'fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) ),
inference(ennf_transformation,[],[f448]) ).
tff(f448,axiom,
! [X0: $real] :
( ( 0.0 != X0 )
=> ( 1.0 = 'fun_app$c'('times$a'(X0),'fun_app$c'('inverse$',X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom446) ).
tff(f7827,plain,
spl183_561,
inference(avatar_split_clause,[],[f2077,f7825]) ).
tff(f2077,plain,
! [X0: $real] :
( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f818]) ).
tff(f818,plain,
! [X0: $real] :
( ( ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) )
| ( 0.0 = X0 ) )
& ( ( 'inverse$a'('ereal$'(X0)) = 'infinity$' )
| ( 0.0 != X0 ) ) ),
inference(ennf_transformation,[],[f21]) ).
tff(f21,axiom,
! [X0: $real] :
( ( ( 0.0 != X0 )
=> ( 'inverse$a'('ereal$'(X0)) = 'ereal$'('fun_app$c'('inverse$',X0)) ) )
& ( ( 0.0 = X0 )
=> ( 'inverse$a'('ereal$'(X0)) = 'infinity$' ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom19) ).
tff(f7822,plain,
spl183_560,
inference(avatar_split_clause,[],[f2066,f7820]) ).
tff(f2066,plain,
! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'nat$'(0)) = 'inverse$a'('fps_nth$a'(X0,'nat$'(0))) ),
inference(cnf_transformation,[],[f186]) ).
tff(f186,axiom,
! [X0: 'Ereal_fps$'] : ( 'fps_nth$a'('inverse$d'(X0),'nat$'(0)) = 'inverse$a'('fps_nth$a'(X0,'nat$'(0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom184) ).
tff(f7818,plain,
spl183_559,
inference(avatar_split_clause,[],[f742,f7816]) ).
tff(f7816,plain,
( spl183_559
<=> ! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_559])]) ).
tff(f742,plain,
! [X2: $real,X0: $real,X1: $real] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f7814,plain,
spl183_558,
inference(avatar_split_clause,[],[f731,f7812]) ).
tff(f7812,plain,
( spl183_558
<=> ! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_558])]) ).
tff(f731,plain,
! [X2: $real,X0: $real,X1: $real] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f7810,plain,
spl183_557,
inference(avatar_split_clause,[],[f724,f7808]) ).
tff(f7808,plain,
( spl183_557
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_557])]) ).
tff(f724,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f7806,plain,
spl183_556,
inference(avatar_split_clause,[],[f713,f7804]) ).
tff(f7804,plain,
( spl183_556
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_556])]) ).
tff(f713,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f7735,plain,
( spl183_555
| ~ spl183_25
| ~ spl183_343 ),
inference(avatar_split_clause,[],[f6525,f5733,f3894,f7732]) ).
tff(f7732,plain,
( spl183_555
<=> ( 'one$a' = 'max$'('one$a','zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_555])]) ).
tff(f3894,plain,
( spl183_25
<=> 'fun_app$b'('less_eq$'('zero$'),'one$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_25])]) ).
tff(f5733,plain,
( spl183_343
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_343])]) ).
tff(f6525,plain,
( ( 'one$a' = 'max$'('one$a','zero$') )
| ~ spl183_25
| ~ spl183_343 ),
inference(resolution,[],[f5734,f3896]) ).
tff(f3896,plain,
( 'fun_app$b'('less_eq$'('zero$'),'one$a')
| ~ spl183_25 ),
inference(avatar_component_clause,[],[f3894]) ).
tff(f5734,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X0),X1)
| ( 'max$'(X1,X0) = X1 ) )
| ~ spl183_343 ),
inference(avatar_component_clause,[],[f5733]) ).
tff(f7718,plain,
( spl183_554
| ~ spl183_25
| ~ spl183_342 ),
inference(avatar_split_clause,[],[f6517,f5729,f3894,f7715]) ).
tff(f7715,plain,
( spl183_554
<=> ( 'one$a' = 'max$'('zero$','one$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_554])]) ).
tff(f5729,plain,
( spl183_342
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_342])]) ).
tff(f6517,plain,
( ( 'one$a' = 'max$'('zero$','one$a') )
| ~ spl183_25
| ~ spl183_342 ),
inference(resolution,[],[f5730,f3896]) ).
tff(f5730,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'(X0),X1)
| ( 'max$'(X0,X1) = X1 ) )
| ~ spl183_342 ),
inference(avatar_component_clause,[],[f5729]) ).
tff(f7616,plain,
( spl183_553
| ~ spl183_140
| ~ spl183_471 ),
inference(avatar_split_clause,[],[f7129,f7126,f4423,f7614]) ).
tff(f7614,plain,
( spl183_553
<=> ! [X2: $real,X0: 'Real_list$',X1: 'Real_list$'] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_553])]) ).
tff(f7126,plain,
( spl183_471
<=> ! [X2: $real,X0: 'Real_list$',X1: 'Real_list$'] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_471])]) ).
tff(f7129,plain,
( ! [X2: $real,X0: 'Real_list$',X1: 'Real_list$'] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'size_ereal$'('one$a')) )
| ~ spl183_140
| ~ spl183_471 ),
inference(forward_demodulation,[],[f7127,f4425]) ).
tff(f7127,plain,
( ! [X2: $real,X0: 'Real_list$',X1: 'Real_list$'] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'nat$'(0)) )
| ~ spl183_471 ),
inference(avatar_component_clause,[],[f7126]) ).
tff(f7587,plain,
( spl183_552
| ~ spl183_140
| ~ spl183_466 ),
inference(avatar_split_clause,[],[f7108,f7105,f4423,f7585]) ).
tff(f7585,plain,
( spl183_552
<=> ! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'size_ereal$'('one$a'),X1),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_552])]) ).
tff(f7105,plain,
( spl183_466
<=> ! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'nat$'(0),X1),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_466])]) ).
tff(f7108,plain,
( ! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'size_ereal$'('one$a'),X1),'size_ereal$'('one$a')) )
| ~ spl183_140
| ~ spl183_466 ),
inference(forward_demodulation,[],[f7106,f4425]) ).
tff(f7106,plain,
( ! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'nat$'(0),X1),'nat$'(0)) )
| ~ spl183_466 ),
inference(avatar_component_clause,[],[f7105]) ).
tff(f7530,plain,
( spl183_551
| ~ spl183_48
| ~ spl183_320 ),
inference(avatar_split_clause,[],[f6278,f5638,f3993,f7527]) ).
tff(f7527,plain,
( spl183_551
<=> ( -1.0 = 'fun_app$c'('inverse$',-1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_551])]) ).
tff(f3993,plain,
( spl183_48
<=> ( 1.0 = 'fun_app$c'('inverse$',1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_48])]) ).
tff(f5638,plain,
( spl183_320
<=> ! [X0: $real] : ( 'fun_app$c'('inverse$',$uminus(X0)) = $uminus('fun_app$c'('inverse$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_320])]) ).
tff(f6278,plain,
( ( -1.0 = 'fun_app$c'('inverse$',-1.0) )
| ~ spl183_48
| ~ spl183_320 ),
inference(evaluation,[],[f6255]) ).
tff(f6255,plain,
( ( $uminus(1.0) = 'fun_app$c'('inverse$',$uminus(1.0)) )
| ~ spl183_48
| ~ spl183_320 ),
inference(superposition,[],[f5639,f3995]) ).
tff(f3995,plain,
( ( 1.0 = 'fun_app$c'('inverse$',1.0) )
| ~ spl183_48 ),
inference(avatar_component_clause,[],[f3993]) ).
tff(f5639,plain,
( ! [X0: $real] : ( 'fun_app$c'('inverse$',$uminus(X0)) = $uminus('fun_app$c'('inverse$',X0)) )
| ~ spl183_320 ),
inference(avatar_component_clause,[],[f5638]) ).
tff(f7472,plain,
spl183_550,
inference(avatar_split_clause,[],[f3666,f7470]) ).
tff(f7470,plain,
( spl183_550
<=> ! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'(X0,sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_550])]) ).
tff(f3666,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'(X0,sK97(X0)) ),
inference(evaluation,[],[f3266]) ).
tff(f3266,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'times$'('infinity$','ereal$'($uminus(1.0))))
| ~ 'fun_app$b'(X0,sK97(X0)) ),
inference(definition_unfolding,[],[f2309,f2063]) ).
tff(f2309,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ~ 'fun_app$b'(X0,sK97(X0)) ),
inference(cnf_transformation,[],[f1413]) ).
tff(f1413,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
| ~ 'fun_app$b'(X0,'ereal$'(sK96(X0)))
| ~ 'fun_app$b'(X0,'infinity$') )
& ( ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X3: $real] : 'fun_app$b'(X0,'ereal$'(X3))
& 'fun_app$b'(X0,'infinity$') )
| ~ 'fun_app$b'(X0,sK97(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f1410,f1412,f1411]) ).
tff(f1411,plain,
! [X0: 'Ereal_bool_fun$'] :
( ? [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
=> ~ 'fun_app$b'(X0,'ereal$'(sK96(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1412,plain,
! [X0: 'Ereal_bool_fun$'] :
( ? [X4: 'Ereal$'] : ~ 'fun_app$b'(X0,X4)
=> ~ 'fun_app$b'(X0,sK97(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1410,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
| ~ 'fun_app$b'(X0,'infinity$') )
& ( ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X3: $real] : 'fun_app$b'(X0,'ereal$'(X3))
& 'fun_app$b'(X0,'infinity$') )
| ? [X4: 'Ereal$'] : ~ 'fun_app$b'(X0,X4) ) ),
inference(rectify,[],[f1409]) ).
tff(f1409,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
| ~ 'fun_app$b'(X0,'infinity$') )
& ( ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
& 'fun_app$b'(X0,'infinity$') )
| ? [X1: 'Ereal$'] : ~ 'fun_app$b'(X0,X1) ) ),
inference(flattening,[],[f1408]) ).
tff(f1408,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
| ~ 'fun_app$b'(X0,'infinity$') )
& ( ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
& 'fun_app$b'(X0,'infinity$') )
| ? [X1: 'Ereal$'] : ~ 'fun_app$b'(X0,X1) ) ),
inference(nnf_transformation,[],[f779]) ).
tff(f779,plain,
! [X0: 'Ereal_bool_fun$'] :
( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
<=> ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
& 'fun_app$b'(X0,'infinity$') ) ),
inference(rectify,[],[f216]) ).
tff(f216,axiom,
! [X0: 'Ereal_bool_fun$'] :
( ! [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
<=> ( 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X1: $real] : 'fun_app$b'(X0,'ereal$'(X1))
& 'fun_app$b'(X0,'infinity$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom214) ).
tff(f7468,plain,
spl183_549,
inference(avatar_split_clause,[],[f3665,f7466]) ).
tff(f7466,plain,
( spl183_549
<=> ! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'times$'('infinity$','ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_549])]) ).
tff(f3665,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'times$'('infinity$','ereal$'(-1.0))) ),
inference(evaluation,[],[f3267]) ).
tff(f3267,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'times$'('infinity$','ereal$'($uminus(1.0)))) ),
inference(definition_unfolding,[],[f2314,f2063]) ).
tff(f2314,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'uminus$'('infinity$')) ),
inference(cnf_transformation,[],[f1419]) ).
tff(f1419,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( 'fun_app$b'(X0,sK98(X0))
| ( ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
& ~ 'fun_app$b'(X0,'infinity$') ) )
& ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| 'fun_app$b'(X0,'ereal$'(sK99(X0)))
| 'fun_app$b'(X0,'infinity$')
| ! [X4: 'Ereal$'] : ~ 'fun_app$b'(X0,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98,sK99])],[f1416,f1418,f1417]) ).
tff(f1417,plain,
! [X0: 'Ereal_bool_fun$'] :
( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
=> 'fun_app$b'(X0,sK98(X0)) ),
introduced(choice_axiom,[]) ).
tff(f1418,plain,
! [X0: 'Ereal_bool_fun$'] :
( ? [X3: $real] : 'fun_app$b'(X0,'ereal$'(X3))
=> 'fun_app$b'(X0,'ereal$'(sK99(X0))) ),
introduced(choice_axiom,[]) ).
tff(f1416,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ( ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
& ~ 'fun_app$b'(X0,'infinity$') ) )
& ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X3: $real] : 'fun_app$b'(X0,'ereal$'(X3))
| 'fun_app$b'(X0,'infinity$')
| ! [X4: 'Ereal$'] : ~ 'fun_app$b'(X0,X4) ) ),
inference(rectify,[],[f1415]) ).
tff(f1415,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ( ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
& ~ 'fun_app$b'(X0,'infinity$') ) )
& ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
| 'fun_app$b'(X0,'infinity$')
| ! [X1: 'Ereal$'] : ~ 'fun_app$b'(X0,X1) ) ),
inference(flattening,[],[f1414]) ).
tff(f1414,plain,
! [X0: 'Ereal_bool_fun$'] :
( ( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
| ( ~ 'fun_app$b'(X0,'uminus$'('infinity$'))
& ! [X2: $real] : ~ 'fun_app$b'(X0,'ereal$'(X2))
& ~ 'fun_app$b'(X0,'infinity$') ) )
& ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
| 'fun_app$b'(X0,'infinity$')
| ! [X1: 'Ereal$'] : ~ 'fun_app$b'(X0,X1) ) ),
inference(nnf_transformation,[],[f780]) ).
tff(f780,plain,
! [X0: 'Ereal_bool_fun$'] :
( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
<=> ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X2: $real] : 'fun_app$b'(X0,'ereal$'(X2))
| 'fun_app$b'(X0,'infinity$') ) ),
inference(rectify,[],[f215]) ).
tff(f215,axiom,
! [X0: 'Ereal_bool_fun$'] :
( ? [X1: 'Ereal$'] : 'fun_app$b'(X0,X1)
<=> ( 'fun_app$b'(X0,'uminus$'('infinity$'))
| ? [X1: $real] : 'fun_app$b'(X0,'ereal$'(X1))
| 'fun_app$b'(X0,'infinity$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom213) ).
tff(f7464,plain,
spl183_548,
inference(avatar_split_clause,[],[f3631,f7462]) ).
tff(f7462,plain,
( spl183_548
<=> ! [X1: 'Ereal$'] :
( sP13('times$'('infinity$','ereal$'(-1.0)),X1)
| ~ 'fun_app$b'('less$'(X1),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_548])]) ).
tff(f3631,plain,
! [X1: 'Ereal$'] :
( sP13('times$'('infinity$','ereal$'(-1.0)),X1)
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(evaluation,[],[f3460]) ).
tff(f3460,plain,
! [X1: 'Ereal$'] :
( sP13('times$'('infinity$','ereal$'($uminus(1.0))),X1)
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(equality_resolution,[],[f3292]) ).
tff(f3292,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ( 'times$'('infinity$','ereal$'($uminus(1.0))) != X0 )
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(definition_unfolding,[],[f2591,f2063]) ).
tff(f2591,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ( 'uminus$'('infinity$') != X0 )
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1544]) ).
tff(f1544,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP13(X0,X1)
| ( ( ( 'uminus$'('infinity$') != X0 )
| ~ 'fun_app$b'('less$'(X1),'zero$') )
& ( ~ 'fun_app$b'('less$'(X0),'zero$')
| ( 'uminus$'('infinity$') != X1 ) )
& ~ sP12(X0,X1)
& ~ sP11(X0,X1) ) )
& ( ( ( 'uminus$'('infinity$') = X0 )
& 'fun_app$b'('less$'(X1),'zero$') )
| ( 'fun_app$b'('less$'(X0),'zero$')
& ( 'uminus$'('infinity$') = X1 ) )
| sP12(X0,X1)
| sP11(X0,X1)
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f1543]) ).
tff(f1543,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP13(X1,X0)
| ( ( ( 'uminus$'('infinity$') != X1 )
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ( 'uminus$'('infinity$') != X0 ) )
& ~ sP12(X1,X0)
& ~ sP11(X1,X0) ) )
& ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'uminus$'('infinity$') = X0 ) )
| sP12(X1,X0)
| sP11(X1,X0)
| ~ sP13(X1,X0) ) ),
inference(flattening,[],[f1542]) ).
tff(f1542,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP13(X1,X0)
| ( ( ( 'uminus$'('infinity$') != X1 )
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ~ 'fun_app$b'('less$'(X1),'zero$')
| ( 'uminus$'('infinity$') != X0 ) )
& ~ sP12(X1,X0)
& ~ sP11(X1,X0) ) )
& ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'uminus$'('infinity$') = X0 ) )
| sP12(X1,X0)
| sP11(X1,X0)
| ~ sP13(X1,X0) ) ),
inference(nnf_transformation,[],[f1205]) ).
tff(f1205,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP13(X1,X0)
<=> ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'uminus$'('infinity$') = X0 ) )
| sP12(X1,X0)
| sP11(X1,X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
tff(f7460,plain,
spl183_547,
inference(avatar_split_clause,[],[f3630,f7458]) ).
tff(f7458,plain,
( spl183_547
<=> ! [X0: 'Ereal$'] :
( sP13(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'(X0),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_547])]) ).
tff(f3630,plain,
! [X0: 'Ereal$'] :
( sP13(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(evaluation,[],[f3461]) ).
tff(f3461,plain,
! [X0: 'Ereal$'] :
( sP13(X0,'times$'('infinity$','ereal$'($uminus(1.0))))
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(equality_resolution,[],[f3293]) ).
tff(f3293,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ( 'times$'('infinity$','ereal$'($uminus(1.0))) != X1 ) ),
inference(definition_unfolding,[],[f2590,f2063]) ).
tff(f2590,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ( 'uminus$'('infinity$') != X1 ) ),
inference(cnf_transformation,[],[f1544]) ).
tff(f7456,plain,
spl183_546,
inference(avatar_split_clause,[],[f3616,f7454]) ).
tff(f7454,plain,
( spl183_546
<=> ! [X1: 'Ereal$'] :
( sP20('times$'('infinity$','ereal$'(-1.0)),X1)
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_546])]) ).
tff(f3616,plain,
! [X1: 'Ereal$'] :
( sP20('times$'('infinity$','ereal$'(-1.0)),X1)
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(evaluation,[],[f3486]) ).
tff(f3486,plain,
! [X1: 'Ereal$'] :
( sP20('times$'('infinity$','ereal$'($uminus(1.0))),X1)
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(equality_resolution,[],[f3308]) ).
tff(f3308,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ( 'times$'('infinity$','ereal$'($uminus(1.0))) != X0 )
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(definition_unfolding,[],[f2689,f2063]) ).
tff(f2689,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ( 'uminus$'('infinity$') != X0 )
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f1602,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP20(X0,X1)
| ( ( ( 'uminus$'('infinity$') != X0 )
| ~ 'fun_app$b'('less$'('zero$'),X1) )
& ( ~ 'fun_app$b'('less$'('zero$'),X0)
| ( 'uminus$'('infinity$') != X1 ) )
& ~ sP19(X0,X1)
& ~ sP18(X0,X1) ) )
& ( ( ( 'uminus$'('infinity$') = X0 )
& 'fun_app$b'('less$'('zero$'),X1) )
| ( 'fun_app$b'('less$'('zero$'),X0)
& ( 'uminus$'('infinity$') = X1 ) )
| sP19(X0,X1)
| sP18(X0,X1)
| ~ sP20(X0,X1) ) ),
inference(rectify,[],[f1601]) ).
tff(f1601,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP20(X1,X0)
| ( ( ( 'uminus$'('infinity$') != X1 )
| ~ 'fun_app$b'('less$'('zero$'),X0) )
& ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ( 'uminus$'('infinity$') != X0 ) )
& ~ sP19(X1,X0)
& ~ sP18(X1,X0) ) )
& ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'uminus$'('infinity$') = X0 ) )
| sP19(X1,X0)
| sP18(X1,X0)
| ~ sP20(X1,X0) ) ),
inference(flattening,[],[f1600]) ).
tff(f1600,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP20(X1,X0)
| ( ( ( 'uminus$'('infinity$') != X1 )
| ~ 'fun_app$b'('less$'('zero$'),X0) )
& ( ~ 'fun_app$b'('less$'('zero$'),X1)
| ( 'uminus$'('infinity$') != X0 ) )
& ~ sP19(X1,X0)
& ~ sP18(X1,X0) ) )
& ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'uminus$'('infinity$') = X0 ) )
| sP19(X1,X0)
| sP18(X1,X0)
| ~ sP20(X1,X0) ) ),
inference(nnf_transformation,[],[f1217]) ).
tff(f7435,plain,
spl183_545,
inference(avatar_split_clause,[],[f3615,f7433]) ).
tff(f7433,plain,
( spl183_545
<=> ! [X0: 'Ereal$'] :
( sP20(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_545])]) ).
tff(f3615,plain,
! [X0: 'Ereal$'] :
( sP20(X0,'times$'('infinity$','ereal$'(-1.0)))
| ~ 'fun_app$b'('less$'('zero$'),X0) ),
inference(evaluation,[],[f3487]) ).
tff(f3487,plain,
! [X0: 'Ereal$'] :
( sP20(X0,'times$'('infinity$','ereal$'($uminus(1.0))))
| ~ 'fun_app$b'('less$'('zero$'),X0) ),
inference(equality_resolution,[],[f3309]) ).
tff(f3309,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ( 'times$'('infinity$','ereal$'($uminus(1.0))) != X1 ) ),
inference(definition_unfolding,[],[f2688,f2063]) ).
tff(f2688,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ( 'uminus$'('infinity$') != X1 ) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f7431,plain,
spl183_544,
inference(avatar_split_clause,[],[f3599,f7429]) ).
tff(f7429,plain,
( spl183_544
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_544])]) ).
tff(f3599,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP43(X0,X1,X2) ),
inference(evaluation,[],[f3319]) ).
tff(f3319,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP43(X0,X1,X2) ),
inference(definition_unfolding,[],[f2948,f2063]) ).
tff(f2948,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f1699,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP43(X0,X1,X2) ),
inference(rectify,[],[f1698]) ).
tff(f1698,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP43(X2,X1,X0) ),
inference(nnf_transformation,[],[f1252]) ).
tff(f1252,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP43(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP43])]) ).
tff(f7427,plain,
spl183_543,
inference(avatar_split_clause,[],[f3598,f7425]) ).
tff(f7425,plain,
( spl183_543
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_543])]) ).
tff(f3598,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP43(X0,X1,X2) ),
inference(evaluation,[],[f3320]) ).
tff(f3320,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP43(X0,X1,X2) ),
inference(definition_unfolding,[],[f2947,f2063]) ).
tff(f2947,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f7423,plain,
spl183_542,
inference(avatar_split_clause,[],[f3597,f7421]) ).
tff(f7421,plain,
( spl183_542
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_542])]) ).
tff(f3597,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP42(X0,X1,X2) ),
inference(evaluation,[],[f3321]) ).
tff(f3321,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP42(X0,X1,X2) ),
inference(definition_unfolding,[],[f2951,f2063]) ).
tff(f2951,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP42(X0,X1,X2) ),
inference(cnf_transformation,[],[f1701]) ).
tff(f1701,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP42(X0,X1,X2) ),
inference(rectify,[],[f1700]) ).
tff(f1700,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP42(X2,X1,X0) ),
inference(nnf_transformation,[],[f1251]) ).
tff(f1251,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP42(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
tff(f7419,plain,
spl183_541,
inference(avatar_split_clause,[],[f3596,f7417]) ).
tff(f7417,plain,
( spl183_541
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_541])]) ).
tff(f3596,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP42(X0,X1,X2) ),
inference(evaluation,[],[f3322]) ).
tff(f3322,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP42(X0,X1,X2) ),
inference(definition_unfolding,[],[f2949,f2063]) ).
tff(f2949,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP42(X0,X1,X2) ),
inference(cnf_transformation,[],[f1701]) ).
tff(f7415,plain,
spl183_540,
inference(avatar_split_clause,[],[f3595,f7413]) ).
tff(f7413,plain,
( spl183_540
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_540])]) ).
tff(f3595,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP39(X0,X1,X2) ),
inference(evaluation,[],[f3323]) ).
tff(f3323,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP39(X0,X1,X2) ),
inference(definition_unfolding,[],[f2958,f2063]) ).
tff(f2958,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f7411,plain,
spl183_539,
inference(avatar_split_clause,[],[f3594,f7409]) ).
tff(f7409,plain,
( spl183_539
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_539])]) ).
tff(f3594,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP38(X0,X1,X2) ),
inference(evaluation,[],[f3324]) ).
tff(f3324,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP38(X0,X1,X2) ),
inference(definition_unfolding,[],[f2963,f2063]) ).
tff(f2963,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1715]) ).
tff(f7407,plain,
spl183_538,
inference(avatar_split_clause,[],[f3587,f7405]) ).
tff(f7405,plain,
( spl183_538
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP49(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_538])]) ).
tff(f3587,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP49(X0,X1,X2) ),
inference(evaluation,[],[f3331]) ).
tff(f3331,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP49(X0,X1,X2) ),
inference(definition_unfolding,[],[f2994,f2063]) ).
tff(f2994,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP49(X0,X1,X2) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f1733,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( tltrue = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP49(X0,X1,X2) ),
inference(rectify,[],[f1732]) ).
tff(f1732,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( tltrue = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP49(X2,X1,X0) ),
inference(nnf_transformation,[],[f1259]) ).
tff(f1259,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( tltrue = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP49(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP49])]) ).
tff(f7403,plain,
spl183_537,
inference(avatar_split_clause,[],[f3586,f7401]) ).
tff(f7401,plain,
( spl183_537
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_537])]) ).
tff(f3586,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP48(X0,X1,X2) ),
inference(evaluation,[],[f3332]) ).
tff(f3332,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP48(X0,X1,X2) ),
inference(definition_unfolding,[],[f2997,f2063]) ).
tff(f2997,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1737]) ).
tff(f7399,plain,
spl183_536,
inference(avatar_split_clause,[],[f3585,f7397]) ).
tff(f7397,plain,
( spl183_536
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_536])]) ).
tff(f3585,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP46(X0,X1,X2) ),
inference(evaluation,[],[f3333]) ).
tff(f3333,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP46(X0,X1,X2) ),
inference(definition_unfolding,[],[f3004,f2063]) ).
tff(f3004,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1745]) ).
tff(f1745,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( tltrue != X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( sK151(X0,X1,X2) = X2 ) )
| ~ sP46(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f1743,f1744]) ).
tff(f1744,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ( tltrue != X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( X2 = X3 ) )
=> ( ( tltrue != X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( sK151(X0,X1,X2) = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1743,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ( tltrue != X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( X2 = X3 ) )
| ~ sP46(X0,X1,X2) ),
inference(rectify,[],[f1742]) ).
tff(f1742,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: 'Ereal$'] :
( ( tltrue != X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( X0 = X5 ) )
| ~ sP46(X2,X1,X0) ),
inference(nnf_transformation,[],[f1256]) ).
tff(f1256,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: 'Ereal$'] :
( ( tltrue != X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( X0 = X5 ) )
| ~ sP46(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP46])]) ).
tff(f7395,plain,
spl183_535,
inference(avatar_split_clause,[],[f3584,f7393]) ).
tff(f7393,plain,
( spl183_535
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP75(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_535])]) ).
tff(f3584,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP75(X0,X1,X2) ),
inference(evaluation,[],[f3334]) ).
tff(f3334,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP75(X0,X1,X2) ),
inference(definition_unfolding,[],[f3016,f2063]) ).
tff(f3016,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP75(X0,X1,X2) ),
inference(cnf_transformation,[],[f1757]) ).
tff(f1757,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP75(X0,X1,X2) ),
inference(rectify,[],[f1756]) ).
tff(f1756,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP75(X2,X1,X0) ),
inference(nnf_transformation,[],[f1286]) ).
tff(f1286,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP75(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP75])]) ).
tff(f7391,plain,
spl183_534,
inference(avatar_split_clause,[],[f3583,f7389]) ).
tff(f7389,plain,
( spl183_534
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP75(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_534])]) ).
tff(f3583,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP75(X0,X1,X2) ),
inference(evaluation,[],[f3335]) ).
tff(f3335,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP75(X0,X1,X2) ),
inference(definition_unfolding,[],[f3015,f2063]) ).
tff(f3015,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP75(X0,X1,X2) ),
inference(cnf_transformation,[],[f1757]) ).
tff(f7387,plain,
spl183_533,
inference(avatar_split_clause,[],[f3582,f7385]) ).
tff(f7385,plain,
( spl183_533
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP74(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_533])]) ).
tff(f3582,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP74(X0,X1,X2) ),
inference(evaluation,[],[f3336]) ).
tff(f3336,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP74(X0,X1,X2) ),
inference(definition_unfolding,[],[f3019,f2063]) ).
tff(f3019,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP74(X0,X1,X2) ),
inference(cnf_transformation,[],[f1761]) ).
tff(f7383,plain,
spl183_532,
inference(avatar_split_clause,[],[f3581,f7381]) ).
tff(f7381,plain,
( spl183_532
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP74(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_532])]) ).
tff(f3581,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP74(X0,X1,X2) ),
inference(evaluation,[],[f3337]) ).
tff(f3337,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP74(X0,X1,X2) ),
inference(definition_unfolding,[],[f3018,f2063]) ).
tff(f3018,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP74(X0,X1,X2) ),
inference(cnf_transformation,[],[f1761]) ).
tff(f7379,plain,
spl183_531,
inference(avatar_split_clause,[],[f3580,f7377]) ).
tff(f7377,plain,
( spl183_531
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP73(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_531])]) ).
tff(f3580,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP73(X0,X1,X2) ),
inference(evaluation,[],[f3338]) ).
tff(f3338,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP73(X0,X1,X2) ),
inference(definition_unfolding,[],[f3023,f2063]) ).
tff(f3023,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP73(X0,X1,X2) ),
inference(cnf_transformation,[],[f1763]) ).
tff(f1763,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP73(X0,X1,X2) ),
inference(rectify,[],[f1762]) ).
tff(f1762,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP73(X2,X1,X0) ),
inference(nnf_transformation,[],[f1284]) ).
tff(f1284,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP73(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP73])]) ).
tff(f7375,plain,
spl183_530,
inference(avatar_split_clause,[],[f3579,f7373]) ).
tff(f7373,plain,
( spl183_530
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP73(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_530])]) ).
tff(f3579,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP73(X0,X1,X2) ),
inference(evaluation,[],[f3339]) ).
tff(f3339,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP73(X0,X1,X2) ),
inference(definition_unfolding,[],[f3021,f2063]) ).
tff(f3021,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP73(X0,X1,X2) ),
inference(cnf_transformation,[],[f1763]) ).
tff(f7371,plain,
spl183_529,
inference(avatar_split_clause,[],[f3578,f7369]) ).
tff(f7369,plain,
( spl183_529
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP72(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_529])]) ).
tff(f3578,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP72(X0,X1,X2) ),
inference(evaluation,[],[f3340]) ).
tff(f3340,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP72(X0,X1,X2) ),
inference(definition_unfolding,[],[f3024,f2063]) ).
tff(f3024,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP72(X0,X1,X2) ),
inference(cnf_transformation,[],[f1765]) ).
tff(f1765,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X2 ) )
| ~ sP72(X0,X1,X2) ),
inference(rectify,[],[f1764]) ).
tff(f1764,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP72(X2,X1,X0) ),
inference(nnf_transformation,[],[f1283]) ).
tff(f1283,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP72(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP72])]) ).
tff(f7367,plain,
spl183_528,
inference(avatar_split_clause,[],[f3577,f7365]) ).
tff(f7365,plain,
( spl183_528
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP71(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_528])]) ).
tff(f3577,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP71(X0,X1,X2) ),
inference(evaluation,[],[f3341]) ).
tff(f3341,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP71(X0,X1,X2) ),
inference(definition_unfolding,[],[f3027,f2063]) ).
tff(f3027,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP71(X0,X1,X2) ),
inference(cnf_transformation,[],[f1769]) ).
tff(f7363,plain,
spl183_527,
inference(avatar_split_clause,[],[f3576,f7361]) ).
tff(f7361,plain,
( spl183_527
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP70(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_527])]) ).
tff(f3576,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP70(X0,X1,X2) ),
inference(evaluation,[],[f3342]) ).
tff(f3342,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP70(X0,X1,X2) ),
inference(definition_unfolding,[],[f3032,f2063]) ).
tff(f3032,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP70(X0,X1,X2) ),
inference(cnf_transformation,[],[f1773]) ).
tff(f7359,plain,
spl183_526,
inference(avatar_split_clause,[],[f3575,f7357]) ).
tff(f7357,plain,
( spl183_526
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP70(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_526])]) ).
tff(f3575,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP70(X0,X1,X2) ),
inference(evaluation,[],[f3343]) ).
tff(f3343,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP70(X0,X1,X2) ),
inference(definition_unfolding,[],[f3030,f2063]) ).
tff(f3030,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP70(X0,X1,X2) ),
inference(cnf_transformation,[],[f1773]) ).
tff(f7355,plain,
spl183_525,
inference(avatar_split_clause,[],[f3574,f7353]) ).
tff(f7353,plain,
( spl183_525
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP69(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_525])]) ).
tff(f3574,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP69(X0,X1,X2) ),
inference(evaluation,[],[f3344]) ).
tff(f3344,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP69(X0,X1,X2) ),
inference(definition_unfolding,[],[f3033,f2063]) ).
tff(f3033,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP69(X0,X1,X2) ),
inference(cnf_transformation,[],[f1777]) ).
tff(f7351,plain,
spl183_524,
inference(avatar_split_clause,[],[f3573,f7349]) ).
tff(f7349,plain,
( spl183_524
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP68(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_524])]) ).
tff(f3573,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X2 )
| ~ sP68(X0,X1,X2) ),
inference(evaluation,[],[f3345]) ).
tff(f3345,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X2 )
| ~ sP68(X0,X1,X2) ),
inference(definition_unfolding,[],[f3036,f2063]) ).
tff(f3036,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X2 )
| ~ sP68(X0,X1,X2) ),
inference(cnf_transformation,[],[f1781]) ).
tff(f7347,plain,
spl183_523,
inference(avatar_split_clause,[],[f3572,f7345]) ).
tff(f7345,plain,
( spl183_523
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP67(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_523])]) ).
tff(f3572,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP67(X0,X1,X2) ),
inference(evaluation,[],[f3346]) ).
tff(f3346,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP67(X0,X1,X2) ),
inference(definition_unfolding,[],[f3041,f2063]) ).
tff(f3041,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP67(X0,X1,X2) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f1783,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP67(X0,X1,X2) ),
inference(rectify,[],[f1782]) ).
tff(f1782,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP67(X2,X1,X0) ),
inference(nnf_transformation,[],[f1278]) ).
tff(f1278,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP67(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP67])]) ).
tff(f7343,plain,
spl183_522,
inference(avatar_split_clause,[],[f3571,f7341]) ).
tff(f7341,plain,
( spl183_522
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP67(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_522])]) ).
tff(f3571,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP67(X0,X1,X2) ),
inference(evaluation,[],[f3347]) ).
tff(f3347,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP67(X0,X1,X2) ),
inference(definition_unfolding,[],[f3040,f2063]) ).
tff(f3040,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP67(X0,X1,X2) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f7339,plain,
spl183_521,
inference(avatar_split_clause,[],[f3570,f7337]) ).
tff(f7337,plain,
( spl183_521
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP66(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_521])]) ).
tff(f3570,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP66(X0,X1,X2) ),
inference(evaluation,[],[f3348]) ).
tff(f3348,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP66(X0,X1,X2) ),
inference(definition_unfolding,[],[f3043,f2063]) ).
tff(f3043,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP66(X0,X1,X2) ),
inference(cnf_transformation,[],[f1785]) ).
tff(f1785,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP66(X0,X1,X2) ),
inference(rectify,[],[f1784]) ).
tff(f1784,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP66(X2,X1,X0) ),
inference(nnf_transformation,[],[f1277]) ).
tff(f1277,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP66(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP66])]) ).
tff(f7335,plain,
spl183_520,
inference(avatar_split_clause,[],[f3569,f7333]) ).
tff(f7333,plain,
( spl183_520
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP65(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_520])]) ).
tff(f3569,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP65(X0,X1,X2) ),
inference(evaluation,[],[f3349]) ).
tff(f3349,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP65(X0,X1,X2) ),
inference(definition_unfolding,[],[f3046,f2063]) ).
tff(f3046,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP65(X0,X1,X2) ),
inference(cnf_transformation,[],[f1789]) ).
tff(f7331,plain,
spl183_519,
inference(avatar_split_clause,[],[f3568,f7329]) ).
tff(f7329,plain,
( spl183_519
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP64(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_519])]) ).
tff(f3568,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP64(X0,X1,X2) ),
inference(evaluation,[],[f3350]) ).
tff(f3350,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP64(X0,X1,X2) ),
inference(definition_unfolding,[],[f3050,f2063]) ).
tff(f3050,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP64(X0,X1,X2) ),
inference(cnf_transformation,[],[f1791]) ).
tff(f1791,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP64(X0,X1,X2) ),
inference(rectify,[],[f1790]) ).
tff(f1790,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP64(X2,X1,X0) ),
inference(nnf_transformation,[],[f1275]) ).
tff(f1275,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP64(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP64])]) ).
tff(f7327,plain,
spl183_518,
inference(avatar_split_clause,[],[f3567,f7325]) ).
tff(f7325,plain,
( spl183_518
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP61(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_518])]) ).
tff(f3567,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP61(X0,X1,X2) ),
inference(evaluation,[],[f3351]) ).
tff(f3351,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP61(X0,X1,X2) ),
inference(definition_unfolding,[],[f3059,f2063]) ).
tff(f3059,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP61(X0,X1,X2) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f7323,plain,
spl183_517,
inference(avatar_split_clause,[],[f3566,f7321]) ).
tff(f7321,plain,
( spl183_517
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP58(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_517])]) ).
tff(f3566,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP58(X0,X1,X2) ),
inference(evaluation,[],[f3352]) ).
tff(f3352,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP58(X0,X1,X2) ),
inference(definition_unfolding,[],[f3068,f2063]) ).
tff(f3068,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP58(X0,X1,X2) ),
inference(cnf_transformation,[],[f1813]) ).
tff(f7319,plain,
spl183_516,
inference(avatar_split_clause,[],[f3565,f7317]) ).
tff(f7317,plain,
( spl183_516
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP58(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_516])]) ).
tff(f3565,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP58(X0,X1,X2) ),
inference(evaluation,[],[f3353]) ).
tff(f3353,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP58(X0,X1,X2) ),
inference(definition_unfolding,[],[f3067,f2063]) ).
tff(f3067,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP58(X0,X1,X2) ),
inference(cnf_transformation,[],[f1813]) ).
tff(f7315,plain,
spl183_515,
inference(avatar_split_clause,[],[f3564,f7313]) ).
tff(f7313,plain,
( spl183_515
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP57(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_515])]) ).
tff(f3564,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP57(X0,X1,X2) ),
inference(evaluation,[],[f3354]) ).
tff(f3354,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP57(X0,X1,X2) ),
inference(definition_unfolding,[],[f3070,f2063]) ).
tff(f3070,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP57(X0,X1,X2) ),
inference(cnf_transformation,[],[f1817]) ).
tff(f7311,plain,
spl183_514,
inference(avatar_split_clause,[],[f3563,f7309]) ).
tff(f7309,plain,
( spl183_514
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_514])]) ).
tff(f3563,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP56(X0,X1,X2) ),
inference(evaluation,[],[f3355]) ).
tff(f3355,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP56(X0,X1,X2) ),
inference(definition_unfolding,[],[f3073,f2063]) ).
tff(f3073,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f1821]) ).
tff(f7307,plain,
spl183_513,
inference(avatar_split_clause,[],[f3562,f7305]) ).
tff(f7305,plain,
( spl183_513
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP55(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_513])]) ).
tff(f3562,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP55(X0,X1,X2) ),
inference(evaluation,[],[f3356]) ).
tff(f3356,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP55(X0,X1,X2) ),
inference(definition_unfolding,[],[f3077,f2063]) ).
tff(f3077,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP55(X0,X1,X2) ),
inference(cnf_transformation,[],[f1825]) ).
tff(f7303,plain,
spl183_512,
inference(avatar_split_clause,[],[f3561,f7301]) ).
tff(f7301,plain,
( spl183_512
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP52(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_512])]) ).
tff(f3561,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP52(X0,X1,X2) ),
inference(evaluation,[],[f3357]) ).
tff(f3357,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP52(X0,X1,X2) ),
inference(definition_unfolding,[],[f3086,f2063]) ).
tff(f3086,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP52(X0,X1,X2) ),
inference(cnf_transformation,[],[f1837]) ).
tff(f7299,plain,
spl183_511,
inference(avatar_split_clause,[],[f3211,f7296]) ).
tff(f3211,plain,
'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(sK182)),
inference(cnf_transformation,[],[f1907]) ).
tff(f1907,plain,
( 'fun_app$b'('less$'('ereal$'(sK182)),'ereal$'('c$a'))
& 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(sK182)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f65,f1906]) ).
tff(f1906,plain,
( ? [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'('c$a'))
& 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(X0)) )
=> ( 'fun_app$b'('less$'('ereal$'(sK182)),'ereal$'('c$a'))
& 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(sK182)) ) ),
introduced(choice_axiom,[]) ).
tff(f65,axiom,
? [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'('c$a'))
& 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom63) ).
tff(f7294,plain,
spl183_510,
inference(avatar_split_clause,[],[f3176,f7292]) ).
tff(f7292,plain,
( spl183_510
<=> ! [X2: $real,X0: $real,X1: $real] :
( sP79(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_510])]) ).
tff(f3176,plain,
! [X2: $real,X0: $real,X1: $real] :
( sP79(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0.0) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f1894,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( sP79(X0,X1,X2)
| ( ( ~ $less(X1,X0)
| ~ $less(X2,0.0) )
& ( ~ $less(X0,X1)
| ~ $less(0.0,X2) ) ) )
& ( ( $less(X1,X0)
& $less(X2,0.0) )
| ( $less(X0,X1)
& $less(0.0,X2) )
| ~ sP79(X0,X1,X2) ) ),
inference(rectify,[],[f1893]) ).
tff(f1893,plain,
! [X1: $real,X2: $real,X0: $real] :
( ( sP79(X1,X2,X0)
| ( ( ~ $less(X2,X1)
| ~ $less(X0,0.0) )
& ( ~ $less(X1,X2)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(X2,X1)
& $less(X0,0.0) )
| ( $less(X1,X2)
& $less(0.0,X0) )
| ~ sP79(X1,X2,X0) ) ),
inference(flattening,[],[f1892]) ).
tff(f1892,plain,
! [X1: $real,X2: $real,X0: $real] :
( ( sP79(X1,X2,X0)
| ( ( ~ $less(X2,X1)
| ~ $less(X0,0.0) )
& ( ~ $less(X1,X2)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(X2,X1)
& $less(X0,0.0) )
| ( $less(X1,X2)
& $less(0.0,X0) )
| ~ sP79(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f1294]) ).
tff(f1294,plain,
! [X1: $real,X2: $real,X0: $real] :
( sP79(X1,X2,X0)
<=> ( ( $less(X2,X1)
& $less(X0,0.0) )
| ( $less(X1,X2)
& $less(0.0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP79])]) ).
tff(f7290,plain,
spl183_509,
inference(avatar_split_clause,[],[f3175,f7288]) ).
tff(f7288,plain,
( spl183_509
<=> ! [X2: $real,X0: $real,X1: $real] :
( sP79(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0.0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_509])]) ).
tff(f3175,plain,
! [X2: $real,X0: $real,X1: $real] :
( sP79(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0.0,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f7286,plain,
spl183_508,
inference(avatar_split_clause,[],[f3174,f7284]) ).
tff(f7284,plain,
( spl183_508
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP79(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_508])]) ).
tff(f3174,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP79(X0,X1,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f7282,plain,
spl183_507,
inference(avatar_split_clause,[],[f3173,f7280]) ).
tff(f7280,plain,
( spl183_507
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(0.0,X2)
| ~ sP79(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_507])]) ).
tff(f3173,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(0.0,X2)
| ~ sP79(X0,X1,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f7278,plain,
spl183_506,
inference(avatar_split_clause,[],[f3172,f7276]) ).
tff(f7276,plain,
( spl183_506
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(X0,X1)
| ~ sP79(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_506])]) ).
tff(f3172,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(X0,X1)
| ~ sP79(X0,X1,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f7274,plain,
( spl183_505
| ~ spl183_231
| ~ spl183_409 ),
inference(avatar_split_clause,[],[f6801,f6007,f4794,f7271]) ).
tff(f7271,plain,
( spl183_505
<=> sP26('ereal$'(-1.0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_505])]) ).
tff(f6007,plain,
( spl183_409
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X1,X0)
| ~ 'fun_app$b'('less$'('times$'(X0,X1)),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_409])]) ).
tff(f6801,plain,
( sP26('ereal$'(-1.0),'infinity$')
| ~ spl183_231
| ~ spl183_409 ),
inference(resolution,[],[f6008,f4796]) ).
tff(f6008,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
| sP26(X1,X0) )
| ~ spl183_409 ),
inference(avatar_component_clause,[],[f6007]) ).
tff(f7269,plain,
spl183_504,
inference(avatar_split_clause,[],[f3171,f7267]) ).
tff(f7267,plain,
( spl183_504
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(0.0,X2)
| ~ sP79(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_504])]) ).
tff(f3171,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(0.0,X2)
| ~ sP79(X0,X1,X2) ),
inference(cnf_transformation,[],[f1894]) ).
tff(f7265,plain,
spl183_503,
inference(avatar_split_clause,[],[f3168,f7263]) ).
tff(f7263,plain,
( spl183_503
<=> ! [X2: $real,X0: $real,X1: $real] :
( sP78(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_503])]) ).
tff(f3168,plain,
! [X2: $real,X0: $real,X1: $real] :
( sP78(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0.0) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f1890,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( sP78(X0,X1,X2)
| ( ( ~ $less(X1,X0)
| ~ $less(X2,0.0) )
& ( ~ $less(X0,X1)
| ~ $less(0.0,X2) ) ) )
& ( ( $less(X1,X0)
& $less(X2,0.0) )
| ( $less(X0,X1)
& $less(0.0,X2) )
| ~ sP78(X0,X1,X2) ) ),
inference(rectify,[],[f1889]) ).
tff(f1889,plain,
! [X0: $real,X2: $real,X1: $real] :
( ( sP78(X0,X2,X1)
| ( ( ~ $less(X2,X0)
| ~ $less(X1,0.0) )
& ( ~ $less(X0,X2)
| ~ $less(0.0,X1) ) ) )
& ( ( $less(X2,X0)
& $less(X1,0.0) )
| ( $less(X0,X2)
& $less(0.0,X1) )
| ~ sP78(X0,X2,X1) ) ),
inference(flattening,[],[f1888]) ).
tff(f1888,plain,
! [X0: $real,X2: $real,X1: $real] :
( ( sP78(X0,X2,X1)
| ( ( ~ $less(X2,X0)
| ~ $less(X1,0.0) )
& ( ~ $less(X0,X2)
| ~ $less(0.0,X1) ) ) )
& ( ( $less(X2,X0)
& $less(X1,0.0) )
| ( $less(X0,X2)
& $less(0.0,X1) )
| ~ sP78(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f1292]) ).
tff(f1292,plain,
! [X0: $real,X2: $real,X1: $real] :
( sP78(X0,X2,X1)
<=> ( ( $less(X2,X0)
& $less(X1,0.0) )
| ( $less(X0,X2)
& $less(0.0,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP78])]) ).
tff(f7261,plain,
spl183_502,
inference(avatar_split_clause,[],[f3167,f7259]) ).
tff(f7259,plain,
( spl183_502
<=> ! [X2: $real,X0: $real,X1: $real] :
( sP78(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0.0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_502])]) ).
tff(f3167,plain,
! [X2: $real,X0: $real,X1: $real] :
( sP78(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0.0,X2) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f7257,plain,
spl183_501,
inference(avatar_split_clause,[],[f3166,f7255]) ).
tff(f7255,plain,
( spl183_501
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP78(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_501])]) ).
tff(f3166,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP78(X0,X1,X2) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f7253,plain,
spl183_500,
inference(avatar_split_clause,[],[f3165,f7251]) ).
tff(f7251,plain,
( spl183_500
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(0.0,X2)
| ~ sP78(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_500])]) ).
tff(f3165,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X0)
| $less(0.0,X2)
| ~ sP78(X0,X1,X2) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f7249,plain,
spl183_499,
inference(avatar_split_clause,[],[f3164,f7247]) ).
tff(f7247,plain,
( spl183_499
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(X0,X1)
| ~ sP78(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_499])]) ).
tff(f3164,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(X0,X1)
| ~ sP78(X0,X1,X2) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f7245,plain,
spl183_498,
inference(avatar_split_clause,[],[f3163,f7243]) ).
tff(f7243,plain,
( spl183_498
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(0.0,X2)
| ~ sP78(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_498])]) ).
tff(f3163,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X2,0.0)
| $less(0.0,X2)
| ~ sP78(X0,X1,X2) ),
inference(cnf_transformation,[],[f1890]) ).
tff(f7241,plain,
spl183_497,
inference(avatar_split_clause,[],[f3142,f7239]) ).
tff(f7239,plain,
( spl183_497
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP77(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_497])]) ).
tff(f3142,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP77(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f1874,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( sP77(X0,X1,X2)
| ( ( ~ $less(X1,X0)
| ~ $less(X2,0) )
& ( ~ $less(X0,X1)
| ~ $less(0,X2) ) ) )
& ( ( $less(X1,X0)
& $less(X2,0) )
| ( $less(X0,X1)
& $less(0,X2) )
| ~ sP77(X0,X1,X2) ) ),
inference(rectify,[],[f1873]) ).
tff(f1873,plain,
! [X1: $int,X2: $int,X0: $int] :
( ( sP77(X1,X2,X0)
| ( ( ~ $less(X2,X1)
| ~ $less(X0,0) )
& ( ~ $less(X1,X2)
| ~ $less(0,X0) ) ) )
& ( ( $less(X2,X1)
& $less(X0,0) )
| ( $less(X1,X2)
& $less(0,X0) )
| ~ sP77(X1,X2,X0) ) ),
inference(flattening,[],[f1872]) ).
tff(f1872,plain,
! [X1: $int,X2: $int,X0: $int] :
( ( sP77(X1,X2,X0)
| ( ( ~ $less(X2,X1)
| ~ $less(X0,0) )
& ( ~ $less(X1,X2)
| ~ $less(0,X0) ) ) )
& ( ( $less(X2,X1)
& $less(X0,0) )
| ( $less(X1,X2)
& $less(0,X0) )
| ~ sP77(X1,X2,X0) ) ),
inference(nnf_transformation,[],[f1290]) ).
tff(f7237,plain,
spl183_496,
inference(avatar_split_clause,[],[f3141,f7235]) ).
tff(f7235,plain,
( spl183_496
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP77(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_496])]) ).
tff(f3141,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP77(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0,X2) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7233,plain,
spl183_495,
inference(avatar_split_clause,[],[f3140,f7231]) ).
tff(f7231,plain,
( spl183_495
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP77(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_495])]) ).
tff(f3140,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP77(X0,X1,X2) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7229,plain,
( spl183_494
| ~ spl183_227
| ~ spl183_407 ),
inference(avatar_split_clause,[],[f6782,f5999,f4777,f7226]) ).
tff(f7226,plain,
( spl183_494
<=> sP25('ereal$'(-1.0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_494])]) ).
tff(f4777,plain,
( spl183_227
<=> ! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('times$'('infinity$','ereal$'(-1.0))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_227])]) ).
tff(f5999,plain,
( spl183_407
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X1,X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_407])]) ).
tff(f6782,plain,
( sP25('ereal$'(-1.0),'infinity$')
| ~ spl183_227
| ~ spl183_407 ),
inference(resolution,[],[f6000,f4778]) ).
tff(f4778,plain,
( ! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('times$'('infinity$','ereal$'(-1.0))),X0)
| ~ spl183_227 ),
inference(avatar_component_clause,[],[f4777]) ).
tff(f6000,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
| sP25(X1,X0) )
| ~ spl183_407 ),
inference(avatar_component_clause,[],[f5999]) ).
tff(f7224,plain,
spl183_493,
inference(avatar_split_clause,[],[f3139,f7222]) ).
tff(f7222,plain,
( spl183_493
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(0,X2)
| ~ sP77(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_493])]) ).
tff(f3139,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(0,X2)
| ~ sP77(X0,X1,X2) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7220,plain,
spl183_492,
inference(avatar_split_clause,[],[f3138,f7218]) ).
tff(f7218,plain,
( spl183_492
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(X0,X1)
| ~ sP77(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_492])]) ).
tff(f3138,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(X0,X1)
| ~ sP77(X0,X1,X2) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7216,plain,
spl183_491,
inference(avatar_split_clause,[],[f3137,f7214]) ).
tff(f7214,plain,
( spl183_491
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(0,X2)
| ~ sP77(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_491])]) ).
tff(f3137,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(0,X2)
| ~ sP77(X0,X1,X2) ),
inference(cnf_transformation,[],[f1874]) ).
tff(f7212,plain,
spl183_490,
inference(avatar_split_clause,[],[f3134,f7210]) ).
tff(f7210,plain,
( spl183_490
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_490])]) ).
tff(f3134,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X1,X2)
| ~ $less(X1,X0)
| ~ $less(X2,0) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f1870,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( sP76(X0,X1,X2)
| ( ( ~ $less(X1,X0)
| ~ $less(X2,0) )
& ( ~ $less(X0,X1)
| ~ $less(0,X2) ) ) )
& ( ( $less(X1,X0)
& $less(X2,0) )
| ( $less(X0,X1)
& $less(0,X2) )
| ~ sP76(X0,X1,X2) ) ),
inference(rectify,[],[f1869]) ).
tff(f1869,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( sP76(X0,X2,X1)
| ( ( ~ $less(X2,X0)
| ~ $less(X1,0) )
& ( ~ $less(X0,X2)
| ~ $less(0,X1) ) ) )
& ( ( $less(X2,X0)
& $less(X1,0) )
| ( $less(X0,X2)
& $less(0,X1) )
| ~ sP76(X0,X2,X1) ) ),
inference(flattening,[],[f1868]) ).
tff(f1868,plain,
! [X0: $int,X2: $int,X1: $int] :
( ( sP76(X0,X2,X1)
| ( ( ~ $less(X2,X0)
| ~ $less(X1,0) )
& ( ~ $less(X0,X2)
| ~ $less(0,X1) ) ) )
& ( ( $less(X2,X0)
& $less(X1,0) )
| ( $less(X0,X2)
& $less(0,X1) )
| ~ sP76(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f1288]) ).
tff(f7208,plain,
spl183_489,
inference(avatar_split_clause,[],[f3133,f7206]) ).
tff(f7206,plain,
( spl183_489
<=> ! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_489])]) ).
tff(f3133,plain,
! [X2: $int,X0: $int,X1: $int] :
( sP76(X0,X1,X2)
| ~ $less(X0,X1)
| ~ $less(0,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7204,plain,
spl183_488,
inference(avatar_split_clause,[],[f3132,f7202]) ).
tff(f7202,plain,
( spl183_488
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP76(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_488])]) ).
tff(f3132,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ~ sP76(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7200,plain,
spl183_487,
inference(avatar_split_clause,[],[f3131,f7198]) ).
tff(f7198,plain,
( spl183_487
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(0,X2)
| ~ sP76(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_487])]) ).
tff(f3131,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X0)
| $less(0,X2)
| ~ sP76(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7196,plain,
spl183_486,
inference(avatar_split_clause,[],[f3130,f7194]) ).
tff(f7194,plain,
( spl183_486
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(X0,X1)
| ~ sP76(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_486])]) ).
tff(f3130,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(X0,X1)
| ~ sP76(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7192,plain,
spl183_485,
inference(avatar_split_clause,[],[f3129,f7190]) ).
tff(f7190,plain,
( spl183_485
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(0,X2)
| ~ sP76(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_485])]) ).
tff(f3129,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X2,0)
| $less(0,X2)
| ~ sP76(X0,X1,X2) ),
inference(cnf_transformation,[],[f1870]) ).
tff(f7188,plain,
spl183_484,
inference(avatar_split_clause,[],[f3112,f7186]) ).
tff(f7186,plain,
( spl183_484
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X2)
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_484])]) ).
tff(f3112,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X1),X2)
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f1857]) ).
tff(f1857,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2)
| ~ 'fun_app$b'('less_eq$'(X1),X2)
| ~ 'fun_app$b'('less_eq$'(X0),X2) )
& ( ( 'fun_app$b'('less_eq$'(X1),X2)
& 'fun_app$b'('less_eq$'(X0),X2) )
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ) ),
inference(flattening,[],[f1856]) ).
tff(f1856,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2)
| ~ 'fun_app$b'('less_eq$'(X1),X2)
| ~ 'fun_app$b'('less_eq$'(X0),X2) )
& ( ( 'fun_app$b'('less_eq$'(X1),X2)
& 'fun_app$b'('less_eq$'(X0),X2) )
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ) ),
inference(nnf_transformation,[],[f551]) ).
tff(f551,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2)
<=> ( 'fun_app$b'('less_eq$'(X1),X2)
& 'fun_app$b'('less_eq$'(X0),X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom549) ).
tff(f7184,plain,
( ~ spl183_483
| ~ spl183_226
| ~ spl183_405 ),
inference(avatar_split_clause,[],[f6762,f5991,f4773,f7181]) ).
tff(f7181,plain,
( spl183_483
<=> sP24('ereal$'(-1.0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_483])]) ).
tff(f4773,plain,
( spl183_226
<=> ! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'times$'('infinity$','ereal$'(-1.0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_226])]) ).
tff(f5991,plain,
( spl183_405
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
| ~ sP24(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_405])]) ).
tff(f6762,plain,
( ~ sP24('ereal$'(-1.0),'infinity$')
| ~ spl183_226
| ~ spl183_405 ),
inference(resolution,[],[f5992,f4774]) ).
tff(f4774,plain,
( ! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'times$'('infinity$','ereal$'(-1.0)))
| ~ spl183_226 ),
inference(avatar_component_clause,[],[f4773]) ).
tff(f5992,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
| ~ sP24(X1,X0) )
| ~ spl183_405 ),
inference(avatar_component_clause,[],[f5991]) ).
tff(f7179,plain,
spl183_482,
inference(avatar_split_clause,[],[f3111,f7177]) ).
tff(f7177,plain,
( spl183_482
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X2)
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_482])]) ).
tff(f3111,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X2)
| ~ 'fun_app$b'('less_eq$'('max$'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f1857]) ).
tff(f7175,plain,
spl183_481,
inference(avatar_split_clause,[],[f3007,f7173]) ).
tff(f7173,plain,
( spl183_481
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( sK152(X0,X1,X2) = X1 )
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_481])]) ).
tff(f3007,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( sK152(X0,X1,X2) = X1 )
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f1749,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( tltrue != X0 )
& ( sK152(X0,X1,X2) = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP45(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152])],[f1747,f1748]) ).
tff(f1748,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ( tltrue != X0 )
& ( X1 = X3 )
& ( 'infinity$' = X2 ) )
=> ( ( tltrue != X0 )
& ( sK152(X0,X1,X2) = X1 )
& ( 'infinity$' = X2 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1747,plain,
! [X0: tlbool,X1: 'Ereal$',X2: 'Ereal$'] :
( ? [X3: 'Ereal$'] :
( ( tltrue != X0 )
& ( X1 = X3 )
& ( 'infinity$' = X2 ) )
| ~ sP45(X0,X1,X2) ),
inference(rectify,[],[f1746]) ).
tff(f1746,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: 'Ereal$'] :
( ( tltrue != X2 )
& ( X1 = X6 )
& ( 'infinity$' = X0 ) )
| ~ sP45(X2,X1,X0) ),
inference(nnf_transformation,[],[f1255]) ).
tff(f1255,plain,
! [X2: tlbool,X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: 'Ereal$'] :
( ( tltrue != X2 )
& ( X1 = X6 )
& ( 'infinity$' = X0 ) )
| ~ sP45(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP45])]) ).
tff(f7171,plain,
spl183_480,
inference(avatar_split_clause,[],[f3003,f7169]) ).
tff(f7169,plain,
( spl183_480
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( sK151(X0,X1,X2) = X2 )
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_480])]) ).
tff(f3003,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( sK151(X0,X1,X2) = X2 )
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1745]) ).
tff(f7167,plain,
spl183_479,
inference(avatar_split_clause,[],[f2990,f7165]) ).
tff(f7165,plain,
( spl183_479
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),X2)
| ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_479])]) ).
tff(f2990,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),X2)
| ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f1154]) ).
tff(f1154,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( 'fun_app$b'('less$'(X1),X2)
& 'fun_app$b'('less$'(X0),X2) )
| ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2) ),
inference(ennf_transformation,[],[f804]) ).
tff(f804,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
~ ( ~ ( 'fun_app$b'('less$'(X1),X2)
& 'fun_app$b'('less$'(X0),X2) )
& 'fun_app$b'('less$'('max$'(X0,X1)),X2) ),
inference(true_and_false_elimination,[],[f106]) ).
tff(f106,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( ( 'fun_app$b'('less$'(X1),X2)
& 'fun_app$b'('less$'(X0),X2) )
=> $false )
& 'fun_app$b'('less$'('max$'(X0,X1)),X2) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom104) ).
tff(f7163,plain,
spl183_478,
inference(avatar_split_clause,[],[f2989,f7161]) ).
tff(f2989,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X2)
| ~ 'fun_app$b'('less$'('max$'(X0,X1)),X2) ),
inference(cnf_transformation,[],[f1154]) ).
tff(f7159,plain,
spl183_477,
inference(avatar_split_clause,[],[f2973,f7157]) ).
tff(f7157,plain,
( spl183_477
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP32(X0,sK148(X0,X1,X2))
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_477])]) ).
tff(f2973,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP32(X0,sK148(X0,X1,X2))
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f7155,plain,
spl183_476,
inference(avatar_split_clause,[],[f2969,f7153]) ).
tff(f7153,plain,
( spl183_476
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP33(X0,sK147(X0,X1,X2))
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_476])]) ).
tff(f2969,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP33(X0,sK147(X0,X1,X2))
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f7151,plain,
spl183_475,
inference(avatar_split_clause,[],[f2965,f7149]) ).
tff(f7149,plain,
( spl183_475
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP34(X0,sK146(X0,X1,X2))
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_475])]) ).
tff(f2965,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP34(X0,sK146(X0,X1,X2))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f1715]) ).
tff(f7147,plain,
spl183_474,
inference(avatar_split_clause,[],[f2961,f7145]) ).
tff(f7145,plain,
( spl183_474
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP35(X0,sK145(X0,X1,X2))
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_474])]) ).
tff(f2961,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( sP35(X0,sK145(X0,X1,X2))
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f1711]) ).
tff(f7143,plain,
spl183_473,
inference(avatar_split_clause,[],[f2913,f7141]) ).
tff(f7141,plain,
( spl183_473
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X2,X1))
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_473])]) ).
tff(f2913,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X2,X1))
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1083]) ).
tff(f1083,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X2,X1))
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(ennf_transformation,[],[f92]) ).
tff(f92,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X1)
=> 'fun_app$b'('less$'(X0),'max$'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom90) ).
tff(f7133,plain,
spl183_472,
inference(avatar_split_clause,[],[f2912,f7131]) ).
tff(f7131,plain,
( spl183_472
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X1,X2))
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_472])]) ).
tff(f2912,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X1,X2))
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1082]) ).
tff(f1082,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'max$'(X1,X2))
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(ennf_transformation,[],[f95]) ).
tff(f95,axiom,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X1)
=> 'fun_app$b'('less$'(X0),'max$'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom93) ).
tff(f7128,plain,
spl183_471,
inference(avatar_split_clause,[],[f2826,f7126]) ).
tff(f2826,plain,
! [X2: $real,X0: 'Real_list$',X1: 'Real_list$'] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'nat$'(0)) ),
inference(cnf_transformation,[],[f512]) ).
tff(f512,axiom,
! [X0: 'Real_list$',X1: 'Real_list$',X2: $real] : ( 1.0 = 'fun_app$f'('fps_nth$'('fps_hypergeo$'(X0,X1,X2)),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom510) ).
tff(f7124,plain,
spl183_470,
inference(avatar_split_clause,[],[f2492,f7122]) ).
tff(f7122,plain,
( spl183_470
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( $less(sK124(X0,X1),sK125(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_470])]) ).
tff(f2492,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( $less(sK124(X0,X1),sK125(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1480]) ).
tff(f1480,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( $less(sK124(X0,X1),sK125(X0,X1))
& ( 'ereal$'(sK125(X0,X1)) = X0 )
& ( 'ereal$'(sK124(X0,X1)) = X1 ) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125])],[f1478,f1479]) ).
tff(f1479,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( $less(X2,X3)
& ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( $less(sK124(X0,X1),sK125(X0,X1))
& ( 'ereal$'(sK125(X0,X1)) = X0 )
& ( 'ereal$'(sK124(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1478,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( $less(X2,X3)
& ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f1477]) ).
tff(f1477,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real,X5: $real] :
( $less(X4,X5)
& ( 'ereal$'(X5) = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f1192]) ).
tff(f1192,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real,X5: $real] :
( $less(X4,X5)
& ( 'ereal$'(X5) = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
tff(f7120,plain,
spl183_469,
inference(avatar_split_clause,[],[f2460,f7118]) ).
tff(f7118,plain,
( spl183_469
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ $less(sK117(X0,X1),sK118(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_469])]) ).
tff(f2460,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ $less(sK117(X0,X1),sK118(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1463]) ).
tff(f1463,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ~ $less(sK117(X0,X1),sK118(X0,X1))
& ( 'ereal$'(sK118(X0,X1)) = X0 )
& ( 'ereal$'(sK117(X0,X1)) = X1 ) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK117,sK118])],[f1461,f1462]) ).
tff(f1462,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( ~ $less(X2,X3)
& ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( ~ $less(sK117(X0,X1),sK118(X0,X1))
& ( 'ereal$'(sK118(X0,X1)) = X0 )
& ( 'ereal$'(sK117(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1461,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( ~ $less(X2,X3)
& ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f1460]) ).
tff(f1460,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real,X5: $real] :
( ~ $less(X4,X5)
& ( 'ereal$'(X5) = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f1188]) ).
tff(f1188,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real,X5: $real] :
( ~ $less(X4,X5)
& ( 'ereal$'(X5) = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f7116,plain,
spl183_468,
inference(avatar_split_clause,[],[f2409,f7114]) ).
tff(f7114,plain,
( spl183_468
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'fun_app$c'('inverse$',X0) != 'fun_app$c'('inverse$',X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_468])]) ).
tff(f2409,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'fun_app$c'('inverse$',X0) != 'fun_app$c'('inverse$',X1) ) ),
inference(cnf_transformation,[],[f911]) ).
tff(f911,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'fun_app$c'('inverse$',X0) != 'fun_app$c'('inverse$',X1) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,axiom,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('inverse$',X0) = 'fun_app$c'('inverse$',X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom13) ).
tff(f7112,plain,
spl183_467,
inference(avatar_split_clause,[],[f2397,f7110]) ).
tff(f7110,plain,
( spl183_467
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X0) != 'of_nat$'(X1) )
| ~ $less('of_nat$'(X0),'of_nat$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_467])]) ).
tff(f2397,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X0) != 'of_nat$'(X1) )
| ~ $less('of_nat$'(X0),'of_nat$'(X1)) ),
inference(cnf_transformation,[],[f899]) ).
tff(f899,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 'of_nat$'(X0) != 'of_nat$'(X1) )
| ~ $less('of_nat$'(X0),'of_nat$'(X1)) ),
inference(ennf_transformation,[],[f126]) ).
tff(f126,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( $less('of_nat$'(X0),'of_nat$'(X1))
=> ( 'of_nat$'(X0) != 'of_nat$'(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom124) ).
tff(f7107,plain,
spl183_466,
inference(avatar_split_clause,[],[f2345,f7105]) ).
tff(f2345,plain,
! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'nat$'(0),X1),'nat$'(0)) ),
inference(cnf_transformation,[],[f495]) ).
tff(f495,axiom,
! [X0: 'Nat_real_real_fun_fun$',X1: 'Real_fps$'] : ( 1.0 = 'fun_app$f'('radical$'(X0,'nat$'(0),X1),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom493) ).
tff(f7103,plain,
spl183_465,
inference(avatar_split_clause,[],[f2329,f7101]) ).
tff(f7101,plain,
( spl183_465
<=> ! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| 'member$'(sK113(X0,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_465])]) ).
tff(f2329,plain,
! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(sK112(X0)),X2)
| 'member$'(sK113(X0,X2),X0) ),
inference(cnf_transformation,[],[f1449]) ).
tff(f7099,plain,
spl183_464,
inference(avatar_split_clause,[],[f2326,f7097]) ).
tff(f7097,plain,
( spl183_464
<=> ! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| 'member$'(sK111(X0,X2),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_464])]) ).
tff(f2326,plain,
! [X2: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(X2),sK110(X0))
| 'member$'(sK111(X0,X2),X0) ),
inference(cnf_transformation,[],[f1446]) ).
tff(f7095,plain,
spl183_463,
inference(avatar_split_clause,[],[f2157,f7093]) ).
tff(f7093,plain,
( spl183_463
<=> ! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK95(X0)) )
| ( 'zero$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_463])]) ).
tff(f2157,plain,
! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK95(X0)) )
| ( 'zero$b' = X0 ) ),
inference(cnf_transformation,[],[f1336]) ).
tff(f1336,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] :
( ( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK94(X0,X1)) )
& $less('of_nat$'(sK94(X0,X1)),'of_nat$'(X1)) )
| ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) ) )
& ( ( ! [X4: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK95(X0))) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK95(X0)) ) )
| ( 'zero$b' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f1333,f1335,f1334]) ).
tff(f1334,plain,
! [X0: 'Real_fps$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
=> ( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK94(X0,X1)) )
& $less('of_nat$'(sK94(X0,X1)),'of_nat$'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1335,plain,
! [X0: 'Real_fps$'] :
( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X3) ) )
=> ( ! [X4: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK95(X0))) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK95(X0)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1333,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) ) )
& ( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X3) ) )
| ( 'zero$b' = X0 ) ) ),
inference(rectify,[],[f1332]) ).
tff(f1332,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) ) )
& ( ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X1) ) )
| ( 'zero$b' = X0 ) ) ),
inference(nnf_transformation,[],[f869]) ).
tff(f869,plain,
! [X0: 'Real_fps$'] :
( ( 'zero$b' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X1) ) ) ),
inference(ennf_transformation,[],[f223]) ).
tff(f223,axiom,
! [X0: 'Real_fps$'] :
( ( 'zero$b' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( $less('of_nat$'(X2),'of_nat$'(X1))
=> ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X2) ) )
& ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom221) ).
tff(f7088,plain,
spl183_462,
inference(avatar_split_clause,[],[f2155,f7086]) ).
tff(f7086,plain,
( spl183_462
<=> ! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK93(X0)) )
| ( 'zero$b' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_462])]) ).
tff(f2155,plain,
! [X0: 'Real_fps$'] :
( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK93(X0)) )
| ( 'zero$b' = X0 ) ),
inference(cnf_transformation,[],[f1331]) ).
tff(f1331,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) )
& ( ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK93(X0)) )
| ( 'zero$b' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f1329,f1330]) ).
tff(f1330,plain,
! [X0: 'Real_fps$'] :
( ? [X2: 'Nat$'] : ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X2) )
=> ( 0.0 != 'fun_app$f'('fps_nth$'(X0),sK93(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1329,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) )
& ( ? [X2: 'Nat$'] : ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X2) )
| ( 'zero$b' = X0 ) ) ),
inference(rectify,[],[f1328]) ).
tff(f1328,plain,
! [X0: 'Real_fps$'] :
( ( ( 'zero$b' != X0 )
| ! [X1: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'(X0),X1) ) )
& ( ? [X1: 'Nat$'] : ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X1) )
| ( 'zero$b' = X0 ) ) ),
inference(nnf_transformation,[],[f208]) ).
tff(f208,axiom,
! [X0: 'Real_fps$'] :
( ( 'zero$b' != X0 )
<=> ? [X1: 'Nat$'] : ( 0.0 != 'fun_app$f'('fps_nth$'(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom206) ).
tff(f7084,plain,
spl183_461,
inference(avatar_split_clause,[],[f2101,f7082]) ).
tff(f7082,plain,
( spl183_461
<=> ! [X0: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 = 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_461])]) ).
tff(f2101,plain,
! [X0: 'Nat$'] :
( ( 0.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 = 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f828]) ).
tff(f828,plain,
! [X0: 'Nat$'] :
( ( ( 0.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 = 'of_nat$'(X0) ) )
& ( ( 1.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
inference(ennf_transformation,[],[f452]) ).
tff(f452,axiom,
! [X0: 'Nat$'] :
( ( ( 0 != 'of_nat$'(X0) )
=> ( 0.0 = 'fun_app$f'('fps_nth$'('one$'),X0) ) )
& ( ( 0 = 'of_nat$'(X0) )
=> ( 1.0 = 'fun_app$f'('fps_nth$'('one$'),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom450) ).
tff(f7080,plain,
spl183_460,
inference(avatar_split_clause,[],[f2100,f7078]) ).
tff(f7078,plain,
( spl183_460
<=> ! [X0: 'Nat$'] :
( ( 1.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_460])]) ).
tff(f2100,plain,
! [X0: 'Nat$'] :
( ( 1.0 = 'fun_app$f'('fps_nth$'('one$'),X0) )
| ( 0 != 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f828]) ).
tff(f7076,plain,
spl183_459,
inference(avatar_split_clause,[],[f2090,f7074]) ).
tff(f7074,plain,
( spl183_459
<=> ! [X0: $real] :
( ( 'ereal$'(X0) = 'max$'('zero$','ereal$'(X0)) )
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_459])]) ).
tff(f2090,plain,
! [X0: $real] :
( ( 'ereal$'(X0) = 'max$'('zero$','ereal$'(X0)) )
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f823]) ).
tff(f823,plain,
! [X0: $real] :
( ( ( 'ereal$'(0.0) = 'max$'('zero$','ereal$'(X0)) )
| ~ $less(X0,0.0) )
& ( ( 'ereal$'(X0) = 'max$'('zero$','ereal$'(X0)) )
| $less(X0,0.0) ) ),
inference(ennf_transformation,[],[f648]) ).
tff(f648,plain,
! [X0: $real] :
( ( $less(X0,0.0)
=> ( 'ereal$'(0.0) = 'max$'('zero$','ereal$'(X0)) ) )
& ( ~ $less(X0,0.0)
=> ( 'ereal$'(X0) = 'max$'('zero$','ereal$'(X0)) ) ) ),
inference(theory_normalization,[],[f101]) ).
tff(f101,axiom,
! [X0: $real] :
( ( ~ $lesseq(0.0,X0)
=> ( 'ereal$'(0.0) = 'max$'('zero$','ereal$'(X0)) ) )
& ( $lesseq(0.0,X0)
=> ( 'ereal$'(X0) = 'max$'('zero$','ereal$'(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom99) ).
tff(f7072,plain,
spl183_458,
inference(avatar_split_clause,[],[f1987,f7069]) ).
tff(f7069,plain,
( spl183_458
<=> 'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'('c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_458])]) ).
tff(f1987,plain,
'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'('c$a')),
inference(cnf_transformation,[],[f66]) ).
tff(f66,axiom,
'fun_app$b'('less$'('max$'('c$b','ereal$'('fun_app$c'('inverse$','u$')))),'ereal$'('c$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom64) ).
tff(f7067,plain,
spl183_457,
inference(avatar_split_clause,[],[f738,f7065]) ).
tff(f7065,plain,
( spl183_457
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_457])]) ).
tff(f738,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f7063,plain,
spl183_456,
inference(avatar_split_clause,[],[f733,f7061]) ).
tff(f7061,plain,
( spl183_456
<=> ! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_456])]) ).
tff(f733,plain,
! [X0: $real,X1: $real] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f7059,plain,
spl183_455,
inference(avatar_split_clause,[],[f720,f7057]) ).
tff(f7057,plain,
( spl183_455
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_455])]) ).
tff(f720,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f7055,plain,
spl183_454,
inference(avatar_split_clause,[],[f715,f7053]) ).
tff(f7053,plain,
( spl183_454
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_454])]) ).
tff(f715,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f7051,plain,
( spl183_453
| ~ spl183_113
| ~ spl183_417 ),
inference(avatar_split_clause,[],[f6864,f6039,f4279,f7048]) ).
tff(f7048,plain,
( spl183_453
<=> sP27(-1.0,-1.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_453])]) ).
tff(f4279,plain,
( spl183_113
<=> ( 1.0 = 'fun_app$c'('times$a'(-1.0),-1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_113])]) ).
tff(f6039,plain,
( spl183_417
<=> ! [X0: $real,X1: $real] :
( sP27(X1,X0)
| ~ $less(0.0,'fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_417])]) ).
tff(f6864,plain,
( sP27(-1.0,-1.0)
| ~ spl183_113
| ~ spl183_417 ),
inference(evaluation,[],[f6863]) ).
tff(f6863,plain,
( ~ $less(0.0,1.0)
| sP27(-1.0,-1.0)
| ~ spl183_113
| ~ spl183_417 ),
inference(superposition,[],[f6040,f4281]) ).
tff(f4281,plain,
( ( 1.0 = 'fun_app$c'('times$a'(-1.0),-1.0) )
| ~ spl183_113 ),
inference(avatar_component_clause,[],[f4279]) ).
tff(f6040,plain,
( ! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
| sP27(X1,X0) )
| ~ spl183_417 ),
inference(avatar_component_clause,[],[f6039]) ).
tff(f6869,plain,
( spl183_452
| ~ spl183_107
| ~ spl183_406 ),
inference(avatar_split_clause,[],[f6777,f5995,f4252,f6866]) ).
tff(f6866,plain,
( spl183_452
<=> $less(sK182,'c$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_452])]) ).
tff(f5995,plain,
( spl183_406
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_406])]) ).
tff(f6777,plain,
( $less(sK182,'c$a')
| ~ spl183_107
| ~ spl183_406 ),
inference(resolution,[],[f5996,f4254]) ).
tff(f5996,plain,
( ! [X0: $real,X1: $real] :
( ~ 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1))
| $less(X0,X1) )
| ~ spl183_406 ),
inference(avatar_component_clause,[],[f5995]) ).
tff(f6827,plain,
( ~ spl183_451
| ~ spl183_113
| ~ spl183_400 ),
inference(avatar_split_clause,[],[f6736,f5970,f4279,f6824]) ).
tff(f6824,plain,
( spl183_451
<=> sP22(-1.0,-1.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_451])]) ).
tff(f5970,plain,
( spl183_400
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP22(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_400])]) ).
tff(f6736,plain,
( ~ sP22(-1.0,-1.0)
| ~ spl183_113
| ~ spl183_400 ),
inference(evaluation,[],[f6735]) ).
tff(f6735,plain,
( ~ $less(0.0,1.0)
| ~ sP22(-1.0,-1.0)
| ~ spl183_113
| ~ spl183_400 ),
inference(superposition,[],[f5971,f4281]) ).
tff(f5971,plain,
( ! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP22(X1,X0) )
| ~ spl183_400 ),
inference(avatar_component_clause,[],[f5970]) ).
tff(f6674,plain,
( spl183_450
| ~ spl183_2
| ~ spl183_297 ),
inference(avatar_split_clause,[],[f5543,f5207,f3781,f6672]) ).
tff(f6672,plain,
( spl183_450
<=> ! [X0: $int,X1: $int] : ~ $less('max$b'(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_450])]) ).
tff(f3781,plain,
( spl183_2
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_2])]) ).
tff(f5207,plain,
( spl183_297
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X1,X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_297])]) ).
tff(f5543,plain,
( ! [X0: $int,X1: $int] : ~ $less('max$b'(X0,X1),X0)
| ~ spl183_2
| ~ spl183_297 ),
inference(resolution,[],[f5208,f3782]) ).
tff(f3782,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl183_2 ),
inference(avatar_component_clause,[],[f3781]) ).
tff(f5208,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X1,X2))
| ~ $less(X0,X1) )
| ~ spl183_297 ),
inference(avatar_component_clause,[],[f5207]) ).
tff(f6640,plain,
( spl183_449
| ~ spl183_2
| ~ spl183_296 ),
inference(avatar_split_clause,[],[f5536,f5203,f3781,f6638]) ).
tff(f6638,plain,
( spl183_449
<=> ! [X0: $int,X1: $int] : ~ $less('max$b'(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_449])]) ).
tff(f5203,plain,
( spl183_296
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X2,X1))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_296])]) ).
tff(f5536,plain,
( ! [X0: $int,X1: $int] : ~ $less('max$b'(X0,X1),X1)
| ~ spl183_2
| ~ spl183_296 ),
inference(resolution,[],[f5204,f3782]) ).
tff(f5204,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X2,X1))
| ~ $less(X0,X1) )
| ~ spl183_296 ),
inference(avatar_component_clause,[],[f5203]) ).
tff(f6601,plain,
( spl183_448
| ~ spl183_233
| ~ spl183_277 ),
inference(avatar_split_clause,[],[f5449,f5121,f4805,f6598]) ).
tff(f6598,plain,
( spl183_448
<=> 'fun_app$b'('less_eq$'('ereal$'(-1.0)),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_448])]) ).
tff(f4805,plain,
( spl183_233
<=> 'fun_app$b'('less$'('ereal$'(-1.0)),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_233])]) ).
tff(f5449,plain,
( 'fun_app$b'('less_eq$'('ereal$'(-1.0)),'zero$')
| ~ spl183_233
| ~ spl183_277 ),
inference(resolution,[],[f5122,f4807]) ).
tff(f4807,plain,
( 'fun_app$b'('less$'('ereal$'(-1.0)),'zero$')
| ~ spl183_233 ),
inference(avatar_component_clause,[],[f4805]) ).
tff(f6581,plain,
( spl183_447
| ~ spl183_58
| ~ spl183_277 ),
inference(avatar_split_clause,[],[f5439,f5121,f4043,f6578]) ).
tff(f6578,plain,
( spl183_447
<=> 'fun_app$b'('less_eq$'('c$b'),'ereal$'(sK80)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_447])]) ).
tff(f4043,plain,
( spl183_58
<=> 'fun_app$b'('less$'('c$b'),'ereal$'(sK80)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_58])]) ).
tff(f5439,plain,
( 'fun_app$b'('less_eq$'('c$b'),'ereal$'(sK80))
| ~ spl183_58
| ~ spl183_277 ),
inference(resolution,[],[f5122,f4045]) ).
tff(f4045,plain,
( 'fun_app$b'('less$'('c$b'),'ereal$'(sK80))
| ~ spl183_58 ),
inference(avatar_component_clause,[],[f4043]) ).
tff(f6575,plain,
( spl183_446
| ~ spl183_52
| ~ spl183_277 ),
inference(avatar_split_clause,[],[f5438,f5121,f4013,f6572]) ).
tff(f6572,plain,
( spl183_446
<=> 'fun_app$b'('less_eq$'('c$b'),'ereal$'('c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_446])]) ).
tff(f4013,plain,
( spl183_52
<=> 'fun_app$b'('less$'('c$b'),'ereal$'('c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_52])]) ).
tff(f5438,plain,
( 'fun_app$b'('less_eq$'('c$b'),'ereal$'('c$a'))
| ~ spl183_52
| ~ spl183_277 ),
inference(resolution,[],[f5122,f4015]) ).
tff(f4015,plain,
( 'fun_app$b'('less$'('c$b'),'ereal$'('c$a'))
| ~ spl183_52 ),
inference(avatar_component_clause,[],[f4013]) ).
tff(f6413,plain,
( spl183_445
| ~ spl183_51
| ~ spl183_277 ),
inference(avatar_split_clause,[],[f5437,f5121,f4008,f6410]) ).
tff(f6410,plain,
( spl183_445
<=> 'fun_app$b'('less_eq$'('c$b'),'ereal$'('c$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_445])]) ).
tff(f5437,plain,
( 'fun_app$b'('less_eq$'('c$b'),'ereal$'('c$'))
| ~ spl183_51
| ~ spl183_277 ),
inference(resolution,[],[f5122,f4010]) ).
tff(f6305,plain,
( spl183_444
| ~ spl183_2
| ~ spl183_269 ),
inference(avatar_split_clause,[],[f5367,f5086,f3781,f6303]) ).
tff(f6303,plain,
( spl183_444
<=> ! [X0: $int] : ( 'max$b'(X0,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_444])]) ).
tff(f5086,plain,
( spl183_269
<=> ! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_269])]) ).
tff(f5367,plain,
( ! [X0: $int] : ( 'max$b'(X0,X0) = X0 )
| ~ spl183_2
| ~ spl183_269 ),
inference(resolution,[],[f5087,f3782]) ).
tff(f5087,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,X0)
| ( 'max$b'(X1,X0) = X1 ) )
| ~ spl183_269 ),
inference(avatar_component_clause,[],[f5086]) ).
tff(f6254,plain,
( spl183_443
| ~ spl183_140
| ~ spl183_319 ),
inference(avatar_split_clause,[],[f5636,f5633,f4423,f6252]) ).
tff(f6252,plain,
( spl183_443
<=> ! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_443])]) ).
tff(f5633,plain,
( spl183_319
<=> ! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_319])]) ).
tff(f5636,plain,
( ! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'size_ereal$'('one$a')) )
| ~ spl183_140
| ~ spl183_319 ),
inference(forward_demodulation,[],[f5634,f4425]) ).
tff(f5634,plain,
( ! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'nat$'(0)) )
| ~ spl183_319 ),
inference(avatar_component_clause,[],[f5633]) ).
tff(f6199,plain,
( spl183_442
| ~ spl183_3
| ~ spl183_240 ),
inference(avatar_split_clause,[],[f5245,f4966,f3785,f6197]) ).
tff(f3785,plain,
( spl183_3
<=> ! [X0: $real] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_3])]) ).
tff(f4966,plain,
( spl183_240
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_240])]) ).
tff(f5245,plain,
( ! [X0: $real] : $less(X0,$sum(X0,1.0))
| ~ spl183_3
| ~ spl183_240 ),
inference(resolution,[],[f4967,f3786]) ).
tff(f3786,plain,
( ! [X0: $real] : ~ $less(X0,X0)
| ~ spl183_3 ),
inference(avatar_component_clause,[],[f3785]) ).
tff(f4967,plain,
( ! [X0: $real,X1: $real] :
( $less(X1,$sum(X0,1.0))
| $less(X0,X1) )
| ~ spl183_240 ),
inference(avatar_component_clause,[],[f4966]) ).
tff(f6137,plain,
spl183_441,
inference(avatar_split_clause,[],[f3743,f6135]) ).
tff(f6135,plain,
( spl183_441
<=> ! [X0: $int,X1: $int] : ( 'times$d'($uminus(X0),X1) = 'times$d'(X0,$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_441])]) ).
tff(f3743,plain,
! [X0: $int,X1: $int] : ( 'times$d'($uminus(X0),X1) = 'times$d'(X0,$uminus(X1)) ),
inference(forward_demodulation,[],[f2342,f2337]) ).
tff(f2337,plain,
! [X0: $int,X1: $int] : ( $uminus('times$d'(X0,X1)) = 'times$d'(X0,$uminus(X1)) ),
inference(cnf_transformation,[],[f308]) ).
tff(f308,axiom,
! [X0: $int,X1: $int] : ( $uminus('times$d'(X0,X1)) = 'times$d'(X0,$uminus(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom306) ).
tff(f2342,plain,
! [X0: $int,X1: $int] : ( 'times$d'($uminus(X0),X1) = $uminus('times$d'(X0,X1)) ),
inference(cnf_transformation,[],[f304]) ).
tff(f304,axiom,
! [X0: $int,X1: $int] : ( 'times$d'($uminus(X0),X1) = $uminus('times$d'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom302) ).
tff(f6133,plain,
spl183_440,
inference(avatar_split_clause,[],[f3736,f6131]) ).
tff(f6131,plain,
( spl183_440
<=> ! [X0: $real] :
( ( 'zero$' = 'max$'('zero$','ereal$'(X0)) )
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_440])]) ).
tff(f3736,plain,
! [X0: $real] :
( ( 'zero$' = 'max$'('zero$','ereal$'(X0)) )
| ~ $less(X0,0.0) ),
inference(forward_demodulation,[],[f2091,f1953]) ).
tff(f1953,plain,
'zero$' = 'ereal$'(0.0),
inference(cnf_transformation,[],[f47]) ).
tff(f47,axiom,
'zero$' = 'ereal$'(0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom45) ).
tff(f2091,plain,
! [X0: $real] :
( ( 'ereal$'(0.0) = 'max$'('zero$','ereal$'(X0)) )
| ~ $less(X0,0.0) ),
inference(cnf_transformation,[],[f823]) ).
tff(f6129,plain,
spl183_439,
inference(avatar_split_clause,[],[f3714,f6127]) ).
tff(f6127,plain,
( spl183_439
<=> ! [X0: 'Ereal$'] : ( 'times$'('times$'(X0,'ereal$'(-1.0)),'ereal$'(-1.0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_439])]) ).
tff(f3714,plain,
! [X0: 'Ereal$'] : ( 'times$'('times$'(X0,'ereal$'(-1.0)),'ereal$'(-1.0)) = X0 ),
inference(evaluation,[],[f3226]) ).
tff(f3226,plain,
! [X0: 'Ereal$'] : ( 'times$'('times$'(X0,'ereal$'($uminus(1.0))),'ereal$'($uminus(1.0))) = X0 ),
inference(definition_unfolding,[],[f2021,f2063,f2063]) ).
tff(f2021,plain,
! [X0: 'Ereal$'] : ( 'uminus$'('uminus$'(X0)) = X0 ),
inference(cnf_transformation,[],[f147]) ).
tff(f147,axiom,
! [X0: 'Ereal$'] : ( 'uminus$'('uminus$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom145) ).
tff(f6125,plain,
spl183_438,
inference(avatar_split_clause,[],[f3706,f6123]) ).
tff(f6123,plain,
( spl183_438
<=> ! [X0: $real] : ( 'ereal$'($uminus(X0)) = 'times$'('ereal$'(X0),'ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_438])]) ).
tff(f3706,plain,
! [X0: $real] : ( 'ereal$'($uminus(X0)) = 'times$'('ereal$'(X0),'ereal$'(-1.0)) ),
inference(evaluation,[],[f3230]) ).
tff(f3230,plain,
! [X0: $real] : ( 'ereal$'($uminus(X0)) = 'times$'('ereal$'(X0),'ereal$'($uminus(1.0))) ),
inference(definition_unfolding,[],[f2059,f2063]) ).
tff(f2059,plain,
! [X0: $real] : ( 'uminus$'('ereal$'(X0)) = 'ereal$'($uminus(X0)) ),
inference(cnf_transformation,[],[f239]) ).
tff(f239,axiom,
! [X0: $real] : ( 'uminus$'('ereal$'(X0)) = 'ereal$'($uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom237) ).
tff(f6121,plain,
spl183_437,
inference(avatar_split_clause,[],[f3684,f6119]) ).
tff(f6119,plain,
( spl183_437
<=> ! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,'ereal$'(-1.0)) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_437])]) ).
tff(f3684,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,'ereal$'(-1.0)) ) ),
inference(evaluation,[],[f3252]) ).
tff(f3252,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'zero$' != 'times$'(X0,'ereal$'($uminus(1.0))) ) ),
inference(definition_unfolding,[],[f2188,f2063]) ).
tff(f2188,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'zero$' != 'uminus$'(X0) ) ),
inference(cnf_transformation,[],[f1350]) ).
tff(f1350,plain,
! [X0: 'Ereal$'] :
( ( ( 'zero$' = 'uminus$'(X0) )
| ( 'zero$' != X0 ) )
& ( ( 'zero$' = X0 )
| ( 'zero$' != 'uminus$'(X0) ) ) ),
inference(nnf_transformation,[],[f164]) ).
tff(f164,axiom,
! [X0: 'Ereal$'] :
( ( 'zero$' = 'uminus$'(X0) )
<=> ( 'zero$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom162) ).
tff(f6117,plain,
spl183_436,
inference(avatar_split_clause,[],[f3641,f6115]) ).
tff(f6115,plain,
( spl183_436
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_436])]) ).
tff(f3641,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X1 )
| ~ sP10(X0,X1) ),
inference(evaluation,[],[f3283]) ).
tff(f3283,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X1 )
| ~ sP10(X0,X1) ),
inference(definition_unfolding,[],[f2507,f2063]) ).
tff(f2507,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X1 )
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f1486]) ).
tff(f1486,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'ereal$'(sK127(X0,X1)) = X0 )
& ( 'uminus$'('infinity$') = X1 ) )
| ~ sP10(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK127])],[f1484,f1485]) ).
tff(f1485,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& ( 'uminus$'('infinity$') = X1 ) )
=> ( ( 'ereal$'(sK127(X0,X1)) = X0 )
& ( 'uminus$'('infinity$') = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1484,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& ( 'uminus$'('infinity$') = X1 ) )
| ~ sP10(X0,X1) ),
inference(rectify,[],[f1483]) ).
tff(f1483,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP10(X1,X0) ),
inference(nnf_transformation,[],[f1201]) ).
tff(f1201,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ~ sP10(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
tff(f6113,plain,
spl183_435,
inference(avatar_split_clause,[],[f3640,f6111]) ).
tff(f6111,plain,
( spl183_435
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_435])]) ).
tff(f3640,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP9(X0,X1) ),
inference(evaluation,[],[f3284]) ).
tff(f3284,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP9(X0,X1) ),
inference(definition_unfolding,[],[f2510,f2063]) ).
tff(f2510,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1488]) ).
tff(f1488,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'infinity$' = X1 ) )
| ~ sP9(X0,X1) ),
inference(rectify,[],[f1487]) ).
tff(f1487,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP9(X1,X0) ),
inference(nnf_transformation,[],[f1200]) ).
tff(f1200,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP9(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
tff(f6109,plain,
spl183_434,
inference(avatar_split_clause,[],[f3639,f6107]) ).
tff(f6107,plain,
( spl183_434
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_434])]) ).
tff(f3639,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'(-1.0)) = X0 )
| ~ sP6(X0,X1) ),
inference(evaluation,[],[f3285]) ).
tff(f3285,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'times$'('infinity$','ereal$'($uminus(1.0))) = X0 )
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f2516,f2063]) ).
tff(f2516,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'uminus$'('infinity$') = X0 )
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1498]) ).
tff(f1498,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK129(X0,X1)) = X1 ) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129])],[f1496,f1497]) ).
tff(f1497,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(sK129(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1496,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'uminus$'('infinity$') = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f1495]) ).
tff(f1495,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP6(X1,X0) ),
inference(nnf_transformation,[],[f1197]) ).
tff(f1197,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X4: $real] :
( ( 'uminus$'('infinity$') = X1 )
& ( 'ereal$'(X4) = X0 ) )
| ~ sP6(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
tff(f6105,plain,
( spl183_433
| ~ spl183_2
| ~ spl183_237 ),
inference(avatar_split_clause,[],[f5237,f4953,f3781,f6103]) ).
tff(f4953,plain,
( spl183_237
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_237])]) ).
tff(f5237,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl183_2
| ~ spl183_237 ),
inference(resolution,[],[f4954,f3782]) ).
tff(f4954,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl183_237 ),
inference(avatar_component_clause,[],[f4953]) ).
tff(f6101,plain,
spl183_432,
inference(avatar_split_clause,[],[f3478,f6099]) ).
tff(f6099,plain,
( spl183_432
<=> ! [X2: $real,X1: $real] :
( 'fun_app$b'('less$'('ereal$'(X2)),'ereal$'(X1))
| ~ $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_432])]) ).
tff(f3478,plain,
! [X2: $real,X1: $real] :
( 'fun_app$b'('less$'('ereal$'(X2)),'ereal$'(X1))
| ~ $less(X2,X1) ),
inference(equality_resolution,[],[f2664]) ).
tff(f2664,plain,
! [X2: $real,X0: 'Ereal$',X1: $real] :
( 'fun_app$b'('less$'(X0),'ereal$'(X1))
| ( 'ereal$'(X2) != X0 )
| ~ $less(X2,X1) ),
inference(cnf_transformation,[],[f1589]) ).
tff(f1589,plain,
! [X0: 'Ereal$',X1: $real] :
( ( 'fun_app$b'('less$'(X0),'ereal$'(X1))
| ( ! [X2: $real] :
( ( 'ereal$'(X2) != X0 )
| ~ $less(X2,X1) )
& ( 'uminus$'('infinity$') != X0 ) ) )
& ( ( ( 'ereal$'(sK138(X0,X1)) = X0 )
& $less(sK138(X0,X1),X1) )
| ( 'uminus$'('infinity$') = X0 )
| ~ 'fun_app$b'('less$'(X0),'ereal$'(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138])],[f1587,f1588]) ).
tff(f1588,plain,
! [X0: 'Ereal$',X1: $real] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& $less(X3,X1) )
=> ( ( 'ereal$'(sK138(X0,X1)) = X0 )
& $less(sK138(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
tff(f1587,plain,
! [X0: 'Ereal$',X1: $real] :
( ( 'fun_app$b'('less$'(X0),'ereal$'(X1))
| ( ! [X2: $real] :
( ( 'ereal$'(X2) != X0 )
| ~ $less(X2,X1) )
& ( 'uminus$'('infinity$') != X0 ) ) )
& ( ? [X3: $real] :
( ( 'ereal$'(X3) = X0 )
& $less(X3,X1) )
| ( 'uminus$'('infinity$') = X0 )
| ~ 'fun_app$b'('less$'(X0),'ereal$'(X1)) ) ),
inference(rectify,[],[f1586]) ).
tff(f1586,plain,
! [X0: 'Ereal$',X1: $real] :
( ( 'fun_app$b'('less$'(X0),'ereal$'(X1))
| ( ! [X2: $real] :
( ( 'ereal$'(X2) != X0 )
| ~ $less(X2,X1) )
& ( 'uminus$'('infinity$') != X0 ) ) )
& ( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& $less(X2,X1) )
| ( 'uminus$'('infinity$') = X0 )
| ~ 'fun_app$b'('less$'(X0),'ereal$'(X1)) ) ),
inference(flattening,[],[f1585]) ).
tff(f1585,plain,
! [X0: 'Ereal$',X1: $real] :
( ( 'fun_app$b'('less$'(X0),'ereal$'(X1))
| ( ! [X2: $real] :
( ( 'ereal$'(X2) != X0 )
| ~ $less(X2,X1) )
& ( 'uminus$'('infinity$') != X0 ) ) )
& ( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& $less(X2,X1) )
| ( 'uminus$'('infinity$') = X0 )
| ~ 'fun_app$b'('less$'(X0),'ereal$'(X1)) ) ),
inference(nnf_transformation,[],[f234]) ).
tff(f234,axiom,
! [X0: 'Ereal$',X1: $real] :
( 'fun_app$b'('less$'(X0),'ereal$'(X1))
<=> ( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& $less(X2,X1) )
| ( 'uminus$'('infinity$') = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom232) ).
tff(f6097,plain,
spl183_431,
inference(avatar_split_clause,[],[f2992,f6095]) ).
tff(f6095,plain,
( spl183_431
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X2)
| ~ $less('fun_app$c'('max$a'(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_431])]) ).
tff(f2992,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X1,X2)
| ~ $less('fun_app$c'('max$a'(X0),X1),X2) ),
inference(cnf_transformation,[],[f1155]) ).
tff(f1155,plain,
! [X0: $real,X1: $real,X2: $real] :
( ( $less(X1,X2)
& $less(X0,X2) )
| ~ $less('fun_app$c'('max$a'(X0),X1),X2) ),
inference(ennf_transformation,[],[f805]) ).
tff(f805,plain,
! [X0: $real,X1: $real,X2: $real] :
~ ( ~ ( $less(X1,X2)
& $less(X0,X2) )
& $less('fun_app$c'('max$a'(X0),X1),X2) ),
inference(true_and_false_elimination,[],[f105]) ).
tff(f105,axiom,
! [X0: $real,X1: $real,X2: $real] :
( ( ( ( $less(X1,X2)
& $less(X0,X2) )
=> $false )
& $less('fun_app$c'('max$a'(X0),X1),X2) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom103) ).
tff(f6093,plain,
spl183_430,
inference(avatar_split_clause,[],[f2991,f6091]) ).
tff(f6091,plain,
( spl183_430
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X0,X2)
| ~ $less('fun_app$c'('max$a'(X0),X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_430])]) ).
tff(f2991,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X0,X2)
| ~ $less('fun_app$c'('max$a'(X0),X1),X2) ),
inference(cnf_transformation,[],[f1155]) ).
tff(f6089,plain,
spl183_429,
inference(avatar_split_clause,[],[f2900,f6087]) ).
tff(f6087,plain,
( spl183_429
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X0,'fun_app$c'('max$a'(X2),X1))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_429])]) ).
tff(f2900,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X0,'fun_app$c'('max$a'(X2),X1))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1075]) ).
tff(f1075,plain,
! [X0: $real,X1: $real,X2: $real] :
( $less(X0,'fun_app$c'('max$a'(X2),X1))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f91]) ).
tff(f91,axiom,
! [X0: $real,X1: $real,X2: $real] :
( $less(X0,X1)
=> $less(X0,'fun_app$c'('max$a'(X2),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom89) ).
tff(f6085,plain,
spl183_428,
inference(avatar_split_clause,[],[f2899,f6083]) ).
tff(f6083,plain,
( spl183_428
<=> ! [X2: $real,X0: $real,X1: $real] :
( $less(X0,'fun_app$c'('max$a'(X1),X2))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_428])]) ).
tff(f2899,plain,
! [X2: $real,X0: $real,X1: $real] :
( $less(X0,'fun_app$c'('max$a'(X1),X2))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1074]) ).
tff(f1074,plain,
! [X0: $real,X1: $real,X2: $real] :
( $less(X0,'fun_app$c'('max$a'(X1),X2))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f94]) ).
tff(f94,axiom,
! [X0: $real,X1: $real,X2: $real] :
( $less(X0,X1)
=> $less(X0,'fun_app$c'('max$a'(X1),X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom92) ).
tff(f6081,plain,
spl183_427,
inference(avatar_split_clause,[],[f2822,f6079]) ).
tff(f6079,plain,
( spl183_427
<=> ! [X4: 'Ereal$',X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$'] :
( $less(0.0,sK142(X0,X1,X4))
| ~ sP31(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_427])]) ).
tff(f2822,plain,
! [X0: 'Ereal_set$',X1: 'Real_ereal_bool_fun_fun$',X4: 'Ereal$'] :
( $less(0.0,sK142(X0,X1,X4))
| ~ sP31(X1,X0) ),
inference(cnf_transformation,[],[f1683]) ).
tff(f6077,plain,
spl183_426,
inference(avatar_split_clause,[],[f2779,f6075]) ).
tff(f6075,plain,
( spl183_426
<=> ! [X0: $real,X1: $real] :
( $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP28(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_426])]) ).
tff(f2779,plain,
! [X0: $real,X1: $real] :
( $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP28(X1,X0) ),
inference(cnf_transformation,[],[f1652]) ).
tff(f1652,plain,
! [X0: $real,X1: $real] :
( ( $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP28(X1,X0) )
& ( sP28(X1,X0)
| ~ $less('fun_app$c'('times$a'(X0),X1),0.0) ) ),
inference(nnf_transformation,[],[f1234]) ).
tff(f1234,plain,
! [X0: $real,X1: $real] :
( $less('fun_app$c'('times$a'(X0),X1),0.0)
<=> sP28(X1,X0) ),
inference(definition_folding,[],[f411,f1233]) ).
tff(f1233,plain,
! [X1: $real,X0: $real] :
( sP28(X1,X0)
<=> ( ( $less(0.0,X1)
& $less(X0,0.0) )
| ( $less(X1,0.0)
& $less(0.0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
tff(f411,axiom,
! [X0: $real,X1: $real] :
( $less('fun_app$c'('times$a'(X0),X1),0.0)
<=> ( ( $less(0.0,X1)
& $less(X0,0.0) )
| ( $less(X1,0.0)
& $less(0.0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom409) ).
tff(f6073,plain,
spl183_425,
inference(avatar_split_clause,[],[f2778,f6071]) ).
tff(f6071,plain,
( spl183_425
<=> ! [X0: $real,X1: $real] :
( sP28(X1,X0)
| ~ $less('fun_app$c'('times$a'(X0),X1),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_425])]) ).
tff(f2778,plain,
! [X0: $real,X1: $real] :
( sP28(X1,X0)
| ~ $less('fun_app$c'('times$a'(X0),X1),0.0) ),
inference(cnf_transformation,[],[f1652]) ).
tff(f6069,plain,
spl183_424,
inference(avatar_split_clause,[],[f2777,f6067]) ).
tff(f6067,plain,
( spl183_424
<=> ! [X0: $real,X1: $real] :
( sP28(X0,X1)
| ~ $less(0.0,X0)
| ~ $less(X1,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_424])]) ).
tff(f2777,plain,
! [X0: $real,X1: $real] :
( sP28(X0,X1)
| ~ $less(0.0,X0)
| ~ $less(X1,0.0) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f1651,plain,
! [X0: $real,X1: $real] :
( ( sP28(X0,X1)
| ( ( ~ $less(0.0,X0)
| ~ $less(X1,0.0) )
& ( ~ $less(X0,0.0)
| ~ $less(0.0,X1) ) ) )
& ( ( $less(0.0,X0)
& $less(X1,0.0) )
| ( $less(X0,0.0)
& $less(0.0,X1) )
| ~ sP28(X0,X1) ) ),
inference(rectify,[],[f1650]) ).
tff(f1650,plain,
! [X1: $real,X0: $real] :
( ( sP28(X1,X0)
| ( ( ~ $less(0.0,X1)
| ~ $less(X0,0.0) )
& ( ~ $less(X1,0.0)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(0.0,X1)
& $less(X0,0.0) )
| ( $less(X1,0.0)
& $less(0.0,X0) )
| ~ sP28(X1,X0) ) ),
inference(flattening,[],[f1649]) ).
tff(f1649,plain,
! [X1: $real,X0: $real] :
( ( sP28(X1,X0)
| ( ( ~ $less(0.0,X1)
| ~ $less(X0,0.0) )
& ( ~ $less(X1,0.0)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(0.0,X1)
& $less(X0,0.0) )
| ( $less(X1,0.0)
& $less(0.0,X0) )
| ~ sP28(X1,X0) ) ),
inference(nnf_transformation,[],[f1233]) ).
tff(f6065,plain,
spl183_423,
inference(avatar_split_clause,[],[f2776,f6063]) ).
tff(f6063,plain,
( spl183_423
<=> ! [X0: $real,X1: $real] :
( sP28(X0,X1)
| ~ $less(X0,0.0)
| ~ $less(0.0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_423])]) ).
tff(f2776,plain,
! [X0: $real,X1: $real] :
( sP28(X0,X1)
| ~ $less(X0,0.0)
| ~ $less(0.0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f6061,plain,
spl183_422,
inference(avatar_split_clause,[],[f2775,f6059]) ).
tff(f6059,plain,
( spl183_422
<=> ! [X0: $real,X1: $real] :
( $less(0.0,X0)
| $less(X0,0.0)
| ~ sP28(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_422])]) ).
tff(f2775,plain,
! [X0: $real,X1: $real] :
( $less(0.0,X0)
| $less(X0,0.0)
| ~ sP28(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f6057,plain,
spl183_421,
inference(avatar_split_clause,[],[f2774,f6055]) ).
tff(f6055,plain,
( spl183_421
<=> ! [X0: $real,X1: $real] :
( $less(0.0,X0)
| $less(0.0,X1)
| ~ sP28(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_421])]) ).
tff(f2774,plain,
! [X0: $real,X1: $real] :
( $less(0.0,X0)
| $less(0.0,X1)
| ~ sP28(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f6053,plain,
spl183_420,
inference(avatar_split_clause,[],[f2773,f6051]) ).
tff(f6051,plain,
( spl183_420
<=> ! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(X0,0.0)
| ~ sP28(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_420])]) ).
tff(f2773,plain,
! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(X0,0.0)
| ~ sP28(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f6049,plain,
spl183_419,
inference(avatar_split_clause,[],[f2772,f6047]) ).
tff(f6047,plain,
( spl183_419
<=> ! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X1)
| ~ sP28(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_419])]) ).
tff(f2772,plain,
! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X1)
| ~ sP28(X0,X1) ),
inference(cnf_transformation,[],[f1651]) ).
tff(f6045,plain,
spl183_418,
inference(avatar_split_clause,[],[f2771,f6043]) ).
tff(f6043,plain,
( spl183_418
<=> ! [X0: $real,X1: $real] :
( $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP27(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_418])]) ).
tff(f2771,plain,
! [X0: $real,X1: $real] :
( $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP27(X1,X0) ),
inference(cnf_transformation,[],[f1648]) ).
tff(f1648,plain,
! [X0: $real,X1: $real] :
( ( $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP27(X1,X0) )
& ( sP27(X1,X0)
| ~ $less(0.0,'fun_app$c'('times$a'(X0),X1)) ) ),
inference(nnf_transformation,[],[f1232]) ).
tff(f1232,plain,
! [X0: $real,X1: $real] :
( $less(0.0,'fun_app$c'('times$a'(X0),X1))
<=> sP27(X1,X0) ),
inference(definition_folding,[],[f397,f1231]) ).
tff(f1231,plain,
! [X1: $real,X0: $real] :
( sP27(X1,X0)
<=> ( ( $less(X1,0.0)
& $less(X0,0.0) )
| ( $less(0.0,X1)
& $less(0.0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
tff(f397,axiom,
! [X0: $real,X1: $real] :
( $less(0.0,'fun_app$c'('times$a'(X0),X1))
<=> ( ( $less(X1,0.0)
& $less(X0,0.0) )
| ( $less(0.0,X1)
& $less(0.0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom395) ).
tff(f6041,plain,
spl183_417,
inference(avatar_split_clause,[],[f2770,f6039]) ).
tff(f2770,plain,
! [X0: $real,X1: $real] :
( sP27(X1,X0)
| ~ $less(0.0,'fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f1648]) ).
tff(f6037,plain,
spl183_416,
inference(avatar_split_clause,[],[f2769,f6035]) ).
tff(f6035,plain,
( spl183_416
<=> ! [X0: $real,X1: $real] :
( sP27(X0,X1)
| ~ $less(X0,0.0)
| ~ $less(X1,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_416])]) ).
tff(f2769,plain,
! [X0: $real,X1: $real] :
( sP27(X0,X1)
| ~ $less(X0,0.0)
| ~ $less(X1,0.0) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f1647,plain,
! [X0: $real,X1: $real] :
( ( sP27(X0,X1)
| ( ( ~ $less(X0,0.0)
| ~ $less(X1,0.0) )
& ( ~ $less(0.0,X0)
| ~ $less(0.0,X1) ) ) )
& ( ( $less(X0,0.0)
& $less(X1,0.0) )
| ( $less(0.0,X0)
& $less(0.0,X1) )
| ~ sP27(X0,X1) ) ),
inference(rectify,[],[f1646]) ).
tff(f1646,plain,
! [X1: $real,X0: $real] :
( ( sP27(X1,X0)
| ( ( ~ $less(X1,0.0)
| ~ $less(X0,0.0) )
& ( ~ $less(0.0,X1)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(X1,0.0)
& $less(X0,0.0) )
| ( $less(0.0,X1)
& $less(0.0,X0) )
| ~ sP27(X1,X0) ) ),
inference(flattening,[],[f1645]) ).
tff(f1645,plain,
! [X1: $real,X0: $real] :
( ( sP27(X1,X0)
| ( ( ~ $less(X1,0.0)
| ~ $less(X0,0.0) )
& ( ~ $less(0.0,X1)
| ~ $less(0.0,X0) ) ) )
& ( ( $less(X1,0.0)
& $less(X0,0.0) )
| ( $less(0.0,X1)
& $less(0.0,X0) )
| ~ sP27(X1,X0) ) ),
inference(nnf_transformation,[],[f1231]) ).
tff(f6033,plain,
spl183_415,
inference(avatar_split_clause,[],[f2768,f6031]) ).
tff(f6031,plain,
( spl183_415
<=> ! [X0: $real,X1: $real] :
( sP27(X0,X1)
| ~ $less(0.0,X0)
| ~ $less(0.0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_415])]) ).
tff(f2768,plain,
! [X0: $real,X1: $real] :
( sP27(X0,X1)
| ~ $less(0.0,X0)
| ~ $less(0.0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f6029,plain,
spl183_414,
inference(avatar_split_clause,[],[f2767,f6027]) ).
tff(f6027,plain,
( spl183_414
<=> ! [X0: $real,X1: $real] :
( $less(X0,0.0)
| $less(0.0,X0)
| ~ sP27(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_414])]) ).
tff(f2767,plain,
! [X0: $real,X1: $real] :
( $less(X0,0.0)
| $less(0.0,X0)
| ~ sP27(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f6025,plain,
spl183_413,
inference(avatar_split_clause,[],[f2766,f6023]) ).
tff(f6023,plain,
( spl183_413
<=> ! [X0: $real,X1: $real] :
( $less(X0,0.0)
| $less(0.0,X1)
| ~ sP27(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_413])]) ).
tff(f2766,plain,
! [X0: $real,X1: $real] :
( $less(X0,0.0)
| $less(0.0,X1)
| ~ sP27(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f6021,plain,
spl183_412,
inference(avatar_split_clause,[],[f2765,f6019]) ).
tff(f6019,plain,
( spl183_412
<=> ! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X0)
| ~ sP27(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_412])]) ).
tff(f2765,plain,
! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X0)
| ~ sP27(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f6017,plain,
spl183_411,
inference(avatar_split_clause,[],[f2764,f6015]) ).
tff(f6015,plain,
( spl183_411
<=> ! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X1)
| ~ sP27(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_411])]) ).
tff(f2764,plain,
! [X0: $real,X1: $real] :
( $less(X1,0.0)
| $less(0.0,X1)
| ~ sP27(X0,X1) ),
inference(cnf_transformation,[],[f1647]) ).
tff(f6013,plain,
spl183_410,
inference(avatar_split_clause,[],[f2763,f6011]) ).
tff(f6011,plain,
( spl183_410
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
| ~ sP26(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_410])]) ).
tff(f2763,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
| ~ sP26(X1,X0) ),
inference(cnf_transformation,[],[f1644]) ).
tff(f1644,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
| ~ sP26(X1,X0) )
& ( sP26(X1,X0)
| ~ 'fun_app$b'('less$'('times$'(X0,X1)),'zero$') ) ),
inference(nnf_transformation,[],[f1230]) ).
tff(f1230,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
<=> sP26(X1,X0) ),
inference(definition_folding,[],[f295,f1229]) ).
tff(f295,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('times$'(X0,X1)),'zero$')
<=> ( ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'('zero$'),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom293) ).
tff(f6009,plain,
spl183_409,
inference(avatar_split_clause,[],[f2762,f6007]) ).
tff(f2762,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP26(X1,X0)
| ~ 'fun_app$b'('less$'('times$'(X0,X1)),'zero$') ),
inference(cnf_transformation,[],[f1644]) ).
tff(f6005,plain,
spl183_408,
inference(avatar_split_clause,[],[f2755,f6003]) ).
tff(f6003,plain,
( spl183_408
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
| ~ sP25(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_408])]) ).
tff(f2755,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
| ~ sP25(X1,X0) ),
inference(cnf_transformation,[],[f1640]) ).
tff(f1640,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
| ~ sP25(X1,X0) )
& ( sP25(X1,X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$') ) ),
inference(nnf_transformation,[],[f1228]) ).
tff(f1228,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
<=> sP25(X1,X0) ),
inference(definition_folding,[],[f621,f1227]) ).
tff(f621,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$')
<=> ( ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'('zero$'),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom619) ).
tff(f6001,plain,
spl183_407,
inference(avatar_split_clause,[],[f2754,f5999]) ).
tff(f2754,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP25(X1,X0)
| ~ 'fun_app$b'('less_eq$'('times$'(X0,X1)),'zero$') ),
inference(cnf_transformation,[],[f1640]) ).
tff(f5997,plain,
spl183_406,
inference(avatar_split_clause,[],[f2744,f5995]) ).
tff(f2744,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1)) ),
inference(cnf_transformation,[],[f1635]) ).
tff(f1635,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1))
| ~ $less(X0,X1) )
& ( $less(X0,X1)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1)) ) ),
inference(nnf_transformation,[],[f46]) ).
tff(f46,axiom,
! [X0: $real,X1: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'ereal$'(X1))
<=> $less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom44) ).
tff(f5993,plain,
spl183_405,
inference(avatar_split_clause,[],[f2741,f5991]) ).
tff(f2741,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
| ~ sP24(X1,X0) ),
inference(cnf_transformation,[],[f1633]) ).
tff(f1633,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
| ~ sP24(X1,X0) )
& ( sP24(X1,X0)
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,X1)) ) ),
inference(nnf_transformation,[],[f1226]) ).
tff(f1226,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
<=> sP24(X1,X0) ),
inference(definition_folding,[],[f296,f1225]) ).
tff(f296,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),'times$'(X0,X1))
<=> ( ( 'fun_app$b'('less$'(X1),'zero$')
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'('zero$'),X1)
& 'fun_app$b'('less$'('zero$'),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom294) ).
tff(f5989,plain,
spl183_404,
inference(avatar_split_clause,[],[f2740,f5987]) ).
tff(f5987,plain,
( spl183_404
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X1,X0)
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_404])]) ).
tff(f2740,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP24(X1,X0)
| ~ 'fun_app$b'('less$'('zero$'),'times$'(X0,X1)) ),
inference(cnf_transformation,[],[f1633]) ).
tff(f5985,plain,
spl183_403,
inference(avatar_split_clause,[],[f2733,f5983]) ).
tff(f5983,plain,
( spl183_403
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1))
| ~ sP23(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_403])]) ).
tff(f2733,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1))
| ~ sP23(X1,X0) ),
inference(cnf_transformation,[],[f1629]) ).
tff(f1629,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1))
| ~ sP23(X1,X0) )
& ( sP23(X1,X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1)) ) ),
inference(nnf_transformation,[],[f1224]) ).
tff(f1224,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1))
<=> sP23(X1,X0) ),
inference(definition_folding,[],[f622,f1223]) ).
tff(f622,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1))
<=> ( ( 'fun_app$b'('less_eq$'(X1),'zero$')
& 'fun_app$b'('less_eq$'(X0),'zero$') )
| ( 'fun_app$b'('less_eq$'('zero$'),X1)
& 'fun_app$b'('less_eq$'('zero$'),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom620) ).
tff(f5981,plain,
( spl183_402
| ~ spl183_103
| ~ spl183_360 ),
inference(avatar_split_clause,[],[f5891,f5802,f4236,f5978]) ).
tff(f5978,plain,
( spl183_402
<=> sP20('ereal$'(-1.0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_402])]) ).
tff(f4236,plain,
( spl183_103
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_103])]) ).
tff(f5802,plain,
( spl183_360
<=> sP18('ereal$'(-1.0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_360])]) ).
tff(f5891,plain,
( sP20('ereal$'(-1.0),'infinity$')
| ~ spl183_103
| ~ spl183_360 ),
inference(resolution,[],[f5804,f4237]) ).
tff(f4237,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ sP18(X0,X1)
| sP20(X0,X1) )
| ~ spl183_103 ),
inference(avatar_component_clause,[],[f4236]) ).
tff(f5804,plain,
( sP18('ereal$'(-1.0),'infinity$')
| ~ spl183_360 ),
inference(avatar_component_clause,[],[f5802]) ).
tff(f5976,plain,
spl183_401,
inference(avatar_split_clause,[],[f2732,f5974]) ).
tff(f5974,plain,
( spl183_401
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X1,X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_401])]) ).
tff(f2732,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP23(X1,X0)
| ~ 'fun_app$b'('less_eq$'('zero$'),'times$'(X0,X1)) ),
inference(cnf_transformation,[],[f1629]) ).
tff(f5972,plain,
spl183_400,
inference(avatar_split_clause,[],[f2725,f5970]) ).
tff(f2725,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP22(X1,X0) ),
inference(cnf_transformation,[],[f1625]) ).
tff(f1625,plain,
! [X0: $real,X1: $real] :
( ( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
| ~ sP22(X1,X0) )
& ( sP22(X1,X0)
| $less(0.0,'fun_app$c'('times$a'(X0),X1)) ) ),
inference(nnf_transformation,[],[f1222]) ).
tff(f1222,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
<=> sP22(X1,X0) ),
inference(definition_folding,[],[f690,f1221]) ).
tff(f1221,plain,
! [X1: $real,X0: $real] :
( sP22(X1,X0)
<=> ( ( ~ $less(X1,0.0)
& ~ $less(0.0,X0) )
| ( ~ $less(0.0,X1)
& ~ $less(X0,0.0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
tff(f690,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X1))
<=> ( ( ~ $less(X1,0.0)
& ~ $less(0.0,X0) )
| ( ~ $less(0.0,X1)
& ~ $less(X0,0.0) ) ) ),
inference(theory_normalization,[],[f593]) ).
tff(f593,axiom,
! [X0: $real,X1: $real] :
( $lesseq('fun_app$c'('times$a'(X0),X1),0.0)
<=> ( ( $lesseq(0.0,X1)
& $lesseq(X0,0.0) )
| ( $lesseq(X1,0.0)
& $lesseq(0.0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom591) ).
tff(f5968,plain,
spl183_399,
inference(avatar_split_clause,[],[f2724,f5966]) ).
tff(f5966,plain,
( spl183_399
<=> ! [X0: $real,X1: $real] :
( sP22(X1,X0)
| $less(0.0,'fun_app$c'('times$a'(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_399])]) ).
tff(f2724,plain,
! [X0: $real,X1: $real] :
( sP22(X1,X0)
| $less(0.0,'fun_app$c'('times$a'(X0),X1)) ),
inference(cnf_transformation,[],[f1625]) ).
tff(f5964,plain,
spl183_398,
inference(avatar_split_clause,[],[f2723,f5962]) ).
tff(f5962,plain,
( spl183_398
<=> ! [X0: $real,X1: $real] :
( sP22(X0,X1)
| $less(X0,0.0)
| $less(0.0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_398])]) ).
tff(f2723,plain,
! [X0: $real,X1: $real] :
( sP22(X0,X1)
| $less(X0,0.0)
| $less(0.0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f1624,plain,
! [X0: $real,X1: $real] :
( ( sP22(X0,X1)
| ( ( $less(X0,0.0)
| $less(0.0,X1) )
& ( $less(0.0,X0)
| $less(X1,0.0) ) ) )
& ( ( ~ $less(X0,0.0)
& ~ $less(0.0,X1) )
| ( ~ $less(0.0,X0)
& ~ $less(X1,0.0) )
| ~ sP22(X0,X1) ) ),
inference(rectify,[],[f1623]) ).
tff(f1623,plain,
! [X1: $real,X0: $real] :
( ( sP22(X1,X0)
| ( ( $less(X1,0.0)
| $less(0.0,X0) )
& ( $less(0.0,X1)
| $less(X0,0.0) ) ) )
& ( ( ~ $less(X1,0.0)
& ~ $less(0.0,X0) )
| ( ~ $less(0.0,X1)
& ~ $less(X0,0.0) )
| ~ sP22(X1,X0) ) ),
inference(flattening,[],[f1622]) ).
tff(f1622,plain,
! [X1: $real,X0: $real] :
( ( sP22(X1,X0)
| ( ( $less(X1,0.0)
| $less(0.0,X0) )
& ( $less(0.0,X1)
| $less(X0,0.0) ) ) )
& ( ( ~ $less(X1,0.0)
& ~ $less(0.0,X0) )
| ( ~ $less(0.0,X1)
& ~ $less(X0,0.0) )
| ~ sP22(X1,X0) ) ),
inference(nnf_transformation,[],[f1221]) ).
tff(f5960,plain,
spl183_397,
inference(avatar_split_clause,[],[f2722,f5958]) ).
tff(f5958,plain,
( spl183_397
<=> ! [X0: $real,X1: $real] :
( sP22(X0,X1)
| $less(0.0,X0)
| $less(X1,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_397])]) ).
tff(f2722,plain,
! [X0: $real,X1: $real] :
( sP22(X0,X1)
| $less(0.0,X0)
| $less(X1,0.0) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f5956,plain,
spl183_396,
inference(avatar_split_clause,[],[f2721,f5954]) ).
tff(f5954,plain,
( spl183_396
<=> ! [X0: $real,X1: $real] :
( ~ $less(X0,0.0)
| ~ $less(0.0,X0)
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_396])]) ).
tff(f2721,plain,
! [X0: $real,X1: $real] :
( ~ $less(X0,0.0)
| ~ $less(0.0,X0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f5952,plain,
spl183_395,
inference(avatar_split_clause,[],[f2720,f5950]) ).
tff(f5950,plain,
( spl183_395
<=> ! [X0: $real,X1: $real] :
( ~ $less(X0,0.0)
| ~ $less(X1,0.0)
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_395])]) ).
tff(f2720,plain,
! [X0: $real,X1: $real] :
( ~ $less(X0,0.0)
| ~ $less(X1,0.0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f5948,plain,
spl183_394,
inference(avatar_split_clause,[],[f2719,f5946]) ).
tff(f5946,plain,
( spl183_394
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(0.0,X0)
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_394])]) ).
tff(f2719,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(0.0,X0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f5944,plain,
spl183_393,
inference(avatar_split_clause,[],[f2718,f5942]) ).
tff(f5942,plain,
( spl183_393
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X1,0.0)
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_393])]) ).
tff(f2718,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X1,0.0)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f1624]) ).
tff(f5940,plain,
spl183_392,
inference(avatar_split_clause,[],[f2717,f5938]) ).
tff(f5938,plain,
( spl183_392
<=> ! [X0: $real,X1: $real] :
( ~ $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP21(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_392])]) ).
tff(f2717,plain,
! [X0: $real,X1: $real] :
( ~ $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP21(X1,X0) ),
inference(cnf_transformation,[],[f1621]) ).
tff(f1621,plain,
! [X0: $real,X1: $real] :
( ( ~ $less('fun_app$c'('times$a'(X0),X1),0.0)
| ~ sP21(X1,X0) )
& ( sP21(X1,X0)
| $less('fun_app$c'('times$a'(X0),X1),0.0) ) ),
inference(nnf_transformation,[],[f1220]) ).
tff(f1220,plain,
! [X0: $real,X1: $real] :
( ~ $less('fun_app$c'('times$a'(X0),X1),0.0)
<=> sP21(X1,X0) ),
inference(definition_folding,[],[f689,f1219]) ).
tff(f1219,plain,
! [X1: $real,X0: $real] :
( sP21(X1,X0)
<=> ( ( ~ $less(0.0,X1)
& ~ $less(0.0,X0) )
| ( ~ $less(X1,0.0)
& ~ $less(X0,0.0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
tff(f689,plain,
! [X0: $real,X1: $real] :
( ~ $less('fun_app$c'('times$a'(X0),X1),0.0)
<=> ( ( ~ $less(0.0,X1)
& ~ $less(0.0,X0) )
| ( ~ $less(X1,0.0)
& ~ $less(X0,0.0) ) ) ),
inference(theory_normalization,[],[f576]) ).
tff(f576,axiom,
! [X0: $real,X1: $real] :
( $lesseq(0.0,'fun_app$c'('times$a'(X0),X1))
<=> ( ( $lesseq(X1,0.0)
& $lesseq(X0,0.0) )
| ( $lesseq(0.0,X1)
& $lesseq(0.0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom574) ).
tff(f5936,plain,
( spl183_391
| ~ spl183_104
| ~ spl183_349 ),
inference(avatar_split_clause,[],[f5848,f5757,f4240,f5933]) ).
tff(f5933,plain,
( spl183_391
<=> sP20('infinity$','ereal$'(-1.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_391])]) ).
tff(f4240,plain,
( spl183_104
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_104])]) ).
tff(f5757,plain,
( spl183_349
<=> sP19('infinity$','ereal$'(-1.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_349])]) ).
tff(f5848,plain,
( sP20('infinity$','ereal$'(-1.0))
| ~ spl183_104
| ~ spl183_349 ),
inference(resolution,[],[f5759,f4241]) ).
tff(f4241,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ sP19(X0,X1)
| sP20(X0,X1) )
| ~ spl183_104 ),
inference(avatar_component_clause,[],[f4240]) ).
tff(f5759,plain,
( sP19('infinity$','ereal$'(-1.0))
| ~ spl183_349 ),
inference(avatar_component_clause,[],[f5757]) ).
tff(f5931,plain,
spl183_390,
inference(avatar_split_clause,[],[f2716,f5929]) ).
tff(f5929,plain,
( spl183_390
<=> ! [X0: $real,X1: $real] :
( sP21(X1,X0)
| $less('fun_app$c'('times$a'(X0),X1),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_390])]) ).
tff(f2716,plain,
! [X0: $real,X1: $real] :
( sP21(X1,X0)
| $less('fun_app$c'('times$a'(X0),X1),0.0) ),
inference(cnf_transformation,[],[f1621]) ).
tff(f5927,plain,
spl183_389,
inference(avatar_split_clause,[],[f2715,f5925]) ).
tff(f5925,plain,
( spl183_389
<=> ! [X0: $real,X1: $real] :
( sP21(X0,X1)
| $less(0.0,X0)
| $less(0.0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_389])]) ).
tff(f2715,plain,
! [X0: $real,X1: $real] :
( sP21(X0,X1)
| $less(0.0,X0)
| $less(0.0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f1620,plain,
! [X0: $real,X1: $real] :
( ( sP21(X0,X1)
| ( ( $less(0.0,X0)
| $less(0.0,X1) )
& ( $less(X0,0.0)
| $less(X1,0.0) ) ) )
& ( ( ~ $less(0.0,X0)
& ~ $less(0.0,X1) )
| ( ~ $less(X0,0.0)
& ~ $less(X1,0.0) )
| ~ sP21(X0,X1) ) ),
inference(rectify,[],[f1619]) ).
tff(f1619,plain,
! [X1: $real,X0: $real] :
( ( sP21(X1,X0)
| ( ( $less(0.0,X1)
| $less(0.0,X0) )
& ( $less(X1,0.0)
| $less(X0,0.0) ) ) )
& ( ( ~ $less(0.0,X1)
& ~ $less(0.0,X0) )
| ( ~ $less(X1,0.0)
& ~ $less(X0,0.0) )
| ~ sP21(X1,X0) ) ),
inference(flattening,[],[f1618]) ).
tff(f1618,plain,
! [X1: $real,X0: $real] :
( ( sP21(X1,X0)
| ( ( $less(0.0,X1)
| $less(0.0,X0) )
& ( $less(X1,0.0)
| $less(X0,0.0) ) ) )
& ( ( ~ $less(0.0,X1)
& ~ $less(0.0,X0) )
| ( ~ $less(X1,0.0)
& ~ $less(X0,0.0) )
| ~ sP21(X1,X0) ) ),
inference(nnf_transformation,[],[f1219]) ).
tff(f5923,plain,
spl183_388,
inference(avatar_split_clause,[],[f2714,f5921]) ).
tff(f5921,plain,
( spl183_388
<=> ! [X0: $real,X1: $real] :
( sP21(X0,X1)
| $less(X0,0.0)
| $less(X1,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_388])]) ).
tff(f2714,plain,
! [X0: $real,X1: $real] :
( sP21(X0,X1)
| $less(X0,0.0)
| $less(X1,0.0) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f5919,plain,
spl183_387,
inference(avatar_split_clause,[],[f2713,f5917]) ).
tff(f5917,plain,
( spl183_387
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X0)
| ~ $less(X0,0.0)
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_387])]) ).
tff(f2713,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X0)
| ~ $less(X0,0.0)
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f5915,plain,
spl183_386,
inference(avatar_split_clause,[],[f2712,f5913]) ).
tff(f5913,plain,
( spl183_386
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X0)
| ~ $less(X1,0.0)
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_386])]) ).
tff(f2712,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X0)
| ~ $less(X1,0.0)
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f5911,plain,
spl183_385,
inference(avatar_split_clause,[],[f2711,f5909]) ).
tff(f5909,plain,
( spl183_385
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X0,0.0)
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_385])]) ).
tff(f2711,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X0,0.0)
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f5907,plain,
spl183_384,
inference(avatar_split_clause,[],[f2710,f5905]) ).
tff(f5905,plain,
( spl183_384
<=> ! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X1,0.0)
| ~ sP21(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_384])]) ).
tff(f2710,plain,
! [X0: $real,X1: $real] :
( ~ $less(0.0,X1)
| ~ $less(X1,0.0)
| ~ sP21(X0,X1) ),
inference(cnf_transformation,[],[f1620]) ).
tff(f5903,plain,
spl183_383,
inference(avatar_split_clause,[],[f2658,f5901]) ).
tff(f5901,plain,
( spl183_383
<=> ! [X0: $int,X1: $int] :
( sP17(X0,X1)
| ~ $less(0,X0)
| ~ $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_383])]) ).
tff(f2658,plain,
! [X0: $int,X1: $int] :
( sP17(X0,X1)
| ~ $less(0,X0)
| ~ $less(X1,0) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f1583,plain,
! [X0: $int,X1: $int] :
( ( sP17(X0,X1)
| ( ( ~ $less(0,X0)
| ~ $less(X1,0) )
& ( ~ $less(X0,0)
| ~ $less(0,X1) ) ) )
& ( ( $less(0,X0)
& $less(X1,0) )
| ( $less(X0,0)
& $less(0,X1) )
| ~ sP17(X0,X1) ) ),
inference(rectify,[],[f1582]) ).
tff(f1582,plain,
! [X1: $int,X0: $int] :
( ( sP17(X1,X0)
| ( ( ~ $less(0,X1)
| ~ $less(X0,0) )
& ( ~ $less(X1,0)
| ~ $less(0,X0) ) ) )
& ( ( $less(0,X1)
& $less(X0,0) )
| ( $less(X1,0)
& $less(0,X0) )
| ~ sP17(X1,X0) ) ),
inference(flattening,[],[f1581]) ).
tff(f1581,plain,
! [X1: $int,X0: $int] :
( ( sP17(X1,X0)
| ( ( ~ $less(0,X1)
| ~ $less(X0,0) )
& ( ~ $less(X1,0)
| ~ $less(0,X0) ) ) )
& ( ( $less(0,X1)
& $less(X0,0) )
| ( $less(X1,0)
& $less(0,X0) )
| ~ sP17(X1,X0) ) ),
inference(nnf_transformation,[],[f1213]) ).
tff(f1213,plain,
! [X1: $int,X0: $int] :
( sP17(X1,X0)
<=> ( ( $less(0,X1)
& $less(X0,0) )
| ( $less(X1,0)
& $less(0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
tff(f5899,plain,
spl183_382,
inference(avatar_split_clause,[],[f2657,f5897]) ).
tff(f5897,plain,
( spl183_382
<=> ! [X0: $int,X1: $int] :
( sP17(X0,X1)
| ~ $less(X0,0)
| ~ $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_382])]) ).
tff(f2657,plain,
! [X0: $int,X1: $int] :
( sP17(X0,X1)
| ~ $less(X0,0)
| ~ $less(0,X1) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f5895,plain,
spl183_381,
inference(avatar_split_clause,[],[f2656,f5893]) ).
tff(f5893,plain,
( spl183_381
<=> ! [X0: $int,X1: $int] :
( $less(0,X0)
| $less(X0,0)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_381])]) ).
tff(f2656,plain,
! [X0: $int,X1: $int] :
( $less(0,X0)
| $less(X0,0)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f5888,plain,
spl183_380,
inference(avatar_split_clause,[],[f2655,f5886]) ).
tff(f5886,plain,
( spl183_380
<=> ! [X0: $int,X1: $int] :
( $less(0,X0)
| $less(0,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_380])]) ).
tff(f2655,plain,
! [X0: $int,X1: $int] :
( $less(0,X0)
| $less(0,X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f5884,plain,
spl183_379,
inference(avatar_split_clause,[],[f2654,f5882]) ).
tff(f5882,plain,
( spl183_379
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_379])]) ).
tff(f2654,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(X0,0)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f5880,plain,
spl183_378,
inference(avatar_split_clause,[],[f2653,f5878]) ).
tff(f5878,plain,
( spl183_378
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X1)
| ~ sP17(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_378])]) ).
tff(f2653,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X1)
| ~ sP17(X0,X1) ),
inference(cnf_transformation,[],[f1583]) ).
tff(f5876,plain,
spl183_377,
inference(avatar_split_clause,[],[f2648,f5874]) ).
tff(f5874,plain,
( spl183_377
<=> ! [X0: $int,X1: $int] :
( sP16(X0,X1)
| ~ $less(X0,0)
| ~ $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_377])]) ).
tff(f2648,plain,
! [X0: $int,X1: $int] :
( sP16(X0,X1)
| ~ $less(X0,0)
| ~ $less(X1,0) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f1578,plain,
! [X0: $int,X1: $int] :
( ( sP16(X0,X1)
| ( ( ~ $less(X0,0)
| ~ $less(X1,0) )
& ( ~ $less(0,X0)
| ~ $less(0,X1) ) ) )
& ( ( $less(X0,0)
& $less(X1,0) )
| ( $less(0,X0)
& $less(0,X1) )
| ~ sP16(X0,X1) ) ),
inference(rectify,[],[f1577]) ).
tff(f1577,plain,
! [X1: $int,X0: $int] :
( ( sP16(X1,X0)
| ( ( ~ $less(X1,0)
| ~ $less(X0,0) )
& ( ~ $less(0,X1)
| ~ $less(0,X0) ) ) )
& ( ( $less(X1,0)
& $less(X0,0) )
| ( $less(0,X1)
& $less(0,X0) )
| ~ sP16(X1,X0) ) ),
inference(flattening,[],[f1576]) ).
tff(f1576,plain,
! [X1: $int,X0: $int] :
( ( sP16(X1,X0)
| ( ( ~ $less(X1,0)
| ~ $less(X0,0) )
& ( ~ $less(0,X1)
| ~ $less(0,X0) ) ) )
& ( ( $less(X1,0)
& $less(X0,0) )
| ( $less(0,X1)
& $less(0,X0) )
| ~ sP16(X1,X0) ) ),
inference(nnf_transformation,[],[f1211]) ).
tff(f1211,plain,
! [X1: $int,X0: $int] :
( sP16(X1,X0)
<=> ( ( $less(X1,0)
& $less(X0,0) )
| ( $less(0,X1)
& $less(0,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
tff(f5872,plain,
spl183_376,
inference(avatar_split_clause,[],[f2647,f5870]) ).
tff(f5870,plain,
( spl183_376
<=> ! [X0: $int,X1: $int] :
( sP16(X0,X1)
| ~ $less(0,X0)
| ~ $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_376])]) ).
tff(f2647,plain,
! [X0: $int,X1: $int] :
( sP16(X0,X1)
| ~ $less(0,X0)
| ~ $less(0,X1) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5868,plain,
spl183_375,
inference(avatar_split_clause,[],[f2646,f5866]) ).
tff(f5866,plain,
( spl183_375
<=> ! [X0: $int,X1: $int] :
( $less(X0,0)
| $less(0,X0)
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_375])]) ).
tff(f2646,plain,
! [X0: $int,X1: $int] :
( $less(X0,0)
| $less(0,X0)
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5864,plain,
spl183_374,
inference(avatar_split_clause,[],[f2645,f5862]) ).
tff(f5862,plain,
( spl183_374
<=> ! [X0: $int,X1: $int] :
( $less(X0,0)
| $less(0,X1)
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_374])]) ).
tff(f2645,plain,
! [X0: $int,X1: $int] :
( $less(X0,0)
| $less(0,X1)
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5860,plain,
spl183_373,
inference(avatar_split_clause,[],[f2644,f5858]) ).
tff(f5858,plain,
( spl183_373
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X0)
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_373])]) ).
tff(f2644,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X0)
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5856,plain,
spl183_372,
inference(avatar_split_clause,[],[f2643,f5854]) ).
tff(f5854,plain,
( spl183_372
<=> ! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X1)
| ~ sP16(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_372])]) ).
tff(f2643,plain,
! [X0: $int,X1: $int] :
( $less(X1,0)
| $less(0,X1)
| ~ sP16(X0,X1) ),
inference(cnf_transformation,[],[f1578]) ).
tff(f5852,plain,
spl183_371,
inference(avatar_split_clause,[],[f2640,f5850]) ).
tff(f5850,plain,
( spl183_371
<=> ! [X0: $int,X1: $int] :
( sP15(X0,X1)
| $less(X0,0)
| $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_371])]) ).
tff(f2640,plain,
! [X0: $int,X1: $int] :
( sP15(X0,X1)
| $less(X0,0)
| $less(0,X1) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f1574,plain,
! [X0: $int,X1: $int] :
( ( sP15(X0,X1)
| ( ( $less(X0,0)
| $less(0,X1) )
& ( $less(0,X0)
| $less(X1,0) ) ) )
& ( ( ~ $less(X0,0)
& ~ $less(0,X1) )
| ( ~ $less(0,X0)
& ~ $less(X1,0) )
| ~ sP15(X0,X1) ) ),
inference(rectify,[],[f1573]) ).
tff(f1573,plain,
! [X1: $int,X0: $int] :
( ( sP15(X1,X0)
| ( ( $less(X1,0)
| $less(0,X0) )
& ( $less(0,X1)
| $less(X0,0) ) ) )
& ( ( ~ $less(X1,0)
& ~ $less(0,X0) )
| ( ~ $less(0,X1)
& ~ $less(X0,0) )
| ~ sP15(X1,X0) ) ),
inference(flattening,[],[f1572]) ).
tff(f1572,plain,
! [X1: $int,X0: $int] :
( ( sP15(X1,X0)
| ( ( $less(X1,0)
| $less(0,X0) )
& ( $less(0,X1)
| $less(X0,0) ) ) )
& ( ( ~ $less(X1,0)
& ~ $less(0,X0) )
| ( ~ $less(0,X1)
& ~ $less(X0,0) )
| ~ sP15(X1,X0) ) ),
inference(nnf_transformation,[],[f1209]) ).
tff(f1209,plain,
! [X1: $int,X0: $int] :
( sP15(X1,X0)
<=> ( ( ~ $less(X1,0)
& ~ $less(0,X0) )
| ( ~ $less(0,X1)
& ~ $less(X0,0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
tff(f5845,plain,
spl183_370,
inference(avatar_split_clause,[],[f2639,f5843]) ).
tff(f5843,plain,
( spl183_370
<=> ! [X0: $int,X1: $int] :
( sP15(X0,X1)
| $less(0,X0)
| $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_370])]) ).
tff(f2639,plain,
! [X0: $int,X1: $int] :
( sP15(X0,X1)
| $less(0,X0)
| $less(X1,0) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5841,plain,
spl183_369,
inference(avatar_split_clause,[],[f2638,f5839]) ).
tff(f5839,plain,
( spl183_369
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(0,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_369])]) ).
tff(f2638,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(0,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5837,plain,
spl183_368,
inference(avatar_split_clause,[],[f2637,f5835]) ).
tff(f5835,plain,
( spl183_368
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_368])]) ).
tff(f2637,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,0)
| ~ $less(X1,0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5833,plain,
spl183_367,
inference(avatar_split_clause,[],[f2636,f5831]) ).
tff(f5831,plain,
( spl183_367
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(0,X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_367])]) ).
tff(f2636,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(0,X0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5829,plain,
spl183_366,
inference(avatar_split_clause,[],[f2635,f5827]) ).
tff(f5827,plain,
( spl183_366
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_366])]) ).
tff(f2635,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,0)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f1574]) ).
tff(f5825,plain,
spl183_365,
inference(avatar_split_clause,[],[f2630,f5823]) ).
tff(f5823,plain,
( spl183_365
<=> ! [X0: $int,X1: $int] :
( sP14(X0,X1)
| $less(0,X0)
| $less(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_365])]) ).
tff(f2630,plain,
! [X0: $int,X1: $int] :
( sP14(X0,X1)
| $less(0,X0)
| $less(0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f1569,plain,
! [X0: $int,X1: $int] :
( ( sP14(X0,X1)
| ( ( $less(0,X0)
| $less(0,X1) )
& ( $less(X0,0)
| $less(X1,0) ) ) )
& ( ( ~ $less(0,X0)
& ~ $less(0,X1) )
| ( ~ $less(X0,0)
& ~ $less(X1,0) )
| ~ sP14(X0,X1) ) ),
inference(rectify,[],[f1568]) ).
tff(f1568,plain,
! [X1: $int,X0: $int] :
( ( sP14(X1,X0)
| ( ( $less(0,X1)
| $less(0,X0) )
& ( $less(X1,0)
| $less(X0,0) ) ) )
& ( ( ~ $less(0,X1)
& ~ $less(0,X0) )
| ( ~ $less(X1,0)
& ~ $less(X0,0) )
| ~ sP14(X1,X0) ) ),
inference(flattening,[],[f1567]) ).
tff(f1567,plain,
! [X1: $int,X0: $int] :
( ( sP14(X1,X0)
| ( ( $less(0,X1)
| $less(0,X0) )
& ( $less(X1,0)
| $less(X0,0) ) ) )
& ( ( ~ $less(0,X1)
& ~ $less(0,X0) )
| ( ~ $less(X1,0)
& ~ $less(X0,0) )
| ~ sP14(X1,X0) ) ),
inference(nnf_transformation,[],[f1207]) ).
tff(f1207,plain,
! [X1: $int,X0: $int] :
( sP14(X1,X0)
<=> ( ( ~ $less(0,X1)
& ~ $less(0,X0) )
| ( ~ $less(X1,0)
& ~ $less(X0,0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
tff(f5821,plain,
spl183_364,
inference(avatar_split_clause,[],[f2629,f5819]) ).
tff(f5819,plain,
( spl183_364
<=> ! [X0: $int,X1: $int] :
( sP14(X0,X1)
| $less(X0,0)
| $less(X1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_364])]) ).
tff(f2629,plain,
! [X0: $int,X1: $int] :
( sP14(X0,X1)
| $less(X0,0)
| $less(X1,0) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f5817,plain,
spl183_363,
inference(avatar_split_clause,[],[f2628,f5815]) ).
tff(f5815,plain,
( spl183_363
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| ~ $less(X0,0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_363])]) ).
tff(f2628,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| ~ $less(X0,0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f5813,plain,
spl183_362,
inference(avatar_split_clause,[],[f2627,f5811]) ).
tff(f5811,plain,
( spl183_362
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| ~ $less(X1,0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_362])]) ).
tff(f2627,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X0)
| ~ $less(X1,0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f5809,plain,
spl183_361,
inference(avatar_split_clause,[],[f2626,f5807]) ).
tff(f5807,plain,
( spl183_361
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X0,0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_361])]) ).
tff(f2626,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X0,0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f5805,plain,
( spl183_360
| ~ spl183_225
| ~ spl183_233 ),
inference(avatar_split_clause,[],[f4941,f4805,f4769,f5802]) ).
tff(f4941,plain,
( sP18('ereal$'(-1.0),'infinity$')
| ~ spl183_225
| ~ spl183_233 ),
inference(resolution,[],[f4770,f4807]) ).
tff(f5800,plain,
spl183_359,
inference(avatar_split_clause,[],[f2625,f5798]) ).
tff(f5798,plain,
( spl183_359
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_359])]) ).
tff(f2625,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,X1)
| ~ $less(X1,0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f1569]) ).
tff(f5796,plain,
spl183_358,
inference(avatar_split_clause,[],[f2520,f5794]) ).
tff(f5794,plain,
( spl183_358
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK132(X0,X1)) = X0 )
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_358])]) ).
tff(f2520,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK132(X0,X1)) = X0 )
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1506]) ).
tff(f1506,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'ereal$'(sK132(X0,X1)) = X0 )
& ( 'ereal$'(sK131(X0,X1)) = X1 ) )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK131,sK132])],[f1504,f1505]) ).
tff(f1505,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( ( 'ereal$'(sK132(X0,X1)) = X0 )
& ( 'ereal$'(sK131(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1504,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real,X3: $real] :
( ( 'ereal$'(X3) = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f1503]) ).
tff(f1503,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real,X7: $real] :
( ( 'ereal$'(X7) = X1 )
& ( 'ereal$'(X6) = X0 ) )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f1195]) ).
tff(f1195,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X6: $real,X7: $real] :
( ( 'ereal$'(X7) = X1 )
& ( 'ereal$'(X6) = X0 ) )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
tff(f5792,plain,
spl183_357,
inference(avatar_split_clause,[],[f2519,f5790]) ).
tff(f5790,plain,
( spl183_357
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK131(X0,X1)) = X1 )
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_357])]) ).
tff(f2519,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK131(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f1506]) ).
tff(f5788,plain,
spl183_356,
inference(avatar_split_clause,[],[f2517,f5786]) ).
tff(f5786,plain,
( spl183_356
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK130(X0,X1)) = X1 )
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_356])]) ).
tff(f2517,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK130(X0,X1)) = X1 )
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f1502]) ).
tff(f1502,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK130(X0,X1)) = X1 ) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK130])],[f1500,f1501]) ).
tff(f1501,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK130(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1500,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f1499]) ).
tff(f1499,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( ( 'infinity$' = X1 )
& ( 'ereal$'(X5) = X0 ) )
| ~ sP5(X1,X0) ),
inference(nnf_transformation,[],[f1196]) ).
tff(f1196,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X5: $real] :
( ( 'infinity$' = X1 )
& ( 'ereal$'(X5) = X0 ) )
| ~ sP5(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
tff(f5784,plain,
spl183_355,
inference(avatar_split_clause,[],[f2515,f5782]) ).
tff(f5782,plain,
( spl183_355
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK129(X0,X1)) = X1 )
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_355])]) ).
tff(f2515,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK129(X0,X1)) = X1 )
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f1498]) ).
tff(f5780,plain,
spl183_354,
inference(avatar_split_clause,[],[f2514,f5778]) ).
tff(f5778,plain,
( spl183_354
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK128(X0,X1)) = X0 )
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_354])]) ).
tff(f2514,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK128(X0,X1)) = X0 )
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f1494]) ).
tff(f1494,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'ereal$'(sK128(X0,X1)) = X0 )
& ( 'infinity$' = X1 ) )
| ~ sP7(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK128])],[f1492,f1493]) ).
tff(f1493,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& ( 'infinity$' = X1 ) )
=> ( ( 'ereal$'(sK128(X0,X1)) = X0 )
& ( 'infinity$' = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1492,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'ereal$'(X2) = X0 )
& ( 'infinity$' = X1 ) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f1491]) ).
tff(f1491,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP7(X1,X0) ),
inference(nnf_transformation,[],[f1198]) ).
tff(f1198,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'ereal$'(X3) = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
tff(f5776,plain,
spl183_353,
inference(avatar_split_clause,[],[f2508,f5774]) ).
tff(f5774,plain,
( spl183_353
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK127(X0,X1)) = X0 )
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_353])]) ).
tff(f2508,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK127(X0,X1)) = X0 )
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f1486]) ).
tff(f5772,plain,
spl183_352,
inference(avatar_split_clause,[],[f2491,f5770]) ).
tff(f5770,plain,
( spl183_352
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK125(X0,X1)) = X0 )
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_352])]) ).
tff(f2491,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK125(X0,X1)) = X0 )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1480]) ).
tff(f5768,plain,
spl183_351,
inference(avatar_split_clause,[],[f2490,f5766]) ).
tff(f5766,plain,
( spl183_351
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK124(X0,X1)) = X1 )
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_351])]) ).
tff(f2490,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK124(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f1480]) ).
tff(f5764,plain,
spl183_350,
inference(avatar_split_clause,[],[f2488,f5762]) ).
tff(f5762,plain,
( spl183_350
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK123(X0,X1)) = X1 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_350])]) ).
tff(f2488,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK123(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f1476]) ).
tff(f1476,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK123(X0,X1)) = X1 ) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK123])],[f1474,f1475]) ).
tff(f1475,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X2) = X1 ) )
=> ( ( 'infinity$' = X0 )
& ( 'ereal$'(sK123(X0,X1)) = X1 ) ) ),
introduced(choice_axiom,[]) ).
tff(f1474,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ? [X2: $real] :
( ( 'infinity$' = X0 )
& ( 'ereal$'(X2) = X1 ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f1473]) ).
tff(f1473,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X0 ) )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f1193]) ).
tff(f1193,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ? [X3: $real] :
( ( 'infinity$' = X1 )
& ( 'ereal$'(X3) = X0 ) )
| ~ sP3(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
tff(f5760,plain,
( spl183_349
| ~ spl183_224
| ~ spl183_233 ),
inference(avatar_split_clause,[],[f4940,f4805,f4765,f5757]) ).
tff(f4940,plain,
( sP19('infinity$','ereal$'(-1.0))
| ~ spl183_224
| ~ spl183_233 ),
inference(resolution,[],[f4766,f4807]) ).
tff(f5755,plain,
spl183_348,
inference(avatar_split_clause,[],[f2465,f5753]) ).
tff(f5753,plain,
( spl183_348
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK121(X0,X1)) = X1 )
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_348])]) ).
tff(f2465,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK121(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f1470]) ).
tff(f5751,plain,
spl183_347,
inference(avatar_split_clause,[],[f2459,f5749]) ).
tff(f5749,plain,
( spl183_347
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK118(X0,X1)) = X0 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_347])]) ).
tff(f2459,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK118(X0,X1)) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1463]) ).
tff(f5747,plain,
spl183_346,
inference(avatar_split_clause,[],[f2458,f5745]) ).
tff(f5745,plain,
( spl183_346
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK117(X0,X1)) = X1 )
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_346])]) ).
tff(f2458,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'ereal$'(sK117(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f1463]) ).
tff(f5743,plain,
spl183_345,
inference(avatar_split_clause,[],[f2388,f5741]) ).
tff(f5741,plain,
( spl183_345
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_345])]) ).
tff(f2388,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f891]) ).
tff(f891,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(ennf_transformation,[],[f82]) ).
tff(f82,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X1)
=> ( 'max$'(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom80) ).
tff(f5739,plain,
spl183_344,
inference(avatar_split_clause,[],[f2387,f5737]) ).
tff(f5737,plain,
( spl183_344
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_344])]) ).
tff(f2387,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f890]) ).
tff(f890,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(ennf_transformation,[],[f85]) ).
tff(f85,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X1)
=> ( 'max$'(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom83) ).
tff(f5735,plain,
spl183_343,
inference(avatar_split_clause,[],[f2386,f5733]) ).
tff(f2386,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ),
inference(cnf_transformation,[],[f889]) ).
tff(f889,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X1,X0) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ),
inference(ennf_transformation,[],[f545]) ).
tff(f545,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
=> ( 'max$'(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom543) ).
tff(f5731,plain,
spl183_342,
inference(avatar_split_clause,[],[f2385,f5729]) ).
tff(f2385,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ),
inference(cnf_transformation,[],[f888]) ).
tff(f888,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'max$'(X0,X1) = X1 )
| ~ 'fun_app$b'('less_eq$'(X0),X1) ),
inference(ennf_transformation,[],[f548]) ).
tff(f548,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
=> ( 'max$'(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom546) ).
tff(f5727,plain,
spl183_341,
inference(avatar_split_clause,[],[f2384,f5725]) ).
tff(f5725,plain,
( spl183_341
<=> ! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_341])]) ).
tff(f2384,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f887]) ).
tff(f887,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f84]) ).
tff(f84,axiom,
! [X0: $real,X1: $real] :
( $less(X0,X1)
=> ( 'fun_app$c'('max$a'(X1),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom82) ).
tff(f5723,plain,
spl183_340,
inference(avatar_split_clause,[],[f2383,f5721]) ).
tff(f5721,plain,
( spl183_340
<=> ! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_340])]) ).
tff(f2383,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f886]) ).
tff(f886,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f81]) ).
tff(f81,axiom,
! [X0: $real,X1: $real] :
( $less(X0,X1)
=> ( 'fun_app$c'('max$a'(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom79) ).
tff(f5719,plain,
spl183_339,
inference(avatar_split_clause,[],[f2376,f5717]) ).
tff(f5717,plain,
( spl183_339
<=> ! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_339])]) ).
tff(f2376,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f879]) ).
tff(f879,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X1),X0) = X1 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f666]) ).
tff(f666,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
=> ( 'fun_app$c'('max$a'(X1),X0) = X1 ) ),
inference(theory_normalization,[],[f543]) ).
tff(f543,axiom,
! [X0: $real,X1: $real] :
( $lesseq(X0,X1)
=> ( 'fun_app$c'('max$a'(X1),X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom541) ).
tff(f5714,plain,
spl183_338,
inference(avatar_split_clause,[],[f2375,f5712]) ).
tff(f5712,plain,
( spl183_338
<=> ! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_338])]) ).
tff(f2375,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f878]) ).
tff(f878,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('max$a'(X0),X1) = X1 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f665]) ).
tff(f665,plain,
! [X0: $real,X1: $real] :
( ~ $less(X1,X0)
=> ( 'fun_app$c'('max$a'(X0),X1) = X1 ) ),
inference(theory_normalization,[],[f546]) ).
tff(f546,axiom,
! [X0: $real,X1: $real] :
( $lesseq(X0,X1)
=> ( 'fun_app$c'('max$a'(X0),X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom544) ).
tff(f5710,plain,
spl183_337,
inference(avatar_split_clause,[],[f2344,f5708]) ).
tff(f5708,plain,
( spl183_337
<=> ! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_337])]) ).
tff(f2344,plain,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'(X1),X0) ),
inference(cnf_transformation,[],[f280]) ).
tff(f280,axiom,
! [X0: $real,X1: $real] : ( 'fun_app$c'('times$a'(X0),X1) = 'fun_app$c'('times$a'(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom278) ).
tff(f5706,plain,
spl183_336,
inference(avatar_split_clause,[],[f2340,f5704]) ).
tff(f5704,plain,
( spl183_336
<=> ! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),X1) = 'fun_app$g'('times$f'(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_336])]) ).
tff(f2340,plain,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),X1) = 'fun_app$g'('times$f'(X1),X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,axiom,
! [X0: 'Nat$',X1: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),X1) = 'fun_app$g'('times$f'(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom277) ).
tff(f5702,plain,
spl183_335,
inference(avatar_split_clause,[],[f2337,f5700]) ).
tff(f5700,plain,
( spl183_335
<=> ! [X0: $int,X1: $int] : ( $uminus('times$d'(X0,X1)) = 'times$d'(X0,$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_335])]) ).
tff(f5698,plain,
spl183_334,
inference(avatar_split_clause,[],[f2336,f5696]) ).
tff(f5696,plain,
( spl183_334
<=> ! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'($uminus(X0),$uminus(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_334])]) ).
tff(f2336,plain,
! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'($uminus(X0),$uminus(X1)) ),
inference(cnf_transformation,[],[f306]) ).
tff(f306,axiom,
! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'($uminus(X0),$uminus(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom304) ).
tff(f5694,plain,
spl183_333,
inference(avatar_split_clause,[],[f2335,f5692]) ).
tff(f5692,plain,
( spl183_333
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'('max$'(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_333])]) ).
tff(f2335,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'('max$'(X0,X1),X1) ),
inference(cnf_transformation,[],[f87]) ).
tff(f87,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'('max$'(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom85) ).
tff(f5690,plain,
spl183_332,
inference(avatar_split_clause,[],[f2334,f5688]) ).
tff(f5688,plain,
( spl183_332
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X0,'max$'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_332])]) ).
tff(f2334,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X0,'max$'(X0,X1)) ),
inference(cnf_transformation,[],[f88]) ).
tff(f88,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X0,'max$'(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom86) ).
tff(f5686,plain,
spl183_331,
inference(avatar_split_clause,[],[f2295,f5684]) ).
tff(f5684,plain,
( spl183_331
<=> ! [X0: $real] :
( ( 0.0 = X0 )
| $less(0.0,'fun_app$c'('times$a'(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_331])]) ).
tff(f2295,plain,
! [X0: $real] :
( ( 0.0 = X0 )
| $less(0.0,'fun_app$c'('times$a'(X0),X0)) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f1402,plain,
! [X0: $real] :
( ( ~ $less(0.0,'fun_app$c'('times$a'(X0),X0))
| ( 0.0 != X0 ) )
& ( ( 0.0 = X0 )
| $less(0.0,'fun_app$c'('times$a'(X0),X0)) ) ),
inference(nnf_transformation,[],[f418]) ).
tff(f418,axiom,
! [X0: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X0))
<=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom416) ).
tff(f5682,plain,
spl183_330,
inference(avatar_split_clause,[],[f2151,f5680]) ).
tff(f5680,plain,
( spl183_330
<=> ! [X0: 'Int_fps$'] :
( ( 0 != 'fps_nth$b'(X0,sK92(X0)) )
| ( 'zero$d' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_330])]) ).
tff(f2151,plain,
! [X0: 'Int_fps$'] :
( ( 0 != 'fps_nth$b'(X0,sK92(X0)) )
| ( 'zero$d' = X0 ) ),
inference(cnf_transformation,[],[f1327]) ).
tff(f1327,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] :
( ( ( 0 != 'fps_nth$b'(X0,sK91(X0,X1)) )
& $less('of_nat$'(sK91(X0,X1)),'of_nat$'(X1)) )
| ( 0 = 'fps_nth$b'(X0,X1) ) ) )
& ( ( ! [X4: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK92(X0))) )
& ( 0 != 'fps_nth$b'(X0,sK92(X0)) ) )
| ( 'zero$d' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f1324,f1326,f1325]) ).
tff(f1325,plain,
! [X0: 'Int_fps$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0 != 'fps_nth$b'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
=> ( ( 0 != 'fps_nth$b'(X0,sK91(X0,X1)) )
& $less('of_nat$'(sK91(X0,X1)),'of_nat$'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1326,plain,
! [X0: 'Int_fps$'] :
( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 0 != 'fps_nth$b'(X0,X3) ) )
=> ( ! [X4: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK92(X0))) )
& ( 0 != 'fps_nth$b'(X0,sK92(X0)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1324,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0 != 'fps_nth$b'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 0 = 'fps_nth$b'(X0,X1) ) ) )
& ( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 0 != 'fps_nth$b'(X0,X3) ) )
| ( 'zero$d' = X0 ) ) ),
inference(rectify,[],[f1323]) ).
tff(f1323,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 0 != 'fps_nth$b'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 0 = 'fps_nth$b'(X0,X1) ) ) )
& ( ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 0 != 'fps_nth$b'(X0,X1) ) )
| ( 'zero$d' = X0 ) ) ),
inference(nnf_transformation,[],[f868]) ).
tff(f868,plain,
! [X0: 'Int_fps$'] :
( ( 'zero$d' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 0 = 'fps_nth$b'(X0,X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 0 != 'fps_nth$b'(X0,X1) ) ) ),
inference(ennf_transformation,[],[f222]) ).
tff(f222,axiom,
! [X0: 'Int_fps$'] :
( ( 'zero$d' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( $less('of_nat$'(X2),'of_nat$'(X1))
=> ( 0 = 'fps_nth$b'(X0,X2) ) )
& ( 0 != 'fps_nth$b'(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom220) ).
tff(f5678,plain,
spl183_329,
inference(avatar_split_clause,[],[f2147,f5676]) ).
tff(f5676,plain,
( spl183_329
<=> ! [X0: 'Ereal_fps$'] :
( ( 'zero$' != 'fps_nth$a'(X0,sK90(X0)) )
| ( 'zero$c' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_329])]) ).
tff(f2147,plain,
! [X0: 'Ereal_fps$'] :
( ( 'zero$' != 'fps_nth$a'(X0,sK90(X0)) )
| ( 'zero$c' = X0 ) ),
inference(cnf_transformation,[],[f1322]) ).
tff(f1322,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] :
( ( ( 'zero$' != 'fps_nth$a'(X0,sK89(X0,X1)) )
& $less('of_nat$'(sK89(X0,X1)),'of_nat$'(X1)) )
| ( 'zero$' = 'fps_nth$a'(X0,X1) ) ) )
& ( ( ! [X4: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK90(X0))) )
& ( 'zero$' != 'fps_nth$a'(X0,sK90(X0)) ) )
| ( 'zero$c' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90])],[f1319,f1321,f1320]) ).
tff(f1320,plain,
! [X0: 'Ereal_fps$',X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'zero$' != 'fps_nth$a'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
=> ( ( 'zero$' != 'fps_nth$a'(X0,sK89(X0,X1)) )
& $less('of_nat$'(sK89(X0,X1)),'of_nat$'(X1)) ) ),
introduced(choice_axiom,[]) ).
tff(f1321,plain,
! [X0: 'Ereal_fps$'] :
( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 'zero$' != 'fps_nth$a'(X0,X3) ) )
=> ( ! [X4: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(sK90(X0))) )
& ( 'zero$' != 'fps_nth$a'(X0,sK90(X0)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1319,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'zero$' != 'fps_nth$a'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 'zero$' = 'fps_nth$a'(X0,X1) ) ) )
& ( ? [X3: 'Nat$'] :
( ! [X4: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X4) )
| ~ $less('of_nat$'(X4),'of_nat$'(X3)) )
& ( 'zero$' != 'fps_nth$a'(X0,X3) ) )
| ( 'zero$c' = X0 ) ) ),
inference(rectify,[],[f1318]) ).
tff(f1318,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] :
( ? [X2: 'Nat$'] :
( ( 'zero$' != 'fps_nth$a'(X0,X2) )
& $less('of_nat$'(X2),'of_nat$'(X1)) )
| ( 'zero$' = 'fps_nth$a'(X0,X1) ) ) )
& ( ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 'zero$' != 'fps_nth$a'(X0,X1) ) )
| ( 'zero$c' = X0 ) ) ),
inference(nnf_transformation,[],[f867]) ).
tff(f867,plain,
! [X0: 'Ereal_fps$'] :
( ( 'zero$c' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'(X0,X2) )
| ~ $less('of_nat$'(X2),'of_nat$'(X1)) )
& ( 'zero$' != 'fps_nth$a'(X0,X1) ) ) ),
inference(ennf_transformation,[],[f221]) ).
tff(f221,axiom,
! [X0: 'Ereal_fps$'] :
( ( 'zero$c' != X0 )
<=> ? [X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( $less('of_nat$'(X2),'of_nat$'(X1))
=> ( 'zero$' = 'fps_nth$a'(X0,X2) ) )
& ( 'zero$' != 'fps_nth$a'(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom219) ).
tff(f5672,plain,
spl183_328,
inference(avatar_split_clause,[],[f2145,f5670]) ).
tff(f5670,plain,
( spl183_328
<=> ! [X0: 'Int_fps$'] :
( ( 0 != 'fps_nth$b'(X0,sK88(X0)) )
| ( 'zero$d' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_328])]) ).
tff(f2145,plain,
! [X0: 'Int_fps$'] :
( ( 0 != 'fps_nth$b'(X0,sK88(X0)) )
| ( 'zero$d' = X0 ) ),
inference(cnf_transformation,[],[f1317]) ).
tff(f1317,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] : ( 0 = 'fps_nth$b'(X0,X1) ) )
& ( ( 0 != 'fps_nth$b'(X0,sK88(X0)) )
| ( 'zero$d' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f1315,f1316]) ).
tff(f1316,plain,
! [X0: 'Int_fps$'] :
( ? [X2: 'Nat$'] : ( 0 != 'fps_nth$b'(X0,X2) )
=> ( 0 != 'fps_nth$b'(X0,sK88(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1315,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] : ( 0 = 'fps_nth$b'(X0,X1) ) )
& ( ? [X2: 'Nat$'] : ( 0 != 'fps_nth$b'(X0,X2) )
| ( 'zero$d' = X0 ) ) ),
inference(rectify,[],[f1314]) ).
tff(f1314,plain,
! [X0: 'Int_fps$'] :
( ( ( 'zero$d' != X0 )
| ! [X1: 'Nat$'] : ( 0 = 'fps_nth$b'(X0,X1) ) )
& ( ? [X1: 'Nat$'] : ( 0 != 'fps_nth$b'(X0,X1) )
| ( 'zero$d' = X0 ) ) ),
inference(nnf_transformation,[],[f207]) ).
tff(f207,axiom,
! [X0: 'Int_fps$'] :
( ( 'zero$d' != X0 )
<=> ? [X1: 'Nat$'] : ( 0 != 'fps_nth$b'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom205) ).
tff(f5668,plain,
spl183_327,
inference(avatar_split_clause,[],[f2143,f5666]) ).
tff(f5666,plain,
( spl183_327
<=> ! [X0: 'Ereal_fps$'] :
( ( 'zero$' != 'fps_nth$a'(X0,sK87(X0)) )
| ( 'zero$c' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_327])]) ).
tff(f2143,plain,
! [X0: 'Ereal_fps$'] :
( ( 'zero$' != 'fps_nth$a'(X0,sK87(X0)) )
| ( 'zero$c' = X0 ) ),
inference(cnf_transformation,[],[f1313]) ).
tff(f1313,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] : ( 'zero$' = 'fps_nth$a'(X0,X1) ) )
& ( ( 'zero$' != 'fps_nth$a'(X0,sK87(X0)) )
| ( 'zero$c' = X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f1311,f1312]) ).
tff(f1312,plain,
! [X0: 'Ereal_fps$'] :
( ? [X2: 'Nat$'] : ( 'zero$' != 'fps_nth$a'(X0,X2) )
=> ( 'zero$' != 'fps_nth$a'(X0,sK87(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1311,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] : ( 'zero$' = 'fps_nth$a'(X0,X1) ) )
& ( ? [X2: 'Nat$'] : ( 'zero$' != 'fps_nth$a'(X0,X2) )
| ( 'zero$c' = X0 ) ) ),
inference(rectify,[],[f1310]) ).
tff(f1310,plain,
! [X0: 'Ereal_fps$'] :
( ( ( 'zero$c' != X0 )
| ! [X1: 'Nat$'] : ( 'zero$' = 'fps_nth$a'(X0,X1) ) )
& ( ? [X1: 'Nat$'] : ( 'zero$' != 'fps_nth$a'(X0,X1) )
| ( 'zero$c' = X0 ) ) ),
inference(nnf_transformation,[],[f206]) ).
tff(f206,axiom,
! [X0: 'Ereal_fps$'] :
( ( 'zero$c' != X0 )
<=> ? [X1: 'Nat$'] : ( 'zero$' != 'fps_nth$a'(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom204) ).
tff(f5664,plain,
spl183_326,
inference(avatar_split_clause,[],[f2142,f5662]) ).
tff(f5662,plain,
( spl183_326
<=> ! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('ereal$'(sK86(X0))),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_326])]) ).
tff(f2142,plain,
! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('ereal$'(sK86(X0))),X0) ),
inference(cnf_transformation,[],[f1309]) ).
tff(f1309,plain,
! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('ereal$'(sK86(X0))),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f866,f1308]) ).
tff(f1308,plain,
! [X0: 'Ereal$'] :
( ? [X1: $real] : ~ 'fun_app$b'('less_eq$'('ereal$'(X1)),X0)
=> ~ 'fun_app$b'('less_eq$'('ereal$'(sK86(X0))),X0) ),
introduced(choice_axiom,[]) ).
tff(f866,plain,
! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ? [X1: $real] : ~ 'fun_app$b'('less_eq$'('ereal$'(X1)),X0) ),
inference(ennf_transformation,[],[f637]) ).
tff(f637,axiom,
! [X0: 'Ereal$'] :
( ! [X1: $real] : 'fun_app$b'('less_eq$'('ereal$'(X1)),X0)
=> ( 'infinity$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom635) ).
tff(f5660,plain,
spl183_325,
inference(avatar_split_clause,[],[f2122,f5658]) ).
tff(f5658,plain,
( spl183_325
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'inverse$a'(X0))
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_325])]) ).
tff(f2122,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'inverse$a'(X0))
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ),
inference(cnf_transformation,[],[f843]) ).
tff(f843,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),'inverse$a'(X0))
| ~ 'fun_app$b'('less_eq$'('zero$'),X0) ),
inference(ennf_transformation,[],[f625]) ).
tff(f625,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('zero$'),X0)
=> 'fun_app$b'('less_eq$'('zero$'),'inverse$a'(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom623) ).
tff(f5656,plain,
spl183_324,
inference(avatar_split_clause,[],[f2099,f5654]) ).
tff(f5654,plain,
( spl183_324
<=> ! [X0: 'Nat$'] :
( ( 0 = 'fps_nth$b'('one$d',X0) )
| ( 0 = 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_324])]) ).
tff(f2099,plain,
! [X0: 'Nat$'] :
( ( 0 = 'fps_nth$b'('one$d',X0) )
| ( 0 = 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f827]) ).
tff(f827,plain,
! [X0: 'Nat$'] :
( ( ( 0 = 'fps_nth$b'('one$d',X0) )
| ( 0 = 'of_nat$'(X0) ) )
& ( ( 1 = 'fps_nth$b'('one$d',X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
inference(ennf_transformation,[],[f451]) ).
tff(f451,axiom,
! [X0: 'Nat$'] :
( ( ( 0 != 'of_nat$'(X0) )
=> ( 0 = 'fps_nth$b'('one$d',X0) ) )
& ( ( 0 = 'of_nat$'(X0) )
=> ( 1 = 'fps_nth$b'('one$d',X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom449) ).
tff(f5652,plain,
spl183_323,
inference(avatar_split_clause,[],[f2098,f5650]) ).
tff(f5650,plain,
( spl183_323
<=> ! [X0: 'Nat$'] :
( ( 1 = 'fps_nth$b'('one$d',X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_323])]) ).
tff(f2098,plain,
! [X0: 'Nat$'] :
( ( 1 = 'fps_nth$b'('one$d',X0) )
| ( 0 != 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f827]) ).
tff(f5648,plain,
spl183_322,
inference(avatar_split_clause,[],[f2097,f5646]) ).
tff(f5646,plain,
( spl183_322
<=> ! [X0: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'('one$c',X0) )
| ( 0 = 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_322])]) ).
tff(f2097,plain,
! [X0: 'Nat$'] :
( ( 'zero$' = 'fps_nth$a'('one$c',X0) )
| ( 0 = 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f826]) ).
tff(f826,plain,
! [X0: 'Nat$'] :
( ( ( 'zero$' = 'fps_nth$a'('one$c',X0) )
| ( 0 = 'of_nat$'(X0) ) )
& ( ( 'one$a' = 'fps_nth$a'('one$c',X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
inference(ennf_transformation,[],[f450]) ).
tff(f450,axiom,
! [X0: 'Nat$'] :
( ( ( 0 != 'of_nat$'(X0) )
=> ( 'zero$' = 'fps_nth$a'('one$c',X0) ) )
& ( ( 0 = 'of_nat$'(X0) )
=> ( 'one$a' = 'fps_nth$a'('one$c',X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom448) ).
tff(f5644,plain,
spl183_321,
inference(avatar_split_clause,[],[f2096,f5642]) ).
tff(f5642,plain,
( spl183_321
<=> ! [X0: 'Nat$'] :
( ( 'one$a' = 'fps_nth$a'('one$c',X0) )
| ( 0 != 'of_nat$'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_321])]) ).
tff(f2096,plain,
! [X0: 'Nat$'] :
( ( 'one$a' = 'fps_nth$a'('one$c',X0) )
| ( 0 != 'of_nat$'(X0) ) ),
inference(cnf_transformation,[],[f826]) ).
tff(f5640,plain,
spl183_320,
inference(avatar_split_clause,[],[f2065,f5638]) ).
tff(f2065,plain,
! [X0: $real] : ( 'fun_app$c'('inverse$',$uminus(X0)) = $uminus('fun_app$c'('inverse$',X0)) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,axiom,
! [X0: $real] : ( 'fun_app$c'('inverse$',$uminus(X0)) = $uminus('fun_app$c'('inverse$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom159) ).
tff(f5635,plain,
spl183_319,
inference(avatar_split_clause,[],[f2064,f5633]) ).
tff(f2064,plain,
! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'nat$'(0)) ),
inference(cnf_transformation,[],[f514]) ).
tff(f514,axiom,
! [X0: 'Real_fps$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('fun_app$i'('fps_XD$a',X0)),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom512) ).
tff(f5629,plain,
( ~ spl183_50
| spl183_318 ),
inference(avatar_split_clause,[],[f1991,f5626,f4003]) ).
tff(f4003,plain,
( spl183_50
<=> ( 0.0 = 'fun_app$c'('inverse$',0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_50])]) ).
tff(f5626,plain,
( spl183_318
<=> ( 'zero$b' = 'inverse$c'('zero$b') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_318])]) ).
tff(f1991,plain,
( ( 'zero$b' = 'inverse$c'('zero$b') )
| ( 0.0 != 'fun_app$c'('inverse$',0.0) ) ),
inference(cnf_transformation,[],[f813]) ).
tff(f813,plain,
( ( 'zero$b' = 'inverse$c'('zero$b') )
| ( 0.0 != 'fun_app$c'('inverse$',0.0) ) ),
inference(ennf_transformation,[],[f71]) ).
tff(f71,axiom,
( ( 0.0 = 'fun_app$c'('inverse$',0.0) )
=> ( 'zero$b' = 'inverse$c'('zero$b') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom69) ).
tff(f5624,plain,
( ~ spl183_50
| spl183_317 ),
inference(avatar_split_clause,[],[f1990,f5621,f4003]) ).
tff(f5621,plain,
( spl183_317
<=> ( 'zero$a' = 'inverse$b'('zero$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_317])]) ).
tff(f1990,plain,
( ( 'zero$a' = 'inverse$b'('zero$a') )
| ( 0.0 != 'fun_app$c'('inverse$',0.0) ) ),
inference(cnf_transformation,[],[f812]) ).
tff(f812,plain,
( ( 'zero$a' = 'inverse$b'('zero$a') )
| ( 0.0 != 'fun_app$c'('inverse$',0.0) ) ),
inference(ennf_transformation,[],[f70]) ).
tff(f70,axiom,
( ( 0.0 = 'fun_app$c'('inverse$',0.0) )
=> ( 'zero$a' = 'inverse$b'('zero$a') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom68) ).
tff(f5619,plain,
( ~ spl183_48
| spl183_316 ),
inference(avatar_split_clause,[],[f1989,f5616,f3993]) ).
tff(f5616,plain,
( spl183_316
<=> ( 'one$' = 'inverse$c'('one$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_316])]) ).
tff(f1989,plain,
( ( 'one$' = 'inverse$c'('one$') )
| ( 1.0 != 'fun_app$c'('inverse$',1.0) ) ),
inference(cnf_transformation,[],[f811]) ).
tff(f811,plain,
( ( 'one$' = 'inverse$c'('one$') )
| ( 1.0 != 'fun_app$c'('inverse$',1.0) ) ),
inference(ennf_transformation,[],[f464]) ).
tff(f464,axiom,
( ( 1.0 = 'fun_app$c'('inverse$',1.0) )
=> ( 'one$' = 'inverse$c'('one$') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom462) ).
tff(f5614,plain,
( ~ spl183_48
| spl183_315 ),
inference(avatar_split_clause,[],[f1988,f5611,f3993]) ).
tff(f5611,plain,
( spl183_315
<=> ( 'one$e' = 'inverse$b'('one$e') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_315])]) ).
tff(f1988,plain,
( ( 'one$e' = 'inverse$b'('one$e') )
| ( 1.0 != 'fun_app$c'('inverse$',1.0) ) ),
inference(cnf_transformation,[],[f810]) ).
tff(f810,plain,
( ( 'one$e' = 'inverse$b'('one$e') )
| ( 1.0 != 'fun_app$c'('inverse$',1.0) ) ),
inference(ennf_transformation,[],[f465]) ).
tff(f465,axiom,
( ( 1.0 = 'fun_app$c'('inverse$',1.0) )
=> ( 'one$e' = 'inverse$b'('one$e') ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom463) ).
tff(f5609,plain,
spl183_314,
inference(avatar_split_clause,[],[f737,f5607]) ).
tff(f5607,plain,
( spl183_314
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_314])]) ).
tff(f737,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f5605,plain,
spl183_313,
inference(avatar_split_clause,[],[f736,f5603]) ).
tff(f5603,plain,
( spl183_313
<=> ! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_313])]) ).
tff(f736,plain,
! [X2: $real,X0: $real,X1: $real] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f5601,plain,
( spl183_312
| ~ spl183_79
| ~ spl183_291 ),
inference(avatar_split_clause,[],[f5524,f5180,f4129,f5598]) ).
tff(f5598,plain,
( spl183_312
<=> sP16(-1,-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_312])]) ).
tff(f4129,plain,
( spl183_79
<=> ( 1 = 'times$d'(-1,-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_79])]) ).
tff(f5180,plain,
( spl183_291
<=> ! [X0: $int,X1: $int] :
( sP16(X1,X0)
| ~ $less(0,'times$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_291])]) ).
tff(f5524,plain,
( sP16(-1,-1)
| ~ spl183_79
| ~ spl183_291 ),
inference(evaluation,[],[f5523]) ).
tff(f5523,plain,
( ~ $less(0,1)
| sP16(-1,-1)
| ~ spl183_79
| ~ spl183_291 ),
inference(superposition,[],[f5181,f4131]) ).
tff(f4131,plain,
( ( 1 = 'times$d'(-1,-1) )
| ~ spl183_79 ),
inference(avatar_component_clause,[],[f4129]) ).
tff(f5181,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| sP16(X1,X0) )
| ~ spl183_291 ),
inference(avatar_component_clause,[],[f5180]) ).
tff(f5596,plain,
spl183_311,
inference(avatar_split_clause,[],[f719,f5594]) ).
tff(f5594,plain,
( spl183_311
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_311])]) ).
tff(f719,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f5592,plain,
spl183_310,
inference(avatar_split_clause,[],[f718,f5590]) ).
tff(f5590,plain,
( spl183_310
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_310])]) ).
tff(f718,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f5554,plain,
( ~ spl183_309
| ~ spl183_79
| ~ spl183_290 ),
inference(avatar_split_clause,[],[f5514,f5176,f4129,f5551]) ).
tff(f5551,plain,
( spl183_309
<=> sP15(-1,-1) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_309])]) ).
tff(f5176,plain,
( spl183_290
<=> ! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| ~ sP15(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_290])]) ).
tff(f5514,plain,
( ~ sP15(-1,-1)
| ~ spl183_79
| ~ spl183_290 ),
inference(evaluation,[],[f5513]) ).
tff(f5513,plain,
( ~ $less(0,1)
| ~ sP15(-1,-1)
| ~ spl183_79
| ~ spl183_290 ),
inference(superposition,[],[f5177,f4131]) ).
tff(f5177,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| ~ sP15(X1,X0) )
| ~ spl183_290 ),
inference(avatar_component_clause,[],[f5176]) ).
tff(f5365,plain,
( spl183_308
| ~ spl183_99
| ~ spl183_261 ),
inference(avatar_split_clause,[],[f5228,f5053,f4220,f5362]) ).
tff(f5362,plain,
( spl183_308
<=> sP13('one$a','infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_308])]) ).
tff(f4220,plain,
( spl183_99
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_99])]) ).
tff(f5053,plain,
( spl183_261
<=> sP11('one$a','infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_261])]) ).
tff(f5228,plain,
( sP13('one$a','infinity$')
| ~ spl183_99
| ~ spl183_261 ),
inference(resolution,[],[f5055,f4221]) ).
tff(f4221,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ sP11(X0,X1)
| sP13(X0,X1) )
| ~ spl183_99 ),
inference(avatar_component_clause,[],[f4220]) ).
tff(f5055,plain,
( sP11('one$a','infinity$')
| ~ spl183_261 ),
inference(avatar_component_clause,[],[f5053]) ).
tff(f5315,plain,
( spl183_307
| ~ spl183_100
| ~ spl183_239 ),
inference(avatar_split_clause,[],[f5142,f4961,f4224,f5312]) ).
tff(f5312,plain,
( spl183_307
<=> sP13('infinity$','one$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_307])]) ).
tff(f4224,plain,
( spl183_100
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_100])]) ).
tff(f4961,plain,
( spl183_239
<=> sP12('infinity$','one$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_239])]) ).
tff(f5142,plain,
( sP13('infinity$','one$a')
| ~ spl183_100
| ~ spl183_239 ),
inference(resolution,[],[f4963,f4225]) ).
tff(f4225,plain,
( ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ~ sP12(X0,X1)
| sP13(X0,X1) )
| ~ spl183_100 ),
inference(avatar_component_clause,[],[f4224]) ).
tff(f4963,plain,
( sP12('infinity$','one$a')
| ~ spl183_239 ),
inference(avatar_component_clause,[],[f4961]) ).
tff(f5275,plain,
( spl183_306
| ~ spl183_100
| ~ spl183_236 ),
inference(avatar_split_clause,[],[f5099,f4943,f4224,f5272]) ).
tff(f5272,plain,
( spl183_306
<=> sP13('infinity$','infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_306])]) ).
tff(f4943,plain,
( spl183_236
<=> sP12('infinity$','infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_236])]) ).
tff(f5099,plain,
( sP13('infinity$','infinity$')
| ~ spl183_100
| ~ spl183_236 ),
inference(resolution,[],[f4945,f4225]) ).
tff(f4945,plain,
( sP12('infinity$','infinity$')
| ~ spl183_236 ),
inference(avatar_component_clause,[],[f4943]) ).
tff(f5256,plain,
( spl183_305
| ~ spl183_140
| ~ spl183_242 ),
inference(avatar_split_clause,[],[f4978,f4975,f4423,f5254]) ).
tff(f5254,plain,
( spl183_305
<=> ! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_305])]) ).
tff(f4975,plain,
( spl183_242
<=> ! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_242])]) ).
tff(f4978,plain,
( ! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'size_ereal$'('one$a')) )
| ~ spl183_140
| ~ spl183_242 ),
inference(forward_demodulation,[],[f4976,f4425]) ).
tff(f4976,plain,
( ! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'nat$'(0)) )
| ~ spl183_242 ),
inference(avatar_component_clause,[],[f4975]) ).
tff(f5252,plain,
( spl183_304
| ~ spl183_140
| ~ spl183_241 ),
inference(avatar_split_clause,[],[f4973,f4970,f4423,f5250]) ).
tff(f5250,plain,
( spl183_304
<=> ! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_304])]) ).
tff(f4970,plain,
( spl183_241
<=> ! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_241])]) ).
tff(f4973,plain,
( ! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'size_ereal$'('one$a')) )
| ~ spl183_140
| ~ spl183_241 ),
inference(forward_demodulation,[],[f4971,f4425]) ).
tff(f4971,plain,
( ! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'nat$'(0)) )
| ~ spl183_241 ),
inference(avatar_component_clause,[],[f4970]) ).
tff(f5236,plain,
spl183_303,
inference(avatar_split_clause,[],[f3712,f5234]) ).
tff(f5234,plain,
( spl183_303
<=> ! [X0: 'Ereal$'] : ( 'max$'(X0,'times$'('infinity$','ereal$'(-1.0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_303])]) ).
tff(f3712,plain,
! [X0: 'Ereal$'] : ( 'max$'(X0,'times$'('infinity$','ereal$'(-1.0))) = X0 ),
inference(evaluation,[],[f3228]) ).
tff(f3228,plain,
! [X0: 'Ereal$'] : ( 'max$'(X0,'times$'('infinity$','ereal$'($uminus(1.0)))) = X0 ),
inference(definition_unfolding,[],[f2044,f2063]) ).
tff(f2044,plain,
! [X0: 'Ereal$'] : ( 'max$'(X0,'uminus$'('infinity$')) = X0 ),
inference(cnf_transformation,[],[f183]) ).
tff(f183,axiom,
! [X0: 'Ereal$'] : ( 'max$'(X0,'uminus$'('infinity$')) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom181) ).
tff(f5232,plain,
spl183_302,
inference(avatar_split_clause,[],[f3711,f5230]) ).
tff(f5230,plain,
( spl183_302
<=> ! [X0: 'Ereal$'] : ( 'max$'('times$'('infinity$','ereal$'(-1.0)),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_302])]) ).
tff(f3711,plain,
! [X0: 'Ereal$'] : ( 'max$'('times$'('infinity$','ereal$'(-1.0)),X0) = X0 ),
inference(evaluation,[],[f3229]) ).
tff(f3229,plain,
! [X0: 'Ereal$'] : ( 'max$'('times$'('infinity$','ereal$'($uminus(1.0))),X0) = X0 ),
inference(definition_unfolding,[],[f2045,f2063]) ).
tff(f2045,plain,
! [X0: 'Ereal$'] : ( 'max$'('uminus$'('infinity$'),X0) = X0 ),
inference(cnf_transformation,[],[f182]) ).
tff(f182,axiom,
! [X0: 'Ereal$'] : ( 'max$'('uminus$'('infinity$'),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom180) ).
tff(f5225,plain,
spl183_301,
inference(avatar_split_clause,[],[f3668,f5223]) ).
tff(f5223,plain,
( spl183_301
<=> ! [X0: $real] : 'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'ereal$'(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_301])]) ).
tff(f3668,plain,
! [X0: $real] : 'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'ereal$'(X0)),
inference(evaluation,[],[f3264]) ).
tff(f3264,plain,
! [X0: $real] : 'fun_app$b'('less$'('times$'('infinity$','ereal$'($uminus(1.0)))),'ereal$'(X0)),
inference(definition_unfolding,[],[f2300,f2063]) ).
tff(f2300,plain,
! [X0: $real] : 'fun_app$b'('less$'('uminus$'('infinity$')),'ereal$'(X0)),
inference(cnf_transformation,[],[f778]) ).
tff(f778,plain,
! [X0: $real] : 'fun_app$b'('less$'('uminus$'('infinity$')),'ereal$'(X0)),
inference(true_and_false_elimination,[],[f224]) ).
tff(f224,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('uminus$'('infinity$')),'ereal$'(X0))
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom222) ).
tff(f5221,plain,
spl183_300,
inference(avatar_split_clause,[],[f3649,f5219]) ).
tff(f5219,plain,
( spl183_300
<=> ! [X0: 'Ereal$'] :
( ( 'zero$' = 'inverse$a'(X0) )
| sP1('inverse$a'(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_300])]) ).
tff(f3649,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = 'inverse$a'(X0) )
| sP1('inverse$a'(X0),X0) ),
inference(duplicate_literal_removal,[],[f3441]) ).
tff(f3441,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = 'inverse$a'(X0) )
| ( 'zero$' = 'inverse$a'(X0) )
| sP1('inverse$a'(X0),X0) ),
inference(equality_resolution,[],[f2471]) ).
tff(f2471,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'zero$' = X1 )
| ( 'zero$' = X1 )
| sP1(X1,X0)
| ( 'inverse$a'(X0) != X1 ) ),
inference(cnf_transformation,[],[f1191]) ).
tff(f1191,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'zero$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ( ( 'zero$' = X1 )
& ( 'infinity$' = X0 ) )
| sP1(X1,X0)
| ( 'inverse$a'(X0) != X1 ) ),
inference(definition_folding,[],[f990,f1190]) ).
tff(f990,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'zero$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
| ( ( 'zero$' = X1 )
& ( 'infinity$' = X0 ) )
| ? [X2: $real] :
( ( ( 'ereal$'('fun_app$c'('inverse$',X2)) = X1 )
| ( 0.0 = X2 ) )
& ( ( 'infinity$' = X1 )
| ( 0.0 != X2 ) )
& ( 'ereal$'(X2) = X0 ) )
| ( 'inverse$a'(X0) != X1 ) ),
inference(ennf_transformation,[],[f793]) ).
tff(f793,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
~ ( ~ ( ( 'zero$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
& ~ ( ( 'zero$' = X1 )
& ( 'infinity$' = X0 ) )
& ! [X2: $real] :
~ ( ( ( 0.0 != X2 )
=> ( 'ereal$'('fun_app$c'('inverse$',X2)) = X1 ) )
& ( ( 0.0 = X2 )
=> ( 'infinity$' = X1 ) )
& ( 'ereal$'(X2) = X0 ) )
& ( 'inverse$a'(X0) = X1 ) ),
inference(true_and_false_elimination,[],[f140]) ).
tff(f140,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( ( ( 'zero$' = X1 )
& ( 'uminus$'('infinity$') = X0 ) )
=> $false )
& ( ( ( 'zero$' = X1 )
& ( 'infinity$' = X0 ) )
=> $false )
& ! [X2: $real] :
( ( ( ( 0.0 != X2 )
=> ( 'ereal$'('fun_app$c'('inverse$',X2)) = X1 ) )
& ( ( 0.0 = X2 )
=> ( 'infinity$' = X1 ) )
& ( 'ereal$'(X2) = X0 ) )
=> $false )
& ( 'inverse$a'(X0) = X1 ) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom138) ).
tff(f5217,plain,
spl183_299,
inference(avatar_split_clause,[],[f2988,f5215]) ).
tff(f5215,plain,
( spl183_299
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X2)
| ~ $less('max$b'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_299])]) ).
tff(f2988,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X1,X2)
| ~ $less('max$b'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1153]) ).
tff(f1153,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less(X1,X2)
& $less(X0,X2) )
| ~ $less('max$b'(X0,X1),X2) ),
inference(ennf_transformation,[],[f803]) ).
tff(f803,plain,
! [X0: $int,X1: $int,X2: $int] :
~ ( ~ ( $less(X1,X2)
& $less(X0,X2) )
& $less('max$b'(X0,X1),X2) ),
inference(true_and_false_elimination,[],[f107]) ).
tff(f107,axiom,
! [X0: $int,X1: $int,X2: $int] :
( ( ( ( $less(X1,X2)
& $less(X0,X2) )
=> $false )
& $less('max$b'(X0,X1),X2) )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom105) ).
tff(f5213,plain,
spl183_298,
inference(avatar_split_clause,[],[f2987,f5211]) ).
tff(f5211,plain,
( spl183_298
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less('max$b'(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_298])]) ).
tff(f2987,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less('max$b'(X0,X1),X2) ),
inference(cnf_transformation,[],[f1153]) ).
tff(f5209,plain,
spl183_297,
inference(avatar_split_clause,[],[f2892,f5207]) ).
tff(f2892,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X1,X2))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1070]) ).
tff(f1070,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,'max$b'(X1,X2))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f96]) ).
tff(f96,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,X1)
=> $less(X0,'max$b'(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom94) ).
tff(f5205,plain,
spl183_296,
inference(avatar_split_clause,[],[f2891,f5203]) ).
tff(f2891,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,'max$b'(X2,X1))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1069]) ).
tff(f1069,plain,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,'max$b'(X2,X1))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f93]) ).
tff(f93,axiom,
! [X0: $int,X1: $int,X2: $int] :
( $less(X0,X1)
=> $less(X0,'max$b'(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom91) ).
tff(f5201,plain,
spl183_295,
inference(avatar_split_clause,[],[f2820,f5199]) ).
tff(f5199,plain,
( spl183_295
<=> ! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( sP31(X0,X1)
| 'member$'(sK139(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_295])]) ).
tff(f2820,plain,
! [X0: 'Real_ereal_bool_fun_fun$',X1: 'Ereal_set$'] :
( sP31(X0,X1)
| 'member$'(sK139(X0,X1),X1) ),
inference(cnf_transformation,[],[f1678]) ).
tff(f5197,plain,
spl183_294,
inference(avatar_split_clause,[],[f2660,f5195]) ).
tff(f5195,plain,
( spl183_294
<=> ! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ sP17(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_294])]) ).
tff(f2660,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
| ~ sP17(X1,X0) ),
inference(cnf_transformation,[],[f1584]) ).
tff(f1584,plain,
! [X0: $int,X1: $int] :
( ( $less('times$d'(X0,X1),0)
| ~ sP17(X1,X0) )
& ( sP17(X1,X0)
| ~ $less('times$d'(X0,X1),0) ) ),
inference(nnf_transformation,[],[f1214]) ).
tff(f1214,plain,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
<=> sP17(X1,X0) ),
inference(definition_folding,[],[f412,f1213]) ).
tff(f412,axiom,
! [X0: $int,X1: $int] :
( $less('times$d'(X0,X1),0)
<=> ( ( $less(0,X1)
& $less(X0,0) )
| ( $less(X1,0)
& $less(0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom410) ).
tff(f5193,plain,
spl183_293,
inference(avatar_split_clause,[],[f2659,f5191]) ).
tff(f5191,plain,
( spl183_293
<=> ! [X0: $int,X1: $int] :
( sP17(X1,X0)
| ~ $less('times$d'(X0,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_293])]) ).
tff(f2659,plain,
! [X0: $int,X1: $int] :
( sP17(X1,X0)
| ~ $less('times$d'(X0,X1),0) ),
inference(cnf_transformation,[],[f1584]) ).
tff(f5189,plain,
spl183_292,
inference(avatar_split_clause,[],[f2650,f5187]) ).
tff(f5187,plain,
( spl183_292
<=> ! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ sP16(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_292])]) ).
tff(f2650,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
| ~ sP16(X1,X0) ),
inference(cnf_transformation,[],[f1579]) ).
tff(f1579,plain,
! [X0: $int,X1: $int] :
( ( $less(0,'times$d'(X0,X1))
| ~ sP16(X1,X0) )
& ( sP16(X1,X0)
| ~ $less(0,'times$d'(X0,X1)) ) ),
inference(nnf_transformation,[],[f1212]) ).
tff(f1212,plain,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
<=> sP16(X1,X0) ),
inference(definition_folding,[],[f398,f1211]) ).
tff(f398,axiom,
! [X0: $int,X1: $int] :
( $less(0,'times$d'(X0,X1))
<=> ( ( $less(X1,0)
& $less(X0,0) )
| ( $less(0,X1)
& $less(0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom396) ).
tff(f5182,plain,
spl183_291,
inference(avatar_split_clause,[],[f2649,f5180]) ).
tff(f2649,plain,
! [X0: $int,X1: $int] :
( sP16(X1,X0)
| ~ $less(0,'times$d'(X0,X1)) ),
inference(cnf_transformation,[],[f1579]) ).
tff(f5178,plain,
spl183_290,
inference(avatar_split_clause,[],[f2642,f5176]) ).
tff(f2642,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
| ~ sP15(X1,X0) ),
inference(cnf_transformation,[],[f1575]) ).
tff(f1575,plain,
! [X0: $int,X1: $int] :
( ( ~ $less(0,'times$d'(X0,X1))
| ~ sP15(X1,X0) )
& ( sP15(X1,X0)
| $less(0,'times$d'(X0,X1)) ) ),
inference(nnf_transformation,[],[f1210]) ).
tff(f1210,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
<=> sP15(X1,X0) ),
inference(definition_folding,[],[f688,f1209]) ).
tff(f688,plain,
! [X0: $int,X1: $int] :
( ~ $less(0,'times$d'(X0,X1))
<=> ( ( ~ $less(X1,0)
& ~ $less(0,X0) )
| ( ~ $less(0,X1)
& ~ $less(X0,0) ) ) ),
inference(theory_normalization,[],[f594]) ).
tff(f594,axiom,
! [X0: $int,X1: $int] :
( $lesseq('times$d'(X0,X1),0)
<=> ( ( $lesseq(0,X1)
& $lesseq(X0,0) )
| ( $lesseq(X1,0)
& $lesseq(0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom592) ).
tff(f5174,plain,
spl183_289,
inference(avatar_split_clause,[],[f2641,f5172]) ).
tff(f5172,plain,
( spl183_289
<=> ! [X0: $int,X1: $int] :
( sP15(X1,X0)
| $less(0,'times$d'(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_289])]) ).
tff(f2641,plain,
! [X0: $int,X1: $int] :
( sP15(X1,X0)
| $less(0,'times$d'(X0,X1)) ),
inference(cnf_transformation,[],[f1575]) ).
tff(f5170,plain,
spl183_288,
inference(avatar_split_clause,[],[f2634,f5168]) ).
tff(f5168,plain,
( spl183_288
<=> ! [X0: $int,X1: $int] :
( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_288])]) ).
tff(f2634,plain,
! [X0: $int,X1: $int] :
( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f1571]) ).
tff(f1571,plain,
! [X0: $int,X1: $int] :
( ( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) )
& ( ~ $less(X0,X1)
| $less($uminus(X1),$uminus(X0)) ) ),
inference(nnf_transformation,[],[f687]) ).
tff(f687,plain,
! [X0: $int,X1: $int] :
( ~ $less($uminus(X1),$uminus(X0))
<=> ~ $less(X0,X1) ),
inference(theory_normalization,[],[f542]) ).
tff(f542,axiom,
! [X0: $int,X1: $int] :
( $lesseq($uminus(X0),$uminus(X1))
<=> $lesseq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom540) ).
tff(f5166,plain,
spl183_287,
inference(avatar_split_clause,[],[f2632,f5164]) ).
tff(f5164,plain,
( spl183_287
<=> ! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| ~ sP14(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_287])]) ).
tff(f2632,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
| ~ sP14(X1,X0) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f1570,plain,
! [X0: $int,X1: $int] :
( ( ~ $less('times$d'(X0,X1),0)
| ~ sP14(X1,X0) )
& ( sP14(X1,X0)
| $less('times$d'(X0,X1),0) ) ),
inference(nnf_transformation,[],[f1208]) ).
tff(f1208,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
<=> sP14(X1,X0) ),
inference(definition_folding,[],[f686,f1207]) ).
tff(f686,plain,
! [X0: $int,X1: $int] :
( ~ $less('times$d'(X0,X1),0)
<=> ( ( ~ $less(0,X1)
& ~ $less(0,X0) )
| ( ~ $less(X1,0)
& ~ $less(X0,0) ) ) ),
inference(theory_normalization,[],[f577]) ).
tff(f577,axiom,
! [X0: $int,X1: $int] :
( $lesseq(0,'times$d'(X0,X1))
<=> ( ( $lesseq(X1,0)
& $lesseq(X0,0) )
| ( $lesseq(0,X1)
& $lesseq(0,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom575) ).
tff(f5162,plain,
spl183_286,
inference(avatar_split_clause,[],[f2631,f5160]) ).
tff(f5160,plain,
( spl183_286
<=> ! [X0: $int,X1: $int] :
( sP14(X1,X0)
| $less('times$d'(X0,X1),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_286])]) ).
tff(f2631,plain,
! [X0: $int,X1: $int] :
( sP14(X1,X0)
| $less('times$d'(X0,X1),0) ),
inference(cnf_transformation,[],[f1570]) ).
tff(f5158,plain,
spl183_285,
inference(avatar_split_clause,[],[f2624,f5156]) ).
tff(f5156,plain,
( spl183_285
<=> ! [X0: $real,X1: $real] :
( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_285])]) ).
tff(f2624,plain,
! [X0: $real,X1: $real] :
( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) ),
inference(cnf_transformation,[],[f1566]) ).
tff(f1566,plain,
! [X0: $real,X1: $real] :
( ( ~ $less($uminus(X1),$uminus(X0))
| $less(X0,X1) )
& ( ~ $less(X0,X1)
| $less($uminus(X1),$uminus(X0)) ) ),
inference(nnf_transformation,[],[f685]) ).
tff(f685,plain,
! [X0: $real,X1: $real] :
( ~ $less($uminus(X1),$uminus(X0))
<=> ~ $less(X0,X1) ),
inference(theory_normalization,[],[f541]) ).
tff(f541,axiom,
! [X0: $real,X1: $real] :
( $lesseq($uminus(X0),$uminus(X1))
<=> $lesseq(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom539) ).
tff(f5154,plain,
spl183_284,
inference(avatar_split_clause,[],[f2607,f5152]) ).
tff(f5152,plain,
( spl183_284
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'ereal$'(X0) != 'ereal$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_284])]) ).
tff(f2607,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( 'ereal$'(X0) != 'ereal$'(X1) ) ),
inference(cnf_transformation,[],[f1556]) ).
tff(f1556,plain,
! [X0: $real,X1: $real] :
( ( ( 'ereal$'(X0) = 'ereal$'(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'ereal$'(X0) != 'ereal$'(X1) ) ) ),
inference(nnf_transformation,[],[f10]) ).
tff(f10,axiom,
! [X0: $real,X1: $real] :
( ( 'ereal$'(X0) = 'ereal$'(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom8) ).
tff(f5150,plain,
spl183_283,
inference(avatar_split_clause,[],[f2605,f5148]) ).
tff(f5148,plain,
( spl183_283
<=> ! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_283])]) ).
tff(f2605,plain,
! [X0: $real,X1: $real] :
( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ),
inference(cnf_transformation,[],[f1555]) ).
tff(f1555,plain,
! [X0: $real,X1: $real] :
( ( ( $uminus(X0) = $uminus(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( $uminus(X0) != $uminus(X1) ) ) ),
inference(nnf_transformation,[],[f145]) ).
tff(f145,axiom,
! [X0: $real,X1: $real] :
( ( $uminus(X0) = $uminus(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom143) ).
tff(f5146,plain,
spl183_282,
inference(avatar_split_clause,[],[f2603,f5144]) ).
tff(f5144,plain,
( spl183_282
<=> ! [X0: 'Real_fps$',X1: 'Real_fps$'] :
( ( X0 = X1 )
| ( 'fps_nth$'(X0) != 'fps_nth$'(X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_282])]) ).
tff(f2603,plain,
! [X0: 'Real_fps$',X1: 'Real_fps$'] :
( ( X0 = X1 )
| ( 'fps_nth$'(X0) != 'fps_nth$'(X1) ) ),
inference(cnf_transformation,[],[f1554]) ).
tff(f1554,plain,
! [X0: 'Real_fps$',X1: 'Real_fps$'] :
( ( ( 'fps_nth$'(X0) = 'fps_nth$'(X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( 'fps_nth$'(X0) != 'fps_nth$'(X1) ) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,axiom,
! [X0: 'Real_fps$',X1: 'Real_fps$'] :
( ( 'fps_nth$'(X0) = 'fps_nth$'(X1) )
<=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom191) ).
tff(f5139,plain,
spl183_281,
inference(avatar_split_clause,[],[f2599,f5137]) ).
tff(f5137,plain,
( spl183_281
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = 'times$'(X0,X1) )
| ~ sP13(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_281])]) ).
tff(f2599,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = 'times$'(X0,X1) )
| ~ sP13(X1,X0) ),
inference(cnf_transformation,[],[f1551]) ).
tff(f1551,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'infinity$' = 'times$'(X0,X1) )
| ~ sP13(X1,X0) )
& ( sP13(X1,X0)
| ( 'infinity$' != 'times$'(X0,X1) ) ) ),
inference(nnf_transformation,[],[f1206]) ).
tff(f1206,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = 'times$'(X0,X1) )
<=> sP13(X1,X0) ),
inference(definition_folding,[],[f264,f1205,f1204,f1203]) ).
tff(f1203,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP11(X1,X0)
<=> ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'infinity$' = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
tff(f1204,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( sP12(X1,X0)
<=> ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'('zero$'),X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
tff(f264,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = 'times$'(X0,X1) )
<=> ( ( ( 'uminus$'('infinity$') = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'uminus$'('infinity$') = X0 ) )
| ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'infinity$' = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom262) ).
tff(f5135,plain,
spl183_280,
inference(avatar_split_clause,[],[f2598,f5133]) ).
tff(f5133,plain,
( spl183_280
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X1,X0)
| ( 'infinity$' != 'times$'(X0,X1) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_280])]) ).
tff(f2598,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X1,X0)
| ( 'infinity$' != 'times$'(X0,X1) ) ),
inference(cnf_transformation,[],[f1551]) ).
tff(f5131,plain,
spl183_279,
inference(avatar_split_clause,[],[f2577,f5129]) ).
tff(f5129,plain,
( spl183_279
<=> ! [X0: $real,X1: $real] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_279])]) ).
tff(f2577,plain,
! [X0: $real,X1: $real] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ),
inference(cnf_transformation,[],[f1537]) ).
tff(f1537,plain,
! [X0: $real,X1: $real] :
( ( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) )
& ( $less($uminus(X1),X0)
| ~ $less($uminus(X0),X1) ) ),
inference(nnf_transformation,[],[f198]) ).
tff(f198,axiom,
! [X0: $real,X1: $real] :
( $less($uminus(X0),X1)
<=> $less($uminus(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom196) ).
tff(f5127,plain,
spl183_278,
inference(avatar_split_clause,[],[f2575,f5125]) ).
tff(f5125,plain,
( spl183_278
<=> ! [X0: $real,X1: $real] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_278])]) ).
tff(f2575,plain,
! [X0: $real,X1: $real] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ),
inference(cnf_transformation,[],[f1536]) ).
tff(f1536,plain,
! [X0: $real,X1: $real] :
( ( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) )
& ( $less(X1,$uminus(X0))
| ~ $less(X0,$uminus(X1)) ) ),
inference(nnf_transformation,[],[f196]) ).
tff(f196,axiom,
! [X0: $real,X1: $real] :
( $less(X0,$uminus(X1))
<=> $less(X1,$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom194) ).
tff(f5123,plain,
spl183_277,
inference(avatar_split_clause,[],[f2569,f5121]) ).
tff(f2569,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
| ~ 'fun_app$b'('less$'(X0),X1) ),
inference(cnf_transformation,[],[f1533]) ).
tff(f5119,plain,
spl183_276,
inference(avatar_split_clause,[],[f2565,f5117]) ).
tff(f5117,plain,
( spl183_276
<=> ! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_276])]) ).
tff(f2565,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) ),
inference(cnf_transformation,[],[f1530]) ).
tff(f1530,plain,
! [X0: $int,X1: $int] :
( ( $less($uminus(X0),X1)
| ~ $less($uminus(X1),X0) )
& ( $less($uminus(X1),X0)
| ~ $less($uminus(X0),X1) ) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,axiom,
! [X0: $int,X1: $int] :
( $less($uminus(X0),X1)
<=> $less($uminus(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom195) ).
tff(f5115,plain,
spl183_275,
inference(avatar_split_clause,[],[f2563,f5113]) ).
tff(f5113,plain,
( spl183_275
<=> ! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_275])]) ).
tff(f2563,plain,
! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) ),
inference(cnf_transformation,[],[f1529]) ).
tff(f1529,plain,
! [X0: $int,X1: $int] :
( ( $less(X0,$uminus(X1))
| ~ $less(X1,$uminus(X0)) )
& ( $less(X1,$uminus(X0))
| ~ $less(X0,$uminus(X1)) ) ),
inference(nnf_transformation,[],[f195]) ).
tff(f195,axiom,
! [X0: $int,X1: $int] :
( $less(X0,$uminus(X1))
<=> $less(X1,$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom193) ).
tff(f5111,plain,
spl183_274,
inference(avatar_split_clause,[],[f2382,f5109]) ).
tff(f5109,plain,
( spl183_274
<=> ! [X0: $real,X1: $real] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_274])]) ).
tff(f2382,plain,
! [X0: $real,X1: $real] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f885]) ).
tff(f885,plain,
! [X0: $real,X1: $real] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f238]) ).
tff(f238,axiom,
! [X0: $real,X1: $real] :
( $less(X0,X1)
=> $less($uminus(X1),$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom236) ).
tff(f5107,plain,
spl183_273,
inference(avatar_split_clause,[],[f2381,f5105]) ).
tff(f5105,plain,
( spl183_273
<=> ! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_273])]) ).
tff(f2381,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f884]) ).
tff(f884,plain,
! [X0: $int,X1: $int] :
( $less($uminus(X1),$uminus(X0))
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f237]) ).
tff(f237,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
=> $less($uminus(X1),$uminus(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom235) ).
tff(f5103,plain,
spl183_272,
inference(avatar_split_clause,[],[f2380,f5101]) ).
tff(f5101,plain,
( spl183_272
<=> ! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_272])]) ).
tff(f2380,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f883]) ).
tff(f883,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f86]) ).
tff(f86,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
=> ( 'max$b'(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom84) ).
tff(f5096,plain,
spl183_271,
inference(avatar_split_clause,[],[f2379,f5094]) ).
tff(f5094,plain,
( spl183_271
<=> ! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_271])]) ).
tff(f2379,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f882]) ).
tff(f882,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| ~ $less(X0,X1) ),
inference(ennf_transformation,[],[f83]) ).
tff(f83,axiom,
! [X0: $int,X1: $int] :
( $less(X0,X1)
=> ( 'max$b'(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom81) ).
tff(f5092,plain,
spl183_270,
inference(avatar_split_clause,[],[f2378,f5090]) ).
tff(f5090,plain,
( spl183_270
<=> ! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_270])]) ).
tff(f2378,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f881]) ).
tff(f881,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X0,X1) = X1 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f668]) ).
tff(f668,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
=> ( 'max$b'(X0,X1) = X1 ) ),
inference(theory_normalization,[],[f547]) ).
tff(f547,axiom,
! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> ( 'max$b'(X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom545) ).
tff(f5088,plain,
spl183_269,
inference(avatar_split_clause,[],[f2377,f5086]) ).
tff(f2377,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| $less(X1,X0) ),
inference(cnf_transformation,[],[f880]) ).
tff(f880,plain,
! [X0: $int,X1: $int] :
( ( 'max$b'(X1,X0) = X1 )
| $less(X1,X0) ),
inference(ennf_transformation,[],[f667]) ).
tff(f667,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
=> ( 'max$b'(X1,X0) = X1 ) ),
inference(theory_normalization,[],[f544]) ).
tff(f544,axiom,
! [X0: $int,X1: $int] :
( $lesseq(X0,X1)
=> ( 'max$b'(X1,X0) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom542) ).
tff(f5084,plain,
spl183_268,
inference(avatar_split_clause,[],[f2328,f5082]) ).
tff(f5082,plain,
( spl183_268
<=> ! [X4: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(X4),sK112(X0))
| ~ 'member$'(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_268])]) ).
tff(f2328,plain,
! [X0: 'Ereal_set$',X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X4),sK112(X0))
| ~ 'member$'(X4,X0) ),
inference(cnf_transformation,[],[f1449]) ).
tff(f5080,plain,
spl183_267,
inference(avatar_split_clause,[],[f2325,f5078]) ).
tff(f5078,plain,
( spl183_267
<=> ! [X4: 'Ereal$',X0: 'Ereal_set$'] :
( 'fun_app$b'('less_eq$'(sK110(X0)),X4)
| ~ 'member$'(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_267])]) ).
tff(f2325,plain,
! [X0: 'Ereal_set$',X4: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(sK110(X0)),X4)
| ~ 'member$'(X4,X0) ),
inference(cnf_transformation,[],[f1446]) ).
tff(f5076,plain,
spl183_266,
inference(avatar_split_clause,[],[f2313,f5074]) ).
tff(f2313,plain,
! [X2: $real,X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'ereal$'(X2)) ),
inference(cnf_transformation,[],[f1419]) ).
tff(f5072,plain,
spl183_265,
inference(avatar_split_clause,[],[f2308,f5070]) ).
tff(f5070,plain,
( spl183_265
<=> ! [X0: 'Ereal_bool_fun$',X3: $real] :
( 'fun_app$b'(X0,'ereal$'(X3))
| ~ 'fun_app$b'(X0,sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_265])]) ).
tff(f2308,plain,
! [X3: $real,X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'ereal$'(X3))
| ~ 'fun_app$b'(X0,sK97(X0)) ),
inference(cnf_transformation,[],[f1413]) ).
tff(f5068,plain,
spl183_264,
inference(avatar_split_clause,[],[f2289,f5066]) ).
tff(f5066,plain,
( spl183_264
<=> ! [X0: $real] :
( $less(X0,1.0)
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_264])]) ).
tff(f2289,plain,
! [X0: $real] :
( $less(X0,1.0)
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ),
inference(cnf_transformation,[],[f1399]) ).
tff(f1399,plain,
! [X0: $real] :
( ( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) )
& ( ( $less(X0,1.0)
& $less(0.0,X0) )
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ) ),
inference(flattening,[],[f1398]) ).
tff(f1398,plain,
! [X0: $real] :
( ( $less(1.0,'fun_app$c'('inverse$',X0))
| ~ $less(X0,1.0)
| ~ $less(0.0,X0) )
& ( ( $less(X0,1.0)
& $less(0.0,X0) )
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ) ),
inference(nnf_transformation,[],[f502]) ).
tff(f502,axiom,
! [X0: $real] :
( $less(1.0,'fun_app$c'('inverse$',X0))
<=> ( $less(X0,1.0)
& $less(0.0,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom500) ).
tff(f5064,plain,
spl183_263,
inference(avatar_split_clause,[],[f2288,f5062]) ).
tff(f5062,plain,
( spl183_263
<=> ! [X0: $real] :
( $less(0.0,X0)
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_263])]) ).
tff(f2288,plain,
! [X0: $real] :
( $less(0.0,X0)
| ~ $less(1.0,'fun_app$c'('inverse$',X0)) ),
inference(cnf_transformation,[],[f1399]) ).
tff(f5060,plain,
spl183_262,
inference(avatar_split_clause,[],[f2286,f5058]) ).
tff(f5058,plain,
( spl183_262
<=> ! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'zero$')
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_262])]) ).
tff(f2286,plain,
! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'zero$')
| ~ $less(X0,0.0) ),
inference(cnf_transformation,[],[f1397]) ).
tff(f1397,plain,
! [X0: $real] :
( ( 'fun_app$b'('less$'('ereal$'(X0)),'zero$')
| ~ $less(X0,0.0) )
& ( $less(X0,0.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'zero$') ) ),
inference(nnf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'zero$')
<=> $less(X0,0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom36) ).
tff(f5056,plain,
( spl183_261
| ~ spl183_26
| ~ spl183_223 ),
inference(avatar_split_clause,[],[f4938,f4761,f3899,f5053]) ).
tff(f3899,plain,
( spl183_26
<=> 'fun_app$b'('less$'('zero$'),'one$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_26])]) ).
tff(f4761,plain,
( spl183_223
<=> ! [X0: 'Ereal$'] :
( sP11(X0,'infinity$')
| ~ 'fun_app$b'('less$'('zero$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_223])]) ).
tff(f4938,plain,
( sP11('one$a','infinity$')
| ~ spl183_26
| ~ spl183_223 ),
inference(resolution,[],[f4762,f3901]) ).
tff(f3901,plain,
( 'fun_app$b'('less$'('zero$'),'one$a')
| ~ spl183_26 ),
inference(avatar_component_clause,[],[f3899]) ).
tff(f4762,plain,
( ! [X0: 'Ereal$'] :
( ~ 'fun_app$b'('less$'('zero$'),X0)
| sP11(X0,'infinity$') )
| ~ spl183_223 ),
inference(avatar_component_clause,[],[f4761]) ).
tff(f5051,plain,
spl183_260,
inference(avatar_split_clause,[],[f2285,f5049]) ).
tff(f5049,plain,
( spl183_260
<=> ! [X0: $real] :
( $less(X0,0.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_260])]) ).
tff(f2285,plain,
! [X0: $real] :
( $less(X0,0.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'zero$') ),
inference(cnf_transformation,[],[f1397]) ).
tff(f5047,plain,
spl183_259,
inference(avatar_split_clause,[],[f2284,f5045]) ).
tff(f5045,plain,
( spl183_259
<=> ! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'one$a')
| ~ $less(X0,1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_259])]) ).
tff(f2284,plain,
! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'one$a')
| ~ $less(X0,1.0) ),
inference(cnf_transformation,[],[f1396]) ).
tff(f1396,plain,
! [X0: $real] :
( ( 'fun_app$b'('less$'('ereal$'(X0)),'one$a')
| ~ $less(X0,1.0) )
& ( $less(X0,1.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'one$a') ) ),
inference(nnf_transformation,[],[f524]) ).
tff(f524,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'one$a')
<=> $less(X0,1.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom522) ).
tff(f5043,plain,
spl183_258,
inference(avatar_split_clause,[],[f2283,f5041]) ).
tff(f5041,plain,
( spl183_258
<=> ! [X0: $real] :
( $less(X0,1.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'one$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_258])]) ).
tff(f2283,plain,
! [X0: $real] :
( $less(X0,1.0)
| ~ 'fun_app$b'('less$'('ereal$'(X0)),'one$a') ),
inference(cnf_transformation,[],[f1396]) ).
tff(f5039,plain,
spl183_257,
inference(avatar_split_clause,[],[f2273,f5037]) ).
tff(f5037,plain,
( spl183_257
<=> ! [X0: $real] :
( 'fun_app$b'('less$'('zero$'),'ereal$'(X0))
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_257])]) ).
tff(f2273,plain,
! [X0: $real] :
( 'fun_app$b'('less$'('zero$'),'ereal$'(X0))
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f1391]) ).
tff(f1391,plain,
! [X0: $real] :
( ( 'fun_app$b'('less$'('zero$'),'ereal$'(X0))
| ~ $less(0.0,X0) )
& ( $less(0.0,X0)
| ~ 'fun_app$b'('less$'('zero$'),'ereal$'(X0)) ) ),
inference(nnf_transformation,[],[f37]) ).
tff(f37,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('zero$'),'ereal$'(X0))
<=> $less(0.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom35) ).
tff(f5035,plain,
spl183_256,
inference(avatar_split_clause,[],[f2272,f5033]) ).
tff(f5033,plain,
( spl183_256
<=> ! [X0: $real] :
( $less(0.0,X0)
| ~ 'fun_app$b'('less$'('zero$'),'ereal$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_256])]) ).
tff(f2272,plain,
! [X0: $real] :
( $less(0.0,X0)
| ~ 'fun_app$b'('less$'('zero$'),'ereal$'(X0)) ),
inference(cnf_transformation,[],[f1391]) ).
tff(f5031,plain,
spl183_255,
inference(avatar_split_clause,[],[f2271,f5029]) ).
tff(f5029,plain,
( spl183_255
<=> ! [X0: $real] :
( 'fun_app$b'('less$'('one$a'),'ereal$'(X0))
| ~ $less(1.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_255])]) ).
tff(f2271,plain,
! [X0: $real] :
( 'fun_app$b'('less$'('one$a'),'ereal$'(X0))
| ~ $less(1.0,X0) ),
inference(cnf_transformation,[],[f1390]) ).
tff(f1390,plain,
! [X0: $real] :
( ( 'fun_app$b'('less$'('one$a'),'ereal$'(X0))
| ~ $less(1.0,X0) )
& ( $less(1.0,X0)
| ~ 'fun_app$b'('less$'('one$a'),'ereal$'(X0)) ) ),
inference(nnf_transformation,[],[f523]) ).
tff(f523,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('one$a'),'ereal$'(X0))
<=> $less(1.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom521) ).
tff(f5027,plain,
spl183_254,
inference(avatar_split_clause,[],[f2270,f5025]) ).
tff(f5025,plain,
( spl183_254
<=> ! [X0: $real] :
( $less(1.0,X0)
| ~ 'fun_app$b'('less$'('one$a'),'ereal$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_254])]) ).
tff(f2270,plain,
! [X0: $real] :
( $less(1.0,X0)
| ~ 'fun_app$b'('less$'('one$a'),'ereal$'(X0)) ),
inference(cnf_transformation,[],[f1390]) ).
tff(f5023,plain,
spl183_253,
inference(avatar_split_clause,[],[f2267,f5021]) ).
tff(f5021,plain,
( spl183_253
<=> ! [X0: $real] :
( ~ $less(0.0,'fun_app$c'('inverse$',X0))
| $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_253])]) ).
tff(f2267,plain,
! [X0: $real] :
( ~ $less(0.0,'fun_app$c'('inverse$',X0))
| $less(0.0,X0) ),
inference(cnf_transformation,[],[f1388]) ).
tff(f1388,plain,
! [X0: $real] :
( ( ~ $less(0.0,'fun_app$c'('inverse$',X0))
| $less(0.0,X0) )
& ( ~ $less(0.0,X0)
| $less(0.0,'fun_app$c'('inverse$',X0)) ) ),
inference(nnf_transformation,[],[f663]) ).
tff(f663,plain,
! [X0: $real] :
( ~ $less(0.0,'fun_app$c'('inverse$',X0))
<=> ~ $less(0.0,X0) ),
inference(theory_normalization,[],[f563]) ).
tff(f563,axiom,
! [X0: $real] :
( $lesseq('fun_app$c'('inverse$',X0),0.0)
<=> $lesseq(X0,0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom561) ).
tff(f5019,plain,
spl183_252,
inference(avatar_split_clause,[],[f2265,f5017]) ).
tff(f5017,plain,
( spl183_252
<=> ! [X0: $real] :
( ~ $less('fun_app$c'('inverse$',X0),0.0)
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_252])]) ).
tff(f2265,plain,
! [X0: $real] :
( ~ $less('fun_app$c'('inverse$',X0),0.0)
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1387]) ).
tff(f1387,plain,
! [X0: $real] :
( ( ~ $less('fun_app$c'('inverse$',X0),0.0)
| $less(X0,0.0) )
& ( ~ $less(X0,0.0)
| $less('fun_app$c'('inverse$',X0),0.0) ) ),
inference(nnf_transformation,[],[f662]) ).
tff(f662,plain,
! [X0: $real] :
( ~ $less('fun_app$c'('inverse$',X0),0.0)
<=> ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f562]) ).
tff(f562,axiom,
! [X0: $real] :
( $lesseq(0.0,'fun_app$c'('inverse$',X0))
<=> $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom560) ).
tff(f5015,plain,
spl183_251,
inference(avatar_split_clause,[],[f2259,f5013]) ).
tff(f5013,plain,
( spl183_251
<=> ! [X0: $real] :
( ( 1.0 = X0 )
| ( 'fun_app$c'('inverse$',X0) != 1.0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_251])]) ).
tff(f2259,plain,
! [X0: $real] :
( ( 1.0 = X0 )
| ( 'fun_app$c'('inverse$',X0) != 1.0 ) ),
inference(cnf_transformation,[],[f1384]) ).
tff(f1384,plain,
! [X0: $real] :
( ( ( 'fun_app$c'('inverse$',X0) = 1.0 )
| ( 1.0 != X0 ) )
& ( ( 1.0 = X0 )
| ( 'fun_app$c'('inverse$',X0) != 1.0 ) ) ),
inference(nnf_transformation,[],[f431]) ).
tff(f431,axiom,
! [X0: $real] :
( ( 'fun_app$c'('inverse$',X0) = 1.0 )
<=> ( 1.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom429) ).
tff(f5011,plain,
( spl183_250
| ~ spl183_27
| ~ spl183_223 ),
inference(avatar_split_clause,[],[f4936,f4761,f3904,f5008]) ).
tff(f5008,plain,
( spl183_250
<=> sP11('infinity$','infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_250])]) ).
tff(f3904,plain,
( spl183_27
<=> 'fun_app$b'('less$'('zero$'),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_27])]) ).
tff(f4936,plain,
( sP11('infinity$','infinity$')
| ~ spl183_27
| ~ spl183_223 ),
inference(resolution,[],[f4762,f3906]) ).
tff(f3906,plain,
( 'fun_app$b'('less$'('zero$'),'infinity$')
| ~ spl183_27 ),
inference(avatar_component_clause,[],[f3904]) ).
tff(f5006,plain,
spl183_249,
inference(avatar_split_clause,[],[f2232,f5004]) ).
tff(f5004,plain,
( spl183_249
<=> ! [X0: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X0),1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_249])]) ).
tff(f2232,plain,
! [X0: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X0),1) ),
inference(cnf_transformation,[],[f1372]) ).
tff(f1372,plain,
! [X0: 'Nat$'] :
( ( $less('of_nat$'(X0),1)
| ( 0 != 'of_nat$'(X0) ) )
& ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X0),1) ) ),
inference(nnf_transformation,[],[f520]) ).
tff(f520,axiom,
! [X0: 'Nat$'] :
( $less('of_nat$'(X0),1)
<=> ( 0 = 'of_nat$'(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom518) ).
tff(f5002,plain,
spl183_248,
inference(avatar_split_clause,[],[f2119,f5000]) ).
tff(f5000,plain,
( spl183_248
<=> ! [X0: $real] :
( $less(0.0,'fun_app$c'('inverse$',X0))
| ~ $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_248])]) ).
tff(f2119,plain,
! [X0: $real] :
( $less(0.0,'fun_app$c'('inverse$',X0))
| ~ $less(0.0,X0) ),
inference(cnf_transformation,[],[f841]) ).
tff(f841,plain,
! [X0: $real] :
( $less(0.0,'fun_app$c'('inverse$',X0))
| ~ $less(0.0,X0) ),
inference(ennf_transformation,[],[f50]) ).
tff(f50,axiom,
! [X0: $real] :
( $less(0.0,X0)
=> $less(0.0,'fun_app$c'('inverse$',X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom48) ).
tff(f4998,plain,
spl183_247,
inference(avatar_split_clause,[],[f2118,f4996]) ).
tff(f4996,plain,
( spl183_247
<=> ! [X0: $real] :
( $less('fun_app$c'('inverse$',X0),0.0)
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_247])]) ).
tff(f2118,plain,
! [X0: $real] :
( $less('fun_app$c'('inverse$',X0),0.0)
| ~ $less(X0,0.0) ),
inference(cnf_transformation,[],[f840]) ).
tff(f840,plain,
! [X0: $real] :
( $less('fun_app$c'('inverse$',X0),0.0)
| ~ $less(X0,0.0) ),
inference(ennf_transformation,[],[f53]) ).
tff(f53,axiom,
! [X0: $real] :
( $less(X0,0.0)
=> $less('fun_app$c'('inverse$',X0),0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom51) ).
tff(f4994,plain,
spl183_246,
inference(avatar_split_clause,[],[f2112,f4992]) ).
tff(f4992,plain,
( spl183_246
<=> ! [X0: $real] :
( ( 0.0 != 'fun_app$c'('inverse$',X0) )
| ( 0.0 = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_246])]) ).
tff(f2112,plain,
! [X0: $real] :
( ( 0.0 != 'fun_app$c'('inverse$',X0) )
| ( 0.0 = X0 ) ),
inference(cnf_transformation,[],[f834]) ).
tff(f834,plain,
! [X0: $real] :
( ( 0.0 != 'fun_app$c'('inverse$',X0) )
| ( 0.0 = X0 ) ),
inference(ennf_transformation,[],[f60]) ).
tff(f60,axiom,
! [X0: $real] :
( ( 0.0 != X0 )
=> ( 0.0 != 'fun_app$c'('inverse$',X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom58) ).
tff(f4990,plain,
spl183_245,
inference(avatar_split_clause,[],[f2106,f4988]) ).
tff(f4988,plain,
( spl183_245
<=> ! [X0: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| $less(0,'of_nat$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_245])]) ).
tff(f2106,plain,
! [X0: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| $less(0,'of_nat$'(X0)) ),
inference(cnf_transformation,[],[f831]) ).
tff(f831,plain,
! [X0: 'Nat$'] :
( ( ( 'of_nat$'(X0) = 'of_nat$'(X0) )
| ~ $less(0,'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X0) )
| $less(0,'of_nat$'(X0)) ) ),
inference(ennf_transformation,[],[f652]) ).
tff(f652,plain,
! [X0: 'Nat$'] :
( ( $less(0,'of_nat$'(X0))
=> ( 'of_nat$'(X0) = 'of_nat$'(X0) ) )
& ( ~ $less(0,'of_nat$'(X0))
=> ( 0 = 'of_nat$'(X0) ) ) ),
inference(theory_normalization,[],[f119]) ).
tff(f119,axiom,
! [X0: 'Nat$'] :
( ( ~ $lesseq('of_nat$'(X0),0)
=> ( 'of_nat$'(X0) = 'of_nat$'(X0) ) )
& ( $lesseq('of_nat$'(X0),0)
=> ( 0 = 'of_nat$'(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom117) ).
tff(f4986,plain,
spl183_244,
inference(avatar_split_clause,[],[f2093,f4984]) ).
tff(f4984,plain,
( spl183_244
<=> ! [X0: $int] :
( ( 0 = 'of_nat$'('nat$'(X0)) )
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_244])]) ).
tff(f2093,plain,
! [X0: $int] :
( ( 0 = 'of_nat$'('nat$'(X0)) )
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f824]) ).
tff(f824,plain,
! [X0: $int] :
( ( ( 0 = 'of_nat$'('nat$'(X0)) )
| ~ $less(X0,0) )
& ( ( 'of_nat$'('nat$'(X0)) = X0 )
| $less(X0,0) ) ),
inference(ennf_transformation,[],[f649]) ).
tff(f649,plain,
! [X0: $int] :
( ( $less(X0,0)
=> ( 0 = 'of_nat$'('nat$'(X0)) ) )
& ( ~ $less(X0,0)
=> ( 'of_nat$'('nat$'(X0)) = X0 ) ) ),
inference(theory_normalization,[],[f640]) ).
tff(f640,axiom,
! [X0: $int] :
( ( ~ $lesseq(0,X0)
=> ( 0 = 'of_nat$'('nat$'(X0)) ) )
& ( $lesseq(0,X0)
=> ( 'of_nat$'('nat$'(X0)) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom638) ).
tff(f4982,plain,
spl183_243,
inference(avatar_split_clause,[],[f2092,f4980]) ).
tff(f4980,plain,
( spl183_243
<=> ! [X0: $int] :
( ( 'of_nat$'('nat$'(X0)) = X0 )
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_243])]) ).
tff(f2092,plain,
! [X0: $int] :
( ( 'of_nat$'('nat$'(X0)) = X0 )
| $less(X0,0) ),
inference(cnf_transformation,[],[f824]) ).
tff(f4977,plain,
spl183_242,
inference(avatar_split_clause,[],[f2062,f4975]) ).
tff(f2062,plain,
! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'nat$'(0)) ),
inference(cnf_transformation,[],[f236]) ).
tff(f236,axiom,
! [X0: $real] : ( 0.0 = 'fun_app$f'('fps_nth$'('fps_ln$'(X0)),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom234) ).
tff(f4972,plain,
spl183_241,
inference(avatar_split_clause,[],[f2061,f4970]) ).
tff(f2061,plain,
! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'nat$'(0)) ),
inference(cnf_transformation,[],[f513]) ).
tff(f513,axiom,
! [X0: 'Int_fps$'] : ( 0 = 'fps_nth$b'('fun_app$h'('fps_XD$',X0),'nat$'(0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom511) ).
tff(f4968,plain,
spl183_240,
inference(avatar_split_clause,[],[f739,f4966]) ).
tff(f739,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| $less(X1,$sum(X0,1.0)) ),
introduced(theory_axiom_147,[]) ).
tff(f4964,plain,
( spl183_239
| ~ spl183_26
| ~ spl183_222 ),
inference(avatar_split_clause,[],[f4934,f4757,f3899,f4961]) ).
tff(f4757,plain,
( spl183_222
<=> ! [X1: 'Ereal$'] :
( sP12('infinity$',X1)
| ~ 'fun_app$b'('less$'('zero$'),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_222])]) ).
tff(f4934,plain,
( sP12('infinity$','one$a')
| ~ spl183_26
| ~ spl183_222 ),
inference(resolution,[],[f4758,f3901]) ).
tff(f4758,plain,
( ! [X1: 'Ereal$'] :
( ~ 'fun_app$b'('less$'('zero$'),X1)
| sP12('infinity$',X1) )
| ~ spl183_222 ),
inference(avatar_component_clause,[],[f4757]) ).
tff(f4959,plain,
spl183_238,
inference(avatar_split_clause,[],[f729,f4957]) ).
tff(f4957,plain,
( spl183_238
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_238])]) ).
tff(f729,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f4955,plain,
spl183_237,
inference(avatar_split_clause,[],[f721,f4953]) ).
tff(f721,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f4946,plain,
( spl183_236
| ~ spl183_27
| ~ spl183_222 ),
inference(avatar_split_clause,[],[f4932,f4757,f3904,f4943]) ).
tff(f4932,plain,
( sP12('infinity$','infinity$')
| ~ spl183_27
| ~ spl183_222 ),
inference(resolution,[],[f4758,f3906]) ).
tff(f4850,plain,
( spl183_235
| ~ spl183_70
| ~ spl183_121
| ~ spl183_128 ),
inference(avatar_split_clause,[],[f4374,f4370,f4324,f4093,f4847]) ).
tff(f4847,plain,
( spl183_235
<=> ( 0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_235])]) ).
tff(f4093,plain,
( spl183_70
<=> ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_70])]) ).
tff(f4324,plain,
( spl183_121
<=> ( 0 = 'of_nat$'('size_ereal$'('one$a')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_121])]) ).
tff(f4370,plain,
( spl183_128
<=> ( 0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_128])]) ).
tff(f4374,plain,
( ( 0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'size_ereal$'('one$a')) )
| ~ spl183_70
| ~ spl183_121
| ~ spl183_128 ),
inference(forward_demodulation,[],[f4372,f4346]) ).
tff(f4346,plain,
( ( 'nat$'(0) = 'size_ereal$'('one$a') )
| ~ spl183_70
| ~ spl183_121 ),
inference(superposition,[],[f4094,f4326]) ).
tff(f4326,plain,
( ( 0 = 'of_nat$'('size_ereal$'('one$a')) )
| ~ spl183_121 ),
inference(avatar_component_clause,[],[f4324]) ).
tff(f4094,plain,
( ! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 )
| ~ spl183_70 ),
inference(avatar_component_clause,[],[f4093]) ).
tff(f4372,plain,
( ( 0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(0)) )
| ~ spl183_128 ),
inference(avatar_component_clause,[],[f4370]) ).
tff(f4813,plain,
spl183_234,
inference(avatar_split_clause,[],[f3723,f4810]) ).
tff(f4810,plain,
( spl183_234
<=> ( 'zero$' = 'inverse$a'('times$'('infinity$','ereal$'(-1.0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_234])]) ).
tff(f3723,plain,
'zero$' = 'inverse$a'('times$'('infinity$','ereal$'(-1.0))),
inference(evaluation,[],[f3217]) ).
tff(f3217,plain,
'zero$' = 'inverse$a'('times$'('infinity$','ereal$'($uminus(1.0)))),
inference(definition_unfolding,[],[f1967,f2063]) ).
tff(f1967,plain,
'zero$' = 'inverse$a'('uminus$'('infinity$')),
inference(cnf_transformation,[],[f226]) ).
tff(f226,axiom,
'zero$' = 'inverse$a'('uminus$'('infinity$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom224) ).
tff(f4808,plain,
( spl183_233
| ~ spl183_72
| ~ spl183_232 ),
inference(avatar_split_clause,[],[f4803,f4799,f4101,f4805]) ).
tff(f4101,plain,
( spl183_72
<=> ! [X0: 'Ereal$'] : ( 'times$'('one$a',X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_72])]) ).
tff(f4799,plain,
( spl183_232
<=> 'fun_app$b'('less$'('times$'('one$a','ereal$'(-1.0))),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_232])]) ).
tff(f4803,plain,
( 'fun_app$b'('less$'('ereal$'(-1.0)),'zero$')
| ~ spl183_72
| ~ spl183_232 ),
inference(forward_demodulation,[],[f4801,f4102]) ).
tff(f4102,plain,
( ! [X0: 'Ereal$'] : ( 'times$'('one$a',X0) = X0 )
| ~ spl183_72 ),
inference(avatar_component_clause,[],[f4101]) ).
tff(f4801,plain,
( 'fun_app$b'('less$'('times$'('one$a','ereal$'(-1.0))),'zero$')
| ~ spl183_232 ),
inference(avatar_component_clause,[],[f4799]) ).
tff(f4802,plain,
spl183_232,
inference(avatar_split_clause,[],[f3722,f4799]) ).
tff(f3722,plain,
'fun_app$b'('less$'('times$'('one$a','ereal$'(-1.0))),'zero$'),
inference(evaluation,[],[f3218]) ).
tff(f3218,plain,
'fun_app$b'('less$'('times$'('one$a','ereal$'($uminus(1.0)))),'zero$'),
inference(definition_unfolding,[],[f1973,f2063]) ).
tff(f1973,plain,
'fun_app$b'('less$'('uminus$'('one$a')),'zero$'),
inference(cnf_transformation,[],[f535]) ).
tff(f535,axiom,
'fun_app$b'('less$'('uminus$'('one$a')),'zero$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom533) ).
tff(f4797,plain,
spl183_231,
inference(avatar_split_clause,[],[f3721,f4794]) ).
tff(f3721,plain,
'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'zero$'),
inference(evaluation,[],[f3219]) ).
tff(f3219,plain,
'fun_app$b'('less$'('times$'('infinity$','ereal$'($uminus(1.0)))),'zero$'),
inference(definition_unfolding,[],[f1974,f2063]) ).
tff(f1974,plain,
'fun_app$b'('less$'('uminus$'('infinity$')),'zero$'),
inference(cnf_transformation,[],[f225]) ).
tff(f225,axiom,
'fun_app$b'('less$'('uminus$'('infinity$')),'zero$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom223) ).
tff(f4792,plain,
spl183_230,
inference(avatar_split_clause,[],[f3717,f4789]) ).
tff(f4789,plain,
( spl183_230
<=> 'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_230])]) ).
tff(f3717,plain,
'fun_app$b'('less$'('times$'('infinity$','ereal$'(-1.0))),'infinity$'),
inference(evaluation,[],[f3223]) ).
tff(f3223,plain,
'fun_app$b'('less$'('times$'('infinity$','ereal$'($uminus(1.0)))),'infinity$'),
inference(definition_unfolding,[],[f1995,f2063]) ).
tff(f1995,plain,
'fun_app$b'('less$'('uminus$'('infinity$')),'infinity$'),
inference(cnf_transformation,[],[f749]) ).
tff(f749,plain,
'fun_app$b'('less$'('uminus$'('infinity$')),'infinity$'),
inference(true_and_false_elimination,[],[f218]) ).
tff(f218,axiom,
( 'fun_app$b'('less$'('uminus$'('infinity$')),'infinity$')
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom216) ).
tff(f4787,plain,
spl183_229,
inference(avatar_split_clause,[],[f3716,f4785]) ).
tff(f4785,plain,
( spl183_229
<=> ! [X0: 'Ereal$'] : ( 'inverse$a'(X0) != 'times$'('infinity$','ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_229])]) ).
tff(f3716,plain,
! [X0: 'Ereal$'] : ( 'inverse$a'(X0) != 'times$'('infinity$','ereal$'(-1.0)) ),
inference(evaluation,[],[f3224]) ).
tff(f3224,plain,
! [X0: 'Ereal$'] : ( 'inverse$a'(X0) != 'times$'('infinity$','ereal$'($uminus(1.0))) ),
inference(definition_unfolding,[],[f2001,f2063]) ).
tff(f2001,plain,
! [X0: 'Ereal$'] : ( 'inverse$a'(X0) != 'uminus$'('infinity$') ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,axiom,
! [X0: 'Ereal$'] : ( 'inverse$a'(X0) != 'uminus$'('infinity$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom218) ).
tff(f4783,plain,
spl183_228,
inference(avatar_split_clause,[],[f3715,f4781]) ).
tff(f4781,plain,
( spl183_228
<=> ! [X0: $real] : ( 'ereal$'(X0) != 'times$'('infinity$','ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_228])]) ).
tff(f3715,plain,
! [X0: $real] : ( 'ereal$'(X0) != 'times$'('infinity$','ereal$'(-1.0)) ),
inference(evaluation,[],[f3225]) ).
tff(f3225,plain,
! [X0: $real] : ( 'ereal$'(X0) != 'times$'('infinity$','ereal$'($uminus(1.0))) ),
inference(definition_unfolding,[],[f2002,f2063]) ).
tff(f2002,plain,
! [X0: $real] : ( 'ereal$'(X0) != 'uminus$'('infinity$') ),
inference(cnf_transformation,[],[f209]) ).
tff(f209,axiom,
! [X0: $real] : ( 'ereal$'(X0) != 'uminus$'('infinity$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom207) ).
tff(f4779,plain,
spl183_227,
inference(avatar_split_clause,[],[f3713,f4777]) ).
tff(f3713,plain,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('times$'('infinity$','ereal$'(-1.0))),X0),
inference(evaluation,[],[f3227]) ).
tff(f3227,plain,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('times$'('infinity$','ereal$'($uminus(1.0)))),X0),
inference(definition_unfolding,[],[f2035,f2063]) ).
tff(f2035,plain,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('uminus$'('infinity$')),X0),
inference(cnf_transformation,[],[f636]) ).
tff(f636,axiom,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'('uminus$'('infinity$')),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom634) ).
tff(f4775,plain,
spl183_226,
inference(avatar_split_clause,[],[f3675,f4773]) ).
tff(f3675,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'times$'('infinity$','ereal$'(-1.0))),
inference(evaluation,[],[f3259]) ).
tff(f3259,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'times$'('infinity$','ereal$'($uminus(1.0)))),
inference(definition_unfolding,[],[f2278,f2063]) ).
tff(f2278,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'uminus$'('infinity$')),
inference(cnf_transformation,[],[f776]) ).
tff(f776,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'uminus$'('infinity$')),
inference(flattening,[],[f775]) ).
tff(f775,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),'uminus$'('infinity$')),
inference(true_and_false_elimination,[],[f219]) ).
tff(f219,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'uminus$'('infinity$'))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom217) ).
tff(f4771,plain,
spl183_225,
inference(avatar_split_clause,[],[f3489,f4769]) ).
tff(f3489,plain,
! [X0: 'Ereal$'] :
( sP18(X0,'infinity$')
| ~ 'fun_app$b'('less$'(X0),'zero$') ),
inference(equality_resolution,[],[f2695]) ).
tff(f2695,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP18(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ( 'infinity$' != X1 ) ),
inference(cnf_transformation,[],[f1608]) ).
tff(f1608,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP18(X0,X1)
| ~ 'fun_app$b'('less$'(X0),'zero$')
| ( 'infinity$' != X1 ) )
& ( ( 'fun_app$b'('less$'(X0),'zero$')
& ( 'infinity$' = X1 ) )
| ~ sP18(X0,X1) ) ),
inference(rectify,[],[f1607]) ).
tff(f1607,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP18(X1,X0)
| ~ 'fun_app$b'('less$'(X1),'zero$')
| ( 'infinity$' != X0 ) )
& ( ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'infinity$' = X0 ) )
| ~ sP18(X1,X0) ) ),
inference(flattening,[],[f1606]) ).
tff(f1606,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP18(X1,X0)
| ~ 'fun_app$b'('less$'(X1),'zero$')
| ( 'infinity$' != X0 ) )
& ( ( 'fun_app$b'('less$'(X1),'zero$')
& ( 'infinity$' = X0 ) )
| ~ sP18(X1,X0) ) ),
inference(nnf_transformation,[],[f1215]) ).
tff(f4767,plain,
spl183_224,
inference(avatar_split_clause,[],[f3488,f4765]) ).
tff(f3488,plain,
! [X1: 'Ereal$'] :
( sP19('infinity$',X1)
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(equality_resolution,[],[f2692]) ).
tff(f2692,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP19(X0,X1)
| ( 'infinity$' != X0 )
| ~ 'fun_app$b'('less$'(X1),'zero$') ),
inference(cnf_transformation,[],[f1605]) ).
tff(f1605,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP19(X0,X1)
| ( 'infinity$' != X0 )
| ~ 'fun_app$b'('less$'(X1),'zero$') )
& ( ( ( 'infinity$' = X0 )
& 'fun_app$b'('less$'(X1),'zero$') )
| ~ sP19(X0,X1) ) ),
inference(rectify,[],[f1604]) ).
tff(f1604,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP19(X1,X0)
| ( 'infinity$' != X1 )
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ~ sP19(X1,X0) ) ),
inference(flattening,[],[f1603]) ).
tff(f1603,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP19(X1,X0)
| ( 'infinity$' != X1 )
| ~ 'fun_app$b'('less$'(X0),'zero$') )
& ( ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'(X0),'zero$') )
| ~ sP19(X1,X0) ) ),
inference(nnf_transformation,[],[f1216]) ).
tff(f4763,plain,
spl183_223,
inference(avatar_split_clause,[],[f3463,f4761]) ).
tff(f3463,plain,
! [X0: 'Ereal$'] :
( sP11(X0,'infinity$')
| ~ 'fun_app$b'('less$'('zero$'),X0) ),
inference(equality_resolution,[],[f2597]) ).
tff(f2597,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP11(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ( 'infinity$' != X1 ) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f1550,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP11(X0,X1)
| ~ 'fun_app$b'('less$'('zero$'),X0)
| ( 'infinity$' != X1 ) )
& ( ( 'fun_app$b'('less$'('zero$'),X0)
& ( 'infinity$' = X1 ) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f1549]) ).
tff(f1549,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP11(X1,X0)
| ~ 'fun_app$b'('less$'('zero$'),X1)
| ( 'infinity$' != X0 ) )
& ( ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'infinity$' = X0 ) )
| ~ sP11(X1,X0) ) ),
inference(flattening,[],[f1548]) ).
tff(f1548,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP11(X1,X0)
| ~ 'fun_app$b'('less$'('zero$'),X1)
| ( 'infinity$' != X0 ) )
& ( ( 'fun_app$b'('less$'('zero$'),X1)
& ( 'infinity$' = X0 ) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f1203]) ).
tff(f4759,plain,
spl183_222,
inference(avatar_split_clause,[],[f3462,f4757]) ).
tff(f3462,plain,
! [X1: 'Ereal$'] :
( sP12('infinity$',X1)
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(equality_resolution,[],[f2594]) ).
tff(f2594,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP12(X0,X1)
| ( 'infinity$' != X0 )
| ~ 'fun_app$b'('less$'('zero$'),X1) ),
inference(cnf_transformation,[],[f1547]) ).
tff(f1547,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( sP12(X0,X1)
| ( 'infinity$' != X0 )
| ~ 'fun_app$b'('less$'('zero$'),X1) )
& ( ( ( 'infinity$' = X0 )
& 'fun_app$b'('less$'('zero$'),X1) )
| ~ sP12(X0,X1) ) ),
inference(rectify,[],[f1546]) ).
tff(f1546,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP12(X1,X0)
| ( 'infinity$' != X1 )
| ~ 'fun_app$b'('less$'('zero$'),X0) )
& ( ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP12(X1,X0) ) ),
inference(flattening,[],[f1545]) ).
tff(f1545,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( sP12(X1,X0)
| ( 'infinity$' != X1 )
| ~ 'fun_app$b'('less$'('zero$'),X0) )
& ( ( ( 'infinity$' = X1 )
& 'fun_app$b'('less$'('zero$'),X0) )
| ~ sP12(X1,X0) ) ),
inference(nnf_transformation,[],[f1204]) ).
tff(f4755,plain,
spl183_221,
inference(avatar_split_clause,[],[f3089,f4753]) ).
tff(f4753,plain,
( spl183_221
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_221])]) ).
tff(f3089,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1841]) ).
tff(f4751,plain,
spl183_220,
inference(avatar_split_clause,[],[f3082,f4749]) ).
tff(f4749,plain,
( spl183_220
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP53(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_220])]) ).
tff(f3082,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP53(X0,X1,X2) ),
inference(cnf_transformation,[],[f1833]) ).
tff(f4747,plain,
spl183_219,
inference(avatar_split_clause,[],[f3080,f4745]) ).
tff(f4745,plain,
( spl183_219
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_219])]) ).
tff(f3080,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f4743,plain,
spl183_218,
inference(avatar_split_clause,[],[f3079,f4741]) ).
tff(f4741,plain,
( spl183_218
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP54(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_218])]) ).
tff(f3079,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP54(X0,X1,X2) ),
inference(cnf_transformation,[],[f1829]) ).
tff(f4739,plain,
spl183_217,
inference(avatar_split_clause,[],[f3076,f4737]) ).
tff(f4737,plain,
( spl183_217
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP55(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_217])]) ).
tff(f3076,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP55(X0,X1,X2) ),
inference(cnf_transformation,[],[f1825]) ).
tff(f4735,plain,
spl183_216,
inference(avatar_split_clause,[],[f3071,f4733]) ).
tff(f4733,plain,
( spl183_216
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP57(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_216])]) ).
tff(f3071,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP57(X0,X1,X2) ),
inference(cnf_transformation,[],[f1817]) ).
tff(f4731,plain,
spl183_215,
inference(avatar_split_clause,[],[f3063,f4729]) ).
tff(f4729,plain,
( spl183_215
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP59(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_215])]) ).
tff(f3063,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP59(X0,X1,X2) ),
inference(cnf_transformation,[],[f1809]) ).
tff(f4727,plain,
spl183_214,
inference(avatar_split_clause,[],[f3062,f4725]) ).
tff(f4725,plain,
( spl183_214
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP60(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_214])]) ).
tff(f3062,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP60(X0,X1,X2) ),
inference(cnf_transformation,[],[f1805]) ).
tff(f4723,plain,
spl183_213,
inference(avatar_split_clause,[],[f3060,f4721]) ).
tff(f4721,plain,
( spl183_213
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP60(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_213])]) ).
tff(f3060,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP60(X0,X1,X2) ),
inference(cnf_transformation,[],[f1805]) ).
tff(f4719,plain,
spl183_212,
inference(avatar_split_clause,[],[f3057,f4717]) ).
tff(f4717,plain,
( spl183_212
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP61(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_212])]) ).
tff(f3057,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP61(X0,X1,X2) ),
inference(cnf_transformation,[],[f1801]) ).
tff(f4715,plain,
spl183_211,
inference(avatar_split_clause,[],[f3055,f4713]) ).
tff(f4713,plain,
( spl183_211
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP62(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_211])]) ).
tff(f3055,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP62(X0,X1,X2) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f4711,plain,
spl183_210,
inference(avatar_split_clause,[],[f3054,f4709]) ).
tff(f4709,plain,
( spl183_210
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP62(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_210])]) ).
tff(f3054,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP62(X0,X1,X2) ),
inference(cnf_transformation,[],[f1797]) ).
tff(f4707,plain,
spl183_209,
inference(avatar_split_clause,[],[f3053,f4705]) ).
tff(f4705,plain,
( spl183_209
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP63(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_209])]) ).
tff(f3053,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP63(X0,X1,X2) ),
inference(cnf_transformation,[],[f1793]) ).
tff(f1793,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP63(X0,X1,X2) ),
inference(rectify,[],[f1792]) ).
tff(f1792,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP63(X2,X1,X0) ),
inference(nnf_transformation,[],[f1274]) ).
tff(f1274,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP63(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP63])]) ).
tff(f4703,plain,
spl183_208,
inference(avatar_split_clause,[],[f3052,f4701]) ).
tff(f4701,plain,
( spl183_208
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP63(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_208])]) ).
tff(f3052,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP63(X0,X1,X2) ),
inference(cnf_transformation,[],[f1793]) ).
tff(f4699,plain,
spl183_207,
inference(avatar_split_clause,[],[f3051,f4697]) ).
tff(f4697,plain,
( spl183_207
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP63(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_207])]) ).
tff(f3051,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP63(X0,X1,X2) ),
inference(cnf_transformation,[],[f1793]) ).
tff(f4695,plain,
spl183_206,
inference(avatar_split_clause,[],[f3049,f4693]) ).
tff(f4693,plain,
( spl183_206
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP64(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_206])]) ).
tff(f3049,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP64(X0,X1,X2) ),
inference(cnf_transformation,[],[f1791]) ).
tff(f4691,plain,
spl183_205,
inference(avatar_split_clause,[],[f3048,f4689]) ).
tff(f4689,plain,
( spl183_205
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP64(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_205])]) ).
tff(f3048,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP64(X0,X1,X2) ),
inference(cnf_transformation,[],[f1791]) ).
tff(f4687,plain,
spl183_204,
inference(avatar_split_clause,[],[f3045,f4685]) ).
tff(f4685,plain,
( spl183_204
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP65(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_204])]) ).
tff(f3045,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP65(X0,X1,X2) ),
inference(cnf_transformation,[],[f1789]) ).
tff(f4681,plain,
spl183_203,
inference(avatar_split_clause,[],[f3044,f4679]) ).
tff(f4679,plain,
( spl183_203
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP66(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_203])]) ).
tff(f3044,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP66(X0,X1,X2) ),
inference(cnf_transformation,[],[f1785]) ).
tff(f4677,plain,
spl183_202,
inference(avatar_split_clause,[],[f3042,f4675]) ).
tff(f4675,plain,
( spl183_202
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP66(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_202])]) ).
tff(f3042,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP66(X0,X1,X2) ),
inference(cnf_transformation,[],[f1785]) ).
tff(f4673,plain,
spl183_201,
inference(avatar_split_clause,[],[f3039,f4671]) ).
tff(f4671,plain,
( spl183_201
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP67(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_201])]) ).
tff(f3039,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP67(X0,X1,X2) ),
inference(cnf_transformation,[],[f1783]) ).
tff(f4669,plain,
spl183_200,
inference(avatar_split_clause,[],[f3035,f4667]) ).
tff(f4667,plain,
( spl183_200
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP69(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_200])]) ).
tff(f3035,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP69(X0,X1,X2) ),
inference(cnf_transformation,[],[f1777]) ).
tff(f4665,plain,
spl183_199,
inference(avatar_split_clause,[],[f3028,f4663]) ).
tff(f4663,plain,
( spl183_199
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP71(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_199])]) ).
tff(f3028,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP71(X0,X1,X2) ),
inference(cnf_transformation,[],[f1769]) ).
tff(f4661,plain,
spl183_198,
inference(avatar_split_clause,[],[f3026,f4659]) ).
tff(f4659,plain,
( spl183_198
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP72(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_198])]) ).
tff(f3026,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP72(X0,X1,X2) ),
inference(cnf_transformation,[],[f1765]) ).
tff(f4657,plain,
spl183_197,
inference(avatar_split_clause,[],[f3025,f4655]) ).
tff(f4655,plain,
( spl183_197
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP72(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_197])]) ).
tff(f3025,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP72(X0,X1,X2) ),
inference(cnf_transformation,[],[f1765]) ).
tff(f4653,plain,
spl183_196,
inference(avatar_split_clause,[],[f3022,f4651]) ).
tff(f4651,plain,
( spl183_196
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP73(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_196])]) ).
tff(f3022,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP73(X0,X1,X2) ),
inference(cnf_transformation,[],[f1763]) ).
tff(f4649,plain,
spl183_195,
inference(avatar_split_clause,[],[f3017,f4647]) ).
tff(f4647,plain,
( spl183_195
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP75(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_195])]) ).
tff(f3017,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP75(X0,X1,X2) ),
inference(cnf_transformation,[],[f1757]) ).
tff(f4645,plain,
spl183_194,
inference(avatar_split_clause,[],[f3006,f4643]) ).
tff(f4643,plain,
( spl183_194
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_194])]) ).
tff(f3006,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f4641,plain,
( spl183_193
| ~ spl183_140
| ~ spl183_182 ),
inference(avatar_split_clause,[],[f4597,f4594,f4423,f4639]) ).
tff(f4639,plain,
( spl183_193
<=> ! [X0: $real] : ( 'size_ereal$'('ereal$'(X0)) = 'size_ereal$'('one$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_193])]) ).
tff(f4594,plain,
( spl183_182
<=> ! [X0: $real] : ( 'nat$'(0) = 'size_ereal$'('ereal$'(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_182])]) ).
tff(f4597,plain,
( ! [X0: $real] : ( 'size_ereal$'('ereal$'(X0)) = 'size_ereal$'('one$a') )
| ~ spl183_140
| ~ spl183_182 ),
inference(forward_demodulation,[],[f4595,f4425]) ).
tff(f4595,plain,
( ! [X0: $real] : ( 'nat$'(0) = 'size_ereal$'('ereal$'(X0)) )
| ~ spl183_182 ),
inference(avatar_component_clause,[],[f4594]) ).
tff(f4637,plain,
spl183_192,
inference(avatar_split_clause,[],[f3002,f4635]) ).
tff(f4635,plain,
( spl183_192
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_192])]) ).
tff(f3002,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1741]) ).
tff(f4633,plain,
spl183_191,
inference(avatar_split_clause,[],[f3001,f4631]) ).
tff(f4631,plain,
( spl183_191
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP47(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_191])]) ).
tff(f3001,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f1741]) ).
tff(f4629,plain,
spl183_190,
inference(avatar_split_clause,[],[f2999,f4627]) ).
tff(f4627,plain,
( spl183_190
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP48(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_190])]) ).
tff(f2999,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f1737]) ).
tff(f4625,plain,
spl183_189,
inference(avatar_split_clause,[],[f2996,f4623]) ).
tff(f4623,plain,
( spl183_189
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP49(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_189])]) ).
tff(f2996,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue = X0 )
| ~ sP49(X0,X1,X2) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f4621,plain,
spl183_188,
inference(avatar_split_clause,[],[f2995,f4619]) ).
tff(f4619,plain,
( spl183_188
<=> ! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP49(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_188])]) ).
tff(f2995,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP49(X0,X1,X2) ),
inference(cnf_transformation,[],[f1733]) ).
tff(f4617,plain,
spl183_187,
inference(avatar_split_clause,[],[f2971,f4615]) ).
tff(f4615,plain,
( spl183_187
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_187])]) ).
tff(f2971,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f1723]) ).
tff(f4613,plain,
spl183_186,
inference(avatar_split_clause,[],[f2966,f4611]) ).
tff(f4611,plain,
( spl183_186
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_186])]) ).
tff(f2966,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f1719]) ).
tff(f4609,plain,
spl183_185,
inference(avatar_split_clause,[],[f2954,f4607]) ).
tff(f4607,plain,
( spl183_185
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_185])]) ).
tff(f2954,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f1703]) ).
tff(f1703,plain,
! [X0: 'Ereal$',X1: 'Ereal$',X2: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X2 ) )
| ~ sP41(X0,X1,X2) ),
inference(rectify,[],[f1702]) ).
tff(f1702,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP41(X2,X1,X0) ),
inference(nnf_transformation,[],[f1250]) ).
tff(f1250,plain,
! [X2: 'Ereal$',X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X2 )
& ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP41(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
tff(f4605,plain,
spl183_184,
inference(avatar_split_clause,[],[f2953,f4603]) ).
tff(f4603,plain,
( spl183_184
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_184])]) ).
tff(f2953,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f1703]) ).
tff(f4601,plain,
spl183_183,
inference(avatar_split_clause,[],[f2952,f4599]) ).
tff(f4599,plain,
( spl183_183
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_183])]) ).
tff(f2952,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f1703]) ).
tff(f4596,plain,
( spl183_182
| ~ spl183_70
| ~ spl183_88 ),
inference(avatar_split_clause,[],[f4316,f4176,f4093,f4594]) ).
tff(f4176,plain,
( spl183_88
<=> ! [X0: $real] : ( 0 = 'of_nat$'('size_ereal$'('ereal$'(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_88])]) ).
tff(f4316,plain,
( ! [X0: $real] : ( 'nat$'(0) = 'size_ereal$'('ereal$'(X0)) )
| ~ spl183_70
| ~ spl183_88 ),
inference(superposition,[],[f4094,f4177]) ).
tff(f4177,plain,
( ! [X0: $real] : ( 0 = 'of_nat$'('size_ereal$'('ereal$'(X0))) )
| ~ spl183_88 ),
inference(avatar_component_clause,[],[f4176]) ).
tff(f4592,plain,
spl183_181,
inference(avatar_split_clause,[],[f2950,f4590]) ).
tff(f4590,plain,
( spl183_181
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_181])]) ).
tff(f2950,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP42(X0,X1,X2) ),
inference(cnf_transformation,[],[f1701]) ).
tff(f4588,plain,
spl183_180,
inference(avatar_split_clause,[],[f2946,f4586]) ).
tff(f4586,plain,
( spl183_180
<=> ! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_180])]) ).
tff(f2946,plain,
! [X2: 'Ereal$',X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X2 )
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f1699]) ).
tff(f4584,plain,
spl183_179,
inference(avatar_split_clause,[],[f2816,f4582]) ).
tff(f4582,plain,
( spl183_179
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X1) )
| ~ sP30(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_179])]) ).
tff(f2816,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X1) )
| ~ sP30(X0,X1) ),
inference(cnf_transformation,[],[f1673]) ).
tff(f1673,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP30(X0,X1)
| ( 0 != 'of_nat$'(X1) )
| ( 0 != 'of_nat$'(X0) ) )
& ( ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) )
| ~ sP30(X0,X1) ) ),
inference(flattening,[],[f1672]) ).
tff(f1672,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP30(X0,X1)
| ( 0 != 'of_nat$'(X1) )
| ( 0 != 'of_nat$'(X0) ) )
& ( ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) )
| ~ sP30(X0,X1) ) ),
inference(nnf_transformation,[],[f1238]) ).
tff(f1238,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP30(X0,X1)
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(definition_folding,[],[f1050,f1237]) ).
tff(f1050,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(ennf_transformation,[],[f692]) ).
tff(f692,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $less('of_nat$'(X1),'of_nat$'(X0))
=> ( 0 = 'of_nat$'(X0) ) )
& ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
=> ( 0 = 'of_nat$'(X1) ) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(theory_normalization,[],[f114]) ).
tff(f114,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ~ $lesseq('of_nat$'(X0),'of_nat$'(X1))
=> ( 0 = 'of_nat$'(X0) ) )
& ( $lesseq('of_nat$'(X0),'of_nat$'(X1))
=> ( 0 = 'of_nat$'(X1) ) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom112) ).
tff(f4580,plain,
spl183_178,
inference(avatar_split_clause,[],[f2815,f4578]) ).
tff(f4578,plain,
( spl183_178
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ sP30(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_178])]) ).
tff(f2815,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ sP30(X0,X1) ),
inference(cnf_transformation,[],[f1673]) ).
tff(f4576,plain,
spl183_177,
inference(avatar_split_clause,[],[f2807,f4574]) ).
tff(f4574,plain,
( spl183_177
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X1) )
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_177])]) ).
tff(f2807,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X1) )
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f1669]) ).
tff(f1669,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP29(X0,X1)
| ( 0 != 'of_nat$'(X1) )
| ( 0 != 'of_nat$'(X0) ) )
& ( ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) )
| ~ sP29(X0,X1) ) ),
inference(flattening,[],[f1668]) ).
tff(f1668,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( sP29(X0,X1)
| ( 0 != 'of_nat$'(X1) )
| ( 0 != 'of_nat$'(X0) ) )
& ( ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) )
| ~ sP29(X0,X1) ) ),
inference(nnf_transformation,[],[f1236]) ).
tff(f1236,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( sP29(X0,X1)
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(definition_folding,[],[f1049,f1235]) ).
tff(f1049,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ( 0 = 'of_nat$'(X0) )
| ~ $less('of_nat$'(X1),'of_nat$'(X0)) )
& ( ( 0 = 'of_nat$'(X1) )
| $less('of_nat$'(X1),'of_nat$'(X0)) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(ennf_transformation,[],[f691]) ).
tff(f691,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( $less('of_nat$'(X1),'of_nat$'(X0))
=> ( 0 = 'of_nat$'(X0) ) )
& ( ~ $less('of_nat$'(X1),'of_nat$'(X0))
=> ( 0 = 'of_nat$'(X1) ) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
inference(theory_normalization,[],[f116]) ).
tff(f116,axiom,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( ( ~ $lesseq('of_nat$'(X0),'of_nat$'(X1))
=> ( 0 = 'of_nat$'(X0) ) )
& ( $lesseq('of_nat$'(X0),'of_nat$'(X1))
=> ( 0 = 'of_nat$'(X1) ) ) )
<=> ( ( 0 = 'of_nat$'(X1) )
& ( 0 = 'of_nat$'(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom114) ).
tff(f4572,plain,
spl183_176,
inference(avatar_split_clause,[],[f2806,f4570]) ).
tff(f4570,plain,
( spl183_176
<=> ! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ sP29(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_176])]) ).
tff(f2806,plain,
! [X0: 'Nat$',X1: 'Nat$'] :
( ( 0 = 'of_nat$'(X0) )
| ~ sP29(X0,X1) ),
inference(cnf_transformation,[],[f1669]) ).
tff(f4568,plain,
spl183_175,
inference(avatar_split_clause,[],[f2694,f4566]) ).
tff(f4566,plain,
( spl183_175
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_175])]) ).
tff(f2694,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'zero$')
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f1608]) ).
tff(f4564,plain,
spl183_174,
inference(avatar_split_clause,[],[f2690,f4562]) ).
tff(f4562,plain,
( spl183_174
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_174])]) ).
tff(f2690,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'(X1),'zero$')
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f1605]) ).
tff(f4560,plain,
spl183_173,
inference(avatar_split_clause,[],[f2596,f4558]) ).
tff(f4558,plain,
( spl183_173
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_173])]) ).
tff(f2596,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X0)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f4556,plain,
spl183_172,
inference(avatar_split_clause,[],[f2592,f4554]) ).
tff(f4554,plain,
( spl183_172
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_172])]) ).
tff(f2592,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less$'('zero$'),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1547]) ).
tff(f4551,plain,
spl183_171,
inference(avatar_split_clause,[],[f2567,f4549]) ).
tff(f4549,plain,
( spl183_171
<=> ! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( 'fun_app$b'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_171])]) ).
tff(f2567,plain,
! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( 'fun_app$b'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) ),
inference(cnf_transformation,[],[f1531]) ).
tff(f1531,plain,
! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( ( 'fun_app$b'('uu$'(X0),X1)
| ~ 'member$'(X1,X0) )
& ( 'member$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f3,axiom,
! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( 'fun_app$b'('uu$'(X0),X1)
<=> 'member$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2) ).
tff(f4547,plain,
spl183_170,
inference(avatar_split_clause,[],[f2566,f4545]) ).
tff(f4545,plain,
( spl183_170
<=> ! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_170])]) ).
tff(f2566,plain,
! [X0: 'Ereal_set$',X1: 'Ereal$'] :
( 'member$'(X1,X0)
| ~ 'fun_app$b'('uu$'(X0),X1) ),
inference(cnf_transformation,[],[f1531]) ).
tff(f4543,plain,
spl183_169,
inference(avatar_split_clause,[],[f2561,f4541]) ).
tff(f4541,plain,
( spl183_169
<=> ! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_169])]) ).
tff(f2561,plain,
! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) ),
inference(cnf_transformation,[],[f1528]) ).
tff(f1528,plain,
! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( ( 'member$'(X0,'collect$'(X1))
| ~ 'fun_app$b'(X1,X0) )
& ( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
inference(nnf_transformation,[],[f51]) ).
tff(f51,axiom,
! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( 'member$'(X0,'collect$'(X1))
<=> 'fun_app$b'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom49) ).
tff(f4539,plain,
spl183_168,
inference(avatar_split_clause,[],[f2560,f4537]) ).
tff(f4537,plain,
( spl183_168
<=> ! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_168])]) ).
tff(f2560,plain,
! [X0: 'Ereal$',X1: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X1,X0)
| ~ 'member$'(X0,'collect$'(X1)) ),
inference(cnf_transformation,[],[f1528]) ).
tff(f4535,plain,
spl183_167,
inference(avatar_split_clause,[],[f2559,f4533]) ).
tff(f4533,plain,
( spl183_167
<=> ! [X0: $real,X1: $real] :
( 'fun_app$'('uua$'(X0),X1)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_167])]) ).
tff(f2559,plain,
! [X0: $real,X1: $real] :
( 'fun_app$'('uua$'(X0),X1)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f1527,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$'('uua$'(X0),X1)
| ~ $less(X0,X1) )
& ( $less(X0,X1)
| ~ 'fun_app$'('uua$'(X0),X1) ) ),
inference(nnf_transformation,[],[f1]) ).
tff(f1,axiom,
! [X0: $real,X1: $real] :
( 'fun_app$'('uua$'(X0),X1)
<=> $less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom0) ).
tff(f4531,plain,
spl183_166,
inference(avatar_split_clause,[],[f2558,f4529]) ).
tff(f4529,plain,
( spl183_166
<=> ! [X0: $real,X1: $real] :
( $less(X0,X1)
| ~ 'fun_app$'('uua$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_166])]) ).
tff(f2558,plain,
! [X0: $real,X1: $real] :
( $less(X0,X1)
| ~ 'fun_app$'('uua$'(X0),X1) ),
inference(cnf_transformation,[],[f1527]) ).
tff(f4527,plain,
spl183_165,
inference(avatar_split_clause,[],[f2557,f4525]) ).
tff(f4525,plain,
( spl183_165
<=> ! [X0: $int,X1: $int] :
( 'fun_app$a'('uub$'(X0),X1)
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_165])]) ).
tff(f2557,plain,
! [X0: $int,X1: $int] :
( 'fun_app$a'('uub$'(X0),X1)
| ~ $less(X0,X1) ),
inference(cnf_transformation,[],[f1526]) ).
tff(f1526,plain,
! [X0: $int,X1: $int] :
( ( 'fun_app$a'('uub$'(X0),X1)
| ~ $less(X0,X1) )
& ( $less(X0,X1)
| ~ 'fun_app$a'('uub$'(X0),X1) ) ),
inference(nnf_transformation,[],[f2]) ).
tff(f2,axiom,
! [X0: $int,X1: $int] :
( 'fun_app$a'('uub$'(X0),X1)
<=> $less(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
tff(f4523,plain,
spl183_164,
inference(avatar_split_clause,[],[f2556,f4521]) ).
tff(f4521,plain,
( spl183_164
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ 'fun_app$a'('uub$'(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_164])]) ).
tff(f2556,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| ~ 'fun_app$a'('uub$'(X0),X1) ),
inference(cnf_transformation,[],[f1526]) ).
tff(f4519,plain,
spl183_163,
inference(avatar_split_clause,[],[f2541,f4517]) ).
tff(f4517,plain,
( spl183_163
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK136(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_163])]) ).
tff(f2541,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK136(X0)) ),
inference(cnf_transformation,[],[f1514]) ).
tff(f1514,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ( ~ 'fun_app$e'(X0,sK136(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK136(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f1048,f1513]) ).
tff(f1513,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ~ 'fun_app$e'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) ) )
=> ( ~ 'fun_app$e'(X0,sK136(X0))
& ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK136(X0))) ) ) ),
introduced(choice_axiom,[]) ).
tff(f1048,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ? [X2: 'Nat$'] :
( ~ 'fun_app$e'(X0,X2)
& ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) ) ) ),
inference(ennf_transformation,[],[f123]) ).
tff(f123,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( $less('of_nat$'(X3),'of_nat$'(X2))
=> 'fun_app$e'(X0,X3) )
=> 'fun_app$e'(X0,X2) )
=> 'fun_app$e'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom121) ).
tff(f4515,plain,
spl183_162,
inference(avatar_split_clause,[],[f2536,f4513]) ).
tff(f4513,plain,
( spl183_162
<=> ! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK134(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_162])]) ).
tff(f2536,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ~ 'fun_app$e'(X0,sK134(X0)) ),
inference(cnf_transformation,[],[f1510]) ).
tff(f1510,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK134(X0))) )
& ~ 'fun_app$e'(X0,sK134(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f1046,f1509]) ).
tff(f1509,plain,
! [X0: 'Nat_bool_fun$'] :
( ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
& ~ 'fun_app$e'(X0,X2) )
=> ( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(sK134(X0))) )
& ~ 'fun_app$e'(X0,sK134(X0)) ) ),
introduced(choice_axiom,[]) ).
tff(f1046,plain,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( 'fun_app$e'(X0,X1)
| ? [X2: 'Nat$'] :
( ! [X3: 'Nat$'] :
( 'fun_app$e'(X0,X3)
| ~ $less('of_nat$'(X3),'of_nat$'(X2)) )
& ~ 'fun_app$e'(X0,X2) ) ),
inference(ennf_transformation,[],[f122]) ).
tff(f122,axiom,
! [X0: 'Nat_bool_fun$',X1: 'Nat$'] :
( ! [X2: 'Nat$'] :
( ~ 'fun_app$e'(X0,X2)
=> ? [X3: 'Nat$'] :
( ~ 'fun_app$e'(X0,X3)
& $less('of_nat$'(X3),'of_nat$'(X2)) ) )
=> 'fun_app$e'(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom120) ).
tff(f4511,plain,
spl183_161,
inference(avatar_split_clause,[],[f2333,f4509]) ).
tff(f4509,plain,
( spl183_161
<=> ! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_161])]) ).
tff(f2333,plain,
! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'(X1,X0) ),
inference(cnf_transformation,[],[f278]) ).
tff(f278,axiom,
! [X0: $int,X1: $int] : ( 'times$d'(X0,X1) = 'times$d'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom276) ).
tff(f4507,plain,
spl183_160,
inference(avatar_split_clause,[],[f2332,f4505]) ).
tff(f4505,plain,
( spl183_160
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,X1) = 'times$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_160])]) ).
tff(f2332,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,X1) = 'times$'(X1,X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'times$'(X0,X1) = 'times$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom275) ).
tff(f4503,plain,
spl183_159,
inference(avatar_split_clause,[],[f2331,f4501]) ).
tff(f4501,plain,
( spl183_159
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_159])]) ).
tff(f2331,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
! [X0: 'Ereal$',X1: 'Ereal$'] : ( 'max$'(X0,X1) = 'max$'(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom97) ).
tff(f4499,plain,
spl183_158,
inference(avatar_split_clause,[],[f2312,f4497]) ).
tff(f4497,plain,
( spl183_158
<=> ! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'infinity$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_158])]) ).
tff(f2312,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,sK98(X0))
| ~ 'fun_app$b'(X0,'infinity$') ),
inference(cnf_transformation,[],[f1419]) ).
tff(f4495,plain,
spl183_157,
inference(avatar_split_clause,[],[f2307,f4493]) ).
tff(f4493,plain,
( spl183_157
<=> ! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'infinity$')
| ~ 'fun_app$b'(X0,sK97(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_157])]) ).
tff(f2307,plain,
! [X0: 'Ereal_bool_fun$'] :
( 'fun_app$b'(X0,'infinity$')
| ~ 'fun_app$b'(X0,sK97(X0)) ),
inference(cnf_transformation,[],[f1413]) ).
tff(f4491,plain,
spl183_156,
inference(avatar_split_clause,[],[f2245,f4489]) ).
tff(f4489,plain,
( spl183_156
<=> ! [X0: $real] :
( ~ $less($uminus(X0),X0)
| $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_156])]) ).
tff(f2245,plain,
! [X0: $real] :
( ~ $less($uminus(X0),X0)
| $less(0.0,X0) ),
inference(cnf_transformation,[],[f1377]) ).
tff(f1377,plain,
! [X0: $real] :
( ( ~ $less($uminus(X0),X0)
| $less(0.0,X0) )
& ( ~ $less(0.0,X0)
| $less($uminus(X0),X0) ) ),
inference(nnf_transformation,[],[f658]) ).
tff(f658,plain,
! [X0: $real] :
( ~ $less($uminus(X0),X0)
<=> ~ $less(0.0,X0) ),
inference(theory_normalization,[],[f558]) ).
tff(f558,axiom,
! [X0: $real] :
( $lesseq(X0,$uminus(X0))
<=> $lesseq(X0,0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom556) ).
tff(f4487,plain,
spl183_155,
inference(avatar_split_clause,[],[f2244,f4485]) ).
tff(f4485,plain,
( spl183_155
<=> ! [X0: $real] :
( ~ $less(0.0,X0)
| $less($uminus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_155])]) ).
tff(f2244,plain,
! [X0: $real] :
( ~ $less(0.0,X0)
| $less($uminus(X0),X0) ),
inference(cnf_transformation,[],[f1377]) ).
tff(f4483,plain,
spl183_154,
inference(avatar_split_clause,[],[f2241,f4481]) ).
tff(f4481,plain,
( spl183_154
<=> ! [X0: $real] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_154])]) ).
tff(f2241,plain,
! [X0: $real] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0.0) ),
inference(cnf_transformation,[],[f1375]) ).
tff(f1375,plain,
! [X0: $real] :
( ( $less(X0,$uminus(X0))
| ~ $less(X0,0.0) )
& ( $less(X0,0.0)
| ~ $less(X0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f168]) ).
tff(f168,axiom,
! [X0: $real] :
( $less(X0,$uminus(X0))
<=> $less(X0,0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom166) ).
tff(f4479,plain,
spl183_153,
inference(avatar_split_clause,[],[f2240,f4477]) ).
tff(f4477,plain,
( spl183_153
<=> ! [X0: $real] :
( $less(X0,0.0)
| ~ $less(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_153])]) ).
tff(f2240,plain,
! [X0: $real] :
( $less(X0,0.0)
| ~ $less(X0,$uminus(X0)) ),
inference(cnf_transformation,[],[f1375]) ).
tff(f4475,plain,
spl183_152,
inference(avatar_split_clause,[],[f2235,f4473]) ).
tff(f4473,plain,
( spl183_152
<=> ! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('infinity$'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_152])]) ).
tff(f2235,plain,
! [X0: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('infinity$'),X0) ),
inference(cnf_transformation,[],[f1373]) ).
tff(f1373,plain,
! [X0: 'Ereal$'] :
( ( 'fun_app$b'('less_eq$'('infinity$'),X0)
| ( 'infinity$' != X0 ) )
& ( ( 'infinity$' = X0 )
| ~ 'fun_app$b'('less_eq$'('infinity$'),X0) ) ),
inference(nnf_transformation,[],[f552]) ).
tff(f552,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less_eq$'('infinity$'),X0)
<=> ( 'infinity$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom550) ).
tff(f4471,plain,
( spl183_151
| ~ spl183_70
| ~ spl183_121
| ~ spl183_122 ),
inference(avatar_split_clause,[],[f4381,f4329,f4324,f4093,f4468]) ).
tff(f4468,plain,
( spl183_151
<=> ( 'size_ereal$'('one$a') = 'size_ereal$'('zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_151])]) ).
tff(f4329,plain,
( spl183_122
<=> ( 0 = 'of_nat$'('size_ereal$'('zero$')) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_122])]) ).
tff(f4381,plain,
( ( 'size_ereal$'('one$a') = 'size_ereal$'('zero$') )
| ~ spl183_70
| ~ spl183_121
| ~ spl183_122 ),
inference(forward_demodulation,[],[f4379,f4346]) ).
tff(f4379,plain,
( ( 'nat$'(0) = 'size_ereal$'('zero$') )
| ~ spl183_70
| ~ spl183_122 ),
inference(superposition,[],[f4094,f4331]) ).
tff(f4331,plain,
( ( 0 = 'of_nat$'('size_ereal$'('zero$')) )
| ~ spl183_122 ),
inference(avatar_component_clause,[],[f4329]) ).
tff(f4466,plain,
spl183_150,
inference(avatar_split_clause,[],[f2229,f4464]) ).
tff(f4464,plain,
( spl183_150
<=> ! [X0: $int] :
( $less($uminus(X0),X0)
| ~ $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_150])]) ).
tff(f2229,plain,
! [X0: $int] :
( $less($uminus(X0),X0)
| ~ $less(0,X0) ),
inference(cnf_transformation,[],[f1370]) ).
tff(f1370,plain,
! [X0: $int] :
( ( $less($uminus(X0),X0)
| ~ $less(0,X0) )
& ( $less(0,X0)
| ~ $less($uminus(X0),X0) ) ),
inference(nnf_transformation,[],[f169]) ).
tff(f169,axiom,
! [X0: $int] :
( $less($uminus(X0),X0)
<=> $less(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom167) ).
tff(f4462,plain,
spl183_149,
inference(avatar_split_clause,[],[f2228,f4460]) ).
tff(f4460,plain,
( spl183_149
<=> ! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_149])]) ).
tff(f2228,plain,
! [X0: $int] :
( $less(0,X0)
| ~ $less($uminus(X0),X0) ),
inference(cnf_transformation,[],[f1370]) ).
tff(f4458,plain,
spl183_148,
inference(avatar_split_clause,[],[f2225,f4456]) ).
tff(f4456,plain,
( spl183_148
<=> ! [X0: $int] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_148])]) ).
tff(f2225,plain,
! [X0: $int] :
( $less(X0,$uminus(X0))
| ~ $less(X0,0) ),
inference(cnf_transformation,[],[f1368]) ).
tff(f1368,plain,
! [X0: $int] :
( ( $less(X0,$uminus(X0))
| ~ $less(X0,0) )
& ( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f167]) ).
tff(f167,axiom,
! [X0: $int] :
( $less(X0,$uminus(X0))
<=> $less(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom165) ).
tff(f4454,plain,
spl183_147,
inference(avatar_split_clause,[],[f2224,f4452]) ).
tff(f4452,plain,
( spl183_147
<=> ! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_147])]) ).
tff(f2224,plain,
! [X0: $int] :
( $less(X0,0)
| ~ $less(X0,$uminus(X0)) ),
inference(cnf_transformation,[],[f1368]) ).
tff(f4450,plain,
spl183_146,
inference(avatar_split_clause,[],[f2223,f4448]) ).
tff(f4448,plain,
( spl183_146
<=> ! [X0: $int] :
( ~ $less(0,$uminus(X0))
| $less(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_146])]) ).
tff(f2223,plain,
! [X0: $int] :
( ~ $less(0,$uminus(X0))
| $less(X0,0) ),
inference(cnf_transformation,[],[f1367]) ).
tff(f1367,plain,
! [X0: $int] :
( ( ~ $less(0,$uminus(X0))
| $less(X0,0) )
& ( ~ $less(X0,0)
| $less(0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f657]) ).
tff(f657,plain,
! [X0: $int] :
( ~ $less(0,$uminus(X0))
<=> ~ $less(X0,0) ),
inference(theory_normalization,[],[f557]) ).
tff(f557,axiom,
! [X0: $int] :
( $lesseq($uminus(X0),0)
<=> $lesseq(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom555) ).
tff(f4446,plain,
spl183_145,
inference(avatar_split_clause,[],[f2222,f4444]) ).
tff(f4444,plain,
( spl183_145
<=> ! [X0: $int] :
( ~ $less(X0,0)
| $less(0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_145])]) ).
tff(f2222,plain,
! [X0: $int] :
( ~ $less(X0,0)
| $less(0,$uminus(X0)) ),
inference(cnf_transformation,[],[f1367]) ).
tff(f4442,plain,
spl183_144,
inference(avatar_split_clause,[],[f2221,f4440]) ).
tff(f4440,plain,
( spl183_144
<=> ! [X0: $int] :
( ~ $less($uminus(X0),0)
| $less(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_144])]) ).
tff(f2221,plain,
! [X0: $int] :
( ~ $less($uminus(X0),0)
| $less(0,X0) ),
inference(cnf_transformation,[],[f1366]) ).
tff(f1366,plain,
! [X0: $int] :
( ( ~ $less($uminus(X0),0)
| $less(0,X0) )
& ( ~ $less(0,X0)
| $less($uminus(X0),0) ) ),
inference(nnf_transformation,[],[f656]) ).
tff(f656,plain,
! [X0: $int] :
( ~ $less($uminus(X0),0)
<=> ~ $less(0,X0) ),
inference(theory_normalization,[],[f555]) ).
tff(f555,axiom,
! [X0: $int] :
( $lesseq(0,$uminus(X0))
<=> $lesseq(X0,0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom553) ).
tff(f4438,plain,
spl183_143,
inference(avatar_split_clause,[],[f2220,f4436]) ).
tff(f4436,plain,
( spl183_143
<=> ! [X0: $int] :
( ~ $less(0,X0)
| $less($uminus(X0),0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_143])]) ).
tff(f2220,plain,
! [X0: $int] :
( ~ $less(0,X0)
| $less($uminus(X0),0) ),
inference(cnf_transformation,[],[f1366]) ).
tff(f4434,plain,
spl183_142,
inference(avatar_split_clause,[],[f2219,f4432]) ).
tff(f4432,plain,
( spl183_142
<=> ! [X0: $real] :
( ~ $less(0.0,$uminus(X0))
| $less(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_142])]) ).
tff(f2219,plain,
! [X0: $real] :
( ~ $less(0.0,$uminus(X0))
| $less(X0,0.0) ),
inference(cnf_transformation,[],[f1365]) ).
tff(f1365,plain,
! [X0: $real] :
( ( ~ $less(0.0,$uminus(X0))
| $less(X0,0.0) )
& ( ~ $less(X0,0.0)
| $less(0.0,$uminus(X0)) ) ),
inference(nnf_transformation,[],[f655]) ).
tff(f655,plain,
! [X0: $real] :
( ~ $less(0.0,$uminus(X0))
<=> ~ $less(X0,0.0) ),
inference(theory_normalization,[],[f556]) ).
tff(f556,axiom,
! [X0: $real] :
( $lesseq($uminus(X0),0.0)
<=> $lesseq(0.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom554) ).
tff(f4430,plain,
spl183_141,
inference(avatar_split_clause,[],[f2218,f4428]) ).
tff(f4428,plain,
( spl183_141
<=> ! [X0: $real] :
( ~ $less(X0,0.0)
| $less(0.0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_141])]) ).
tff(f2218,plain,
! [X0: $real] :
( ~ $less(X0,0.0)
| $less(0.0,$uminus(X0)) ),
inference(cnf_transformation,[],[f1365]) ).
tff(f4426,plain,
( spl183_140
| ~ spl183_70
| ~ spl183_121 ),
inference(avatar_split_clause,[],[f4346,f4324,f4093,f4423]) ).
tff(f4421,plain,
spl183_139,
inference(avatar_split_clause,[],[f2217,f4419]) ).
tff(f4419,plain,
( spl183_139
<=> ! [X0: $real] :
( ~ $less($uminus(X0),0.0)
| $less(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_139])]) ).
tff(f2217,plain,
! [X0: $real] :
( ~ $less($uminus(X0),0.0)
| $less(0.0,X0) ),
inference(cnf_transformation,[],[f1364]) ).
tff(f1364,plain,
! [X0: $real] :
( ( ~ $less($uminus(X0),0.0)
| $less(0.0,X0) )
& ( ~ $less(0.0,X0)
| $less($uminus(X0),0.0) ) ),
inference(nnf_transformation,[],[f654]) ).
tff(f654,plain,
! [X0: $real] :
( ~ $less($uminus(X0),0.0)
<=> ~ $less(0.0,X0) ),
inference(theory_normalization,[],[f554]) ).
tff(f554,axiom,
! [X0: $real] :
( $lesseq(0.0,$uminus(X0))
<=> $lesseq(X0,0.0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom552) ).
tff(f4417,plain,
spl183_138,
inference(avatar_split_clause,[],[f2216,f4415]) ).
tff(f4415,plain,
( spl183_138
<=> ! [X0: $real] :
( ~ $less(0.0,X0)
| $less($uminus(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_138])]) ).
tff(f2216,plain,
! [X0: $real] :
( ~ $less(0.0,X0)
| $less($uminus(X0),0.0) ),
inference(cnf_transformation,[],[f1364]) ).
tff(f4413,plain,
spl183_137,
inference(avatar_split_clause,[],[f2212,f4411]) ).
tff(f4411,plain,
( spl183_137
<=> ! [X0: $real] :
( ( 0.0 = X0 )
| ( 'ereal$'(X0) != 'zero$' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_137])]) ).
tff(f2212,plain,
! [X0: $real] :
( ( 0.0 = X0 )
| ( 'ereal$'(X0) != 'zero$' ) ),
inference(cnf_transformation,[],[f1362]) ).
tff(f1362,plain,
! [X0: $real] :
( ( ( 'ereal$'(X0) = 'zero$' )
| ( 0.0 != X0 ) )
& ( ( 0.0 = X0 )
| ( 'ereal$'(X0) != 'zero$' ) ) ),
inference(nnf_transformation,[],[f27]) ).
tff(f27,axiom,
! [X0: $real] :
( ( 'ereal$'(X0) = 'zero$' )
<=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom25) ).
tff(f4409,plain,
spl183_136,
inference(avatar_split_clause,[],[f2208,f4407]) ).
tff(f4407,plain,
( spl183_136
<=> ! [X0: $real] :
( ( 1.0 = X0 )
| ( 'ereal$'(X0) != 'one$a' ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_136])]) ).
tff(f2208,plain,
! [X0: $real] :
( ( 1.0 = X0 )
| ( 'ereal$'(X0) != 'one$a' ) ),
inference(cnf_transformation,[],[f1360]) ).
tff(f1360,plain,
! [X0: $real] :
( ( ( 'ereal$'(X0) = 'one$a' )
| ( 1.0 != X0 ) )
& ( ( 1.0 = X0 )
| ( 'ereal$'(X0) != 'one$a' ) ) ),
inference(nnf_transformation,[],[f515]) ).
tff(f515,axiom,
! [X0: $real] :
( ( 'ereal$'(X0) = 'one$a' )
<=> ( 1.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom513) ).
tff(f4405,plain,
spl183_135,
inference(avatar_split_clause,[],[f2204,f4403]) ).
tff(f4403,plain,
( spl183_135
<=> ! [X0: $real] :
( ( 0.0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_135])]) ).
tff(f2204,plain,
! [X0: $real] :
( ( 0.0 = X0 )
| ( $uminus(X0) != X0 ) ),
inference(cnf_transformation,[],[f1358]) ).
tff(f1358,plain,
! [X0: $real] :
( ( ( $uminus(X0) = X0 )
| ( 0.0 != X0 ) )
& ( ( 0.0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
inference(nnf_transformation,[],[f158]) ).
tff(f158,axiom,
! [X0: $real] :
( ( $uminus(X0) = X0 )
<=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom156) ).
tff(f4401,plain,
spl183_134,
inference(avatar_split_clause,[],[f2200,f4399]) ).
tff(f4399,plain,
( spl183_134
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_134])]) ).
tff(f2200,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ),
inference(cnf_transformation,[],[f1356]) ).
tff(f1356,plain,
! [X0: $int] :
( ( ( $uminus(X0) = X0 )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( $uminus(X0) != X0 ) ) ),
inference(nnf_transformation,[],[f157]) ).
tff(f157,axiom,
! [X0: $int] :
( ( $uminus(X0) = X0 )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom155) ).
tff(f4397,plain,
spl183_133,
inference(avatar_split_clause,[],[f2196,f4395]) ).
tff(f4395,plain,
( spl183_133
<=> ! [X0: $real] :
( ( 0.0 = X0 )
| ( 0.0 != $uminus(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_133])]) ).
tff(f2196,plain,
! [X0: $real] :
( ( 0.0 = X0 )
| ( 0.0 != $uminus(X0) ) ),
inference(cnf_transformation,[],[f1354]) ).
tff(f1354,plain,
! [X0: $real] :
( ( ( 0.0 = $uminus(X0) )
| ( 0.0 != X0 ) )
& ( ( 0.0 = X0 )
| ( 0.0 != $uminus(X0) ) ) ),
inference(nnf_transformation,[],[f154]) ).
tff(f154,axiom,
! [X0: $real] :
( ( 0.0 = $uminus(X0) )
<=> ( 0.0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom152) ).
tff(f4393,plain,
spl183_132,
inference(avatar_split_clause,[],[f2192,f4391]) ).
tff(f4391,plain,
( spl183_132
<=> ! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_132])]) ).
tff(f2192,plain,
! [X0: $int] :
( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ),
inference(cnf_transformation,[],[f1352]) ).
tff(f1352,plain,
! [X0: $int] :
( ( ( 0 = $uminus(X0) )
| ( 0 != X0 ) )
& ( ( 0 = X0 )
| ( 0 != $uminus(X0) ) ) ),
inference(nnf_transformation,[],[f151]) ).
tff(f151,axiom,
! [X0: $int] :
( ( 0 = $uminus(X0) )
<=> ( 0 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom149) ).
tff(f4389,plain,
spl183_131,
inference(avatar_split_clause,[],[f2190,f4387]) ).
tff(f4387,plain,
( spl183_131
<=> ! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'infinity$' != 'inverse$a'(X0) ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_131])]) ).
tff(f2190,plain,
! [X0: 'Ereal$'] :
( ( 'zero$' = X0 )
| ( 'infinity$' != 'inverse$a'(X0) ) ),
inference(cnf_transformation,[],[f1351]) ).
tff(f1351,plain,
! [X0: 'Ereal$'] :
( ( ( 'infinity$' = 'inverse$a'(X0) )
| ( 'zero$' != X0 ) )
& ( ( 'zero$' = X0 )
| ( 'infinity$' != 'inverse$a'(X0) ) ) ),
inference(nnf_transformation,[],[f30]) ).
tff(f30,axiom,
! [X0: 'Ereal$'] :
( ( 'infinity$' = 'inverse$a'(X0) )
<=> ( 'zero$' = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom28) ).
tff(f4385,plain,
spl183_130,
inference(avatar_split_clause,[],[f2111,f4383]) ).
tff(f4383,plain,
( spl183_130
<=> ! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'infinity$')
| ( 'infinity$' = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_130])]) ).
tff(f2111,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'infinity$')
| ( 'infinity$' = X0 ) ),
inference(cnf_transformation,[],[f833]) ).
tff(f833,plain,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),'infinity$')
| ( 'infinity$' = X0 ) ),
inference(ennf_transformation,[],[f29]) ).
tff(f29,axiom,
! [X0: 'Ereal$'] :
( ( 'infinity$' != X0 )
=> 'fun_app$b'('less$'(X0),'infinity$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom27) ).
tff(f4378,plain,
spl183_129,
inference(avatar_split_clause,[],[f2060,f4376]) ).
tff(f4376,plain,
( spl183_129
<=> ! [X0: $real] : ( 'fun_app$c'('inverse$','fun_app$c'('inverse$',X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_129])]) ).
tff(f2060,plain,
! [X0: $real] : ( 'fun_app$c'('inverse$','fun_app$c'('inverse$',X0)) = X0 ),
inference(cnf_transformation,[],[f13]) ).
tff(f13,axiom,
! [X0: $real] : ( 'fun_app$c'('inverse$','fun_app$c'('inverse$',X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom11) ).
tff(f4373,plain,
spl183_128,
inference(avatar_split_clause,[],[f1984,f4370]) ).
tff(f1984,plain,
0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(0)),
inference(cnf_transformation,[],[f244]) ).
tff(f244,axiom,
0.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom242) ).
tff(f4368,plain,
spl183_127,
inference(avatar_split_clause,[],[f1982,f4365]) ).
tff(f4365,plain,
( spl183_127
<=> ( 1.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_127])]) ).
tff(f1982,plain,
1.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(1)),
inference(cnf_transformation,[],[f525]) ).
tff(f525,axiom,
1.0 = 'fun_app$f'('fps_nth$'('fps_Lambert_W$'),'nat$'(1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom523) ).
tff(f4363,plain,
spl183_126,
inference(avatar_split_clause,[],[f741,f4361]) ).
tff(f4361,plain,
( spl183_126
<=> ! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_126])]) ).
tff(f741,plain,
! [X0: $real,X1: $real] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f4359,plain,
spl183_125,
inference(avatar_split_clause,[],[f730,f4357]) ).
tff(f730,plain,
! [X0: $real,X1: $real] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f4355,plain,
spl183_124,
inference(avatar_split_clause,[],[f723,f4353]) ).
tff(f4353,plain,
( spl183_124
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_124])]) ).
tff(f723,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f4351,plain,
spl183_123,
inference(avatar_split_clause,[],[f712,f4349]) ).
tff(f712,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f4332,plain,
( spl183_122
| ~ spl183_22
| ~ spl183_88 ),
inference(avatar_split_clause,[],[f4315,f4176,f3879,f4329]) ).
tff(f3879,plain,
( spl183_22
<=> ( 'zero$' = 'ereal$'(0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_22])]) ).
tff(f4315,plain,
( ( 0 = 'of_nat$'('size_ereal$'('zero$')) )
| ~ spl183_22
| ~ spl183_88 ),
inference(superposition,[],[f4177,f3881]) ).
tff(f3881,plain,
( ( 'zero$' = 'ereal$'(0.0) )
| ~ spl183_22 ),
inference(avatar_component_clause,[],[f3879]) ).
tff(f4327,plain,
( spl183_121
| ~ spl183_20
| ~ spl183_88 ),
inference(avatar_split_clause,[],[f4314,f4176,f3869,f4324]) ).
tff(f3869,plain,
( spl183_20
<=> ( 'one$a' = 'ereal$'(1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_20])]) ).
tff(f4314,plain,
( ( 0 = 'of_nat$'('size_ereal$'('one$a')) )
| ~ spl183_20
| ~ spl183_88 ),
inference(superposition,[],[f4177,f3871]) ).
tff(f3871,plain,
( ( 'one$a' = 'ereal$'(1.0) )
| ~ spl183_20 ),
inference(avatar_component_clause,[],[f3869]) ).
tff(f4313,plain,
~ spl183_120,
inference(avatar_split_clause,[],[f3727,f4310]) ).
tff(f4310,plain,
( spl183_120
<=> ( 'zero$' = 'times$'('infinity$','ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_120])]) ).
tff(f3727,plain,
'zero$' != 'times$'('infinity$','ereal$'(-1.0)),
inference(evaluation,[],[f3213]) ).
tff(f3213,plain,
'zero$' != 'times$'('infinity$','ereal$'($uminus(1.0))),
inference(definition_unfolding,[],[f1936,f2063]) ).
tff(f1936,plain,
'zero$' != 'uminus$'('infinity$'),
inference(cnf_transformation,[],[f217]) ).
tff(f217,axiom,
'zero$' != 'uminus$'('infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom215) ).
tff(f4308,plain,
~ spl183_119,
inference(avatar_split_clause,[],[f3726,f4305]) ).
tff(f4305,plain,
( spl183_119
<=> ( 'infinity$' = 'times$'('infinity$','ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_119])]) ).
tff(f3726,plain,
'infinity$' != 'times$'('infinity$','ereal$'(-1.0)),
inference(evaluation,[],[f3214]) ).
tff(f3214,plain,
'infinity$' != 'times$'('infinity$','ereal$'($uminus(1.0))),
inference(definition_unfolding,[],[f1937,f2063]) ).
tff(f1937,plain,
'infinity$' != 'uminus$'('infinity$'),
inference(cnf_transformation,[],[f199]) ).
tff(f199,axiom,
'infinity$' != 'uminus$'('infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom197) ).
tff(f4303,plain,
~ spl183_118,
inference(avatar_split_clause,[],[f3725,f4300]) ).
tff(f4300,plain,
( spl183_118
<=> ( 'one$a' = 'times$'('infinity$','ereal$'(-1.0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_118])]) ).
tff(f3725,plain,
'one$a' != 'times$'('infinity$','ereal$'(-1.0)),
inference(evaluation,[],[f3215]) ).
tff(f3215,plain,
'one$a' != 'times$'('infinity$','ereal$'($uminus(1.0))),
inference(definition_unfolding,[],[f1940,f2063]) ).
tff(f1940,plain,
'uminus$'('infinity$') != 'one$a',
inference(cnf_transformation,[],[f532]) ).
tff(f532,axiom,
'uminus$'('infinity$') != 'one$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom530) ).
tff(f4298,plain,
spl183_117,
inference(avatar_split_clause,[],[f3710,f4296]) ).
tff(f4296,plain,
( spl183_117
<=> ! [X0: $int] : ( $uminus(X0) = $product(X0,-1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_117])]) ).
tff(f3710,plain,
! [X0: $int] : ( $uminus(X0) = $product(X0,-1) ),
inference(evaluation,[],[f2053]) ).
tff(f2053,plain,
! [X0: $int] : ( $uminus(X0) = $product(X0,$uminus(1)) ),
inference(cnf_transformation,[],[f442]) ).
tff(f442,axiom,
! [X0: $int] : ( $uminus(X0) = $product(X0,$uminus(1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom440) ).
tff(f4294,plain,
spl183_116,
inference(avatar_split_clause,[],[f3709,f4292]) ).
tff(f4292,plain,
( spl183_116
<=> ! [X0: $int] : ( $uminus(X0) = $product(-1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_116])]) ).
tff(f3709,plain,
! [X0: $int] : ( $uminus(X0) = $product(-1,X0) ),
inference(evaluation,[],[f2054]) ).
tff(f2054,plain,
! [X0: $int] : ( $uminus(X0) = $product($uminus(1),X0) ),
inference(cnf_transformation,[],[f440]) ).
tff(f440,axiom,
! [X0: $int] : ( $uminus(X0) = $product($uminus(1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom438) ).
tff(f4290,plain,
spl183_115,
inference(avatar_split_clause,[],[f3708,f4288]) ).
tff(f4288,plain,
( spl183_115
<=> ! [X0: $real] : ( $uminus(X0) = $product(X0,-1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_115])]) ).
tff(f3708,plain,
! [X0: $real] : ( $uminus(X0) = $product(X0,-1.0) ),
inference(evaluation,[],[f2055]) ).
tff(f2055,plain,
! [X0: $real] : ( $uminus(X0) = $product(X0,$uminus(1.0)) ),
inference(cnf_transformation,[],[f443]) ).
tff(f443,axiom,
! [X0: $real] : ( $uminus(X0) = $product(X0,$uminus(1.0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom441) ).
tff(f4286,plain,
spl183_114,
inference(avatar_split_clause,[],[f3707,f4284]) ).
tff(f4284,plain,
( spl183_114
<=> ! [X0: $real] : ( $uminus(X0) = $product(-1.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_114])]) ).
tff(f3707,plain,
! [X0: $real] : ( $uminus(X0) = $product(-1.0,X0) ),
inference(evaluation,[],[f2056]) ).
tff(f2056,plain,
! [X0: $real] : ( $uminus(X0) = $product($uminus(1.0),X0) ),
inference(cnf_transformation,[],[f441]) ).
tff(f441,axiom,
! [X0: $real] : ( $uminus(X0) = $product($uminus(1.0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom439) ).
tff(f4282,plain,
spl183_113,
inference(avatar_split_clause,[],[f3670,f4279]) ).
tff(f3670,plain,
1.0 = 'fun_app$c'('times$a'(-1.0),-1.0),
inference(evaluation,[],[f3418]) ).
tff(f3418,plain,
1.0 = 'fun_app$c'('times$a'($uminus(1.0)),$uminus(1.0)),
inference(equality_resolution,[],[f2299]) ).
tff(f2299,plain,
! [X0: $real] :
( ( 'fun_app$c'('times$a'(X0),X0) = 1.0 )
| ( $uminus(1.0) != X0 ) ),
inference(cnf_transformation,[],[f1404]) ).
tff(f1404,plain,
! [X0: $real] :
( ( ( 'fun_app$c'('times$a'(X0),X0) = 1.0 )
| ( ( $uminus(1.0) != X0 )
& ( 1.0 != X0 ) ) )
& ( ( $uminus(1.0) = X0 )
| ( 1.0 = X0 )
| ( 'fun_app$c'('times$a'(X0),X0) != 1.0 ) ) ),
inference(flattening,[],[f1403]) ).
tff(f1403,plain,
! [X0: $real] :
( ( ( 'fun_app$c'('times$a'(X0),X0) = 1.0 )
| ( ( $uminus(1.0) != X0 )
& ( 1.0 != X0 ) ) )
& ( ( $uminus(1.0) = X0 )
| ( 1.0 = X0 )
| ( 'fun_app$c'('times$a'(X0),X0) != 1.0 ) ) ),
inference(nnf_transformation,[],[f489]) ).
tff(f489,axiom,
! [X0: $real] :
( ( 'fun_app$c'('times$a'(X0),X0) = 1.0 )
<=> ( ( $uminus(1.0) = X0 )
| ( 1.0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom487) ).
tff(f4277,plain,
spl183_112,
inference(avatar_split_clause,[],[f3655,f4275]) ).
tff(f4275,plain,
( spl183_112
<=> ! [X1: $real] : ( 'fun_app$c'('times$a'(1.0),X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_112])]) ).
tff(f3655,plain,
! [X1: $real] : ( 'fun_app$c'('times$a'(1.0),X1) = X1 ),
inference(trivial_inequality_removal,[],[f3428]) ).
tff(f3428,plain,
! [X1: $real] :
( ( 'fun_app$c'('times$a'(1.0),X1) = X1 )
| ( tltrue != tltrue ) ),
inference(equality_resolution,[],[f2367]) ).
tff(f2367,plain,
! [X0: tlbool,X1: $real] :
( ( 'fun_app$c'('times$a'(1.0),X1) = X1 )
| ( tltrue != X0 )
| ( tltrue != X0 ) ),
inference(cnf_transformation,[],[f874]) ).
tff(f874,plain,
! [X0: tlbool,X1: $real] :
( ( ( ( ( 0.0 = 'fun_app$c'('times$a'(0.0),X1) )
| ( tltrue = X0 ) )
& ( ( 'fun_app$c'('times$a'(0.0),X1) = X1 )
| ( tltrue != X0 ) ) )
| ( tltrue = X0 ) )
& ( ( ( ( 0.0 = 'fun_app$c'('times$a'(1.0),X1) )
| ( tltrue = X0 ) )
& ( ( 'fun_app$c'('times$a'(1.0),X1) = X1 )
| ( tltrue != X0 ) ) )
| ( tltrue != X0 ) ) ),
inference(ennf_transformation,[],[f511]) ).
tff(f511,axiom,
! [X0: tlbool,X1: $real] :
( ( ( tltrue != X0 )
=> ( ( ( tltrue != X0 )
=> ( 0.0 = 'fun_app$c'('times$a'(0.0),X1) ) )
& ( ( tltrue = X0 )
=> ( 'fun_app$c'('times$a'(0.0),X1) = X1 ) ) ) )
& ( ( tltrue = X0 )
=> ( ( ( tltrue != X0 )
=> ( 0.0 = 'fun_app$c'('times$a'(1.0),X1) ) )
& ( ( tltrue = X0 )
=> ( 'fun_app$c'('times$a'(1.0),X1) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom509) ).
tff(f4273,plain,
spl183_111,
inference(avatar_split_clause,[],[f3494,f4271]) ).
tff(f4271,plain,
( spl183_111
<=> ! [X0: $real] : ( 'fun_app$c'('times$a'(X0),1.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_111])]) ).
tff(f3494,plain,
! [X0: $real] : ( 'fun_app$c'('times$a'(X0),1.0) = X0 ),
inference(equality_resolution,[],[f2706]) ).
tff(f2706,plain,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('times$a'(X0),X1) = X0 )
| ( 1.0 != X1 ) ),
inference(cnf_transformation,[],[f1615]) ).
tff(f1615,plain,
! [X0: $real,X1: $real] :
( ( ( 'fun_app$c'('times$a'(X0),X1) = X0 )
| ( ( 1.0 != X1 )
& ( 0.0 != X0 ) ) )
& ( ( 1.0 = X1 )
| ( 0.0 = X0 )
| ( 'fun_app$c'('times$a'(X0),X1) != X0 ) ) ),
inference(flattening,[],[f1614]) ).
tff(f1614,plain,
! [X0: $real,X1: $real] :
( ( ( 'fun_app$c'('times$a'(X0),X1) = X0 )
| ( ( 1.0 != X1 )
& ( 0.0 != X0 ) ) )
& ( ( 1.0 = X1 )
| ( 0.0 = X0 )
| ( 'fun_app$c'('times$a'(X0),X1) != X0 ) ) ),
inference(nnf_transformation,[],[f439]) ).
tff(f439,axiom,
! [X0: $real,X1: $real] :
( ( 'fun_app$c'('times$a'(X0),X1) = X0 )
<=> ( ( 1.0 = X1 )
| ( 0.0 = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom437) ).
tff(f4269,plain,
spl183_110,
inference(avatar_split_clause,[],[f3439,f4267]) ).
tff(f4267,plain,
( spl183_110
<=> ! [X1: $real] : ( 0.0 = 'fun_app$c'('times$a'(0.0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_110])]) ).
tff(f3439,plain,
! [X1: $real] : ( 0.0 = 'fun_app$c'('times$a'(0.0),X1) ),
inference(equality_resolution,[],[f2404]) ).
tff(f2404,plain,
! [X0: $real,X1: $real] :
( ( 0.0 != X0 )
| ( 0.0 = 'fun_app$c'('times$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f905]) ).
tff(f905,plain,
! [X0: $real,X1: $real] :
( ( ( 0.0 != X1 )
& ( 0.0 != X0 ) )
| ( 0.0 = 'fun_app$c'('times$a'(X0),X1) ) ),
inference(ennf_transformation,[],[f364]) ).
tff(f364,axiom,
! [X0: $real,X1: $real] :
( ( 0.0 != 'fun_app$c'('times$a'(X0),X1) )
=> ( ( 0.0 != X1 )
& ( 0.0 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom362) ).
tff(f4265,plain,
spl183_109,
inference(avatar_split_clause,[],[f3438,f4263]) ).
tff(f4263,plain,
( spl183_109
<=> ! [X0: $real] : ( 0.0 = 'fun_app$c'('times$a'(X0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_109])]) ).
tff(f3438,plain,
! [X0: $real] : ( 0.0 = 'fun_app$c'('times$a'(X0),0.0) ),
inference(equality_resolution,[],[f2405]) ).
tff(f2405,plain,
! [X0: $real,X1: $real] :
( ( 0.0 != X1 )
| ( 0.0 = 'fun_app$c'('times$a'(X0),X1) ) ),
inference(cnf_transformation,[],[f905]) ).
tff(f4260,plain,
~ spl183_108,
inference(avatar_split_clause,[],[f3417,f4257]) ).
tff(f4257,plain,
( spl183_108
<=> $less(0.0,'fun_app$c'('times$a'(0.0),0.0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_108])]) ).
tff(f3417,plain,
~ $less(0.0,'fun_app$c'('times$a'(0.0),0.0)),
inference(equality_resolution,[],[f2296]) ).
tff(f2296,plain,
! [X0: $real] :
( ~ $less(0.0,'fun_app$c'('times$a'(X0),X0))
| ( 0.0 != X0 ) ),
inference(cnf_transformation,[],[f1402]) ).
tff(f4255,plain,
spl183_107,
inference(avatar_split_clause,[],[f3212,f4252]) ).
tff(f3212,plain,
'fun_app$b'('less$'('ereal$'(sK182)),'ereal$'('c$a')),
inference(cnf_transformation,[],[f1907]) ).
tff(f4250,plain,
spl183_106,
inference(avatar_split_clause,[],[f2693,f4248]) ).
tff(f4248,plain,
( spl183_106
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP18(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_106])]) ).
tff(f2693,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f1608]) ).
tff(f4246,plain,
spl183_105,
inference(avatar_split_clause,[],[f2691,f4244]) ).
tff(f4244,plain,
( spl183_105
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP19(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_105])]) ).
tff(f2691,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f1605]) ).
tff(f4242,plain,
spl183_104,
inference(avatar_split_clause,[],[f2687,f4240]) ).
tff(f2687,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ sP19(X0,X1) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f4238,plain,
spl183_103,
inference(avatar_split_clause,[],[f2686,f4236]) ).
tff(f2686,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP20(X0,X1)
| ~ sP18(X0,X1) ),
inference(cnf_transformation,[],[f1602]) ).
tff(f4234,plain,
spl183_102,
inference(avatar_split_clause,[],[f2595,f4232]) ).
tff(f4232,plain,
( spl183_102
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_102])]) ).
tff(f2595,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1550]) ).
tff(f4230,plain,
spl183_101,
inference(avatar_split_clause,[],[f2593,f4228]) ).
tff(f4228,plain,
( spl183_101
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_101])]) ).
tff(f2593,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1547]) ).
tff(f4226,plain,
spl183_100,
inference(avatar_split_clause,[],[f2589,f4224]) ).
tff(f2589,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f1544]) ).
tff(f4222,plain,
spl183_99,
inference(avatar_split_clause,[],[f2588,f4220]) ).
tff(f2588,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( sP13(X0,X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f1544]) ).
tff(f4218,plain,
spl183_98,
inference(avatar_split_clause,[],[f2518,f4216]) ).
tff(f4216,plain,
( spl183_98
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_98])]) ).
tff(f2518,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f1502]) ).
tff(f4214,plain,
spl183_97,
inference(avatar_split_clause,[],[f2513,f4212]) ).
tff(f4212,plain,
( spl183_97
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_97])]) ).
tff(f2513,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f1494]) ).
tff(f4210,plain,
spl183_96,
inference(avatar_split_clause,[],[f2512,f4208]) ).
tff(f4208,plain,
( spl183_96
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_96])]) ).
tff(f2512,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1490]) ).
tff(f1490,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( ( 'infinity$' = X0 )
& ( 'infinity$' = X1 ) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f1489]) ).
tff(f1489,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP8(X1,X0) ),
inference(nnf_transformation,[],[f1199]) ).
tff(f1199,plain,
! [X1: 'Ereal$',X0: 'Ereal$'] :
( ( ( 'infinity$' = X1 )
& ( 'infinity$' = X0 ) )
| ~ sP8(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
tff(f4206,plain,
spl183_95,
inference(avatar_split_clause,[],[f2511,f4204]) ).
tff(f4204,plain,
( spl183_95
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_95])]) ).
tff(f2511,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f1490]) ).
tff(f4202,plain,
spl183_94,
inference(avatar_split_clause,[],[f2509,f4200]) ).
tff(f4200,plain,
( spl183_94
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_94])]) ).
tff(f2509,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X1 )
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f1488]) ).
tff(f4198,plain,
spl183_93,
inference(avatar_split_clause,[],[f2489,f4196]) ).
tff(f4196,plain,
( spl183_93
<=> ! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_93])]) ).
tff(f2489,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( ( 'infinity$' = X0 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f1476]) ).
tff(f4194,plain,
spl183_92,
inference(avatar_split_clause,[],[f2110,f4192]) ).
tff(f4192,plain,
( spl183_92
<=> ! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_92])]) ).
tff(f2110,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(cnf_transformation,[],[f750]) ).
tff(f750,plain,
! [X0: tlbool] :
( ( tlfalse = X0 )
| ( tltrue = X0 ) ),
inference(rectify,[],[f641]) ).
tff(f641,axiom,
! [X6: tlbool] :
( ( tlfalse = X6 )
| ( tltrue = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_640) ).
tff(f4190,plain,
spl183_91,
inference(avatar_split_clause,[],[f2048,f4188]) ).
tff(f4188,plain,
( spl183_91
<=> ! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),'one$b') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_91])]) ).
tff(f2048,plain,
! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),'one$b') = X0 ),
inference(cnf_transformation,[],[f455]) ).
tff(f455,axiom,
! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'(X0),'one$b') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom453) ).
tff(f4186,plain,
spl183_90,
inference(avatar_split_clause,[],[f2046,f4184]) ).
tff(f4184,plain,
( spl183_90
<=> ! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'('one$b'),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_90])]) ).
tff(f2046,plain,
! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'('one$b'),X0) = X0 ),
inference(cnf_transformation,[],[f428]) ).
tff(f428,axiom,
! [X0: 'Nat$'] : ( 'fun_app$g'('times$f'('one$b'),X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom426) ).
tff(f4182,plain,
spl183_89,
inference(avatar_split_clause,[],[f2043,f4180]) ).
tff(f4180,plain,
( spl183_89
<=> ! [X0: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('zero$b'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_89])]) ).
tff(f2043,plain,
! [X0: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('zero$b'),X0) ),
inference(cnf_transformation,[],[f177]) ).
tff(f177,axiom,
! [X0: 'Nat$'] : ( 0.0 = 'fun_app$f'('fps_nth$'('zero$b'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom175) ).
tff(f4178,plain,
spl183_88,
inference(avatar_split_clause,[],[f2040,f4176]) ).
tff(f2040,plain,
! [X0: $real] : ( 0 = 'of_nat$'('size_ereal$'('ereal$'(X0))) ),
inference(cnf_transformation,[],[f136]) ).
tff(f136,axiom,
! [X0: $real] : ( 0 = 'of_nat$'('size_ereal$'('ereal$'(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom134) ).
tff(f4174,plain,
spl183_87,
inference(avatar_split_clause,[],[f2039,f4172]) ).
tff(f4172,plain,
( spl183_87
<=> ! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'(X0),'zero$e') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_87])]) ).
tff(f2039,plain,
! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'(X0),'zero$e') ),
inference(cnf_transformation,[],[f319]) ).
tff(f319,axiom,
! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'(X0),'zero$e') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom317) ).
tff(f4170,plain,
spl183_86,
inference(avatar_split_clause,[],[f2038,f4168]) ).
tff(f4168,plain,
( spl183_86
<=> ! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'('zero$e'),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_86])]) ).
tff(f2038,plain,
! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'('zero$e'),X0) ),
inference(cnf_transformation,[],[f316]) ).
tff(f316,axiom,
! [X0: 'Nat$'] : ( 'zero$e' = 'fun_app$g'('times$f'('zero$e'),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom314) ).
tff(f4166,plain,
spl183_85,
inference(avatar_split_clause,[],[f2037,f4164]) ).
tff(f4164,plain,
( spl183_85
<=> ! [X0: $real] : ~ $less('fun_app$c'('times$a'(X0),X0),0.0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_85])]) ).
tff(f2037,plain,
! [X0: $real] : ~ $less('fun_app$c'('times$a'(X0),X0),0.0),
inference(cnf_transformation,[],[f413]) ).
tff(f413,axiom,
! [X0: $real] : ~ $less('fun_app$c'('times$a'(X0),X0),0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom411) ).
tff(f4162,plain,
spl183_84,
inference(avatar_split_clause,[],[f1981,f4159]) ).
tff(f4159,plain,
( spl183_84
<=> ( 1.0 = 'fun_app$c'('max$a'(0.0),1.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_84])]) ).
tff(f1981,plain,
1.0 = 'fun_app$c'('max$a'(0.0),1.0),
inference(cnf_transformation,[],[f444]) ).
tff(f444,axiom,
1.0 = 'fun_app$c'('max$a'(0.0),1.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom442) ).
tff(f4157,plain,
( spl183_83
| ~ spl183_20
| ~ spl183_74 ),
inference(avatar_split_clause,[],[f4133,f4109,f3869,f4154]) ).
tff(f4154,plain,
( spl183_83
<=> 'fun_app$b'('less$'('one$a'),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_83])]) ).
tff(f4109,plain,
( spl183_74
<=> ! [X0: $real] : 'fun_app$b'('less$'('ereal$'(X0)),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_74])]) ).
tff(f4133,plain,
( 'fun_app$b'('less$'('one$a'),'infinity$')
| ~ spl183_20
| ~ spl183_74 ),
inference(superposition,[],[f4110,f3871]) ).
tff(f4110,plain,
( ! [X0: $real] : 'fun_app$b'('less$'('ereal$'(X0)),'infinity$')
| ~ spl183_74 ),
inference(avatar_component_clause,[],[f4109]) ).
tff(f4152,plain,
spl183_82,
inference(avatar_split_clause,[],[f1980,f4149]) ).
tff(f4149,plain,
( spl183_82
<=> ( 1.0 = 'fun_app$c'('max$a'(1.0),0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_82])]) ).
tff(f1980,plain,
1.0 = 'fun_app$c'('max$a'(1.0),0.0),
inference(cnf_transformation,[],[f446]) ).
tff(f446,axiom,
1.0 = 'fun_app$c'('max$a'(1.0),0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom444) ).
tff(f4147,plain,
spl183_81,
inference(avatar_split_clause,[],[f734,f4145]) ).
tff(f4145,plain,
( spl183_81
<=> ! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_81])]) ).
tff(f734,plain,
! [X0: $real] : ( 0.0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f4143,plain,
spl183_80,
inference(avatar_split_clause,[],[f716,f4141]) ).
tff(f4141,plain,
( spl183_80
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_80])]) ).
tff(f716,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f4132,plain,
spl183_79,
inference(avatar_split_clause,[],[f3683,f4129]) ).
tff(f3683,plain,
1 = 'times$d'(-1,-1),
inference(evaluation,[],[f3413]) ).
tff(f3413,plain,
1 = 'times$d'($uminus(1),$uminus(1)),
inference(equality_resolution,[],[f2263]) ).
tff(f2263,plain,
! [X0: $int] :
( ( 'times$d'(X0,X0) = 1 )
| ( $uminus(1) != X0 ) ),
inference(cnf_transformation,[],[f1386]) ).
tff(f4127,plain,
spl183_78,
inference(avatar_split_clause,[],[f3659,f4125]) ).
tff(f4125,plain,
( spl183_78
<=> ! [X1: $int] : ( 'times$d'(1,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_78])]) ).
tff(f3659,plain,
! [X1: $int] : ( 'times$d'(1,X1) = X1 ),
inference(trivial_inequality_removal,[],[f3422]) ).
tff(f3422,plain,
! [X1: $int] :
( ( 'times$d'(1,X1) = X1 )
| ( tltrue != tltrue ) ),
inference(equality_resolution,[],[f2359]) ).
tff(f2359,plain,
! [X0: tlbool,X1: $int] :
( ( 'times$d'(1,X1) = X1 )
| ( tltrue != X0 )
| ( tltrue != X0 ) ),
inference(cnf_transformation,[],[f872]) ).
tff(f872,plain,
! [X0: tlbool,X1: $int] :
( ( ( ( ( 0 = 'times$d'(0,X1) )
| ( tltrue = X0 ) )
& ( ( 'times$d'(0,X1) = X1 )
| ( tltrue != X0 ) ) )
| ( tltrue = X0 ) )
& ( ( ( ( 0 = 'times$d'(1,X1) )
| ( tltrue = X0 ) )
& ( ( 'times$d'(1,X1) = X1 )
| ( tltrue != X0 ) ) )
| ( tltrue != X0 ) ) ),
inference(ennf_transformation,[],[f509]) ).
tff(f509,axiom,
! [X0: tlbool,X1: $int] :
( ( ( tltrue != X0 )
=> ( ( ( tltrue != X0 )
=> ( 0 = 'times$d'(0,X1) ) )
& ( ( tltrue = X0 )
=> ( 'times$d'(0,X1) = X1 ) ) ) )
& ( ( tltrue = X0 )
=> ( ( ( tltrue != X0 )
=> ( 0 = 'times$d'(1,X1) ) )
& ( ( tltrue = X0 )
=> ( 'times$d'(1,X1) = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom507) ).
tff(f4123,plain,
spl183_77,
inference(avatar_split_clause,[],[f3470,f4121]) ).
tff(f4121,plain,
( spl183_77
<=> ! [X0: $int] : ( 'times$d'(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_77])]) ).
tff(f3470,plain,
! [X0: $int] : ( 'times$d'(X0,1) = X0 ),
inference(equality_resolution,[],[f2613]) ).
tff(f2613,plain,
! [X0: $int,X1: $int] :
( ( 'times$d'(X0,X1) = X0 )
| ( 1 != X1 ) ),
inference(cnf_transformation,[],[f1559]) ).
tff(f4119,plain,
spl183_76,
inference(avatar_split_clause,[],[f3434,f4117]) ).
tff(f4117,plain,
( spl183_76
<=> ! [X1: $int] : ( 0 = 'times$d'(0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_76])]) ).
tff(f3434,plain,
! [X1: $int] : ( 0 = 'times$d'(0,X1) ),
inference(equality_resolution,[],[f2393]) ).
tff(f2393,plain,
! [X0: $int,X1: $int] :
( ( 0 != X0 )
| ( 0 = 'times$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f895]) ).
tff(f895,plain,
! [X0: $int,X1: $int] :
( ( ( 0 != X1 )
& ( 0 != X0 ) )
| ( 0 = 'times$d'(X0,X1) ) ),
inference(ennf_transformation,[],[f362]) ).
tff(f362,axiom,
! [X0: $int,X1: $int] :
( ( 0 != 'times$d'(X0,X1) )
=> ( ( 0 != X1 )
& ( 0 != X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom360) ).
tff(f4115,plain,
spl183_75,
inference(avatar_split_clause,[],[f3433,f4113]) ).
tff(f4113,plain,
( spl183_75
<=> ! [X0: $int] : ( 0 = 'times$d'(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_75])]) ).
tff(f3433,plain,
! [X0: $int] : ( 0 = 'times$d'(X0,0) ),
inference(equality_resolution,[],[f2394]) ).
tff(f2394,plain,
! [X0: $int,X1: $int] :
( ( 0 != X1 )
| ( 0 = 'times$d'(X0,X1) ) ),
inference(cnf_transformation,[],[f895]) ).
tff(f4111,plain,
spl183_74,
inference(avatar_split_clause,[],[f2287,f4109]) ).
tff(f2287,plain,
! [X0: $real] : 'fun_app$b'('less$'('ereal$'(X0)),'infinity$'),
inference(cnf_transformation,[],[f777]) ).
tff(f777,plain,
! [X0: $real] : 'fun_app$b'('less$'('ereal$'(X0)),'infinity$'),
inference(true_and_false_elimination,[],[f41]) ).
tff(f41,axiom,
! [X0: $real] :
( 'fun_app$b'('less$'('ereal$'(X0)),'infinity$')
<=> $true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom39) ).
tff(f4107,plain,
spl183_73,
inference(avatar_split_clause,[],[f2034,f4105]) ).
tff(f4105,plain,
( spl183_73
<=> ! [X0: 'Ereal$'] : ( 'max$'(X0,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_73])]) ).
tff(f2034,plain,
! [X0: 'Ereal$'] : ( 'max$'(X0,X0) = X0 ),
inference(cnf_transformation,[],[f89]) ).
tff(f89,axiom,
! [X0: 'Ereal$'] : ( 'max$'(X0,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom87) ).
tff(f4103,plain,
spl183_72,
inference(avatar_split_clause,[],[f2032,f4101]) ).
tff(f2032,plain,
! [X0: 'Ereal$'] : ( 'times$'('one$a',X0) = X0 ),
inference(cnf_transformation,[],[f457]) ).
tff(f457,axiom,
! [X0: 'Ereal$'] : ( 'times$'('one$a',X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom455) ).
tff(f4099,plain,
spl183_71,
inference(avatar_split_clause,[],[f2030,f4097]) ).
tff(f4097,plain,
( spl183_71
<=> ! [X0: 'Ereal$'] : ( 'times$'(X0,'one$a') = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_71])]) ).
tff(f2030,plain,
! [X0: 'Ereal$'] : ( 'times$'(X0,'one$a') = X0 ),
inference(cnf_transformation,[],[f453]) ).
tff(f453,axiom,
! [X0: 'Ereal$'] : ( 'times$'(X0,'one$a') = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom451) ).
tff(f4095,plain,
spl183_70,
inference(avatar_split_clause,[],[f2018,f4093]) ).
tff(f2018,plain,
! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
inference(cnf_transformation,[],[f639]) ).
tff(f639,axiom,
! [X0: 'Nat$'] : ( 'nat$'('of_nat$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom637) ).
tff(f4091,plain,
spl183_69,
inference(avatar_split_clause,[],[f2017,f4089]) ).
tff(f4089,plain,
( spl183_69
<=> ! [X0: 'Ereal_set$'] : ( 'collect$'('uu$'(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_69])]) ).
tff(f2017,plain,
! [X0: 'Ereal_set$'] : ( 'collect$'('uu$'(X0)) = X0 ),
inference(cnf_transformation,[],[f52]) ).
tff(f52,axiom,
! [X0: 'Ereal_set$'] : ( 'collect$'('uu$'(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom50) ).
tff(f4087,plain,
spl183_68,
inference(avatar_split_clause,[],[f2015,f4085]) ).
tff(f4085,plain,
( spl183_68
<=> ! [X0: $real] : ( 0.0 = $product(0.0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_68])]) ).
tff(f2015,plain,
! [X0: $real] : ( 0.0 = $product(0.0,X0) ),
inference(cnf_transformation,[],[f317]) ).
tff(f317,axiom,
! [X0: $real] : ( 0.0 = $product(0.0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom315) ).
tff(f4083,plain,
spl183_67,
inference(avatar_split_clause,[],[f2012,f4081]) ).
tff(f4081,plain,
( spl183_67
<=> ! [X0: 'Nat$'] : ( 0 = 'fps_nth$b'('zero$d',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_67])]) ).
tff(f2012,plain,
! [X0: 'Nat$'] : ( 0 = 'fps_nth$b'('zero$d',X0) ),
inference(cnf_transformation,[],[f176]) ).
tff(f176,axiom,
! [X0: 'Nat$'] : ( 0 = 'fps_nth$b'('zero$d',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom174) ).
tff(f4079,plain,
spl183_66,
inference(avatar_split_clause,[],[f2011,f4077]) ).
tff(f4077,plain,
( spl183_66
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_66])]) ).
tff(f2011,plain,
! [X0: $int] : ( 0 = $product(0,X0) ),
inference(cnf_transformation,[],[f315]) ).
tff(f315,axiom,
! [X0: $int] : ( 0 = $product(0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom313) ).
tff(f4075,plain,
spl183_65,
inference(avatar_split_clause,[],[f2009,f4073]) ).
tff(f4073,plain,
( spl183_65
<=> ! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'('infinity$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_65])]) ).
tff(f2009,plain,
! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'('infinity$',X0) ),
inference(cnf_transformation,[],[f74]) ).
tff(f74,axiom,
! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'('infinity$',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom72) ).
tff(f4071,plain,
spl183_64,
inference(avatar_split_clause,[],[f2008,f4069]) ).
tff(f4069,plain,
( spl183_64
<=> ! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'(X0,'infinity$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_64])]) ).
tff(f2008,plain,
! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'(X0,'infinity$') ),
inference(cnf_transformation,[],[f73]) ).
tff(f73,axiom,
! [X0: 'Ereal$'] : ( 'infinity$' = 'max$'(X0,'infinity$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom71) ).
tff(f4067,plain,
spl183_63,
inference(avatar_split_clause,[],[f2007,f4065]) ).
tff(f4065,plain,
( spl183_63
<=> ! [X0: 'Ereal$'] : ( 'zero$' = 'times$'('zero$',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_63])]) ).
tff(f2007,plain,
! [X0: 'Ereal$'] : ( 'zero$' = 'times$'('zero$',X0) ),
inference(cnf_transformation,[],[f255]) ).
tff(f255,axiom,
! [X0: 'Ereal$'] : ( 'zero$' = 'times$'('zero$',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom253) ).
tff(f4063,plain,
spl183_62,
inference(avatar_split_clause,[],[f2006,f4061]) ).
tff(f4061,plain,
( spl183_62
<=> ! [X0: 'Ereal$'] : ( 'zero$' = 'times$'(X0,'zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_62])]) ).
tff(f2006,plain,
! [X0: 'Ereal$'] : ( 'zero$' = 'times$'(X0,'zero$') ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,axiom,
! [X0: 'Ereal$'] : ( 'zero$' = 'times$'(X0,'zero$') ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom254) ).
tff(f4059,plain,
spl183_61,
inference(avatar_split_clause,[],[f2005,f4057]) ).
tff(f4057,plain,
( spl183_61
<=> ! [X0: 'Nat$'] : ( 'zero$' = 'fps_nth$a'('zero$c',X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_61])]) ).
tff(f2005,plain,
! [X0: 'Nat$'] : ( 'zero$' = 'fps_nth$a'('zero$c',X0) ),
inference(cnf_transformation,[],[f175]) ).
tff(f175,axiom,
! [X0: 'Nat$'] : ( 'zero$' = 'fps_nth$a'('zero$c',X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom173) ).
tff(f4055,plain,
spl183_60,
inference(avatar_split_clause,[],[f2004,f4053]) ).
tff(f4053,plain,
( spl183_60
<=> ! [X0: $int] : ~ $less('times$d'(X0,X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_60])]) ).
tff(f2004,plain,
! [X0: $int] : ~ $less('times$d'(X0,X0),0),
inference(cnf_transformation,[],[f414]) ).
tff(f414,axiom,
! [X0: $int] : ~ $less('times$d'(X0,X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom412) ).
tff(f4051,plain,
spl183_59,
inference(avatar_split_clause,[],[f1993,f4048]) ).
tff(f4048,plain,
( spl183_59
<=> $less('fun_app$c'('inverse$','u$'),sK80) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_59])]) ).
tff(f1993,plain,
$less('fun_app$c'('inverse$','u$'),sK80),
inference(cnf_transformation,[],[f1297]) ).
tff(f1297,plain,
( $less(sK80,'c$a')
& $less('fun_app$c'('inverse$','u$'),sK80)
& 'fun_app$b'('less$'('c$b'),'ereal$'(sK80)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f814,f1296]) ).
tff(f1296,plain,
( ? [X0: $real] :
( $less(X0,'c$a')
& $less('fun_app$c'('inverse$','u$'),X0)
& 'fun_app$b'('less$'('c$b'),'ereal$'(X0)) )
=> ( $less(sK80,'c$a')
& $less('fun_app$c'('inverse$','u$'),sK80)
& 'fun_app$b'('less$'('c$b'),'ereal$'(sK80)) ) ),
introduced(choice_axiom,[]) ).
tff(f814,plain,
? [X0: $real] :
( $less(X0,'c$a')
& $less('fun_app$c'('inverse$','u$'),X0)
& 'fun_app$b'('less$'('c$b'),'ereal$'(X0)) ),
inference(ennf_transformation,[],[f748]) ).
tff(f748,plain,
~ ! [X0: $real] :
~ ( $less(X0,'c$a')
& $less('fun_app$c'('inverse$','u$'),X0)
& 'fun_app$b'('less$'('c$b'),'ereal$'(X0)) ),
inference(true_and_false_elimination,[],[f32]) ).
tff(f32,axiom,
( ! [X0: $real] :
( ( $less(X0,'c$a')
& $less('fun_app$c'('inverse$','u$'),X0)
& 'fun_app$b'('less$'('c$b'),'ereal$'(X0)) )
=> $false )
=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom30) ).
tff(f4046,plain,
spl183_58,
inference(avatar_split_clause,[],[f1992,f4043]) ).
tff(f1992,plain,
'fun_app$b'('less$'('c$b'),'ereal$'(sK80)),
inference(cnf_transformation,[],[f1297]) ).
tff(f4041,plain,
spl183_57,
inference(avatar_split_clause,[],[f1979,f4038]) ).
tff(f4038,plain,
( spl183_57
<=> $less('fun_app$c'('inverse$','c$a'),'u$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_57])]) ).
tff(f1979,plain,
$less('fun_app$c'('inverse$','c$a'),'u$'),
inference(cnf_transformation,[],[f22]) ).
tff(f22,axiom,
$less('fun_app$c'('inverse$','c$a'),'u$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom20) ).
tff(f4036,plain,
spl183_56,
inference(avatar_split_clause,[],[f1978,f4033]) ).
tff(f4033,plain,
( spl183_56
<=> $less('fun_app$c'('inverse$','u$'),'c$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_56])]) ).
tff(f1978,plain,
$less('fun_app$c'('inverse$','u$'),'c$'),
inference(cnf_transformation,[],[f8]) ).
tff(f8,axiom,
$less('fun_app$c'('inverse$','u$'),'c$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6) ).
tff(f4031,plain,
spl183_55,
inference(avatar_split_clause,[],[f1977,f4028]) ).
tff(f4028,plain,
( spl183_55
<=> $less(0.0,'fun_app$c'('inverse$','c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_55])]) ).
tff(f1977,plain,
$less(0.0,'fun_app$c'('inverse$','c$a')),
inference(cnf_transformation,[],[f25]) ).
tff(f25,axiom,
$less(0.0,'fun_app$c'('inverse$','c$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom23) ).
tff(f4026,plain,
spl183_54,
inference(avatar_split_clause,[],[f1976,f4023]) ).
tff(f4023,plain,
( spl183_54
<=> $less(0.0,'fun_app$c'('inverse$','u$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_54])]) ).
tff(f1976,plain,
$less(0.0,'fun_app$c'('inverse$','u$')),
inference(cnf_transformation,[],[f20]) ).
tff(f20,axiom,
$less(0.0,'fun_app$c'('inverse$','u$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom18) ).
tff(f4021,plain,
spl183_53,
inference(avatar_split_clause,[],[f1975,f4018]) ).
tff(f4018,plain,
( spl183_53
<=> $less('l$','fun_app$c'('inverse$','c$a')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_53])]) ).
tff(f1975,plain,
$less('l$','fun_app$c'('inverse$','c$a')),
inference(cnf_transformation,[],[f16]) ).
tff(f16,axiom,
$less('l$','fun_app$c'('inverse$','c$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom14) ).
tff(f4016,plain,
spl183_52,
inference(avatar_split_clause,[],[f1972,f4013]) ).
tff(f1972,plain,
'fun_app$b'('less$'('c$b'),'ereal$'('c$a')),
inference(cnf_transformation,[],[f23]) ).
tff(f23,axiom,
'fun_app$b'('less$'('c$b'),'ereal$'('c$a')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom21) ).
tff(f4011,plain,
spl183_51,
inference(avatar_split_clause,[],[f1971,f4008]) ).
tff(f1971,plain,
'fun_app$b'('less$'('c$b'),'ereal$'('c$')),
inference(cnf_transformation,[],[f14]) ).
tff(f14,axiom,
'fun_app$b'('less$'('c$b'),'ereal$'('c$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom12) ).
tff(f4006,plain,
spl183_50,
inference(avatar_split_clause,[],[f1969,f4003]) ).
tff(f1969,plain,
0.0 = 'fun_app$c'('inverse$',0.0),
inference(cnf_transformation,[],[f17]) ).
tff(f17,axiom,
0.0 = 'fun_app$c'('inverse$',0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom15) ).
tff(f4001,plain,
spl183_49,
inference(avatar_split_clause,[],[f1968,f3998]) ).
tff(f3998,plain,
( spl183_49
<=> ( 'infinity$' = 'times$'('infinity$','infinity$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_49])]) ).
tff(f1968,plain,
'infinity$' = 'times$'('infinity$','infinity$'),
inference(cnf_transformation,[],[f272]) ).
tff(f272,axiom,
'infinity$' = 'times$'('infinity$','infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom270) ).
tff(f3996,plain,
spl183_48,
inference(avatar_split_clause,[],[f1966,f3993]) ).
tff(f1966,plain,
1.0 = 'fun_app$c'('inverse$',1.0),
inference(cnf_transformation,[],[f430]) ).
tff(f430,axiom,
1.0 = 'fun_app$c'('inverse$',1.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom428) ).
tff(f3991,plain,
spl183_47,
inference(avatar_split_clause,[],[f1965,f3988]) ).
tff(f3988,plain,
( spl183_47
<=> ( 1 = 'max$b'(0,1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_47])]) ).
tff(f1965,plain,
1 = 'max$b'(0,1),
inference(cnf_transformation,[],[f445]) ).
tff(f445,axiom,
1 = 'max$b'(0,1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom443) ).
tff(f3986,plain,
spl183_46,
inference(avatar_split_clause,[],[f1964,f3983]) ).
tff(f3983,plain,
( spl183_46
<=> ( 1 = 'max$b'(1,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_46])]) ).
tff(f1964,plain,
1 = 'max$b'(1,0),
inference(cnf_transformation,[],[f447]) ).
tff(f447,axiom,
1 = 'max$b'(1,0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom445) ).
tff(f3981,plain,
spl183_45,
inference(avatar_split_clause,[],[f744,f3979]) ).
tff(f3979,plain,
( spl183_45
<=> ! [X0: $real] : ( 0.0 = $product(X0,0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_45])]) ).
tff(f744,plain,
! [X0: $real] : ( 0.0 = $product(X0,0.0) ),
introduced(theory_axiom_149,[]) ).
tff(f3977,plain,
spl183_44,
inference(avatar_split_clause,[],[f743,f3975]) ).
tff(f3975,plain,
( spl183_44
<=> ! [X0: $real] : ( $product(X0,1.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_44])]) ).
tff(f743,plain,
! [X0: $real] : ( $product(X0,1.0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3973,plain,
spl183_43,
inference(avatar_split_clause,[],[f740,f3971]) ).
tff(f3971,plain,
( spl183_43
<=> ! [X0: $real] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_43])]) ).
tff(f740,plain,
! [X0: $real] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f3969,plain,
spl183_42,
inference(avatar_split_clause,[],[f732,f3967]) ).
tff(f3967,plain,
( spl183_42
<=> ! [X0: $real] : ( $sum(X0,0.0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_42])]) ).
tff(f732,plain,
! [X0: $real] : ( $sum(X0,0.0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3965,plain,
spl183_41,
inference(avatar_split_clause,[],[f726,f3963]) ).
tff(f3963,plain,
( spl183_41
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_41])]) ).
tff(f726,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f3961,plain,
spl183_40,
inference(avatar_split_clause,[],[f725,f3959]) ).
tff(f3959,plain,
( spl183_40
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_40])]) ).
tff(f725,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3957,plain,
spl183_39,
inference(avatar_split_clause,[],[f722,f3955]) ).
tff(f3955,plain,
( spl183_39
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_39])]) ).
tff(f722,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f3953,plain,
spl183_38,
inference(avatar_split_clause,[],[f714,f3951]) ).
tff(f3951,plain,
( spl183_38
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_38])]) ).
tff(f714,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f3947,plain,
spl183_37,
inference(avatar_split_clause,[],[f3531,f3945]) ).
tff(f3945,plain,
( spl183_37
<=> ! [X2: 'Ereal$',X1: 'Ereal$'] : ~ sP45(tltrue,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_37])]) ).
tff(f3531,plain,
! [X2: 'Ereal$',X1: 'Ereal$'] : ~ sP45(tltrue,X1,X2),
inference(equality_resolution,[],[f3008]) ).
tff(f3008,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue != X0 )
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f1749]) ).
tff(f3943,plain,
spl183_36,
inference(avatar_split_clause,[],[f3530,f3941]) ).
tff(f3941,plain,
( spl183_36
<=> ! [X2: 'Ereal$',X1: 'Ereal$'] : ~ sP46(tltrue,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_36])]) ).
tff(f3530,plain,
! [X2: 'Ereal$',X1: 'Ereal$'] : ~ sP46(tltrue,X1,X2),
inference(equality_resolution,[],[f3005]) ).
tff(f3005,plain,
! [X2: 'Ereal$',X0: tlbool,X1: 'Ereal$'] :
( ( tltrue != X0 )
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f1745]) ).
tff(f3939,plain,
spl183_35,
inference(avatar_split_clause,[],[f3456,f3937]) ).
tff(f3937,plain,
( spl183_35
<=> ! [X1: 'Ereal$'] : 'fun_app$b'('less_eq$'(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_35])]) ).
tff(f3456,plain,
! [X1: 'Ereal$'] : 'fun_app$b'('less_eq$'(X1),X1),
inference(equality_resolution,[],[f2570]) ).
tff(f2570,plain,
! [X0: 'Ereal$',X1: 'Ereal$'] :
( 'fun_app$b'('less_eq$'(X0),X1)
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f1533]) ).
tff(f3935,plain,
spl183_34,
inference(avatar_split_clause,[],[f2324,f3933]) ).
tff(f3933,plain,
( spl183_34
<=> ! [X0: $real] : $less(X0,sK109(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_34])]) ).
tff(f2324,plain,
! [X0: $real] : $less(X0,sK109(X0)),
inference(cnf_transformation,[],[f1443]) ).
tff(f1443,plain,
! [X0: $real] : $less(X0,sK109(X0)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f45,f1442]) ).
tff(f1442,plain,
! [X0: $real] :
( ? [X1: $real] : $less(X0,X1)
=> $less(X0,sK109(X0)) ),
introduced(choice_axiom,[]) ).
tff(f45,axiom,
! [X0: $real] :
? [X1: $real] : $less(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom43) ).
tff(f3931,plain,
spl183_33,
inference(avatar_split_clause,[],[f2323,f3929]) ).
tff(f3929,plain,
( spl183_33
<=> ! [X0: $real] : $less(sK108(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_33])]) ).
tff(f2323,plain,
! [X0: $real] : $less(sK108(X0),X0),
inference(cnf_transformation,[],[f1441]) ).
tff(f1441,plain,
! [X0: $real] : $less(sK108(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f44,f1440]) ).
tff(f1440,plain,
! [X0: $real] :
( ? [X1: $real] : $less(X1,X0)
=> $less(sK108(X0),X0) ),
introduced(choice_axiom,[]) ).
tff(f44,axiom,
! [X0: $real] :
? [X1: $real] : $less(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom42) ).
tff(f3927,plain,
spl183_32,
inference(avatar_split_clause,[],[f2252,f3925]) ).
tff(f3925,plain,
( spl183_32
<=> ! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_32])]) ).
tff(f2252,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),X0),
inference(cnf_transformation,[],[f774]) ).
tff(f774,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),X0),
inference(flattening,[],[f773]) ).
tff(f773,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'(X0),X0),
inference(true_and_false_elimination,[],[f241]) ).
tff(f241,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'(X0),X0)
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom239) ).
tff(f3923,plain,
spl183_31,
inference(avatar_split_clause,[],[f2237,f3921]) ).
tff(f3921,plain,
( spl183_31
<=> ! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'('infinity$'),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_31])]) ).
tff(f2237,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'('infinity$'),X0),
inference(cnf_transformation,[],[f772]) ).
tff(f772,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'('infinity$'),X0),
inference(flattening,[],[f771]) ).
tff(f771,plain,
! [X0: 'Ereal$'] : ~ 'fun_app$b'('less$'('infinity$'),X0),
inference(true_and_false_elimination,[],[f42]) ).
tff(f42,axiom,
! [X0: 'Ereal$'] :
( 'fun_app$b'('less$'('infinity$'),X0)
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom40) ).
tff(f3919,plain,
spl183_30,
inference(avatar_split_clause,[],[f2000,f3917]) ).
tff(f3917,plain,
( spl183_30
<=> ! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'(X0),'infinity$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_30])]) ).
tff(f2000,plain,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'(X0),'infinity$'),
inference(cnf_transformation,[],[f632]) ).
tff(f632,axiom,
! [X0: 'Ereal$'] : 'fun_app$b'('less_eq$'(X0),'infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom630) ).
tff(f3915,plain,
spl183_29,
inference(avatar_split_clause,[],[f1997,f3913]) ).
tff(f3913,plain,
( spl183_29
<=> ! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_29])]) ).
tff(f1997,plain,
! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0),
inference(cnf_transformation,[],[f135]) ).
tff(f135,axiom,
! [X0: 'Nat$'] : ~ $less('of_nat$'(X0),0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom133) ).
tff(f3911,plain,
spl183_28,
inference(avatar_split_clause,[],[f1996,f3909]) ).
tff(f3909,plain,
( spl183_28
<=> ! [X0: $real] : ( 'ereal$'(X0) != 'infinity$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_28])]) ).
tff(f1996,plain,
! [X0: $real] : ( 'ereal$'(X0) != 'infinity$' ),
inference(cnf_transformation,[],[f49]) ).
tff(f49,axiom,
! [X0: $real] : ( 'ereal$'(X0) != 'infinity$' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom47) ).
tff(f3907,plain,
spl183_27,
inference(avatar_split_clause,[],[f1961,f3904]) ).
tff(f1961,plain,
'fun_app$b'('less$'('zero$'),'infinity$'),
inference(cnf_transformation,[],[f39]) ).
tff(f39,axiom,
'fun_app$b'('less$'('zero$'),'infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom37) ).
tff(f3902,plain,
spl183_26,
inference(avatar_split_clause,[],[f1960,f3899]) ).
tff(f1960,plain,
'fun_app$b'('less$'('zero$'),'one$a'),
inference(cnf_transformation,[],[f534]) ).
tff(f534,axiom,
'fun_app$b'('less$'('zero$'),'one$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom532) ).
tff(f3897,plain,
spl183_25,
inference(avatar_split_clause,[],[f1959,f3894]) ).
tff(f1959,plain,
'fun_app$b'('less_eq$'('zero$'),'one$a'),
inference(cnf_transformation,[],[f570]) ).
tff(f570,axiom,
'fun_app$b'('less_eq$'('zero$'),'one$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom568) ).
tff(f3892,plain,
spl183_24,
inference(avatar_split_clause,[],[f1956,f3889]) ).
tff(f3889,plain,
( spl183_24
<=> $less(0,'of_nat$'('n$')) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_24])]) ).
tff(f1956,plain,
$less(0,'of_nat$'('n$')),
inference(cnf_transformation,[],[f72]) ).
tff(f72,axiom,
$less(0,'of_nat$'('n$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom70) ).
tff(f3887,plain,
spl183_23,
inference(avatar_split_clause,[],[f1955,f3884]) ).
tff(f3884,plain,
( spl183_23
<=> ( 'infinity$' = 'inverse$a'('zero$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_23])]) ).
tff(f1955,plain,
'infinity$' = 'inverse$a'('zero$'),
inference(cnf_transformation,[],[f31]) ).
tff(f31,axiom,
'infinity$' = 'inverse$a'('zero$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom29) ).
tff(f3882,plain,
spl183_22,
inference(avatar_split_clause,[],[f1953,f3879]) ).
tff(f3877,plain,
spl183_21,
inference(avatar_split_clause,[],[f1952,f3874]) ).
tff(f3874,plain,
( spl183_21
<=> ( 'zero$' = 'inverse$a'('infinity$') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_21])]) ).
tff(f1952,plain,
'zero$' = 'inverse$a'('infinity$'),
inference(cnf_transformation,[],[f43]) ).
tff(f43,axiom,
'zero$' = 'inverse$a'('infinity$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom41) ).
tff(f3872,plain,
spl183_20,
inference(avatar_split_clause,[],[f1951,f3869]) ).
tff(f1951,plain,
'one$a' = 'ereal$'(1.0),
inference(cnf_transformation,[],[f529]) ).
tff(f529,axiom,
'one$a' = 'ereal$'(1.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom527) ).
tff(f3867,plain,
spl183_19,
inference(avatar_split_clause,[],[f1950,f3864]) ).
tff(f3864,plain,
( spl183_19
<=> ( 'one$a' = 'inverse$a'('one$a') ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_19])]) ).
tff(f1950,plain,
'one$a' = 'inverse$a'('one$a'),
inference(cnf_transformation,[],[f519]) ).
tff(f519,axiom,
'one$a' = 'inverse$a'('one$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom517) ).
tff(f3862,plain,
spl183_18,
inference(avatar_split_clause,[],[f1949,f3859]) ).
tff(f3859,plain,
( spl183_18
<=> ( 'zero$b' = 'fps_tan$'(0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_18])]) ).
tff(f1949,plain,
'zero$b' = 'fps_tan$'(0.0),
inference(cnf_transformation,[],[f90]) ).
tff(f90,axiom,
'zero$b' = 'fps_tan$'(0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom88) ).
tff(f3857,plain,
spl183_17,
inference(avatar_split_clause,[],[f1948,f3854]) ).
tff(f3854,plain,
( spl183_17
<=> ( 'fps_XD$a' = 'fps_XDp$'(0.0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_17])]) ).
tff(f1948,plain,
'fps_XD$a' = 'fps_XDp$'(0.0),
inference(cnf_transformation,[],[f536]) ).
tff(f536,axiom,
'fps_XD$a' = 'fps_XDp$'(0.0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom534) ).
tff(f3852,plain,
spl183_16,
inference(avatar_split_clause,[],[f1947,f3849]) ).
tff(f3849,plain,
( spl183_16
<=> ( 'fps_XD$' = 'fps_XDp$a'(0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_16])]) ).
tff(f1947,plain,
'fps_XD$' = 'fps_XDp$a'(0),
inference(cnf_transformation,[],[f537]) ).
tff(f537,axiom,
'fps_XD$' = 'fps_XDp$a'(0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom535) ).
tff(f3847,plain,
~ spl183_15,
inference(avatar_split_clause,[],[f1944,f3844]) ).
tff(f3844,plain,
( spl183_15
<=> 'fun_app$b'('less$'('one$a'),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_15])]) ).
tff(f1944,plain,
~ 'fun_app$b'('less$'('one$a'),'zero$'),
inference(cnf_transformation,[],[f533]) ).
tff(f533,axiom,
~ 'fun_app$b'('less$'('one$a'),'zero$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom531) ).
tff(f3842,plain,
~ spl183_14,
inference(avatar_split_clause,[],[f1943,f3839]) ).
tff(f3839,plain,
( spl183_14
<=> 'fun_app$b'('less_eq$'('one$a'),'zero$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_14])]) ).
tff(f1943,plain,
~ 'fun_app$b'('less_eq$'('one$a'),'zero$'),
inference(cnf_transformation,[],[f569]) ).
tff(f569,axiom,
~ 'fun_app$b'('less_eq$'('one$a'),'zero$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom567) ).
tff(f3837,plain,
spl183_13,
inference(avatar_split_clause,[],[f1994,f3834]) ).
tff(f3834,plain,
( spl183_13
<=> $less(sK80,'c$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_13])]) ).
tff(f1994,plain,
$less(sK80,'c$a'),
inference(cnf_transformation,[],[f1297]) ).
tff(f3832,plain,
spl183_12,
inference(avatar_split_clause,[],[f1931,f3829]) ).
tff(f3829,plain,
( spl183_12
<=> $less(0.0,'c$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_12])]) ).
tff(f1931,plain,
$less(0.0,'c$a'),
inference(cnf_transformation,[],[f19]) ).
tff(f19,axiom,
$less(0.0,'c$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom17) ).
tff(f3827,plain,
spl183_11,
inference(avatar_split_clause,[],[f1930,f3824]) ).
tff(f3824,plain,
( spl183_11
<=> $less(0.0,'u$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_11])]) ).
tff(f1930,plain,
$less(0.0,'u$'),
inference(cnf_transformation,[],[f24]) ).
tff(f24,axiom,
$less(0.0,'u$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom22) ).
tff(f3822,plain,
spl183_10,
inference(avatar_split_clause,[],[f1929,f3819]) ).
tff(f1929,plain,
$less(0.0,'c$'),
inference(cnf_transformation,[],[f7]) ).
tff(f7,axiom,
$less(0.0,'c$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5) ).
tff(f3817,plain,
spl183_9,
inference(avatar_split_clause,[],[f1928,f3814]) ).
tff(f3814,plain,
( spl183_9
<=> $less(0.0,'l$') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_9])]) ).
tff(f1928,plain,
$less(0.0,'l$'),
inference(cnf_transformation,[],[f6]) ).
tff(f6,axiom,
$less(0.0,'l$'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4) ).
tff(f3812,plain,
spl183_8,
inference(avatar_split_clause,[],[f1927,f3809]) ).
tff(f3809,plain,
( spl183_8
<=> $less('c$','c$a') ),
introduced(avatar_definition,[new_symbols(naming,[spl183_8])]) ).
tff(f1927,plain,
$less('c$','c$a'),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
$less('c$','c$a'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom7) ).
tff(f3807,plain,
~ spl183_7,
inference(avatar_split_clause,[],[f1912,f3804]) ).
tff(f3804,plain,
( spl183_7
<=> ( 'infinity$' = 'zero$' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_7])]) ).
tff(f1912,plain,
'infinity$' != 'zero$',
inference(cnf_transformation,[],[f40]) ).
tff(f40,axiom,
'infinity$' != 'zero$',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom38) ).
tff(f3802,plain,
~ spl183_6,
inference(avatar_split_clause,[],[f1911,f3799]) ).
tff(f3799,plain,
( spl183_6
<=> ( 'infinity$' = 'one$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_6])]) ).
tff(f1911,plain,
'infinity$' != 'one$a',
inference(cnf_transformation,[],[f530]) ).
tff(f530,axiom,
'infinity$' != 'one$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom528) ).
tff(f3797,plain,
~ spl183_5,
inference(avatar_split_clause,[],[f1910,f3794]) ).
tff(f3794,plain,
( spl183_5
<=> ( 'zero$' = 'one$a' ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_5])]) ).
tff(f1910,plain,
'zero$' != 'one$a',
inference(cnf_transformation,[],[f462]) ).
tff(f462,axiom,
'zero$' != 'one$a',
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom460) ).
tff(f3792,plain,
~ spl183_4,
inference(avatar_split_clause,[],[f1909,f3789]) ).
tff(f3789,plain,
( spl183_4
<=> ( tltrue = tlfalse ) ),
introduced(avatar_definition,[new_symbols(naming,[spl183_4])]) ).
tff(f1909,plain,
tltrue != tlfalse,
inference(cnf_transformation,[],[f642]) ).
tff(f642,axiom,
tltrue != tlfalse,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',formula_641) ).
tff(f3787,plain,
spl183_3,
inference(avatar_split_clause,[],[f735,f3785]) ).
tff(f735,plain,
! [X0: $real] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f3783,plain,
spl183_2,
inference(avatar_split_clause,[],[f717,f3781]) ).
tff(f717,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f3779,plain,
~ spl183_1,
inference(avatar_split_clause,[],[f1908,f3776]) ).
tff(f1908,plain,
'ereal$'('fun_app$c'('inverse$','c$')) != 'inverse$a'('ereal$'('c$')),
inference(cnf_transformation,[],[f747]) ).
tff(f747,plain,
'ereal$'('fun_app$c'('inverse$','c$')) != 'inverse$a'('ereal$'('c$')),
inference(flattening,[],[f5]) ).
tff(f5,negated_conjecture,
( ~ 'ereal$'('fun_app$c'('inverse$','c$')) = 'inverse$a'('ereal$'('c$')) ),
inference(negated_conjecture,[],[f4]) ).
tff(f4,conjecture,
'ereal$'('fun_app$c'('inverse$','c$')) = 'inverse$a'('ereal$'('c$')),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat May 18 18:09:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (26802)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.40 % (26819)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)
% 0.20/0.40 % (26816)WARNING: value z3 for option sas not known
% 0.20/0.40 % (26815)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.40 % (26814)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.40 % (26816)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)
% 0.20/0.40 % (26817)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.40 % (26818)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)
% 0.20/0.41 % (26820)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)
% 0.20/0.46 % (26817)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.46 % (26817)Terminated due to inappropriate strategy.
% 0.20/0.46 % (26817)------------------------------
% 0.20/0.46 % (26817)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.46 % (26817)Termination reason: Inappropriate
% 0.20/0.46
% 0.20/0.46 % (26817)Memory used [KB]: 2314
% 0.20/0.46 % (26817)Time elapsed: 0.057 s
% 0.20/0.46 % (26817)Instructions burned: 133 (million)
% 0.20/0.46 % (26817)------------------------------
% 0.20/0.46 % (26817)------------------------------
% 0.20/0.48 % (26853)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.51 % (26853)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.20/0.51 % (26853)Terminated due to inappropriate strategy.
% 0.20/0.51 % (26853)------------------------------
% 0.20/0.51 % (26853)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.51 % (26853)Termination reason: Inappropriate
% 0.20/0.51
% 0.20/0.51 % (26853)Memory used [KB]: 2251
% 0.20/0.51 % (26853)Time elapsed: 0.034 s
% 0.20/0.51 % (26853)Instructions burned: 75 (million)
% 0.20/0.51 % (26853)------------------------------
% 0.20/0.51 % (26853)------------------------------
% 0.20/0.52 % (26873)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)
% 0.20/0.56 % (26818)First to succeed.
% 0.20/0.59 % (26818)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-26802"
% 1.57/0.60 % (26818)Refutation found. Thanks to Tanya!
% 1.57/0.60 % SZS status Theorem for theBenchmark
% 1.57/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.57/0.62 % (26818)------------------------------
% 1.57/0.62 % (26818)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.57/0.62 % (26818)Termination reason: Refutation
% 1.57/0.62
% 1.57/0.62 % (26818)Memory used [KB]: 4685
% 1.57/0.62 % (26818)Time elapsed: 0.183 s
% 1.57/0.62 % (26818)Instructions burned: 434 (million)
% 1.57/0.62 % (26802)Success in time 0.237 s
%------------------------------------------------------------------------------